The total sustained load on the concrete footing of a planned building is the sum of the dead load plus the occupancy load. Suppose that the dead load

$$X _ { 1 }$$

has a gamma distribution with

$$\alpha _ { 1 } = 50 \text { and } \beta _ { 1 } = 2$$

, whereas the occupancy load

$$X _ { 2 }$$

has a gamma distribution with

$$\alpha _ { 2 } = 20 \operatorname { and } \beta _ { 2 } = 2$$

. (Units are in kips.) Assume that

$$X _ { 1 } \text { and } X _ { 2 }$$

are independent. Find a value for the sustained load that will be exceeded with probability less than 1/16.

You plan to conduct an experiment to test the effectiveness of Sleepeze, a new drug that is supposed to reduce insomnia. You will use a sample of subjects that are treated with the drug and another sample of subjects that are given a placebo. What is a completely randomized design?

Algebraically solve each system of equations using any method you wish.

$$\left\{\begin{aligned} 2 x+8 y &=-8 \\ x+7 y &=-13 \end{aligned}\right.$$

Which expression(s) are not equal to

$$\tan ^ { 2 } \theta ?$$

$$\mathrm { I }. \sec ^ { 2 } \theta + 1$$

$$\mathrm { II } . \sec ^ { 2 } \theta – 1$$

$$\Pi \mathrm { I } \cdot \frac { \sin ^ { 2 } \theta } { \cos ^ { 2 } \theta }$$

$$\mathrm { I } \mathrm { V } . \frac { 1 } { \cot ^ { 2 } \theta }$$

A. I B. II C. III D. I and IV

Forest Products, Inc. invested $50 million. The company’s overall D-E mix is 60–40. What is the return on the company’s equity, if the net income is$5 million on a revenue base of $6 million?

Which number is a solution of | 4x - 1|+ 2 = 1? (A)

$$- \frac { 1 } { 2 }$$

(B) 0 (C) 1 (D) There is no solution.

Find intervals for x and y that describe a good viewing window for the graph of the polynomial function.

$$f(x) = 2x^4 - 7x^3 + x - 8$$

Use an area formula to find the unknown measurement. A rectangular band-aid covers

$$2 \frac { 1 } { 2 } \mathrm { in. } ^ { 2 }$$

of skin. If the width of the band-aid is

$$\frac { 5 } { 8 } \text { in. }$$

, find its length.

Calculate the mass of the Sun based on data for average Earth's orbit and compare the value obtained with the Sun's commonly listed value of

$$1.989 × 10^{30} kg.$$

In a video game, players earn 10 points for finishing the first level and twice as many points for each additional level. How many points does a player earn for finishing the fifth level? How many points will the p!ayer have earned in the game up to that point?

Write each decimal as a fraction or a mixed number in simplest form.

$$2.48$$

Use the minimum or maximum feature of a graphing calculator to approximate the vertex of the graph of the function.

$$y = 0.25 x ^ { 2 } - 5 ^ { 2 / 3 } x + 2$$

Multiply. Write each answer in simplest form. -3(1 5/6)

Explain how a motor neuron action potential can trigger a skeletal muscle fiber contraction.