Numerade

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1. (2 points) In an arithmetic sequence a? = 3 and a?? = 23. What is the common difference, i.e., a? - a???? Show your work. 2. (4 points) Solve the recurrence b? = 2 and b? = 3b??? - 1 for n > 1. Find a closed-form expression. 3. (3 points) List the steps taken by Binary Search to find 11 in the sequence (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11). How many comparisons are performed with 11? 4. (4 points) Sort the sequence (4, 1, 3, 2, 5) using Bubble Sort (smallest to largest). Show the lists obtained at each step. 5. (4 points) Evaluate the summation $\sum_{i=1}^{n} \sum_{j=i}^{n} (j - i)$. 6. (4 points) Prove by induction that 3? - 1 is a multiple of 2 for all positive integers n. 7. (4 points) Prove by induction that $\sum_{i=0}^{n} i = 2^{n+1} - 1$. 8. (4 points) What is the output of the following code? Justify your answer using summations. s = 0 for i = 1 to n j = n while (j >= i) do s = s + 1 j = j - 1 print s

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On a rural highway the speeds of all vehicles are normally distributed with a mean of 43 mph and a standard deviation of 5 mph. Find the probability that the mean speed of a random sample of 16 cars traveling on this highway is greater than 45 mph (the posted speed limit)? Round your answer to 3 decimal places.

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1- To understand how a moving charge can also create a magnetic field, consider a particle with charge q moving with velocity v. Define the position vector r = rf leading from the particle to some location. (a) Show that the magnetic field at that location is B = (μ₀*q*v)/(4π*r^2) (b) Find the magnitude of the magnetic field 1.00 mm to the side of a proton moving at a velocity of 2.00 x 10^7 m/s. [3.2 × 10^-13 T]

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What is the most likely reason that Vredenburg chose to use a large-scale experimental design such as this, rather than a single lake or laboratory experiments?

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In the figure, a 5.00-kg block is moving at 5.00 m/s along a horizontal frictionless surface toward an ideal massless spring that is attached to a wall. After the block collides with the spring, the spring is compressed a maximum distance of 0.68 m. What is the speed of the block when it has moved so that the spring is compressed to only one-half of the maximum distance?

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Which of the following is true of emotions? Question 14 options: Emotions are false and deceiving. People should never feel guilty or fearful. Patients must discover the thoughts that are behind the emotion. Problem solving is independent of emotional state.

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All work will be done in Python. It's important that this is kept in mind. I will follow up on this question and will give a thumbs up once the question is correctly answered in Python. 2. Show that the identity (cos x)2 = (1 + cos(2x)) holds for the following values of x: TT a) x = 6 b) x=1.25 c) Since this is an identity, f(x) = (cos x)2 (1 + cos(2x)) should be zero for all x. Plot f on the domain x e [0, 2r]. If you do not get the line y = 0, explain why (hint: look at the y-axis scale).

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Below are the comparative Balance Sheets for JME for 20x1 and 20x2, as well as the 20x2 Income Statement. 20x1 20x2 Cash 6,878 8,912 Accounts Receivable 639 980 Inventory 260 427 Prepaid Rent 62 54 Equipment (net) 1,326 1,465 Land 675 2,346 Other LT Assets 253 203 Total Assets 10,093 14,387 Sales 11,358 Cost of Goods Sold 1,085 Gross Profit 10,273 Salary Expense 2,856 Misc Expense 362 Depr Exp - Eq 1,925 Operating Income 5,130 Interest Expense 443 Income Before Tax 4,687 Income Tax 1,233 Net Income 3,454 Accounts Payable 808 721 Salary Payable 202 336 Income Tax Payable 484 466 Unearned Revenue 560 1,718 Other Current Liab 371 369 Mortgage Payable 3,000 2,500 Pref Stock - 100 par -0- 1,000 Common Stock and APIC 2,924 3,333 Retained Earnings 1,744 3,944 Total Liab and Equity 10,093 14,387 Be careful of the subtotals - they are in bold. Watch the order of the years. REQUIRED: Prepare JME's SCF for 2Ox2. Make sure you prepare the Operations section under BOTH the indirect and direct methods.

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Problem 3: Using a Lagrange Interpolation polynomial of 1st and 2nd order, evaluate $\log_e(8)$. Given $\log_e(6) = 1.792$, $\log_e(10) = 2.303$, $\log_e(12) = 2.485$ Evaluate the true error (exact value vs interpolated value) for $\log_e(8)$ obtained from both the 1st order and 2nd order Lagrange Interpolation polynomial. Problem 4: A set with the following four data points is given: $\begin{array}{|c|c|c|c|c|} \hline x & 6 & 12 & 18 & 24 \\ \hline y & 6 & 26 & 35 & 51 \\ \hline \end{array}$ a) Determine the linear splines that fit the entire data set b) Determine the interpolated value for $x = 33$

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Chapter 07 Homework (Application) Petty Cash Fund Prepare journal entries for each of the following: a. Issued a check to establish a petty cash fund of $600. If an amount box does not require an entry, leave it blank. b. The amount of cash in the petty cash fund is $190. Issued a check to replenish the fund, based on the following summary of petty cash receipts: store supplies, $240 and miscellaneous selling expense, $152. Record any missing funds in the cash short and over account. If an amount box does not require an entry, leave it blank.

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