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Algebra Q&A Archive of December 20, 2024

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December 20 of 2024

5. (10 pts) Find the following for each function. $f(x) = \begin{cases} -x+1 & -3 \le x < 0 \\ 2x-3 & 0 \le x \le 4 \end{cases}$ a. Find the domain b. Evaluate $f(0)$ c. Is $f$ continuous? d. Graph $f$

The inability to forgive could lead to ill health. false true

Write the system of equations associated with the augmented matrix. Do not solve. $\begin{bmatrix} -7 & -2 & | & 7 \\ -4 & -8 & | & -7 \end{bmatrix}$

Question 8 Translate $1 \cdot 0 + \overline{(0 + 1)}$ into a logical equivalence

The following Maximize: $7X_1 + 3X_2$ Subject to: $5X_1 + 7X_2 \leq 27$ $4X_1 + X_2 \leq 14$ $3X_1 - 2X_2 \leq 9$ $X_1, X_2 \geq 0$ $X_1$ integer represents a: goal programming problem. mixed integer programming problem. nonlinear programming problem. 0-1 integer programming problem.

Find B - A. $A = \begin{bmatrix} 2 & 1 \\ 2 & 7 \end{bmatrix}$ $B = \begin{bmatrix} -6 & 3 \\ 2 & -2 \end{bmatrix}$ $B - A = \square$

1. Let A = {1,2,3} and B = {3,4,5}. Find the following. (A) n(A) (B) n(A∩B)

52. Genes A/a and B/b are linked and known to be 30 map units apart. Individuals heterozygous for both of these genes (genotypes= Ab/aB) were mated with each other. If there 1000 offspring from this cross, how many of the offspring would you expect to show Ab or aB phenotypes? A) 500 B) 360 C)…

Required Information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the following zero-one matrix $\begin{bmatrix} 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$ representing a relation on…

1. Show that if $n$ is a positive odd integer, then $1 + 3 + 5 + ... + (2n - 1) = n^2$

Use Cramer's rule to solve for $x_2$. Write your answers using integers or simplified fractions. $-3x_1 - 3x_2 + 8x_3 - 3x_4 = 3$ $-6x_2 + 5x_4 = 9$ $x_1 + 6x_3 = -2$ $6x_3 + 2x_4 = 7$ Part 1 of 2 Evaluate the determinants $D$ and $D_{x_2}$.

Consider the polynomial function $f(t) = -2t^8 + 3t^7 - 4t^3 + 4 - 5t + 2t^4$. As $t \to -\infty$, $f(t) \to$ ? As $t \to \infty$, $f(t) \to$ ?

The logistic growth model $H(t) = \frac{8000}{1 + 3e^{-0.53t}}$ represents the number of families that own a home in a certain small (but growing) city t years after 1990. a) What is the maximum number of families that will own a home in this city? b) How many families owned a home in 1990? c)…

15. Solve the system: $x_1' = 3x_1 - x_2$, $x_1(0) = 3$ $x_2' = x_1 + x_2$, $x_2(0) = 0$

5. Convert the following function from the $a-b-c$ or standard form to the $a-h-k$ or vertex form $f(x) = x^2 + 6x + 5$

5x^(2)-4x=4 Solve for x using the quadratic formula

g^(-1)(x) for g(x)=(6)/(x-3) What is the inverse function

Graphs and Functions Domain and range from the graph of a discrete relation The graph of the relation $H$ is shown below. Give the domain and range of $H$. Write your answers using set notation. domain = range =

Consider the graph Γ: Which of the graphs below is isomorphic to Γ? Indicate the isomorphism by listing the vertices separated by commas in the order they correspond to A,B,C,D,E,F, respectively.

True or false: If $a \equiv b \pmod{m}$, then $2a \equiv 2b \pmod{m}$. True False

Consider the relation, R on the set of integers with $R = \{(a,b) | a = b \text{ or } a = -b\}$. Which one of the following is true? A. transitive B. not symmetry C. not transitive D. one-to-one relation

Q4. (a) [5 MARKS] Given any matrix, A, show that if x is in the left null space of A, and y is in the column space of A, then x and y are orthogonal. (b) [8 MARKS] Let $u_1 = \begin{bmatrix} 2 \\ 1 \\ 1 \end{bmatrix}$, $u_2 = \begin{bmatrix} -2 \\ 3 \\ 1 \end{bmatrix}$, and $v = \begin{bmatrix}…

9) Solve the following exponential equations: (20pts) i) $8^{x+2} = 4^{3x-1}$ ii) $10^{2x+3} = 7$ iii) $e^{4x-1} = 6$ iv) $5^{x+2} = 6^{3x-1}$ 10) Evaluate the following log expressions exactly (no decimals). (15pts) a) $\log_3 81 =$ b) $\log_5 \sqrt{5} =$ c) $\log_2(\frac{1}{8}) =$ d) $\log_3…

Question 11 Does the graph have an Euler circuit? 10 pts True False

Question 3 At a school dance, 6 girls and 4 boys take turns dancing (as couples) with each other. (a) How many couples dance if every girl dances with every boy? (b) How many couples dance if everyone dances with everyone else (regardless of gender)? (c) Explain what graphs can be used to…

Problem 7. Suppose you take out a loan for $12,543 on a used car. This loan has a 3% interest rate that compounds monthly for 4 years. What will the monthly payment be?

2. A body at a temperature of 50°F is placed outdoors where the temperature is 100°F. If after 5 minutes the temperature of the body is 60°F, how long will it take the body to reach a temperature of 75°F?

1. (7 points) Suppose $f$ is a function whose graph is shown below. Find the value of $f^{-1}(2)$. No explanation necessary. You may assume that each square is 1 unit $\times$ 1 unit, that all of the pieces of the graph that look like straight lines are actually straight lines, and that points…

2. Solve the given differential equation $$(D^2 + 2D + 5)y = e^{2x}\sin x$$ 3. Solve the given differential equation $$x^2\frac{d^2y}{dx^2} + x\frac{dy}{dx} - 3y = x^2(\ln x)$$ 4. Solve the given differential equation $$(D^2 - 3D + 2)y = xe^{3x} + \sin 2x$$

Question 9 The relation R on Z where aRb means $|a - b| \le 1$. Determine whether R is an equivalence relation. True False 5 pts

A parabola has a vertex of (3, 6) and passes through the point (0, -6). (a) Calculate the value of $a$, the leading coefficient. SHOW ALL WORK and leave your answer as a FRACTION.

Suppose a store sells pairs of shoes for $30 each and is running a "buy one, get one 50% off" sale. Suppose further that you buy four pairs of shoes. The marginal cost of the second pair of shoes purchased is Select one: A. $0. B. $15. C. $30. D. $45. E. $60. F. $75. G. $90. H. $120.

(a) Find the smallest possible positive integer N such that $N! > N^3$. Then prove by mathematical induction that $n! > n^3$ for all positive integers $n \ge N$. [8 marks] (b) A sequence $\{a_n\}$ is defined by $a_1 = 3$, $a_2 = 11$ and $a_{n+2} = 6a_{n+1} - 7a_n$ for $n = 1, 2, 3, \dots$ Prove…

The triad on the 3rd quarter-note beat (chord 3) below is [Select] [Select] in [Select] Given that the key is Ab Major, its Roman numeral is [Select]

John rode 2 kilometers on his bike. His sister Sally rode 300 meters on her bike. Who rode the farthest?

Graphs and Functions Domain and range from the graph of a discrete relation The graph of the relation $T$ is shown below. Give the domain and range of $T$. Write your answers using set notation. domain = range =

What is the row 3, column 1 entry for the answer to the following? $\begin{bmatrix} -87 & -30 \\ -69 & -51 \\ -54 & -66 \end{bmatrix} - \begin{bmatrix} -93 & 74 \\ -52 & -44 \\ 33 & -3 \end{bmatrix}$ Enter your answer as a whole number with no additional spaces. Examples

If $A = \begin{bmatrix} 2 & -2 & 1 \\ 4 & -2 & 3 \\ -1 & 3 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 4 & 4 & 1 \\ 3 & 2 & 1 \\ -1 & -2 & 2 \end{bmatrix}$, then $4A - 3B = \begin{bmatrix} \Box & \Box & \Box \\ \Box & \Box & \Box \\ \Box & \Box & \Box \end{bmatrix}$ and $A^T = \begin{bmatrix}…

Given the function $P(r) = (r - 7)(-7r + 5)^9(r - 6)^5$, its roots are and their multiplicities are

7. If $2x^2 + Ax + 15 = (Bx – 5)(x – 3)$, where A and B are constants. Find A.

Question 4 1 pts Find the interest paid on a 2-year lease for a $29,951 car if the car depreciates at an annual rate of 15% and the lease has an annual interest rate of 5.9%. Round your answer to the nearest dollar.

Determine the difference in clock 12 arithmetic by starting at the first number and counting counterclockwise on the clock the number of units given by the second number. 2 - 2 2 - 2 = $\boxed{}$

2. Given $g(x) = (x-5)^2(x+2)(1-x)$, find the following: Degree of the polynomial: All x intercepts: Sign of the leading coefficient: The y intercept: End behavior diagram: Domain: Range:

Problem 5. Let $$ f_n(x) = \begin{cases} n & \text{if } 0 < x \le \frac{1}{n} \\ 0 & \text{if } \frac{1}{n} < x \le 1 \\ 0 & \text{if } x = 0 \end{cases} $$ for all $n \in \mathbb{N}$. (a) Show that $f_n \to 0$ pointwise on $[0, 1]$. (b) Show that the above convergence is not uniform. (Hint:…

There are 52 chipmunks per square kilometer in Ames. What is this a measure of? Dispersion Range Density Carrying capactiy Diversity

(x^(2))/(2)+(3)/(2)x-4=0 Solve for x by completing the square $\frac{x^2}{2} + \frac{3}{2}x - 4 = 0$

Question Is the following infinite sum defined? 15 - 15 + 15 - ... Select the correct answer below: The sum is defined. The sum is not defined. It is impossible to tell if the sum is defined.

