The Chase family spends 20% of their income on rent and $\frac { 1 } { 3 }$ of their income on groceries. What percent of their income does the Chase family spend on rent and groceries combined?

Suppose that the population of oxygen-dependent bacteria in a pond is modeled by the equation $P ( t ) = \frac { 60 } { 5 + 7 e ^ { - l } }$ where $P ( t )$ is the population (in billions) $t$ days after an initial observation at time $t = 0$
(a) Use a graphing utility to graph the function $P ( t )$. (b)In words, explain what happens to the population over time? Check your conclusion by finding $\lim _ { t \rightarrow + \infty } P ( t )$ (c)In words, what happens to the rate of population growth over time? Check your conclusion by graphing $P ^ { \prime } ( t )$ .

a. Calculate each difference without using a calculator : $\dfrac{1}{\sqrt{2}} - \dfrac{\sqrt{2}}{2}$ b Calculate each difference without using a calculator : $\dfrac{1}{\sqrt{3}} - \dfrac{\sqrt{3}}{3}$ c. Calculate each difference without using a calculator : $\dfrac{1}{\sqrt{4}} - \dfrac{\sqrt{4}}{4}$ d. Calculate each difference without using a calculator : $\dfrac{1}{\sqrt{5}} - \dfrac{\sqrt{5}}{5}$ e. What is the pattern in the differences ?

Solve $\left(2x+\frac{2}{3}\right)(x+5)=0$. Is each of the following a solution of the equation?

$$x=-5$$

The Public Service Board (PSB) awarded two contracts worth a combined $1.07 million to improve (i.e., deepen) a retention basin and reconstruct the spillway that was severely damaged in a flood 2 years ago. The PSB said that, because of the weak economy, the bids came in$950,000 lower than engineers expected. If the projects are assumed to have a 20-year life, what is the annual worth of the savings at an interest rate of 6% per year?

Mercury was the messenger of the Roman gods. Mercury is identified with manual skill, eloquence, cleverness, travel, and thievery. What is meant when a person is described as $\underline{mercurial}$?

Use the discriminant to find the number of real solutions of the equation $9 x ^ { 2 } - 24 x + 16 = 0$

A renewable source forms at a rate that is much slower than the rate in which the resource is used.

The original height of the Pyramid of Khafre, located next to the Great Pyramid in Egypt, was about 47 ft. Each side of its square base was about 708 ft. What is the lateral area, to the nearest square foot, of a pyramid with those dimensions?

What causes electrons to move through a wire as a current?

Arrange the following structures in the order in which sperm pass by or travel through them: epididymis; vas deferens; testes; prostate gland; seminal vesicles

Complete each cause-to-effect analogy by choosing the best answer. quarrel : discord :: _____ : merriment a. joking b. talking

The huge number of capillaries and venules is needed to (a) provide nutrients (such as $O_{2}$) and remove waste products from all of the body cells. (b) distribute water uniformly throughout the body. (c) reduce the resistance of the circulatory system. (d) b and c (e) a, b, and c

In designing a spherical weather balloon, it is decided to double the diameter of the balloon so that it can carry a heavier instrument load. What is the ratio of the final surface area to the original surface area?