Both situations have the same expected value. Find the missing information. Situation 1: Paul hits a dart target worth 15 points 45% of the time. Situation 2: He hits a dart target worth 10 points x% of the time.

A quadratic relation has roots 0 and -6 and a maximum at (-3, 4). Determine the equation of the relation.

Either evaluate the given improper integral or show that it diverges. $\int_{0}^{+\infty} x^{2} e^{-x} d x$

Use the given information about the angle $\theta$ to find the exact value of a. $\sin 2 \theta .$ b. $\cos 2 \theta .$ c. $\tan 2 \theta.$ $\tan \theta = - 2 , \frac { \pi } { 2 } < \theta < \pi$

Find the arc length of the curve over the given interval. $r=6 \cos \theta, 0 \leq \theta \leq 2 \pi.$ Check your answer by geometry.

Mentally calculate each quotient. Write each answer as a decimal number.

$$2.5\div100$$

An epidemic hits a city. Each person is classified by the Health Department as either well, sick, or a carrier. The proportion of people in each category by age groups is given by the matrix

$$\begin{array}{lll}{0-15} & {16-35} & {\text { Over } 35} \\ {\text { Sick }} & {0.25} & {0.60} & {0.70} \\ {\text { Sick }} & {0.25} & {0.35} & {0.20} \\ {\text { Carrier }} & {0.10} & {0.05} & {0.10}\end{array} ]=A$$

The population of the city by age and gender is

$$\begin{array}{lll}{0-15} & {35,000} & {30,000} \\ {16-35} & {55,000} & {50,000} \\ {\text { Over } 35} & {70,000} & {75,000}\end{array} ]=B$$

(a) Compute AB. Interpret the meaning of the entries in AB. (b) How many sick males are there? (c) How many females are well?

Metabolic activity in the human body releases approximately $1.0\times10^4\;\mathrm{kJ}$ of heat per day. Assume that a 55-kg body has the same specific heat as water; how much would the body temperature rise if it were an isolated system? How much water must the body eliminate as perspiration to maintain the normal body temperature (98.6 °F)? Comment on your results. (The heat of vaporization of water is 2.41 kJ/g.)

Simplify each product. Use an area model as needed.

$$2 x ( 3 x + 1 )$$

(A) Identify the type of equation or inequality (some may fit more than one category). (B) Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible.

$$(2p+1)(p+5)=2p+40$$

A basketball team scored 43, 55, 41, and 37 points in their first four matches. Find the mean number of points scored for the first four matches.

How would you say 'tools' in Spanish?

A and B are events for which P(A) = 0.3 + x, P(B) = 0.2 + x, and $P(A \cap B)=x$. Find x if A and B are mutually exclusive events.

When a guitar string is sounded along with a 440-Hz tuning fork, a beat frequency of 5 Hz is heard. When the same string is sounded along with a 436-Hz tuning fork, the beat frequency is 9 Hz. What is the frequency of the string?