Question Which of the following are geometric sequences? Select all correct answers. Select all that apply: -5, 15, -45, -135, 405, ... $6, 4, \frac{8}{3}, \frac{16}{9}, \frac{32}{27}, ...$ $5, -\frac{5}{3}, \frac{5}{9}, -\frac{5}{27}, \frac{5}{81}, ...$ $3, 2, \frac{4}{3}, \frac{8}{9},…

8-:2(2+2)= $8 \div 2 (2 + 2) = ?$

3) Given $f(x) = \frac{3x}{x^2 - 1}$, find the following: (3 points each) a) $f(2)$ b) $f(-2)$ c) $f(-x)$ d) $-f(x)$ e) $f(x-2)$ f) $f(2x)$

Question 4 (2 points) An account is opened with an initial deposit of $2,400 and earns 3.9% interest compounded monthly. What will the account be worth in 21 years? (round to 2 decimal places)

$\begin{cases} 2x_1 - 7x_2 + 4x_3 = 9 \\ x_1 + 9x_2 - 6x_3 = 1 \\ -3x_1 + 8x_2 + 5x_3 = 6 \end{cases}$

A bag of flour contains 5.00 lbs of flour. You have 3.20 tons of flour. There are 2000lbs per ton How many bags of flour can you make? 1.28 x 10$^5$ bags 8.00 x 10$^2$ bags 1.28 x 10$^2$ bags 1.28 x 10$^3$ bags 8.00 x 10$^3$ bags

(2 points) D 3 G 7 J 4 10 5 11 6 C F 9 2 I 12 13 14 B E 8 H Consider the graph given above. Use Kruskal's algorithm to find the minimum spanning tree. a. What is the total weight of the spanning tree? b. List the weights of the selected edges separated by commas in the order of selection. Note:…

1. (a) For each of the following sets $H_1, H_2, \dots, H_6$, state whether or not they are subspaces of $M_{2 \times 3}$, the set of $2 \times 3$ matrices with real entries. If so, explain why and if not, explain why. (i) $H_1 = \left\{ \begin{bmatrix} x_1 & x_2 & x_3 \\ x_4 & 0 & 0…

Travon is training for a bike race in the Alps, so he is training on hills. Each time he does a training ride, he measures how long he can continuously pedal without stopping once he begins biking uphill. What dimension of behavior is he measuring? Duration Latency Topography Frequency

6. The function $\log : (0, \infty) \to \mathbb{R}$ is often defined by $$ \log x = \int_1^x \frac{1}{t} dt. $$ Use this definition to verify the following: (b) $\log(xy) = \log x + \log y$, $x, y > 0$.

A fraction representing less than a whole unit where the numerator is less than the denominator is called a mixed number.

9. Joanna has a credit card whose billing period begins on the 17th day of each month. On July 17th her balance was $815.49. She made a $250 payment on July 28. She also made new charges of $27.55 on July 21, $129.99 on August 5, and $74.45 on August 10th. Find her average daily balance. Use a…

Simplify the rational expression. If the rational expression cannot be simplified, so state. $\frac{3y - 21}{2y - 14}$

Question 6 5 pts Suppose f: R → Z, where $f(x) = \lfloor 2x - 1 \rfloor$. Is f is onto Z? True False

The function $f$ is defined below. $$f(x) = \frac{x-8}{x^2+6x+5}$$ Find all values of $x$ that are NOT in the domain of $f$.

32. The greatest common factor between $a^2b^3$ and $a^4b$ is 12. Which of the following could be the value of $a$?

Consider the graph Γ: Which of the graphs below is isomorphic to Γ? Indicate the isomorphism by listing the vertices separated by commas in the order they correspond to A,B,C,D,E,F,G, respectively.

2. In the table below is the population of Los Osos for the period 1970-2020. Use this information to answer the following questions. Do not forget your units! Year 1970 1980 1990 2000 2010 2020 Population 3,487 10,933 14,377 14,351 14,276 16,533 (a) What is the average rate of change of the…

How many solutions (using only nonnegative integers) are there to the following equations? $x_1 + x_2 + x_3 + x_4 + x_5 = 32$. Show your work.

Question 2 Carol Anne makes candles. If she charges $20 for each candle, her total revenue will be $500 if she sells 25 candles. $20 regardless of how many candles she sells. $1,000 if she sells 100 candles. $200 if she sells 5 candles.

z-:4;z=824 9. $z \div 4$; $z = 824$

The hold on a drill bit is tightened by turning a A chuck key. B crimping tool. C ratchet handle. D crescent wrench.

Find the next number: 1, 3, 6, 11, 18, 29, ?

Dr. Ecco wants to meet with you to discuss an event. He sent you an encoded message which will give you a clue. The clue was encoded with the linear code which produced the following ciphertext: XOBRAFNJ You are told that the letter X decodes to the letter O and the letter J decodes to S. The…

(x-7)^(10)(x+5)^(5)+(x-7)^(9)(x+5)^(6)=0

2. A body at a temperature of 50°F is placed outdoors where the temperature is 100°F. If after 5 minutes the temperature of the body is 60°F, how long will it take the body to reach a temperature of 75°F?

3. Solve the system of equations. Write answer as an ordered triple: $x + 2y - z = 8$ $-2x + 3y - z = 1$ $2x + y + 3z = 5$

Let $f(x) = 4x + \frac{1}{x}$ and $g(x) = \frac{x}{x-3}$. Find $f \circ g$.

7) Solve the following system of equations below by the matrix inverse method. Show your work. 6 points $\begin{cases} x + y - z = 4 \\ -3x + 2y - z = 1 \\ 3x - 3y + 2z = 3 \end{cases}$ 8) Find the inverse of the following matrix A. Show your work. Check your work.. i.e. $AA^{-1} = I$ 6…

1. Which of the following is an example of deductive reasoning? (a) John noticed 2 dogs at a pound on Monday, 4 dogs on Tuesday, 6 dogs on Wednesday, he concludes there will be 8 dogs Thursday (b) Helen saw 5 students in the school on Monday, then 7 on Tuesday, then 9 on Wednesday, she…

Question 25 If 3 | $x$ and 25 | $x$, then... 75 | $x$ 28 | $x$ 15 | $x$ 5 | $x$

Ibuprofen can be found in 600 mg doses in over-the-counter analgesics, such as Advil and Motrin. How many grams of ibuprofen does such a tablet contain? 600 mg = g

Find the equation of the line and graph the line through the points (1, 2) and (2, -3). Write the equation in slope-intercept form. Type your equation below and submit your graph after the test.

Questions 16 – 19 are worth ten points each. There are instructions for each question. Please read the instructions carefully before answering the question. ~ $\bullet$ $\lor$ $\supset$ = Construct a truth table for the following statement. 16. $\sim(\sim L \lor N) \supset L$

If all other factors are equal, what effect will higher property taxes have on the value of the home a buyer can afford? O Increase the value for smaller homes and decrease the value for larger homes. O Decrease the value. O Increase the value. O Have no effect on the value.

Write out the next 4 terms of the sequence: $a_1 = -1$, $a_2 = 4$, and $a_{n+1} = a_n + a_{n-1}$ $a_3 = $ $a_4 = $ $a_5 = $ $a_6 = $

Suppose that the polynomial function $f$ is defined as follows. $f(x) = 5x^3 (x-6)(x+11)(x-11)$ List each zero of $f$ according to its multiplicity in the categories below If there is more than one answer for a multiplicity, separate them with Zero(s) of multiplicity one: Zero(s) of…

4. [0/12.5 Points] DETAILS LARPCALC11 7.T.009. PREVIOUS ANSWERS Solve the system of linear equations and check any solutions algebraically. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express x, y, and z in terms of the real number a.) $\begin{cases} x -…

f(x)=(6x)/(9x-7)

yd. What is its volume in ft³. There are 3ft in a yard (yd) 3.0 cubic feet 27 cubic feet .11 cubic feet 81 cubic feet 9.0 cubic feet

Question 2 1 pts "If Watson had bought stamps then he would not already have a drawer full of stamps. But Watson does have a drawer full of stamps.” Which of the following is guaranteed to be true so long as these two premises are true? Watson couldn't have a drawer full of stamps None of…

Column1 Combo Total # Of Puppies Variables Model 2 Wagons 1-2 3 X=0, Y=3 2-3 5 X=1, Y=5 3-4 7 X=2, Y=7 4-5 9 X=3, Y=9 5-6 11 X=4, Y= 11 6-7 13 X=5, Y=13 7-8 15 X=6, Y=15 8-9 17 X=7, Y=17 9-10 19 X=8, Y=19 (Y=MX+B)

(d) Let $f: X \to Y$. If for each pair of sets A, B, with $A \subset X$ and $B \subset X$, $f(A \cap B) = f(A) \cap f(B)$, then the function is one-to-one.

Match each of the following for the given function. The answers may be used more than once. $y = x^3 - 12x + 16$ zeros are starts in quadrant ends in quadrant behavior at the first zero on the left behavior at the second zero from the left

8. Given that we know the mean cholesterol of HIV patient receiving antiretroviral therapy at Livingstone Central Hospital and is normally distributed, with a mean of 2.5mmol/l, and a corresponding standard deviation of 0.6mmol/l. Using the empirical rule, we can say that about 95% of all HIV…

From the textbook: Find a possible formula for the exponential function represented by the data in the following table. x | 0 | 1 | 2 | 3 f(x) | 2.67 | 7.02 | 18.954 | 51.1758 Answer: $f(x) = $

Q2. (a) [5 MARKS] In each of the following let S denote some subset of $\mathbb{R}^3$. (i) Can there be an S which is a subspace of $\mathbb{R}^3$ and for which $|S| < \infty$? If so, give an example. If not, explain why. (ii) Can there be an S which is a subspace of $\mathbb{R}^3$ of dimension…

The goal in simplifying complex fractions is to create a reduced \_\_\_ expression.

Carry out the indicated algebraic operation. (If not possible, enter IMPOSSIBLE in any cell of the matrix.) $A = \begin{bmatrix} -4 & 9 \\ 4 & 5 \end{bmatrix}$ $B = \begin{bmatrix} -2 & \frac{3}{2} & -4 \\ 0 & 2 & -2 \end{bmatrix}$ $C = \begin{bmatrix} 0 & -\frac{3}{2} & 1 \\ 1 & 0 & 2…

Solve the equation. $\log_5(2x+5) - \log_5(x+5) = 1$ What is the equivalent equation that must be solved? A. $(2x+5) - (x+5) = 5$ B. $(2x+5) - (x+5) = 1$ C. $\frac{2x+5}{x+5} = 1$ D. $\frac{2x+5}{x+5} = 5$ Select the correct choice below and, if necessary, fill in the answer box to complete…

2. A fruit grower uses two types of fertilizer in an orange orchard, brand A and brand B. Each bag of brand A contains 8 pounds of nitrogen and 4 pounds of phosphoric acid. Each bag of brand B contains 7 pounds of nitrogen and 6 pounds of phosphoric acid. Tests indicate that the orchard needs…

Determine whether the following argument is valid. Use a truth table to JUSTIFY your answer (make sure to show the table). (15 points) 17. $\sim(J \vee G)$ $K \supset G$ $\sim G \vee K$

Representative democracy is when the people vote directly on issues before the government. O True O False

Find a value of c so that when $3b^4 + 4b^3 - 6b^2 + cb + 5$ is divided $b - 2$ the remainder is 85.

What is a good rule of thumb when buying a home? O It should not cost more than 10 times your annual income. O It should not cost more than 28% of your monthly income. O The monthly payment should be more than 2/3 your monthly salary. O You should wait until you have been married five years.

$5,000 is invested at a simple interest rate of 4.6%. If the future value of the investment is $5,782, how many years was the investment?

