A rabbit can run 35 miles per hour. A fox can run 21 miles in half an hour. Which animal is faster, and by how much? (A) The rabbit is faster by 7 miles per hour. (B) The fox is faster by 7 miles per hour. (C) The rabbit is faster by 14 miles per hour. (D) The fox is faster by 14 miles per hour.

Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x = 8. y = 1 2/9 when x = 3 2/3.

y varies directly with x. If y = 7 when x = 3, find x when y = 21.

A company is planning to produce and sell a new line of computers. The fixed cost will be $360,000 and it will cost$850 to produce each computer. Determine the break-even point. Describe what this means.

The information for two pay-as-you-go cell phone companies is given. On Call 3.5 hours: $10, Talk Time 1/2 hours:$1.25. a. What is the unit rate in dollars per hour for each company? b. Which company offers the best deal? Explain your answer. c. Another company offers a rate of $0.05 per minute. How would you find the unit rate per hour? d. Is the rate in part c a better deal than On Call or Talk Time? Explain.

Expand the given function in a Laurent series valid for the indicated annular domain. $f(z)=\frac{1-e^{z}}{z^{2}}, 0<|z|$

Write the structural formula of ATP. Circle the bond that breaks when ADP forms.

What lessons did the experience of the blitz teach the British?

Determine whether the function is even, odd, or neither (a) algebraically, (b) graphically by using a graphing utility to graph the function, and (c) numerically by using the table feature of the graphing utility to compare f(x) and f(-x) for several values of x. $f(x)=x^{6}-2 x^{2}+3$

Use properties of determinants to evaluate the given determinant by inspection. Explain your reasoning.

$$\left| \begin{array} { c c c c } { 1 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 1 } & { 0 } \\ { 0 } & { 1 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { 1 } \end{array} \right|$$

Solve the inequality. Express the solution using interval notation and graph the solution set on the real number line.

$$12 - x \geq 7 x$$

A Secchi disk is an 8-inch-diameter weighted disk that is painted black and white and attached to a rope. The disk is lowered into water and the depth (in inches) at which it is no longer visible is recorded. The measurement is an indication of water clarity. An environmental biologist interested in determining whether the water clarity of the Jake at Joliet Junior College is improving takes measurements at the same location on eight date during the course of a year and repeats the measurements on the same dates five years later. She obtain s the following results:

$$\begin{matrix} \text{Observation} & \text{1} & \text{2} & \text{3} & \text{4} & \text{5} & \text{6} & \text{7} & \text{8}\\ \text{Date} & \text{5/11} & \text{6/7} & \text{6/24} & \text{7/8} & \text{7/27} & \text{8/31} & \text{9/30} & \text{10/12}\\ \text{Initial depth, }{X_{i}} & \text{38} & \text{58} & \text{65} & \text{74} & \text{56} & \text{36} & \text{56} & \text{52}\\ \text{Depth five years later, }{Y_i} & \text{52} & \text{60} & \text{72} & \text{72} & \text{54} & \text{48} & \text{58} & \text{60}\\ \end{matrix}$$

Why is it important to take the measurements on the same date?

Evaluate

$$\int _ { C } \mathbf { F } \cdot d \mathbf { r }$$

along the curve C.

$$\left. \begin{array} { l } { \mathbf { F } ( x , y ) = x ^ { 2 } y \mathbf { i } + 4 \mathbf { j } } \\ { C : \mathbf { r } ( t ) = e ^ { t } \mathbf { \mathbf { i } } + e ^ { - t } \mathbf { j } } \end{array} \right.$$

(0≤t≤1)

A new sunblock product claims to have an SPF rating of 60. This means that you get 60 times your body’s natural defence against the Suns UVB rays, (a) How could you test this claim? Comment on the ethics of your test (b) If many skin cancers are associated with UVA rays, what impact could this product have on cancer rates?