The $100\,\text{m}$ dash can be run by the best sprinters in $10.0 \mathrm{~s}$. A $66-\mathrm{kg}$ sprinter accelerates uniformly for the first $45 \mathrm{~m}$ to reach top speed, which he maintains for the remaining $55 \mathrm{~m}$. What is the average horizontal component of the force exerted on his feet by the ground during acceleration?

In the long run, all costs become controllable. Is this statement true? Why or why not?

Write R for each run-on and S for each correctly written sentence. Then correct the run-ons using techniques from the lesson.

In 1998 a meteoroid streaked into the earth's atmosphere and exploded over a back yard near Portales, New Mexico.

Write R for each run-on and S for each correctly written sentence. Then correct the run-ons using techniques from the lesson.

This was a rare occurrence most meteoroids do not fall in populated areas.

Let

$$Q_n$$

denote the probability that no run of 3 consecutive heads appears in n tosses of a fair coin. Show that

$$Q _ { n } = \frac { 1 } { 2 } Q _ { n - 1 } + \frac { 1 } { 4 } Q _ { n - 2 } + \frac { 1 } { 8 } Q _ { n - 3 }$$

$$Q _ { 0 } = Q _ { 1 } = Q _ { 2 } = 1$$

Find

$$Q_8$$

. Hint: Condition on the first tail.

Leeanne plans to sell her car and places an x-line ad. The newspaper charges p dollars for the first k lines and e dollars per extra line, to run the ad for a week. a. When x > k, write an algebraic expression for the cost of running the ad for a week. b. When x < k, write an algebraic expression for the cost of running the ad for two weeks.

Larissa ran 15 mi per week before she decided to train for a marathon. The first week of training she ran 17 mi. The second week she ran 19 mi. If she continued her pattern, how far did she run the fifth week?

Write R for each run-on and S for each correctly written sentence. Then correct the run-ons using techniques from the lesson.

It left behind a black meteorite that was as large as a basketball and weighed 37 pounds.

Leeanne plans to sell her car and places an x-line ad. The newspaper charges p dollars for the first k lines and e dollars per extra line, to run the ad for a week. a. When x > k, write an algebraic expression for the cost of running the ad for a week. b. When x < k, write an algebraic expression for the cost of running the ad for two weeks.

What should a company do in the long run to be able to provide a return to investors and creditors?

Write R for each run-on or S for each correctly written sentence. Then correct the run-ons using the techniques in this lesson.

Most students use computers on a daily basis now many students are using their computer skills to earn money.

In the wheelchair ramp problem, Troy used 1:12 as the ratio of the rise of each ramp to the run of each ramp.

What does the ratio of the rise of the ramp to the run of the ramp represent?

What can you conclude about the ratios of the rise to the run in similar right triangles?

Felipe and Armani conducted an experiment to determine if high school sprinters run faster with shoes on or barefoot. They had 20 athletes run a 40-yard dash in their regular track shoes and another 40-yard dash barefoot, randomly determining which they ran first. The data show the difference in 40-yard dash times (in seconds) for each runner (Shoes - Barefoot). A positive number means the athlete took longer with shoes on.

$$\begin{array}{rrrrrrrrrr}0.4 & -0.3 & -0.2 & 0.3 & -0.3 & 0.4 & 0.1 & 0.2 & 0.2 & 0\\ 0.3 & 0.1 & 0.1 & 0.3 & -0.1 & 0.4 & 0.5 & 0.1 & 0.5 & 0\end{array}$$

Can we conclude that runners like these will run faster without shoes? Justify your answer.