$5x + 7y = -4$ $8x - 9y = 12$ Select the correct choice below and, if necessary, fill in the answer box A. There is one solution. The solution is $\boxed{ }$ . (Simplify your answer. Type an ordered pair) B. There are infinitely many solutions of the form $(x, \boxed{ })$. (Type an expression…

Discuss the validity of the statement. If the statement is true, explain why. If not, give a counterexample. $\sqrt{x^2} = x$ for all real numbers $x$ Choose the correct answer below. A. False, because if $x = -7$, then $\sqrt{x^2} = \pm \sqrt{(-7)^2} = \pm \sqrt{49} = \pm 7 \ne x$ B. False,…

Question 9 (Mandatory) (1 point) A furniture designer builds a trapezoidal desk with a semicircular cutout. What is the area of the desk? 126 cm 300 cm 60 cm a) About 26 460 cm² b) About 22 680 cm² c) About 20 805 cm² d) About 11 370 cm²

Question 1 Which (if any) of the graphs below are the same? Which are different? Explain.

According to the rules of tennis, a regulation ball "shall have a bounce of more than 53 inches and less than 58 inches when dropped 100 inches upon a concrete base." Which number sentence reflects the bounce height restrictions for tennis balls? A. 53 inches $<$ bounce height $<$ 58 inches B.…

8. The lease on Kimm's SUV allows her 15,000 miles per year, with a 45 cents per mile penalty for overcharges. At the end of her 3-year lease, she returns the vehicle with 47,321 miles on it. How much of a mileage penalty, if any, does she owe?

1. Let $f: \mathbb{R}^3 \to \mathbb{R}^2$ and $g: \mathbb{R}^2 \to \mathbb{R}^3$ be differentiable functions with $f(1, -1, 0) = (2, 1)$, $$Df(1, -1, 0) = \begin{bmatrix} 3 & 0 & 2 \\ 2 & 1 & 1 \end{bmatrix}$$ and $$Dg(2, 1) = \begin{bmatrix} 0 & 2 \\ 1 & 0 \\ -1 & 1 \end{bmatrix}$$ Which of…

13. Match each graph to the appropriate discriminant. A. $b^2 - 4ac < 0$ B. $b^2 - 4ac > 0$ C. $b^2 - 4ac = 0$

Solve the equation $-7 - \frac{3}{5}x = -3$ algebraically. Answer as a "reduced Proper or Improper" fraction only.

1. Hank bought a policy from an insurance company that he pays \$550 a month guaranteed for the next 10 years. Is the amount he paid a present value or future value?

[-/1 Points] DETAILS ASK YOUR TEACHER A pure sample of a newly discovered radioactive isotope is discovered. It has a half-life of 75 s. Determine how long until only 1/16 of the original amount remains.

Consider the following pattern. 3 $\diamond$ 14 = 42 33 $\diamond$ 14 = 462 333 $\diamond$ 14 = 4662 3333 $\diamond$ 14 = 46662 Predict the result of 333333 $\diamond$ 14. Answer

The following money market account rates were available from a particular bank. Find the compound amount and the interest earned. $10,000 at 1.16% compounded daily for one year The compound amount is $ (Do not round until the final answer. Then round to the nearest cent as needed.)

$x = 2$ Move the two points to define a parabola and then write its equation. $(-3, -3)$

Sketch the graph of the solution set of the system of inequalities. (Use only lines to sketch the boundaries of your solution set. Do not use rays.) $$4x + y \le 8$$ $$4x - y \ge 0$$ $$x \ge 0$$

6. Find the sales tax on a purchase of $154.59 if the sales tax rate is 7%.

12.) Write the matrix $A = \begin{bmatrix} 3 \\ 1 \end{bmatrix} \begin{bmatrix} 1 \\ 2 \end{bmatrix}$ as a product of elementary matrices. 13.) Consider the system of equations. $2x + 2y = 7$ $kx + 2y = 8$ (a) For what value(s) of $k$, if any, does the system have a unique solution? Circle…

2. [0/12.5 Points] DETAILS LARPCALC11 7.T.004. Solve the system of equations graphically. (If there is no solution, enter NO SOLUTION.) $\begin{cases} 3x - 6y = 0 \\ 2x + 5y = 36 \end{cases}$

rewrite the quadratic function $y = 4x^2 - 24x + 29$ in the form $y = a(x - p)^2 + q$ by completing the square

Write the first four terms of the sequence $\{a_n\}_{n=1}^{\infty}$. $a_n = \frac{(-1)^n}{-2^n}$ $a_1 = \square$ (Simplify your answer.) $a_2 = \square$ (Simplify your answer.) $a_3 = \square$ (Simplify your answer.) $a_4 = \square$ (Simplify your answer.)

10. a) Solve by Substitution, the following systems $x^2 + y^2 = 25$ $y = 3x - 5$ b) Confirm your results from part "a" by graphing both equations on same set of axes and finding and labeling the points of intersection.

Q3. (a) [6 MARKS] Explain the term isomorphism. Give an explanation as to why $P_3$ is not isomorphic to $\mathbb{R}^3$. Give an example of a subspace of $P_3$ that is isomorphic to $\mathbb{R}^3$. (b) [6 MARKS] (i) What is the largest possible rank of a 10 × 8 matrix? (ii) If the null space of…

17. For given matrices A, and b, we know $Ax = b$ has solutions $x_1 = \begin{bmatrix} 1 \\ 3 \\ 9 \end{bmatrix}$ and $x_2 = \begin{bmatrix} -1 \\ 2 \\ 6 \end{bmatrix}$. Which of the following must be a solution to $Ax = 0$? a) $\begin{bmatrix} 2 \\ 3 \\ 9 \end{bmatrix}$ b) $\begin{bmatrix} 2…

The following graph has no Hamilton circuit has exactly one Hamilton circuit has several Hamilton circuits, none of which contain the edge AB has several Hamilton circuits, all of which contain the edge AB none of the above

The actual color a viewer sees on a screen is influenced by the specific type and amount of phosphors on the screen. So each computer screen manufacturer must convert between the (R, G, B) data and an international CIE standard for color, which uses three primary colors, called X, Y, and Z. A…

In a certain city there is a river running through the middle of the city. There are 3 islands and 9 bridges as shown in the figure below. North Bank A B C River South Bank In the graph that models this situation, what is the degree of the vertex that represents Island B?

19. Puzzle: Age difference A man and his grandson share their birthday in day and month. On one of their birthdays, the grandfather's age in years is same as his grandson's age in months. After how many years will grandfather's age in years be a multiple of grandson's age in years? Pick ONE…

i- $(p \to q) \lor (p \to r) \equiv \neg r \to (\neg p \lor q)$ ii- $(p \to \neg q) \land \neg p \equiv p \to (\neg q \land \neg p)$

Name a relationship between sets A, B, and/or C as illustrated in the figure below. Your relationship can involve 2 or more sets--you don't need to use all of them. You can find set notation symbols by clicking on the + in the menu above the answer box and choosing "Equation," then "Graphical…

Find the principal needed now to get the given amount; that is, find the present value. To get \$2000 after $1\frac{1}{4}$ years at 8% compounded daily The present value of \$2000 is \$ $\boxed{}$. (Round to the nearest cent as needed.)

A wave function can be expanded in basis states as $|\psi\rangle = \sum_n a_n |\psi_n\rangle$ What must be true of the expansion coefficients? There is no restrictions on the coefficients. $\sum_n a_n = 1$ They must be real numbers. $\sum_n |a_n|^2 = 1$

Suppose that the functions $q$ and $r$ are defined as follows. $q(x) = -x + 3$ $r(x) = 4x + 2$ Find the following. $(r \circ q)(5) = \text{☐}$ $(q \circ r)(5) = \text{☐}$

Range: [-5, 63 Given the graph of f, use interval notation to state the: Domain: Range: Find f(-5) = Find all value(s) of x, for which f(x) = 0.

Which of the following graphs have Euler circuits or Euler trails? A: Has Euler trail. A: Has Euler circuit. B: Has Euler trail. B: Has Euler circuit. C: Has Euler trail. C: Has Euler circuit. D: Has Euler trail. D: Has Euler circuit.

Q3) Transform the boundary value initial problem by $u(x, t)$, $u_t = Du_{xx} - B(u - S)$, $u(x, 0) = \sin(\frac{\pi x}{L}) + S$ into a familiar one by setting: $v(x, t) = e^{Bt}[u(x, t) - S]$ and determine the boundary condition that satisfied by $v(x, t)$ where D, B,S,L are constant.

For $f(x) = \frac{9}{x+5}$ and $g(x) = \frac{7}{x}$, find a. $(f \circ g)(x)$; b. the domain of $f \circ g$ a. $(f \circ g)(x) = \boxed{}$ (Simplify your answer.) b. What is the domain of $f \circ g$? The domain is $\boxed{}$ (Simplify your answer. Type your answer in interval notation. Use…

2log(3-x)=1 $2 \log(3 - x) = 1$

Question 8 1 pts Your employer offers a 401(k) plan with a 42% match, and you set a goal of retiring in 28 years with an amount of money which has the same buying power that 1.5 million dollars has today. If the account earns an annual interest rate of 5.6% and the expected annual rate of…

7. (4 pts.) Use the graph of the polynomial function below to answer the following. a. Determine the minimum degree of the polynomial: b. Is the leading coefficient positive or negative?

Does the graph have a Hamilton circuit? True False Does the graph have a Hamilton circuit? True False

Part 3 (3 pts) 2-Car Combo Total # of Puppies Change 1-2 3 2-3 5 2 Create a table of your data for the various combinations. (Feel free to copy and modify this table for each type of combination) What is the change from one total to the next? Is this change the same or does it change? Can you…

The linear system (S): $\begin{cases} mx - 2y = 1 \\ x + 4y = 0 \end{cases}$ can be solved using Cramer's method if:

Suppose the matrix representation of a relation $R$ on the set $\{1, 2, 3\}$ is $\begin{bmatrix} 1 & 1 & 1 \\ 1 & 0 & 0 \\ 1 & 0 & 1 \end{bmatrix}$ Then $R$ is 1. reflexive [Select] 2. symmetric [Select] 3. transitive [Select]

3. Michael and Kathryn borrowed $282,500 to buy their house, for which they took out a 30-year loan at 3.75%. (a) Find their monthly payment. (b) What would their payment have been if they had instead taken out a 15-year loan at the same interest rate?

Multiple Choice 1 point Which equation is not parallel to $y = \frac{2}{3}x - 5$? $y = \frac{2}{3}x$ $-2x + 3y = 15$ $3x + 2y = 6$ $4x - 6y = 22$

11) Given $a_1 = -2$ and $a_{k+1} = a_k + 4$. 5 points. a) Write the first 5 terms of the sequence. b) What type of sequence is determined by the terms in (a)? c) What is formula for the nth term? d) Find the twenty-first term. e) Compute the sum of the first twenty-one terms. 12) Given $a_1 =…

Choose 7 problems out of the 10 on this exam to complete. If you wish, you may attempt more than 10, but I will only grade 7 of them. Circle the problem numbers for each of the 7 problems you would like me to grade. 1. Let A = \{1,3,5,7,9\} and B = \{x|x is an integer between -5 and 5\}.…

Question 9 Find the value of $1 \cdot 0 + \overline{(0+1)}$

Find $f(x)$ and $g(x)$ such that $h(x) = (f \circ g)(x)$. Answers may vary. (Use no $h(x) = (x - 8)^3$ $\{f(x), g(x)\} = \{\}$

4. Using algebraic methods, find the solution sets for the following. Give your solutions in interval notation. (a) $6x^2 \ge 24x - 18$ (b) $\frac{3}{x+1} < 15$

Use the graph to determine a. open intervals on which the function is increasing, if any. b. open intervals on which the function is decreasing, if any. c. open intervals on which the function is constant, if any.

