Recommended heart rates during exercise vary with age and physical condition. For a healthy person doing moderate to intense exercise, such as hiking, the inequality $0.5(220-a) \leq R \leq 0.9(220-a)$ gives a target range for the heart rate R (in beats per minute), based on age a (in years). a. What is the target range for heart rates for a person 15 years old? b. How old is a person whose target range is between 99 and 178.2 beats per minute?

A student wants to compare the volumes of two metal blocks. Block A has a mass of 128.45 g and a density of 8.80 g/cm³. Block B has a mass of 92.2 g and a density of 7.14 g/cm³. Which block has a greater volume? Show your calculations.

Describe the translation of the point to its image. $(4,-2) \rightarrow(-9,3)$

Your fitness traker overestimates the number of steps you take by 5%. The tracker indicates that you took 7350 steps today. Write and solve an equation to find the actual number of steps you took today.

Solve each equation. $0.25(d-12)=4$

According to a poll for an upcoming school board election, 40% of voters are likely to vote for the incumbent. The poll shows a margin of error of

$$\pm 3$$

percentage points. Write and solve an absolute value equation to find the least and the greatest percents of voters v likely to vote for the incumbent.

a. Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 5 ft by 8 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this way. b. Squares with sides of length x are cut out of each corner of a square piece of cardboard with sides of length $\ell$. Find the volume of the largest open box that can be formed in this way.

Sketch the graph of the equation. Identify any intercepts and test for symmetry. $y=x^{2}+3$

Prove the following statements. a. $|\sin a-\sin b| \leq|a-b|$, for any real numbers a and b. b. $|\sin a| \leq|a|$, for any real number a.

The following table shows the average body mass m(t) (in grams) and average wing chord length w(t) (in millimeters), along with the derivatives m'(t) and w'(t), oft-week-old Indian spotted owlets. The flight formula function f(t)=w(t)/m(t), which is the ratio of wing chord length to mass, is used to predict when these fledglings are old enough to fly. The values off are less than 1, but approach 1 as t increases. When f is close to 1, the fledglings are capable of flying, which is important for determining when rescued fledglings can be released back into the wild.

$$\begin{array}{ccccc}{t} & {m(t)} & {m^{\prime}(t)} & {w(t)} & {w^{\prime}(t)} \\ \hline 1 & {23.32} & {41.45} & {10.14} & {14.5} \\ {1.5} & {50.59} & {64.94} & {20.13} & {26.17} \\ {2} & {82.83} & {57.95} & {36.7} & {39.86} \\ {2.5} & {105.13} & {31.08} & {58.92} & {47.38} \\ {3} & {119.76} & {12.48} & {98.99} & {27.94} \\ {4} & {121.37} & {0.51} & {118.34} & {15.74} \\ {4.5} & {121.37} & {0.17} & {118.34} & {3.85} \\ {5} & {121.42} & {0.06} & {119.34} & {1.8} \\ {6} & {121.44} & {0.02} & {120.32} & {0.84} \\ {6.5} & {121.45} & {0.01} & {120.61} & {0.38}\end{array}$$

Complete the following steps to examine the behavior of the flight formula. a. Sketch an approximate graph of y=f(t) by plotting and connecting the points (1, f(1)), (1.5, f(1.5) ), ... , (6.5, f(6.5)) with a smooth curve. b. For what value oft does f appear to be changing most rapidly? Round t to the nearest whole number. c. For the value oft found in part (b), use the table and the Quotient Rule to find f'(t). Describe what is happening to the bird at this stage in its life. d. Use your graph off to predict what happens to f'(t) as t grows larger and confirm your prediction by evaluating f'(6.5) using the Quotient Rule. Describe what is happening in the physical development of the fledglings as t grows larger.

Consider the following definition. Definition: An integer n is sane if $3 |\left(n^{2}+2 n\right).$ (a) Give a counterexample to the following: All odd integers are sane. (b) Give a direct proof of the following: If 3 | n, then n is sane. (c) Prove by contradiction: If n = 3j + 2 for some integer j, then n is not sane.

Shaft a in the figure has a power input of 75 kW at a speed of 1000 rev/min in the counterclockwise direction. The gears have a module of 5 mm and a $20^{\circ}$ pressure angle. Gear 3 is an idler. a) Find the force $F_{3 b}$ that gear 3 exerts against shaft b. b) Find the torque $T_{4 \mathrm{c}}$ that gear 4 exerts on shaft c.

Graph the equation using x- and y-intercepts. -3x + y = 6

Mr. Swanson bought a package of 10 disposable razors fqr $6.30. He found that each razor lasted for 1 week. What was the cost per day?