A ball is placed inside a box into which it will fit tightly. If the radius of the ball is 10 cm, calculate: a) the volume of the ball, b) the volume of the box, c) the percentage volume of the box not occupied by the ball.

Simplify the following fractions: a) $\frac{1}{7}+\frac{3}{7}$ b) $\frac{a}{7}+\frac{b}{7}$ c) $\frac{5}{13}+\frac{6}{13}$ d) $\frac{c}{13}+\frac{d}{13}$ e) $\frac{x}{3}+\frac{y}{3}+\frac{z}{3}$ f) $\frac{p^{2}}{5}+\frac{q^{2}}{5}$

Determine the mean and variance of the random variable in Exercise 4.1.8.

Roughly estimate the volume of a tennis ball in cubic centimeters by using 6 cm for the diameter and 3 for π. Round the answer to the nearest ten cubic centimeters.

Calculate the volume of material used to make the hemispherical bowl on the left, if the inner radius of the bowl is 5 cm and its outer radius 5.5 cm.

At the end of a football season the leading goal scorer in a league has scored eight more goals than the second leading goal scorer. The second has scored fifteen more than the third. The total number of goals scored by all three players is 134. a) Write an expression for each of the three scores. b) Form an equation and then solve it to find the number of goals scored by each player.

A manufacturer of precision digital switches has daily revenue R (in dollars) of $R(x)=5 x-\frac{x^{2}}{2000}$, where x is the number of switches produced daily. What is the rate of change of revenue with respect to x? What are the units of $R^{\prime}(x)$?

The volume of the material used to make the sphere and hemispherical bowl are the same. Given that the radius of the sphere is 7cm and the inner radius of the bowl is 10cm, calculate, to 1 d.p., the outer radius rcm of the bowl.

Draw a graph of $y=4^{x}$ for values of x between -1 and 3. Use your graph to find approximate solutions to the following equations: a) $4^{x}=30$ b) $4^{x}=\frac{1}{2}$

A prep chef has just made two dozen meatballs. Each meatball has a 2 inch diameter. Right now, before the meatballs are added, the sauce is 2 inches from the top of the 14 inch diameter pot. Will the sauce spill over when the chef adds the meatballs to the pot?

Complete the sentence in a way that shows you understand the meaning of the italicized vocabulary word. Neil $\mathit{feigned}$ sickness in an effort to...

Expand and simplify the following: a) $3 a-2(2 a+4)$ b) $8 x-4(x+5)$ c) $3(p-4)-4$ d) $7(3 m-2 n)+8 n$ e) $6 x-3(2 x-1)$ f) $5 p-3 p(p+2)$

Calculate the volume of material used to make the hemispherical bowl if the inner radius of the bowl is 5 cm and its outer radius 5.5 cm. Give your answer in terms of $\pi$.

A plane leaves London for Boston, a distance of 5200 km, at 0945. The plane travels at an average speed of 800 km/h. If Boston time is five hours behind British time, what is the time in Boston when the aircraft lands?