6. [0/12.5 Points] DETAILS LARPCALC11 7.Τ.011. Write the partial fraction decomposition of the rational expression. Check your result algebraically. $$ \frac{5x + 8}{x^2 - x - 2} $$

Question 14 4 pts A new vaccine claims to reduce the risk of contracting chicken pox from 50% to 20%. Which of the following statements is true regarding this claim? This vaccine decreases the risk of contracting chicken pox by 150 percentage points This vaccine decreases the risk of…

Ex. 4) Find the $10^{th}$ term in a geometric sequence which has a $2^{nd}$ term equal to 7 and a $5^{th}$ term equal to 35. [First, find the common ratio, $r$. Then, since the initial term, $b$, is not given, you must express the $10^{th}$ term of the sequence in terms of one of the given…

Draw the graph of f(x)=-((1)/(6))^(x+2) Draw the graph of $f(x) = - \left( \frac{1}{6} \right)^{x+2}$

Let A = \{1, 3, 5, 7\} B = \{5, 6, 7, 8\} C = \{5, 8\} D = \{2, 5, 8\} U = \{1, 2, 3, 4, 5, 6, 7, 8\} Determine whether the statement is true or false. $C \subset A$ False; A is a subset of C. False; C is equal to A. True False; C has one different element than A does.

(b) Let $P_n$ denote the vector space of polynomials in $t \in \mathbb{R}$ of degree at most $n$. (i) Can $1 + t \in P_1$ be written as a linear combination of $2 + 7t$ and $-3 + 4t$? Explain your answer. (ii) Can $2 - 4t \in P_1$ be written as a linear combination of $2 + 6t$ and $-1 + 3t$?…

Solve the following for $v$ algebraically. $\log_2(4v - 1) - \log_2 v = \log_2 3$

$h(x) = \begin{cases} -4x - 17 & \text{for } x < -8 \\ 3 & \text{for } -8 \le x < 3 \\ x + 2 & \text{for } x \ge 3 \end{cases}$ $h(-8) = ?$ $h(-4) = ?$ $h(3) = ?$ $h(6) = ?$

3. Misalkan himpunan A = {0, 1, 2, 3}. Pada A didefinisikan relasi : R = {(x, y) | x ≤ y}. Jelaskan, apakah relasi R tersebut merupakan relasi ekivalen atau bukan !

Let $\mathcal{P}(A)$ denote the power set of $A$. If $\mathcal{P}(A) \subseteq B$ then (a) $2^{|A|} \le |B|$ (b) $2^{|A|} \ge |B|$ (c) $2^{|A|} < |B|$ (d) $|A| + 2 \le |B|$ (e) $2^{|A|} \ge 2^{|B|}$

To the nearest cent, how much loan can you afford, if you can pay \$700, monthly for 15 years at 3.8\% interest? (Identify or find each) P = d = As a decimal, r = n = t =

Evaluate the following syllogism by using a Venn Diagram (You do not have to show your Venn Diagram.): Some beliefs are items that have propositional reference. Some judgments are items that have propositional reference. So, it follows that some judgments are beliefs. valid invalid

4) Evaluate the following determinants. Show your work. Check your work. 8 points a) $ \begin{vmatrix} 1 & -1 & 2 \\ -1 & 3 & 0 \\ 0 & 1 & -1 \end{vmatrix} $ b) $ \begin{vmatrix} 0 & -1 & 2 \\ 1 & 1 & 0 \\ 2 & 0 & 1 \end{vmatrix} $ c) $ \begin{vmatrix} -1 & 3 & 0 \\ 0 & 1 & 2 \\ 0 & 1 & 2…

Question 3 4 pts A new vaccine claims to reduce the risk of contracting chicken pox from 50% to 20%. Which of the following statements is true regarding this claim? This vaccine decreases the risk of contracting chicken pox by 60 percentage points This vaccine decreases the risk of contracting…

10. If $f(x) = a^x$ and $f(6) = 64$, find the following values of $f(x)$. a. $f(4)$ b. $f(-3)$

Sketch the graph of the solution set of the system of inequalities. $\begin{cases} y < -x^2 + x + 4 \\ y > 3x \end{cases}$

Question 2 1 pts Find the monthly payments on a 2-year lease for a $29,481 car if the car depreciates at an annual rate of 16% and the lease has an annual interest rate of 5.7%. Round your answer to the nearest dollar.

Mary purchased 4 tires by mail order. She paid $45.80 per tire plus $6.50 per tire for shipping and handling. There is no sales tax, because the tires were purchased out of state. She also had to pay $8.17 per tire for mounting and balancing. At a local store, Mary's total for the 4 tires with…

Which of the following is a major seventh (M7) below the given note? Enharmonic equivalents are not acceptable answers. O Eb O C O F O E

9. What is the x-intercept of the line given by the equation? $x + y = 8$ (8, 0) (4, 4) (7, 1)

Which of the following are trees and which are forests? A: Is a forest A: Is a tree B: Is a forest B: Is a tree C: Is a forest C: Is a tree D: Is a forest D: Is a tree

Let the graph of polynomial $g(x)$ be given below. 28. What is the domain and range of $g(x)$? a. D = $(-\infty, \infty)$ and R = $(-\infty, \infty)$ b. D = $(-1, 3)$ and R = $(-\infty, \infty)$ c. D = $(-\infty, \infty)$ and R = $(-\infty, 5]$ d. D = $[-1, 3]$ and R = $[0, 5]$ e. Can't…

4. Companion matrix of the polynomial $f(x) = x^3 + 2x^2 + 1$ is A: $\begin{bmatrix} 0 & 0 & -1 \\ 1 & 0 & 0 \\ 0 & 1 & -2 \end{bmatrix}$ B: $\begin{bmatrix} 1 & 0 & -1 \\ 0 & 1 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ C: $\begin{bmatrix} 1 & 0 & -1 \\ 0 & 1 & -2 \\ 0 & 0 & -1 \end{bmatrix}$ D:…

The following triad is ✓ [Select] F A D C in Given that the key is C Major, its Roman numeral is [Select] 8

Consider the relation, R on the set of integers with $R = \{(a,b) | a = b \text{ or } a = -b\}$. Which one of the following is true? A. transitive B. not symmetry C. not transitive D. one-to-one relation

Determine whether the activity can be used to illustrate the associative property. In a store, buying cereal, soap, and dog food Choose the correct answer below. No Yes

Arnold Brown has a Visa Card with an annual percentage rate of 18.0%. The unpaid balance for his June billing cycle is $1,227.55. During the billing cycle he purchased a printer cartridge for $43.44, books for $232.77 and gasoline for $15.33. He made a payment of $1,100. If the account applies…

Q3. (a) [5 MARKS] Find the matrix of the linear transformation defined by $T\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} -3x_1 + 2x_2 \\ x_1 + 4x_3 \end{bmatrix}$. Is this linear transformation an isomorphism? Explain your answer. (b) [5 MARKS] Is it possible for a matrix…

Suppose, at a given point in time, Sally's Smoothie Shack operates in a perfectly competitive market and is producing its profit-maximizing level of output. Suppose further that at this level of production its average fixed cost of producing a smoothie is $1.30, average variable cost is $2.50,…

Identify $f(x) = \frac{3}{5} - \frac{7}{8}x$ as being linear, quadratic, or neither. If $f$ is quadratic, identify the leading coefficient $a$ and evaluate $f(-2)$.

Use the graph of $f(x)$ to find the $x$-intercepts of the graph and the zeros of the function. The x-intercepts are $\boxed{}$. (Type ordered pairs. Use a comma to separate answers.) The zeros are $x = \boxed{}$. (Use a comma to separate answers.)

A political party's ultimate aim is to A. canvass voters B. nominate candidates in the primary or convention and get them elected C. serve as advisors to county administrators D. finance party candidates

If you want $180,000 in 20 years after collecting 8% simple interest, rounded to the nearest cent, what is the present value? (Identify or find each) A = P = As a decimal, r = t=

Analytics Exercise 4-2 (Algo) You work for a company that makes cell phones and have been made project manager for the design of a new cell phone. Your supervisors have already scoped the project, so you have a list showing the work breakdown structure, and this includes major project…

Solve the inequality $\frac{x+4}{x+7} < -2$ Give your answer in interval notation.

Q1. (a) [12 MARKS] Decide, with justification, whether $H_1$, $H_2$ and $H_3$ are subspaces of $\mathbb{R}^3$, where $H_1 = \begin{Bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} \in \mathbb{R}^3 : x_2 = x_1, x_3 = 0 \end{Bmatrix}$, $H_2 = \begin{Bmatrix} \begin{bmatrix} x_1 \\ x_2 \\…

A land reclamation has 90.2 square feet of land and costs 325.26. What is the cost per square foot to the nearest cent? Enter your answer to the whole nearest whole cent. Do NOT include units with your answer.

Question 6 5 pts Suppose f: R → Z, where $f(x) = \lfloor 2x - 1 \rfloor$. Is f is onto Z? True False

1) Solve the following system of equations by the Gauss-Jordan method. Write the solution if a unique solution exists. If no solution exists, write no solution. If infinitely many solutions exist, write infinitely many solutions, and express $x$, $y$, and $z$ in terms of a parameter $t$. Show…

6. For the system of equations. $\begin{cases} 4x - y + 7z = -21 \\ -x + 2y - 2z = 9 \\ 8y + 9z = 7 \end{cases}$ (a) Write the corresponding augmented matrix. (b) Use the matrix to solve the system. (c) Be sure to write the solution as an ordered triple.

10. It is given that $\frac{1}{x} + \frac{1}{2z} = \frac{6}{5y}$. If $x = -3$ and $y = 12$, find $z$.

Marysia has saved $65.00 in quarters and loonies. If she has 4 quarters fewer than two-fifths the number of loonies, how many coins of each type does Marysia have? Marysia has $\boxed{ }$ loonies and $\boxed{ }$ quarters.

