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Assefa Dedefa

Assefa D.

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Books Assigned

Introductory Statistics

Introductory Statistics

Neil A. Weiss 9th Edition
Achievement 1,372 solutions

Viewed Questions

Write down the number of vertices, the number of edges and the degree of each vertex in: (i) the graph in Fig. 0.3; (ii) the tree in Fig. 0.14.

Introduction to Graph Theory

The chi-square goodness-of-fit test provides a method for performing a hypothesis test about the distribution of a variable that has $c$ possible values. If the number of possible values is 2 that is, $c=2,$ the chi-square goodness-of-fit test is equivalent to a procedure that you studied earlier. a. Which procedure is that? Explain your answer. b. Suppose that you want to perform a hypothesis test to decide whether the proportion of a population that has a specified attribute is different from $p_{0}$. Discuss the method for performing such a test if you use (1) the one-proportion z-test (page 558 ) or (2) the chi-square goodness-of-fit test.

The chi-square goodness-of-fit test provides a method for performing a hypothesis test about the distribution of a variable that has $c$ possible values. If the number of possible values is 2 that is, $c=2,$ the chi-square goodness-of-fit test is equivalent to a procedure that you studied earlier. a. Which procedure is that? Explain your answer. b. Suppose that you want to perform a hypothesis test to decide whether the proportion of a population that has a specified attribute is different from $p_{0}$. Discuss the method for performing such a test if you use (1) the one-proportion z-test (page 558 ) or (2) the chi-square goodness-of-fit test.

Introductory Statistics

Chi-Square Procedures

Chi-Square Goodness-of-Fit Test
Use the graph to approximate the number of points of intersection of the graphs of $y_{1}$ and $y_{2}$. $$\begin{aligned} &y_{1}=2 \sin x\\ &y_{2}=\frac{1}{2} x+1 \end{aligned}$$

Use the graph to approximate the number of points of intersection of the graphs of $y_{1}$ and $y_{2}$. $$\begin{aligned} &y_{1}=2 \sin x\\ &y_{2}=\frac{1}{2} x+1 \end{aligned}$$

Algebra and Trigonometry Real Mathematics, Real People

Analytic Trigonometry

Solving Trigonometric Equations
Use the graph of $y=(x-1)^{2}-4$ to answer each question. (a) Describe the viewing window of the graph. (b) Approximate any $x$ - or $y$ -intercepts of the graph. (c) Determine whether (-4,1) and (2,-3) are solution points of the equation. Explain.

Use the graph of $y=(x-1)^{2}-4$ to answer each question. (a) Describe the viewing window of the graph. (b) Approximate any $x$ - or $y$ -intercepts of the graph. (c) Determine whether (-4,1) and (2,-3) are solution points of the equation. Explain.

Algebra and Trigonometry Real Mathematics, Real People

Functions and Their Graphs

Graphs of Equations

Questions asked

INSTANT ANSWER

A set of stairs is 10 feet tall and covers a horizontal distance of 12 feet. If a handrail is to be installed that extends the entire length of the stairs, what length must it be?

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INSTANT ANSWER

\( -5= \) 8823-7210 \( \square \) -4- 2 Photern ment 1 ? \begin{tabular}{|c|c|} \hline Hrigh \( (\mathrm{cm}) \) & Frequency \\ \hline \( 140 \leq h<160 \) & 11 \\ \hline \( 160 \leq h<170 \) & 51 \\ \hline \( 170 \leq h<180 \) & 68 \\ \hline \( 180 \leq h<190 \) & 47 \\ \hline \( 190 \leq h<210 \) & 23 \\ \hline \end{tabular} (a) (i) Wite down the mid intierval value of \( 140 \leq h<160 \). (ii) Calaculte an ertinute of the memin height of the 200 students. Thes tathe is used to create the following curnulative frequency graph. (b) Use the cumulative frequency curve to estimste the interquartile range. (2) Laszo is e chident in the date set and his height is 204 cm . (c) Use your answer to pat: (b) to estimate whether Laszio's haight is an outlier for this data Justify yourarsiwer \( \qquad \) (This question continues on the following page)

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INSTANT ANSWER

\( -5= \) 8823-7210 \( \square \) -4- 2 Photern ment 1 ? \begin{tabular}{|c|c|} \hline Hrigh \( (\mathrm{cm}) \) & Frequency \\ \hline \( 140 \leq h<160 \) & 11 \\ \hline \( 160 \leq h<170 \) & 51 \\ \hline \( 170 \leq h<180 \) & 68 \\ \hline \( 180 \leq h<190 \) & 47 \\ \hline \( 190 \leq h<210 \) & 23 \\ \hline \end{tabular} (a) (i) Wite down the mid intierval value of \( 140 \leq h<160 \). (ii) Calaculte an ertinute of the memin height of the 200 students. Thes tathe is used to create the following curnulative frequency graph. (b) Use the cumulative frequency curve to estimste the interquartile range. (2) Laszo is e chident in the date set and his height is 204 cm . (c) Use your answer to pat: (b) to estimate whether Laszio's haight is an outlier for this data Justify yourarsiwer \( \qquad \) (This question continues on the following page)

