Numerade

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Suppose that the distribution of the scores of all high school seniors who took the SAT Math (SAT-M) test this year is Normal with a mean of μ and a standard deviation σ=100. To estimate μ, a random sample of 10 students was drawn. If the sample size is changed to 20, which one of the following statements is TRUE? Group of answer choices The sampling standard deviation of the sample mean X¯ would be changed to its 1/2. The sampling standard deviation of the sample mean X¯ would be changed to its half. The population standard deviation would be changed to its 1/2. The sampling standard deviation of the sample mean X¯ would be doubled.

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What is the impact of disease states/conditions that cause prolonged hypercapnia?

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You drive your speedboat at 25.8 (m/s) at 26 degrees west of north. Calculate the westerly component of your speed.

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[30 points] A disc of radius R is supported by a rope (with no inertia) attached to a vertical wall as shown and at the point P of the disc, as shown in the figure. The rope makes an angle $\theta$ with respect to the wall. The point at which the rope is attached to the disc is such that if the line of the rope is extended, it crosses the horizontal line through the center of the disc at a distance $\frac{3}{2}R$ from the wall. Derive a relation for the minimum coefficient of static equilibrium ($\mu_s$), only in terms of the variable $\theta$, for this system to remain in static equilibrium.

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[2] The linkage below has the dimensions and crank angle as shown. Use the polygon method to find $\alpha_3$, $A_A$, $A_B$ and $A_C$ given $\omega_2 = 15$ rad/sec, $\omega_3 = 5.69$ rad/sec and $\alpha_2 = 10$ rad/sec$^2$ in the directions shown and $O_2A = 0.8$ in, $AB = 1.93$ in, $AC = 1.33$ in.

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Unit #1: Thinking Task This is an evaluation, make sure you are completing the work on your own. To earn full marks, you must justify your solution. Include the following as needed: Show diagram, define variables, state formula, theorem, equation or function used, Show substitutions and or steps in solving an equation, State restrictions, state concluding statement, Use correct notation. No marks are given if your solution includes: e or ln, differentiation, integration. 1. The polynomial $P(x) = 6x^3 + mx^2 + nx - 5$ has a factor of $x + 1$. When $P(x)$ is divided by $x - 1$, the remainder is -4. What are the values of m and n? (3 marks)

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Supplemental Problem 3. For a system described by the differential equation \frac{d^2y}{dt^2}(t) + 2\frac{dy}{dt}(t) + 10y(t) = \frac{dx}{dt}(t) + x(t) determine the Laplace transform Y(s) if x(t) = 10u(t), x(0) = 0, y'(0) = 1, and y(0) = 2. Use the inverse Laplace transform to now determine y(t). Plot the response y(t) using MATLAB.

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What is the value of c to the nearest unit? * c b 15 40° 22 20 23 17

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If $1+4=5$ $2+5=12$ $3+6=21$ $8+11=?$

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F. Determine whether the following functions are continuous or not using the three conditions to be satisfied. 1. $f(x) = \frac{x^2 - 36}{x + 6}$ if $x = -12$ 2. $f(x) = \frac{x^2 - 1}{x + 1}$ if $x = -7$

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