Which functions are the same as their inverse functions? $f(x) = \frac{x-1}{x+5}, x \neq -5$ $g(x) = \frac{x-2}{x-1}, x \neq 1$ $h(x) = \frac{x+3}{x-2}, x \neq 2$ $k(x) = \frac{x+1}{x-1}, x \neq 1$

x^(2)+5x-5=0 Slove for x by using the quadratic formula 15. $x^2 + 5x - 5 = 0$

1. A man wants to use cottage cheese and yogurt to increase the amount of protein and calcium in his daily diet. An ounce of cottage cheese contains 3 grams of protein and 15 milligrams of calcium. An ounce of yogurt contains 1 gram of protein and 41 milligrams of calcium. How many ounces of…

4. Find n(F), given that n(B × F) = 18 and B = {1, 3}.

5. (10 pts) Find the following for each function. $f(x) = \begin{cases} -x+1 & -3 \le x < 0 \\ 2x-3 & 0 \le x \le 4 \end{cases}$ a. Find the domain b. Evaluate $f(0)$ c. Is $f$ continuous? d. Graph $f$

The inability to forgive could lead to ill health. false true

Write the system of equations associated with the augmented matrix. Do not solve. $\begin{bmatrix} -7 & -2 & | & 7 \\ -4 & -8 & | & -7 \end{bmatrix}$

Question 8 Translate $1 \cdot 0 + \overline{(0 + 1)}$ into a logical equivalence

The following Maximize: $7X_1 + 3X_2$ Subject to: $5X_1 + 7X_2 \leq 27$ $4X_1 + X_2 \leq 14$ $3X_1 - 2X_2 \leq 9$ $X_1, X_2 \geq 0$ $X_1$ integer represents a: goal programming problem. mixed integer programming problem. nonlinear programming problem. 0-1 integer programming problem.

Find B - A. $A = \begin{bmatrix} 2 & 1 \\ 2 & 7 \end{bmatrix}$ $B = \begin{bmatrix} -6 & 3 \\ 2 & -2 \end{bmatrix}$ $B - A = \square$

1. Let A = {1,2,3} and B = {3,4,5}. Find the following. (A) n(A) (B) n(A∩B)

52. Genes A/a and B/b are linked and known to be 30 map units apart. Individuals heterozygous for both of these genes (genotypes= Ab/aB) were mated with each other. If there 1000 offspring from this cross, how many of the offspring would you expect to show Ab or aB phenotypes? A) 500 B) 360 C)…

Required Information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the following zero-one matrix $\begin{bmatrix} 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$ representing a relation on…

1. Show that if $n$ is a positive odd integer, then $1 + 3 + 5 + ... + (2n - 1) = n^2$

Use Cramer's rule to solve for $x_2$. Write your answers using integers or simplified fractions. $-3x_1 - 3x_2 + 8x_3 - 3x_4 = 3$ $-6x_2 + 5x_4 = 9$ $x_1 + 6x_3 = -2$ $6x_3 + 2x_4 = 7$ Part 1 of 2 Evaluate the determinants $D$ and $D_{x_2}$.

Consider the polynomial function $f(t) = -2t^8 + 3t^7 - 4t^3 + 4 - 5t + 2t^4$. As $t \to -\infty$, $f(t) \to$ ? As $t \to \infty$, $f(t) \to$ ?

The logistic growth model $H(t) = \frac{8000}{1 + 3e^{-0.53t}}$ represents the number of families that own a home in a certain small (but growing) city t years after 1990. a) What is the maximum number of families that will own a home in this city? b) How many families owned a home in 1990? c)…

15. Solve the system: $x_1' = 3x_1 - x_2$, $x_1(0) = 3$ $x_2' = x_1 + x_2$, $x_2(0) = 0$

5. Convert the following function from the $a-b-c$ or standard form to the $a-h-k$ or vertex form $f(x) = x^2 + 6x + 5$

5x^(2)-4x=4 Solve for x using the quadratic formula

g^(-1)(x) for g(x)=(6)/(x-3) What is the inverse function

Graphs and Functions Domain and range from the graph of a discrete relation The graph of the relation $H$ is shown below. Give the domain and range of $H$. Write your answers using set notation. domain = range =

Consider the graph Γ: Which of the graphs below is isomorphic to Γ? Indicate the isomorphism by listing the vertices separated by commas in the order they correspond to A,B,C,D,E,F, respectively.

True or false: If $a \equiv b \pmod{m}$, then $2a \equiv 2b \pmod{m}$. True False

Consider the relation, R on the set of integers with $R = \{(a,b) | a = b \text{ or } a = -b\}$. Which one of the following is true? A. transitive B. not symmetry C. not transitive D. one-to-one relation

Q4. (a) [5 MARKS] Given any matrix, A, show that if x is in the left null space of A, and y is in the column space of A, then x and y are orthogonal. (b) [8 MARKS] Let $u_1 = \begin{bmatrix} 2 \\ 1 \\ 1 \end{bmatrix}$, $u_2 = \begin{bmatrix} -2 \\ 3 \\ 1 \end{bmatrix}$, and $v = \begin{bmatrix}…

9) Solve the following exponential equations: (20pts) i) $8^{x+2} = 4^{3x-1}$ ii) $10^{2x+3} = 7$ iii) $e^{4x-1} = 6$ iv) $5^{x+2} = 6^{3x-1}$ 10) Evaluate the following log expressions exactly (no decimals). (15pts) a) $\log_3 81 =$ b) $\log_5 \sqrt{5} =$ c) $\log_2(\frac{1}{8}) =$ d) $\log_3…

Question 11 Does the graph have an Euler circuit? 10 pts True False

Question 3 At a school dance, 6 girls and 4 boys take turns dancing (as couples) with each other. (a) How many couples dance if every girl dances with every boy? (b) How many couples dance if everyone dances with everyone else (regardless of gender)? (c) Explain what graphs can be used to…

Problem 7. Suppose you take out a loan for $12,543 on a used car. This loan has a 3% interest rate that compounds monthly for 4 years. What will the monthly payment be?

2. A body at a temperature of 50°F is placed outdoors where the temperature is 100°F. If after 5 minutes the temperature of the body is 60°F, how long will it take the body to reach a temperature of 75°F?

1. (7 points) Suppose $f$ is a function whose graph is shown below. Find the value of $f^{-1}(2)$. No explanation necessary. You may assume that each square is 1 unit $\times$ 1 unit, that all of the pieces of the graph that look like straight lines are actually straight lines, and that points…

2. Solve the given differential equation $$(D^2 + 2D + 5)y = e^{2x}\sin x$$ 3. Solve the given differential equation $$x^2\frac{d^2y}{dx^2} + x\frac{dy}{dx} - 3y = x^2(\ln x)$$ 4. Solve the given differential equation $$(D^2 - 3D + 2)y = xe^{3x} + \sin 2x$$

Question 9 The relation R on Z where aRb means $|a - b| \le 1$. Determine whether R is an equivalence relation. True False 5 pts

A parabola has a vertex of (3, 6) and passes through the point (0, -6). (a) Calculate the value of $a$, the leading coefficient. SHOW ALL WORK and leave your answer as a FRACTION.

Suppose a store sells pairs of shoes for $30 each and is running a "buy one, get one 50% off" sale. Suppose further that you buy four pairs of shoes. The marginal cost of the second pair of shoes purchased is Select one: A. $0. B. $15. C. $30. D. $45. E. $60. F. $75. G. $90. H. $120.

(a) Find the smallest possible positive integer N such that $N! > N^3$. Then prove by mathematical induction that $n! > n^3$ for all positive integers $n \ge N$. [8 marks] (b) A sequence $\{a_n\}$ is defined by $a_1 = 3$, $a_2 = 11$ and $a_{n+2} = 6a_{n+1} - 7a_n$ for $n = 1, 2, 3, \dots$ Prove…

The triad on the 3rd quarter-note beat (chord 3) below is [Select] [Select] in [Select] Given that the key is Ab Major, its Roman numeral is [Select]

John rode 2 kilometers on his bike. His sister Sally rode 300 meters on her bike. Who rode the farthest?

Graphs and Functions Domain and range from the graph of a discrete relation The graph of the relation $T$ is shown below. Give the domain and range of $T$. Write your answers using set notation. domain = range =

What is the row 3, column 1 entry for the answer to the following? $\begin{bmatrix} -87 & -30 \\ -69 & -51 \\ -54 & -66 \end{bmatrix} - \begin{bmatrix} -93 & 74 \\ -52 & -44 \\ 33 & -3 \end{bmatrix}$ Enter your answer as a whole number with no additional spaces. Examples

If $A = \begin{bmatrix} 2 & -2 & 1 \\ 4 & -2 & 3 \\ -1 & 3 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 4 & 4 & 1 \\ 3 & 2 & 1 \\ -1 & -2 & 2 \end{bmatrix}$, then $4A - 3B = \begin{bmatrix} \Box & \Box & \Box \\ \Box & \Box & \Box \\ \Box & \Box & \Box \end{bmatrix}$ and $A^T = \begin{bmatrix}…

Given the function $P(r) = (r - 7)(-7r + 5)^9(r - 6)^5$, its roots are and their multiplicities are

7. If $2x^2 + Ax + 15 = (Bx – 5)(x – 3)$, where A and B are constants. Find A.

Question 4 1 pts Find the interest paid on a 2-year lease for a $29,951 car if the car depreciates at an annual rate of 15% and the lease has an annual interest rate of 5.9%. Round your answer to the nearest dollar.

Determine the difference in clock 12 arithmetic by starting at the first number and counting counterclockwise on the clock the number of units given by the second number. 2 - 2 2 - 2 = $\boxed{}$

2. Given $g(x) = (x-5)^2(x+2)(1-x)$, find the following: Degree of the polynomial: All x intercepts: Sign of the leading coefficient: The y intercept: End behavior diagram: Domain: Range:

Problem 5. Let $$ f_n(x) = \begin{cases} n & \text{if } 0 < x \le \frac{1}{n} \\ 0 & \text{if } \frac{1}{n} < x \le 1 \\ 0 & \text{if } x = 0 \end{cases} $$ for all $n \in \mathbb{N}$. (a) Show that $f_n \to 0$ pointwise on $[0, 1]$. (b) Show that the above convergence is not uniform. (Hint:…

There are 52 chipmunks per square kilometer in Ames. What is this a measure of? Dispersion Range Density Carrying capactiy Diversity

(x^(2))/(2)+(3)/(2)x-4=0 Solve for x by completing the square $\frac{x^2}{2} + \frac{3}{2}x - 4 = 0$

Question Is the following infinite sum defined? 15 - 15 + 15 - ... Select the correct answer below: The sum is defined. The sum is not defined. It is impossible to tell if the sum is defined.

