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You borrow 990 from your brother and you agree to pay back $1080 in 16 months. What simple interest rate will you pay?

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Problem #3: An isosceles triangle gate in a wall is hinged at location A. Determine the magnitude of force $F_H$ just required to hold the gate closed at location B. Assume a specific weight of 9810 N/m³ for water. $X_2$ FLUID Y $X_3$ $F_H$ B Known are the following: $SG_y = 0.9$ $X_1 = 1.2 m$ $X_2 = 2 m$ $X_3 = 2.5 m$ $\alpha = 60°$

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In which, if any, of the following cases is f differentiable at a ? (Select all that apply.) a=2; domain of f : all real numbers; lim_(h->0^(+))(f(2+h)-f(2))/(h)=3,lim_(h->0^(-))(f(2+h)-f(2))/(h)=5 a=0; domain of f:(0,2);lim_(h->0)(f(1+h)-f(1))/(h)=3 a=3; domain of f:[0,2];lim_(h->0)(f(3+h)-f(3))/(h)=5 a=0; domain of f : all real numbers; lim_(h->0)(f(h)-f(0))/(h)=infty none of the above [-/1 Points] In which, if any, of the following cases is f differentiable at a? (Select all that apply.) a=4; domain of f : all real numbers except 5; lim_(h->0^(+))(f(4+h)-f(4))/(h)=5,lim_(h->0^(-))(f(4+h)-f(4))/(h)=5 a=0; domain of f:[0,2);lim_(h->0)(f(h)-f(0))/(h)=3 a=3; domain of f : all real numbers except 3; lim_(h->0)(f(4+h)-f(4))/(h)=5 a=0; domain of f:(-0.0001,0.0001);lim_(h->0)(f(h)-f(0))/(h)=30 none of the above In which, if any, of the following cases is f differentiable at a? (Select all that apply.) a=2; domain of f: all real numbers; lim f(2 + h) -f(2)= 3, lim f(2 + h) - f(2) = 5 h0+ h h0 h a = 0; domain of f: (0, 2);lim f(1+h)-f1=3 h a = 3; domain of f: [0, 2]; lim. f(3 + h) - f(3) = 5 h a=0;domain of f:all real numbers; lim 0y-4 h0 h none of the above Submit Answer [-/1 Points] DETAILS MY In which, if any, of the following cases is f differentiable at a? (Select all that apply. a=4; domain of f:all real numbers except 5; lim h0+ h h0 h a=0;domain of f:[0,2; lim 04 h a=3;domain of f:all real numbers except 3; lim f(4 + h) - f(4) = 5 h a=0;domain of f:-0.0001,0.0001 Jim. h0 h none of the above

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Find the zeros of the function and state the multiplicities.\ f(x) = 2x^5 + 9x^4 + 7x^3\ Select one:\ a. 1 (multiplicity 2.5), \frac{7}{2} (multiplicity 2.5)\ b. -1 (multiplicity 2.5), -\frac{7}{2} (multiplicity 2.5)\ c. 0 (multiplicity 3), 1 (multiplicity 1), \frac{7}{2} (multiplicity 1)\ d. 0 (multiplicity 3), -1 (multiplicity 1), -\frac{7}{2} (multiplicity 1)

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A random sample of 50 plastic items is obtained, and their breaking strengths are measured. The sample mean is 7.154 and the sample standard deviation is 0.548. Conduct a hypothesis test to assess whether there is any evidence that the average breaking strength is not 7.000? Use a level of significance of 1% using Approach 1 and Approach 2. Show calculations. Write out your final conclusion in one short sentence.

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The expression 74x + 52 - 2x + 6 - 5x + 6x - 3 equals + ++. Enter the correct number in each box.

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1. (2 pts) Let $Y_1, Y_2, \dots, Y_n$ be a random sample from a distribution with density function $\qquad f(y) = \begin{cases} \frac{m}{\theta} y^{m-1} e^{-y^m/\theta} & y > 0 \\ 0 & y \le 0 \end{cases}$ where $m$ is known and $\theta$ is unknown. Find the uniformly most powerful test for testing $H_0: \theta = \theta_0$ against $H_a: \theta > \theta_0$.

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2: Conservative or not? (8 points) For each of the following fields, tell me whether $\oint \vec{F} \cdot d\vec{r} = 0$ for all possible closed paths. I suggest that you either perform a test on the field, construct a path for which the integral is non-zero, or construct a scalar function that the field is the derivative of. $\circ \vec{F} = a(x)\hat{x} + b(y)\hat{y} + c(z)\hat{z}$ where $a$, $b$, and $c$ are differentiable functions. $\circ \vec{F} = \frac{2\cos\theta}{r^3}\hat{r} + \frac{\sin\theta}{r^3}\hat{\theta}$ (Assume that this field is specified in spherical polar coordinates.) $\circ \vec{F} = g(x)\hat{y}$ where $\frac{d}{dx}g(x) > 0$ for all $x$. $\circ \vec{F} = (\hat{x} + \hat{y})\cos kz$, where $k$ is a constant.

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Barker Office Supply Store is budgeting for the fiscal year ending March 31, 2020. During the fiscal year ended March 31, 2019, sales totaled $1,200,000 and cost of goods sold was $660,000. At March 31, 2019, inventory was $200,000. During the upcoming fiscal year, Barker estimates that cost of goods sold will increase by 9% and that ending inventory will be $225,000. How much inventory should Barker purchase during the fiscal year ending March 31, 2020?

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Question Completion Status: Click Submit to complete this assessment. Question 1 Question 1 of 1 25 points Save Answer A 130-lb box is loaded onto the 65-lb tailgate of a pickup truck. The tailgate is supported by a single cable AB. Note CG's for the tailgate and box are at G1 and G2 respectively. Set $d_1 = 12$-in and $d_2 = 17$-in. a) Calculate the tension developed in the cable AB and enter the value (in units of lb) in the answer box below. b) Calculate the horizontal and vertical components of the reactions at pin O. Indicate the directions with arrows. Note: the answer for part b) will be graded on the pdf submission. Be sure to draw the \textit{free-body} diagram of the tailgate, clearly label all equations of equilibrium and box in your final answers for parts a) and b) on the pdf in order to receive any partial credit.

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cameron d.