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ANSWERED

Ivan Kochetkov verified

Numerade educator

4. [Maximum mark: 12] A type of generator will only function if a particular switch is working. The generator has a main switch, A, and a 'back up' switch, B. The manufacturer claims the probability of switch A failing within one month of being fitted is 0.1 and the probability of the cheaper switch B failing within one month is 0.3. Whether or not a switch fails is independent of the state of the other switch. If both switches fail, the generator needs to shut down to replace the switches. Both switches are replaced after a month of use (whether they have failed or not) or whenever the generator needs to be shut down. The following tree diagram shows the probabilities of a switch failing within one month of them both being replaced, assuming the manufacturer's claim is correct. switch A switch B fail b fail 0.1 c not fail a b fail not fail c not fail (a) Write down the values of (i) a (ii) b (iii) c [2] (b) Hence find the probability that the generator needs to shut down within one month of the switches being replaced. [1] The owner of the generator is suspicious of the switch manufacturer's claims, so they look back through the past 200 occasions when the switches were replaced. The records show whether no switches, one switch or two switches had failed. The data the owner collected are shown in the following table. No switch fails One switch fails Two switches fail 118 72 10 (c) Perform a ?² goodness of fit test at the 5% significance level to test whether the manufacturer's claims are correct using the following hypotheses. H?: The manufacturer's claims are correct. H?: The manufacturer's claims are not both correct.

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ANSWERED

Brian Beasley verified

Numerade educator

A shop uses the following model to estimate ( n ), the number of smoothies sold per day, in terms of ( x ), the price of a single smoothie in pesos. [ n=frac{40000}{x^{2}} ] The maximum number of smoothies the shop can make in a day is 400 . (a) Find the maximum price they could charge per smoothie for the shop to sell 400 in one day. (b) On a day when the shop sells smoothies at 50 pesos each, use the model to find (i) the number of smoothies sold. (ii) the total income from the smoothies sold. The cost of making each smoothie is 20 pesos. The profit per day ( (P) ) is the total income from the sale of smoothies that day minus the cost of making them. (c) (i) Show that, according to the model, ( P=frac{40000}{x}-frac{800000}{x^{2}} ). (ii) Find ( frac{mathrm{d} P}{mathrm{~d} x} ). (iii) Find the value of ( x ) for which ( frac{mathrm{d} P}{mathrm{dx}}=0 ) (iv) Find the number of smoothies sold when the profit is maximized

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ANSWERED

Melissa Munoz verified

Numerade educator

A national park contains three mountains whose summits are at points A, B and C. According to a coordinate system, the position of A is (0, 0, 2.8) and the position of B is (7.2, 5.1, 2.4). All the values are in kilometres. diagram not to scale (a) (i) Find the vector AB. (ii) Hence find AB, the distance between A and B. The vector AC is parallel to the vector (1.1 8.4 0.2). (b) Find the angle between (1.1 8.4 0.2) and AB. The angle between BA and BC is 55.2 . (c) Use the sine rule to find AC.

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ANSWERED

Daniel Carr verified

Numerade educator

The company Fred Express delivers packages. From past experience, the time taken, T, to deliver a package follows a normal distribution with mean 64 hours and standard deviation 12 hours. (a) State P(T < 64). (b) Find P(44 < T < 64). 30% of packages are delivered in less than k hours. (c) (i) Sketch a diagram of this normal distribution, shading the region that represents P(T < k). (ii) Find the value of k. For quality control, the manager randomly selects five outgoing packages. These selections are independent. (d) Find the probability that exactly two of these packages are delivered in less than k hours. Fred Express charges a fixed amount of $4.50 for any package weighing 1 kg or less. Heavier packages are charged an additional fee of $2.00 per kg. This fee is applied for any weight in excess of 1 kg. For example, a 1.5 kg package is charged an additional $1.00. (e) Write down an expression for the amount charged to deliver a package of weight x kg, where x > 1. (f) Find the amount Fred Express charges for a 5.3 kg package. Meiling is charged $7.20 for the delivery of a package. (g) Find the weight of Meiling's package.

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ANSWERED

Melissa Munoz verified

Numerade educator

Consider the following system of coupled differential equations. [ egin{array}{l} frac{d x}{d t}=-4 x \ frac{d y}{d t}=3 x-2 y end{array} ] (a) Find the eigenvalues and corresponding eigenvectors of the matrix ( left(egin{array}{cc}-4 & 0 \ 3 & -2end{array} ight) ). (b) Hence, write down the general solution of the system. (c) Determine, with justification, whether the equilibrium point ( (0,0) ) is stable or unstable. (d) Find the value of ( frac{mathrm{d} y}{mathrm{~d} x} ) (i) at ( (4,0) ). (ii) at ( (-4,0) ). (e) Sketch a phase portrait for the general solution to the system of coupled differential equations for ( -6 leq x leq 6,-6 leq y leq 6 ).

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ANSWERED

Supratim Pal verified

Numerade educator

A particle P moves along the \( x \)-axis. The velocity of P is \( \mathrm{vms}^{-1} \) at time \( t \) seconds, where \( v=-2 t^{2}+16 t-24 \) for \( t \geq 0 \). (a) Find the times when P is at instantaneous rest. (b) Find the magnitude of the particle's acceleration at 6 seconds. (c) Find the greatest speed of P in the interval \( 0 \leq t \leq 6 \). (d) The particle starts from the origin O . Find an expression for the displacement of P from O at time \( t \) seconds. (e) Find the total distance travelled by P in the interval \( 0 \leq t \leq 4 \).

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ANSWERED

Ivan Kochetkov verified

Numerade educator

4. A particle P moves on the x-axis. At time t seconds the velocity of P is v m s^-1 in the direction of x increasing, where v = 2t^2 - 14t + 20, t >= 0 Find (a) the times when P is instantaneously at rest, (b) the greatest speed of P in the interval 0 <= t <= 4 (c) the total distance travelled by P in the interval 0 <= t <= 4

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