Question Which of the following are geometric sequences? Select all correct answers. Select all that apply: -5, 15, -45, -135, 405, ... $6, 4, \frac{8}{3}, \frac{16}{9}, \frac{32}{27}, ...$ $5, -\frac{5}{3}, \frac{5}{9}, -\frac{5}{27}, \frac{5}{81}, ...$ $3, 2, \frac{4}{3}, \frac{8}{9},…

8-:2(2+2)= $8 \div 2 (2 + 2) = ?$

3) Given $f(x) = \frac{3x}{x^2 - 1}$, find the following: (3 points each) a) $f(2)$ b) $f(-2)$ c) $f(-x)$ d) $-f(x)$ e) $f(x-2)$ f) $f(2x)$

Question 4 (2 points) An account is opened with an initial deposit of $2,400 and earns 3.9% interest compounded monthly. What will the account be worth in 21 years? (round to 2 decimal places)

$\begin{cases} 2x_1 - 7x_2 + 4x_3 = 9 \\ x_1 + 9x_2 - 6x_3 = 1 \\ -3x_1 + 8x_2 + 5x_3 = 6 \end{cases}$

A bag of flour contains 5.00 lbs of flour. You have 3.20 tons of flour. There are 2000lbs per ton How many bags of flour can you make? 1.28 x 10$^5$ bags 8.00 x 10$^2$ bags 1.28 x 10$^2$ bags 1.28 x 10$^3$ bags 8.00 x 10$^3$ bags

(2 points) D 3 G 7 J 4 10 5 11 6 C F 9 2 I 12 13 14 B E 8 H Consider the graph given above. Use Kruskal's algorithm to find the minimum spanning tree. a. What is the total weight of the spanning tree? b. List the weights of the selected edges separated by commas in the order of selection. Note:…

1. (a) For each of the following sets $H_1, H_2, \dots, H_6$, state whether or not they are subspaces of $M_{2 \times 3}$, the set of $2 \times 3$ matrices with real entries. If so, explain why and if not, explain why. (i) $H_1 = \left\{ \begin{bmatrix} x_1 & x_2 & x_3 \\ x_4 & 0 & 0…

Travon is training for a bike race in the Alps, so he is training on hills. Each time he does a training ride, he measures how long he can continuously pedal without stopping once he begins biking uphill. What dimension of behavior is he measuring? Duration Latency Topography Frequency

6. The function $\log : (0, \infty) \to \mathbb{R}$ is often defined by $$ \log x = \int_1^x \frac{1}{t} dt. $$ Use this definition to verify the following: (b) $\log(xy) = \log x + \log y$, $x, y > 0$.

A fraction representing less than a whole unit where the numerator is less than the denominator is called a mixed number.

9. Joanna has a credit card whose billing period begins on the 17th day of each month. On July 17th her balance was $815.49. She made a $250 payment on July 28. She also made new charges of $27.55 on July 21, $129.99 on August 5, and $74.45 on August 10th. Find her average daily balance. Use a…

Simplify the rational expression. If the rational expression cannot be simplified, so state. $\frac{3y - 21}{2y - 14}$

Question 6 5 pts Suppose f: R → Z, where $f(x) = \lfloor 2x - 1 \rfloor$. Is f is onto Z? True False

The function $f$ is defined below. $$f(x) = \frac{x-8}{x^2+6x+5}$$ Find all values of $x$ that are NOT in the domain of $f$.

32. The greatest common factor between $a^2b^3$ and $a^4b$ is 12. Which of the following could be the value of $a$?

Consider the graph Γ: Which of the graphs below is isomorphic to Γ? Indicate the isomorphism by listing the vertices separated by commas in the order they correspond to A,B,C,D,E,F,G, respectively.

2. In the table below is the population of Los Osos for the period 1970-2020. Use this information to answer the following questions. Do not forget your units! Year 1970 1980 1990 2000 2010 2020 Population 3,487 10,933 14,377 14,351 14,276 16,533 (a) What is the average rate of change of the…

How many solutions (using only nonnegative integers) are there to the following equations? $x_1 + x_2 + x_3 + x_4 + x_5 = 32$. Show your work.

Question 2 Carol Anne makes candles. If she charges $20 for each candle, her total revenue will be $500 if she sells 25 candles. $20 regardless of how many candles she sells. $1,000 if she sells 100 candles. $200 if she sells 5 candles.

z-:4;z=824 9. $z \div 4$; $z = 824$

The hold on a drill bit is tightened by turning a A chuck key. B crimping tool. C ratchet handle. D crescent wrench.

Find the next number: 1, 3, 6, 11, 18, 29, ?

Dr. Ecco wants to meet with you to discuss an event. He sent you an encoded message which will give you a clue. The clue was encoded with the linear code which produced the following ciphertext: XOBRAFNJ You are told that the letter X decodes to the letter O and the letter J decodes to S. The…

(x-7)^(10)(x+5)^(5)+(x-7)^(9)(x+5)^(6)=0

2. A body at a temperature of 50°F is placed outdoors where the temperature is 100°F. If after 5 minutes the temperature of the body is 60°F, how long will it take the body to reach a temperature of 75°F?

3. Solve the system of equations. Write answer as an ordered triple: $x + 2y - z = 8$ $-2x + 3y - z = 1$ $2x + y + 3z = 5$

Let $f(x) = 4x + \frac{1}{x}$ and $g(x) = \frac{x}{x-3}$. Find $f \circ g$.

7) Solve the following system of equations below by the matrix inverse method. Show your work. 6 points $\begin{cases} x + y - z = 4 \\ -3x + 2y - z = 1 \\ 3x - 3y + 2z = 3 \end{cases}$ 8) Find the inverse of the following matrix A. Show your work. Check your work.. i.e. $AA^{-1} = I$ 6…

1. Which of the following is an example of deductive reasoning? (a) John noticed 2 dogs at a pound on Monday, 4 dogs on Tuesday, 6 dogs on Wednesday, he concludes there will be 8 dogs Thursday (b) Helen saw 5 students in the school on Monday, then 7 on Tuesday, then 9 on Wednesday, she…

Question 25 If 3 | $x$ and 25 | $x$, then... 75 | $x$ 28 | $x$ 15 | $x$ 5 | $x$

Ibuprofen can be found in 600 mg doses in over-the-counter analgesics, such as Advil and Motrin. How many grams of ibuprofen does such a tablet contain? 600 mg = g

Find the equation of the line and graph the line through the points (1, 2) and (2, -3). Write the equation in slope-intercept form. Type your equation below and submit your graph after the test.

Questions 16 – 19 are worth ten points each. There are instructions for each question. Please read the instructions carefully before answering the question. ~ $\bullet$ $\lor$ $\supset$ = Construct a truth table for the following statement. 16. $\sim(\sim L \lor N) \supset L$

If all other factors are equal, what effect will higher property taxes have on the value of the home a buyer can afford? O Increase the value for smaller homes and decrease the value for larger homes. O Decrease the value. O Increase the value. O Have no effect on the value.

Write out the next 4 terms of the sequence: $a_1 = -1$, $a_2 = 4$, and $a_{n+1} = a_n + a_{n-1}$ $a_3 = $ $a_4 = $ $a_5 = $ $a_6 = $

Suppose that the polynomial function $f$ is defined as follows. $f(x) = 5x^3 (x-6)(x+11)(x-11)$ List each zero of $f$ according to its multiplicity in the categories below If there is more than one answer for a multiplicity, separate them with Zero(s) of multiplicity one: Zero(s) of…

4. [0/12.5 Points] DETAILS LARPCALC11 7.T.009. PREVIOUS ANSWERS Solve the system of linear equations and check any solutions algebraically. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express x, y, and z in terms of the real number a.) $\begin{cases} x -…

f(x)=(6x)/(9x-7)

yd. What is its volume in ft³. There are 3ft in a yard (yd) 3.0 cubic feet 27 cubic feet .11 cubic feet 81 cubic feet 9.0 cubic feet

Question 2 1 pts "If Watson had bought stamps then he would not already have a drawer full of stamps. But Watson does have a drawer full of stamps.” Which of the following is guaranteed to be true so long as these two premises are true? Watson couldn't have a drawer full of stamps None of…

Column1 Combo Total # Of Puppies Variables Model 2 Wagons 1-2 3 X=0, Y=3 2-3 5 X=1, Y=5 3-4 7 X=2, Y=7 4-5 9 X=3, Y=9 5-6 11 X=4, Y= 11 6-7 13 X=5, Y=13 7-8 15 X=6, Y=15 8-9 17 X=7, Y=17 9-10 19 X=8, Y=19 (Y=MX+B)

(d) Let $f: X \to Y$. If for each pair of sets A, B, with $A \subset X$ and $B \subset X$, $f(A \cap B) = f(A) \cap f(B)$, then the function is one-to-one.

Match each of the following for the given function. The answers may be used more than once. $y = x^3 - 12x + 16$ zeros are starts in quadrant ends in quadrant behavior at the first zero on the left behavior at the second zero from the left

8. Given that we know the mean cholesterol of HIV patient receiving antiretroviral therapy at Livingstone Central Hospital and is normally distributed, with a mean of 2.5mmol/l, and a corresponding standard deviation of 0.6mmol/l. Using the empirical rule, we can say that about 95% of all HIV…

From the textbook: Find a possible formula for the exponential function represented by the data in the following table. x | 0 | 1 | 2 | 3 f(x) | 2.67 | 7.02 | 18.954 | 51.1758 Answer: $f(x) = $

Q2. (a) [5 MARKS] In each of the following let S denote some subset of $\mathbb{R}^3$. (i) Can there be an S which is a subspace of $\mathbb{R}^3$ and for which $|S| < \infty$? If so, give an example. If not, explain why. (ii) Can there be an S which is a subspace of $\mathbb{R}^3$ of dimension…

The goal in simplifying complex fractions is to create a reduced \_\_\_ expression.

Carry out the indicated algebraic operation. (If not possible, enter IMPOSSIBLE in any cell of the matrix.) $A = \begin{bmatrix} -4 & 9 \\ 4 & 5 \end{bmatrix}$ $B = \begin{bmatrix} -2 & \frac{3}{2} & -4 \\ 0 & 2 & -2 \end{bmatrix}$ $C = \begin{bmatrix} 0 & -\frac{3}{2} & 1 \\ 1 & 0 & 2…

Solve the equation. $\log_5(2x+5) - \log_5(x+5) = 1$ What is the equivalent equation that must be solved? A. $(2x+5) - (x+5) = 5$ B. $(2x+5) - (x+5) = 1$ C. $\frac{2x+5}{x+5} = 1$ D. $\frac{2x+5}{x+5} = 5$ Select the correct choice below and, if necessary, fill in the answer box to complete…

2. A fruit grower uses two types of fertilizer in an orange orchard, brand A and brand B. Each bag of brand A contains 8 pounds of nitrogen and 4 pounds of phosphoric acid. Each bag of brand B contains 7 pounds of nitrogen and 6 pounds of phosphoric acid. Tests indicate that the orchard needs…

Determine whether the following argument is valid. Use a truth table to JUSTIFY your answer (make sure to show the table). (15 points) 17. $\sim(J \vee G)$ $K \supset G$ $\sim G \vee K$

Representative democracy is when the people vote directly on issues before the government. O True O False

Find a value of c so that when $3b^4 + 4b^3 - 6b^2 + cb + 5$ is divided $b - 2$ the remainder is 85.

What is a good rule of thumb when buying a home? O It should not cost more than 10 times your annual income. O It should not cost more than 28% of your monthly income. O The monthly payment should be more than 2/3 your monthly salary. O You should wait until you have been married five years.

$5,000 is invested at a simple interest rate of 4.6%. If the future value of the investment is $5,782, how many years was the investment?

