Consider a hypothesis test of difference of proportions for two independent populations. Suppose random samples produce $r_{1}$ successes out of $n_{1}$ trials for the first population and $r_{2}$ successes out of $n_{2}$ trials for the second population. What is the formula for the sample test statistic?

Joints like knees and elbows are designed to move freely. Find out how friction is reduced in a joint.

Zoom out sufficiently far so that the graph appears as a line. What equation does this line appear to have? (Note that the points at which the function is not continuous are not readily seen when you zoom out.) \

$$f(x)=\dfrac{x^3-3 x^2+2}{x(x-3)}$$

$g(x)=x+\dfrac{2}{x(x-3)} \quad$

Rewrite each sentence, adding a noun clause introduced by the underlined word. Example: Original Mr. Mayherne tries to figure out how. Rewritten Mr. Mayherne tries to figure out how he can prove Leonard Vole's innocence.

Mr. Mayheme thirks about who.

An urn contains K green and N−K blue balls. (a) You take n balls out of the urn. Find the probability that k of the n balls are green. (b) You take a ball out of the urn, note its color, and replace it. You repeat these steps n times. Find the probability that k of the n balls are green.

A cube with a side length of 6 cm has a square pyramid with a 6 cm by 6 cm base and 6 cm height cut out of it. Which has the greatest volume? F. the cut out pyramid shape G. the remainder of the cube H. they have an equal volume J. none of these

Plants have many adaptations to stop them from drying out. Briefly describe two of these adaptations.

You can move a constant across the integral sign, but can you do the same with a variable? Find out by carrying out the following steps:

a. Find $\int x \cdot x d x$ by evaluating $\int x^2 d x$.

b. Find $x \cdot \int x d x$.

c. Do the answers for parts (a) and (b) agree?

Your teacher will give you and your partner different incomplete charts about what four employees at Almacén Gigante did last weekend. After you fill out the chart based on each other's information, you will fill out the final column about your partner.

What are the components of the PAR and where would a federal agency go to find out the requirements for preparing a PAR?

Mica and Joan are on the same softball team. Mica got 8 hits out of 48 times at bat, while Joan got 12 hits out of 40 times at bat. Who do you think is more likely to get a hit her next time at bat? Explain.

For each Vocabulary word, choose the letter of the correct definition.

decrepit

a. careless

b. slow

c. worn out

You put a mirror at the bottom of a 1.4-m-deep pool. A laser beam enters the water at $30^{\circ}$ relative to the normal, hits the mirror, reflects, and comes back out of the water. How far from the water entry point will the beam come out of the water? Draw a ray diagram.

A fighter plane is diving toward the earth. At the last instant, the pilot pulls out of the dive on a vertical circle and begins climbing upward. In such maneuvers, the pilot can black out if too much blood drains from his head. Why does blood drain from his head?