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Question 1 1 pts If a test of hypothesis has a Type I error probability (a) of 0.01 , we mean Bene nul hypotheis is true, we reject it 1% of the time. If the rull irpotheris is false, we reject it 1 K of the time.

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Evan’s presentation topic is complex, so he wants to use a PowerPoint to help his audience follow along, grasp his ideas, and remain interested. How can Evan use his PowerPoint to accomplish his goals while avoiding common visual aid pitfalls?

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uits are one means interest groups use to achieve policy goals. Group of answer choices Class action Mass action Collective action Inaction

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Find the derivative. $y = 6 - 5x^3$

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2. The trapezium ABCD is shown below. Determine the value of the acute angle $x$ (in degrees) when the area of the trapezium is a maximum. (3 marks) 3. Let $f(x) = \begin{cases} \cos x, & x < 0 \\ 1, & x \ge 0 \end{cases}$ Using the appropriate definition(s), determine whether $f$ is differentiable and continuous at $x = 0$.

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QUESTION 25 Alpha computers Inc ships fifty hard drives to Omega Stores via Delta Transport Company. If the shipment is destroyed during transit, the risk of loss will fall on A. Delta only. B. Alpha or Delta, depending on the terms of the contract and the applicable sections of the UCC. C. Alpha only. D. none of the other answers.

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9. A West Coast firm wants to estimate the average fuel savings that will result when people use its gasoline additive. A city police agency conducted an experiment by using the additive in 8 of its cars for a one-week period. The recorded gasoline savings, as measured by the percentage decrease in fuel usage per mile after using the additive, are: 15.2 14.1 13.7 15.2 18.6 14.5 15.0 and 13.8 Some summary information is $\sum X = 120.1$ and $\sum X^2 = 1820.23$ Estimate the true population mean at a 99% confidence level. 10. Weekly ratings published by the A.C. Nielsen Company have made television producers and advertisers very sensitive to claims regarding the proportion of the total viewing audience reached by a particular program. A television station claims that its 6 o'clock evening news reaches 50% of the viewing audience in the area. A firm considering the purchase of advertising time during the 6 o'clock time slot wishes to test the validity of the station's claim. How large a sample should the firm select if it wants the bound on the error of estimation (margin of error) to be 5%?

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QUESTION 13 Consider the nonlinear system $\dot{x}_1 = -x_2$ $\dot{x}_2 = x_1 - 2x_2 + ax_1^3$ where $a = 2$. Consider the Lyapunov function $V(x) = x^T P x + \eta x_1^4$ where $P = \begin{pmatrix} 1.5 & -0.5 \ -0.5 & 0.5 \end{pmatrix}$. For which value of $\eta$ the function $V(x)$ can be used to prove stability of the system? Enter your answer to 2 decimal places in the box below.

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A 3 kg big-toy roller-coaster starts at floor level, pushed 240 mm into a compression spring whose stiffness in 1900 N/m, then released from rest How fast is the coaster moving at the top of hill #1, 1.6 m tall hill? IGNORE FRICTION here, and other inefficiencies (such as spring's mass) (a) determine the spring's Energy before release ] (b) determine the coaster's gravity Energy at the hilltop ] c) find the coaster's speed from its Kinetic Energy at the hilltop 8.54 $m/s$ 22.05 $m/s$ 1.60 $m/s$ 2.26 $m/s$ 6.45 $m/s$ 8.24 $m/s$

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Find \frac{5}{6}(-4 \cdot \frac{2}{7}). Write your answer in simplest form.

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joshua m.