$5x + 7y = -4$ $8x - 9y = 12$ Select the correct choice below and, if necessary, fill in the answer box A. There is one solution. The solution is $\boxed{ }$ . (Simplify your answer. Type an ordered pair) B. There are infinitely many solutions of the form $(x, \boxed{ })$. (Type an expression…

Discuss the validity of the statement. If the statement is true, explain why. If not, give a counterexample. $\sqrt{x^2} = x$ for all real numbers $x$ Choose the correct answer below. A. False, because if $x = -7$, then $\sqrt{x^2} = \pm \sqrt{(-7)^2} = \pm \sqrt{49} = \pm 7 \ne x$ B. False,…

Question 9 (Mandatory) (1 point) A furniture designer builds a trapezoidal desk with a semicircular cutout. What is the area of the desk? 126 cm 300 cm 60 cm a) About 26 460 cm² b) About 22 680 cm² c) About 20 805 cm² d) About 11 370 cm²

Question 1 Which (if any) of the graphs below are the same? Which are different? Explain.

According to the rules of tennis, a regulation ball "shall have a bounce of more than 53 inches and less than 58 inches when dropped 100 inches upon a concrete base." Which number sentence reflects the bounce height restrictions for tennis balls? A. 53 inches $<$ bounce height $<$ 58 inches B.…

8. The lease on Kimm's SUV allows her 15,000 miles per year, with a 45 cents per mile penalty for overcharges. At the end of her 3-year lease, she returns the vehicle with 47,321 miles on it. How much of a mileage penalty, if any, does she owe?

1. Let $f: \mathbb{R}^3 \to \mathbb{R}^2$ and $g: \mathbb{R}^2 \to \mathbb{R}^3$ be differentiable functions with $f(1, -1, 0) = (2, 1)$, $$Df(1, -1, 0) = \begin{bmatrix} 3 & 0 & 2 \\ 2 & 1 & 1 \end{bmatrix}$$ and $$Dg(2, 1) = \begin{bmatrix} 0 & 2 \\ 1 & 0 \\ -1 & 1 \end{bmatrix}$$ Which of…

13. Match each graph to the appropriate discriminant. A. $b^2 - 4ac < 0$ B. $b^2 - 4ac > 0$ C. $b^2 - 4ac = 0$

Solve the equation $-7 - \frac{3}{5}x = -3$ algebraically. Answer as a "reduced Proper or Improper" fraction only.

1. Hank bought a policy from an insurance company that he pays \$550 a month guaranteed for the next 10 years. Is the amount he paid a present value or future value?

[-/1 Points] DETAILS ASK YOUR TEACHER A pure sample of a newly discovered radioactive isotope is discovered. It has a half-life of 75 s. Determine how long until only 1/16 of the original amount remains.

Consider the following pattern. 3 $\diamond$ 14 = 42 33 $\diamond$ 14 = 462 333 $\diamond$ 14 = 4662 3333 $\diamond$ 14 = 46662 Predict the result of 333333 $\diamond$ 14. Answer

The following money market account rates were available from a particular bank. Find the compound amount and the interest earned. $10,000 at 1.16% compounded daily for one year The compound amount is $ (Do not round until the final answer. Then round to the nearest cent as needed.)

$x = 2$ Move the two points to define a parabola and then write its equation. $(-3, -3)$

Sketch the graph of the solution set of the system of inequalities. (Use only lines to sketch the boundaries of your solution set. Do not use rays.) $$4x + y \le 8$$ $$4x - y \ge 0$$ $$x \ge 0$$

6. Find the sales tax on a purchase of $154.59 if the sales tax rate is 7%.

12.) Write the matrix $A = \begin{bmatrix} 3 \\ 1 \end{bmatrix} \begin{bmatrix} 1 \\ 2 \end{bmatrix}$ as a product of elementary matrices. 13.) Consider the system of equations. $2x + 2y = 7$ $kx + 2y = 8$ (a) For what value(s) of $k$, if any, does the system have a unique solution? Circle…

2. [0/12.5 Points] DETAILS LARPCALC11 7.T.004. Solve the system of equations graphically. (If there is no solution, enter NO SOLUTION.) $\begin{cases} 3x - 6y = 0 \\ 2x + 5y = 36 \end{cases}$

rewrite the quadratic function $y = 4x^2 - 24x + 29$ in the form $y = a(x - p)^2 + q$ by completing the square

Write the first four terms of the sequence $\{a_n\}_{n=1}^{\infty}$. $a_n = \frac{(-1)^n}{-2^n}$ $a_1 = \square$ (Simplify your answer.) $a_2 = \square$ (Simplify your answer.) $a_3 = \square$ (Simplify your answer.) $a_4 = \square$ (Simplify your answer.)

10. a) Solve by Substitution, the following systems $x^2 + y^2 = 25$ $y = 3x - 5$ b) Confirm your results from part "a" by graphing both equations on same set of axes and finding and labeling the points of intersection.

Q3. (a) [6 MARKS] Explain the term isomorphism. Give an explanation as to why $P_3$ is not isomorphic to $\mathbb{R}^3$. Give an example of a subspace of $P_3$ that is isomorphic to $\mathbb{R}^3$. (b) [6 MARKS] (i) What is the largest possible rank of a 10 × 8 matrix? (ii) If the null space of…

17. For given matrices A, and b, we know $Ax = b$ has solutions $x_1 = \begin{bmatrix} 1 \\ 3 \\ 9 \end{bmatrix}$ and $x_2 = \begin{bmatrix} -1 \\ 2 \\ 6 \end{bmatrix}$. Which of the following must be a solution to $Ax = 0$? a) $\begin{bmatrix} 2 \\ 3 \\ 9 \end{bmatrix}$ b) $\begin{bmatrix} 2…

The following graph has no Hamilton circuit has exactly one Hamilton circuit has several Hamilton circuits, none of which contain the edge AB has several Hamilton circuits, all of which contain the edge AB none of the above

The actual color a viewer sees on a screen is influenced by the specific type and amount of phosphors on the screen. So each computer screen manufacturer must convert between the (R, G, B) data and an international CIE standard for color, which uses three primary colors, called X, Y, and Z. A…

In a certain city there is a river running through the middle of the city. There are 3 islands and 9 bridges as shown in the figure below. North Bank A B C River South Bank In the graph that models this situation, what is the degree of the vertex that represents Island B?

19. Puzzle: Age difference A man and his grandson share their birthday in day and month. On one of their birthdays, the grandfather's age in years is same as his grandson's age in months. After how many years will grandfather's age in years be a multiple of grandson's age in years? Pick ONE…

i- $(p \to q) \lor (p \to r) \equiv \neg r \to (\neg p \lor q)$ ii- $(p \to \neg q) \land \neg p \equiv p \to (\neg q \land \neg p)$

Name a relationship between sets A, B, and/or C as illustrated in the figure below. Your relationship can involve 2 or more sets--you don't need to use all of them. You can find set notation symbols by clicking on the + in the menu above the answer box and choosing "Equation," then "Graphical…

Find the principal needed now to get the given amount; that is, find the present value. To get \$2000 after $1\frac{1}{4}$ years at 8% compounded daily The present value of \$2000 is \$ $\boxed{}$. (Round to the nearest cent as needed.)

A wave function can be expanded in basis states as $|\psi\rangle = \sum_n a_n |\psi_n\rangle$ What must be true of the expansion coefficients? There is no restrictions on the coefficients. $\sum_n a_n = 1$ They must be real numbers. $\sum_n |a_n|^2 = 1$

Suppose that the functions $q$ and $r$ are defined as follows. $q(x) = -x + 3$ $r(x) = 4x + 2$ Find the following. $(r \circ q)(5) = \text{☐}$ $(q \circ r)(5) = \text{☐}$

Range: [-5, 63 Given the graph of f, use interval notation to state the: Domain: Range: Find f(-5) = Find all value(s) of x, for which f(x) = 0.

Which of the following graphs have Euler circuits or Euler trails? A: Has Euler trail. A: Has Euler circuit. B: Has Euler trail. B: Has Euler circuit. C: Has Euler trail. C: Has Euler circuit. D: Has Euler trail. D: Has Euler circuit.

Q3) Transform the boundary value initial problem by $u(x, t)$, $u_t = Du_{xx} - B(u - S)$, $u(x, 0) = \sin(\frac{\pi x}{L}) + S$ into a familiar one by setting: $v(x, t) = e^{Bt}[u(x, t) - S]$ and determine the boundary condition that satisfied by $v(x, t)$ where D, B,S,L are constant.

For $f(x) = \frac{9}{x+5}$ and $g(x) = \frac{7}{x}$, find a. $(f \circ g)(x)$; b. the domain of $f \circ g$ a. $(f \circ g)(x) = \boxed{}$ (Simplify your answer.) b. What is the domain of $f \circ g$? The domain is $\boxed{}$ (Simplify your answer. Type your answer in interval notation. Use…

2log(3-x)=1 $2 \log(3 - x) = 1$

Question 8 1 pts Your employer offers a 401(k) plan with a 42% match, and you set a goal of retiring in 28 years with an amount of money which has the same buying power that 1.5 million dollars has today. If the account earns an annual interest rate of 5.6% and the expected annual rate of…

7. (4 pts.) Use the graph of the polynomial function below to answer the following. a. Determine the minimum degree of the polynomial: b. Is the leading coefficient positive or negative?

Does the graph have a Hamilton circuit? True False Does the graph have a Hamilton circuit? True False

Part 3 (3 pts) 2-Car Combo Total # of Puppies Change 1-2 3 2-3 5 2 Create a table of your data for the various combinations. (Feel free to copy and modify this table for each type of combination) What is the change from one total to the next? Is this change the same or does it change? Can you…

The linear system (S): $\begin{cases} mx - 2y = 1 \\ x + 4y = 0 \end{cases}$ can be solved using Cramer's method if:

Suppose the matrix representation of a relation $R$ on the set $\{1, 2, 3\}$ is $\begin{bmatrix} 1 & 1 & 1 \\ 1 & 0 & 0 \\ 1 & 0 & 1 \end{bmatrix}$ Then $R$ is 1. reflexive [Select] 2. symmetric [Select] 3. transitive [Select]

3. Michael and Kathryn borrowed $282,500 to buy their house, for which they took out a 30-year loan at 3.75%. (a) Find their monthly payment. (b) What would their payment have been if they had instead taken out a 15-year loan at the same interest rate?

Multiple Choice 1 point Which equation is not parallel to $y = \frac{2}{3}x - 5$? $y = \frac{2}{3}x$ $-2x + 3y = 15$ $3x + 2y = 6$ $4x - 6y = 22$

11) Given $a_1 = -2$ and $a_{k+1} = a_k + 4$. 5 points. a) Write the first 5 terms of the sequence. b) What type of sequence is determined by the terms in (a)? c) What is formula for the nth term? d) Find the twenty-first term. e) Compute the sum of the first twenty-one terms. 12) Given $a_1 =…

Choose 7 problems out of the 10 on this exam to complete. If you wish, you may attempt more than 10, but I will only grade 7 of them. Circle the problem numbers for each of the 7 problems you would like me to grade. 1. Let A = \{1,3,5,7,9\} and B = \{x|x is an integer between -5 and 5\}.…

Question 9 Find the value of $1 \cdot 0 + \overline{(0+1)}$

Find $f(x)$ and $g(x)$ such that $h(x) = (f \circ g)(x)$. Answers may vary. (Use no $h(x) = (x - 8)^3$ $\{f(x), g(x)\} = \{\}$

4. Using algebraic methods, find the solution sets for the following. Give your solutions in interval notation. (a) $6x^2 \ge 24x - 18$ (b) $\frac{3}{x+1} < 15$

Use the graph to determine a. open intervals on which the function is increasing, if any. b. open intervals on which the function is decreasing, if any. c. open intervals on which the function is constant, if any.

