Numerade

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Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb into C as much as possible.) $$ \int \frac{15}{44} dx = $$

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Problem 2.1 Consider the system: \begin{bmatrix} 1 & 2 & -1 \\ 2 & 5 & -1 \\ 1 & 3 & -3 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 3 \\ 6 \\ 0 \end{bmatrix}, (1) as discussed in the module notes. Define the coefficient matrix $A$ and the right-hand side vector $b$ in a Matlab script. Use the 'det' function to determine whether the coefficient matrix is singular or non-singular. Call the determinant of A 'detA'. Use the 'rref' function to determine the RREF of the augmented matrix. Based on inspection of this reduced form, does the system have a unique solution? Why? Imagine that you need to solve the above linear system $Ax = b$. You could either use the \ operator, or find the inverse $A^{-1}$ and then calculate $x = A^{-1}b$. Using the 'tic' and 'toc' functions in a script, show that the solution of the linear system is more efficiently performed using the former approach rather than the latter. Note - due to the small size of the system, you may have to perform the calculation a large number of times (in a loop say) so that there is a noticeable difference in timing between the two approaches.

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Note: Use the z-score methodology learned in class to solve the next problem even though we usually use this methodology for sample sizes of 30 or more. Please ignore the fact our sample in this problem is only 10. Display the problem visually by drawing the normal curve with vertical lines indicating the average and points of interest. HINT: Use the Minitab's Distribution Plot or the methodology described in Chapter VIII of the Greenbelt Primer. 5. Using the average and standard deviation from the previous problem, what percent of rivets have lengths between 3.20 and 3.60 inches? ANSWER: 6. A Two-Replication/Two Operator/5 Part Gage Capability Study was conducted for a bushing outside diameter with a total tolerance equal to 020 of an inch. The following are the recorded measurements: Part Caroline-Rep 1 Caroline-Rep 2 David-Rep 1 David-Rep 2 1 0.494 0.494 0.489 0.488 2 0.497 0.498 0.493 0.490 3 0.514 0.513 0.505 0.505 4 0.503 0.503 0.498 0.497 5 0.506 0.507 0.503 0.501 What is the Gage R&R as a percent of engineering tolerance and as a percent to study variation? Show all work. Feel free to use Minitab or appropriate M/S Excel template. Gage Capability (% to Tolerance): Gage Capability (% to Study Variation):

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Q16a. Responsibility accounting (10 pts) Classico's Pizza, a chain of pizza parlors, views each branch location as an investment center. The local branch reported the following results for the current year: Sales Variable expenses Traceable fixed costs Average total assets of the branch $3,600,000 $2,970,000 $270,000 $1,440,000 Compute the following measures for this investment center: (a) Contribution margin: $ (b) Contribution margin ratio: (c) Responsibility margin: $ (d) Increase in annual responsibility margin that would be expected to result from a 10% increase in sales volume: $ Show work (Label your answers):

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11.2 A steel block [E = 29 \times 10^3 ksi and \nu = 0.33] has initial side lengths all equal to 56 inches. After stresses are applied in the x, y, and z directions, the new lengths in the x, y, and z directions are 56.06 in., 56.10 in., and 55.95 in., respectively. Determine the stress components \sigma_x, \sigma_y, and \sigma_z that cause these deformations.

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1 Complete the following statements. (a) 40 000 m$^2$ = ....... hectares (b) 5673 kg = ....... tonnes (c) 8000 cm$^3$ = ....... litres (d) 20 miles = ....... km 2 Solve the equation. 8b + 22 = 78

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Use the information to answer the question. Alex has $5\frac{1}{2}$ cups of dog food. A serving of dog food is $\frac{4}{5}$ cup. How many servings does Alex have? A. $\frac{8}{55}$ serving B. $4\frac{2}{5}$ servings C. $5\frac{5}{8}$ servings D. $6\frac{7}{8}$ servings

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E. Use the values of a, b and c or roots of each of the ff. quadratic equations in determining the sum and product of its roots. EQUATION/ROOTS 1) x²+4x-21 = 0 2) 2x² - 5x = 2 3) 4) X?= 11 & X?= -11 SUM PRODUCT -16 60

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5.) A company is deciding which box to use for their merchandise. The first box measures 8 inches by 6.25 inches by 10.5 inches. The second box measures 9 inches by 5.5 inches by 11.75 inches. Which box required more material to make? SA = 2(8 \times 6.25 + 8 \times 10.5 + 6.25 \times 10.5) = 399.25 in$^2$ SA = 2(9 \times 5.5 + 5.5 \times 11.75 + 11.75 \times 9) = 439.75 in$^2$ 439.75 > 399.25 6.) If each box (from #5) used material that cost $0.03 per square inch to make, how much does a company save by choosing to make fifty boxes of the smaller box in comparison to fifty boxes of the larger box?

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1) Show that $f(b) - f(a) = f'(a)(b - a) - \int_a^b f''(x)(x - b)dx$.

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tom-s f.