6. [0/12.5 Points] DETAILS LARPCALC11 7.Τ.011. Write the partial fraction decomposition of the rational expression. Check your result algebraically. $$ \frac{5x + 8}{x^2 - x - 2} $$

Question 14 4 pts A new vaccine claims to reduce the risk of contracting chicken pox from 50% to 20%. Which of the following statements is true regarding this claim? This vaccine decreases the risk of contracting chicken pox by 150 percentage points This vaccine decreases the risk of…

Ex. 4) Find the $10^{th}$ term in a geometric sequence which has a $2^{nd}$ term equal to 7 and a $5^{th}$ term equal to 35. [First, find the common ratio, $r$. Then, since the initial term, $b$, is not given, you must express the $10^{th}$ term of the sequence in terms of one of the given…

Draw the graph of f(x)=-((1)/(6))^(x+2) Draw the graph of $f(x) = - \left( \frac{1}{6} \right)^{x+2}$

Let A = \{1, 3, 5, 7\} B = \{5, 6, 7, 8\} C = \{5, 8\} D = \{2, 5, 8\} U = \{1, 2, 3, 4, 5, 6, 7, 8\} Determine whether the statement is true or false. $C \subset A$ False; A is a subset of C. False; C is equal to A. True False; C has one different element than A does.

(b) Let $P_n$ denote the vector space of polynomials in $t \in \mathbb{R}$ of degree at most $n$. (i) Can $1 + t \in P_1$ be written as a linear combination of $2 + 7t$ and $-3 + 4t$? Explain your answer. (ii) Can $2 - 4t \in P_1$ be written as a linear combination of $2 + 6t$ and $-1 + 3t$?…

Solve the following for $v$ algebraically. $\log_2(4v - 1) - \log_2 v = \log_2 3$

$h(x) = \begin{cases} -4x - 17 & \text{for } x < -8 \\ 3 & \text{for } -8 \le x < 3 \\ x + 2 & \text{for } x \ge 3 \end{cases}$ $h(-8) = ?$ $h(-4) = ?$ $h(3) = ?$ $h(6) = ?$

3. Misalkan himpunan A = {0, 1, 2, 3}. Pada A didefinisikan relasi : R = {(x, y) | x ≤ y}. Jelaskan, apakah relasi R tersebut merupakan relasi ekivalen atau bukan !

Let $\mathcal{P}(A)$ denote the power set of $A$. If $\mathcal{P}(A) \subseteq B$ then (a) $2^{|A|} \le |B|$ (b) $2^{|A|} \ge |B|$ (c) $2^{|A|} < |B|$ (d) $|A| + 2 \le |B|$ (e) $2^{|A|} \ge 2^{|B|}$

To the nearest cent, how much loan can you afford, if you can pay \$700, monthly for 15 years at 3.8\% interest? (Identify or find each) P = d = As a decimal, r = n = t =

Evaluate the following syllogism by using a Venn Diagram (You do not have to show your Venn Diagram.): Some beliefs are items that have propositional reference. Some judgments are items that have propositional reference. So, it follows that some judgments are beliefs. valid invalid

4) Evaluate the following determinants. Show your work. Check your work. 8 points a) $ \begin{vmatrix} 1 & -1 & 2 \\ -1 & 3 & 0 \\ 0 & 1 & -1 \end{vmatrix} $ b) $ \begin{vmatrix} 0 & -1 & 2 \\ 1 & 1 & 0 \\ 2 & 0 & 1 \end{vmatrix} $ c) $ \begin{vmatrix} -1 & 3 & 0 \\ 0 & 1 & 2 \\ 0 & 1 & 2…

Question 3 4 pts A new vaccine claims to reduce the risk of contracting chicken pox from 50% to 20%. Which of the following statements is true regarding this claim? This vaccine decreases the risk of contracting chicken pox by 60 percentage points This vaccine decreases the risk of contracting…

10. If $f(x) = a^x$ and $f(6) = 64$, find the following values of $f(x)$. a. $f(4)$ b. $f(-3)$

Sketch the graph of the solution set of the system of inequalities. $\begin{cases} y < -x^2 + x + 4 \\ y > 3x \end{cases}$

Question 2 1 pts Find the monthly payments on a 2-year lease for a $29,481 car if the car depreciates at an annual rate of 16% and the lease has an annual interest rate of 5.7%. Round your answer to the nearest dollar.

Mary purchased 4 tires by mail order. She paid $45.80 per tire plus $6.50 per tire for shipping and handling. There is no sales tax, because the tires were purchased out of state. She also had to pay $8.17 per tire for mounting and balancing. At a local store, Mary's total for the 4 tires with…

Which of the following is a major seventh (M7) below the given note? Enharmonic equivalents are not acceptable answers. O Eb O C O F O E

9. What is the x-intercept of the line given by the equation? $x + y = 8$ (8, 0) (4, 4) (7, 1)

Which of the following are trees and which are forests? A: Is a forest A: Is a tree B: Is a forest B: Is a tree C: Is a forest C: Is a tree D: Is a forest D: Is a tree

Let the graph of polynomial $g(x)$ be given below. 28. What is the domain and range of $g(x)$? a. D = $(-\infty, \infty)$ and R = $(-\infty, \infty)$ b. D = $(-1, 3)$ and R = $(-\infty, \infty)$ c. D = $(-\infty, \infty)$ and R = $(-\infty, 5]$ d. D = $[-1, 3]$ and R = $[0, 5]$ e. Can't…

4. Companion matrix of the polynomial $f(x) = x^3 + 2x^2 + 1$ is A: $\begin{bmatrix} 0 & 0 & -1 \\ 1 & 0 & 0 \\ 0 & 1 & -2 \end{bmatrix}$ B: $\begin{bmatrix} 1 & 0 & -1 \\ 0 & 1 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ C: $\begin{bmatrix} 1 & 0 & -1 \\ 0 & 1 & -2 \\ 0 & 0 & -1 \end{bmatrix}$ D:…

The following triad is ✓ [Select] F A D C in Given that the key is C Major, its Roman numeral is [Select] 8

Consider the relation, R on the set of integers with $R = \{(a,b) | a = b \text{ or } a = -b\}$. Which one of the following is true? A. transitive B. not symmetry C. not transitive D. one-to-one relation

Determine whether the activity can be used to illustrate the associative property. In a store, buying cereal, soap, and dog food Choose the correct answer below. No Yes

Arnold Brown has a Visa Card with an annual percentage rate of 18.0%. The unpaid balance for his June billing cycle is $1,227.55. During the billing cycle he purchased a printer cartridge for $43.44, books for $232.77 and gasoline for $15.33. He made a payment of $1,100. If the account applies…

Q3. (a) [5 MARKS] Find the matrix of the linear transformation defined by $T\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} -3x_1 + 2x_2 \\ x_1 + 4x_3 \end{bmatrix}$. Is this linear transformation an isomorphism? Explain your answer. (b) [5 MARKS] Is it possible for a matrix…

Suppose, at a given point in time, Sally's Smoothie Shack operates in a perfectly competitive market and is producing its profit-maximizing level of output. Suppose further that at this level of production its average fixed cost of producing a smoothie is $1.30, average variable cost is $2.50,…

Identify $f(x) = \frac{3}{5} - \frac{7}{8}x$ as being linear, quadratic, or neither. If $f$ is quadratic, identify the leading coefficient $a$ and evaluate $f(-2)$.

Use the graph of $f(x)$ to find the $x$-intercepts of the graph and the zeros of the function. The x-intercepts are $\boxed{}$. (Type ordered pairs. Use a comma to separate answers.) The zeros are $x = \boxed{}$. (Use a comma to separate answers.)

A political party's ultimate aim is to A. canvass voters B. nominate candidates in the primary or convention and get them elected C. serve as advisors to county administrators D. finance party candidates

If you want $180,000 in 20 years after collecting 8% simple interest, rounded to the nearest cent, what is the present value? (Identify or find each) A = P = As a decimal, r = t=

Analytics Exercise 4-2 (Algo) You work for a company that makes cell phones and have been made project manager for the design of a new cell phone. Your supervisors have already scoped the project, so you have a list showing the work breakdown structure, and this includes major project…

Solve the inequality $\frac{x+4}{x+7} < -2$ Give your answer in interval notation.

Q1. (a) [12 MARKS] Decide, with justification, whether $H_1$, $H_2$ and $H_3$ are subspaces of $\mathbb{R}^3$, where $H_1 = \begin{Bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} \in \mathbb{R}^3 : x_2 = x_1, x_3 = 0 \end{Bmatrix}$, $H_2 = \begin{Bmatrix} \begin{bmatrix} x_1 \\ x_2 \\…

A land reclamation has 90.2 square feet of land and costs 325.26. What is the cost per square foot to the nearest cent? Enter your answer to the whole nearest whole cent. Do NOT include units with your answer.

Question 6 5 pts Suppose f: R → Z, where $f(x) = \lfloor 2x - 1 \rfloor$. Is f is onto Z? True False

1) Solve the following system of equations by the Gauss-Jordan method. Write the solution if a unique solution exists. If no solution exists, write no solution. If infinitely many solutions exist, write infinitely many solutions, and express $x$, $y$, and $z$ in terms of a parameter $t$. Show…

6. For the system of equations. $\begin{cases} 4x - y + 7z = -21 \\ -x + 2y - 2z = 9 \\ 8y + 9z = 7 \end{cases}$ (a) Write the corresponding augmented matrix. (b) Use the matrix to solve the system. (c) Be sure to write the solution as an ordered triple.

10. It is given that $\frac{1}{x} + \frac{1}{2z} = \frac{6}{5y}$. If $x = -3$ and $y = 12$, find $z$.

Marysia has saved $65.00 in quarters and loonies. If she has 4 quarters fewer than two-fifths the number of loonies, how many coins of each type does Marysia have? Marysia has $\boxed{ }$ loonies and $\boxed{ }$ quarters.

Which functions are the same as their inverse functions? $f(x) = \frac{x-1}{x+5}, x \neq -5$ $g(x) = \frac{x-2}{x-1}, x \neq 1$ $h(x) = \frac{x+3}{x-2}, x \neq 2$ $k(x) = \frac{x+1}{x-1}, x \neq 1$

x^(2)+5x-5=0 Slove for x by using the quadratic formula 15. $x^2 + 5x - 5 = 0$

1. A man wants to use cottage cheese and yogurt to increase the amount of protein and calcium in his daily diet. An ounce of cottage cheese contains 3 grams of protein and 15 milligrams of calcium. An ounce of yogurt contains 1 gram of protein and 41 milligrams of calcium. How many ounces of…

4. Find n(F), given that n(B × F) = 18 and B = {1, 3}.

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