91Ó°ÊÓ

A basketball player's hang time is the time spent in the air when shooting a basket. The formula \(t-\frac{\sqrt{d}}{2}\) models hang time, \(t\), in seconds, in terms of the vertical distance of \(a\) player's jump, \(d,\) in feet. When Michael Wilson of the Harlem Globetrotters slamdunked a basketball, his hang time for the shot was approximately 1.16 seconds. What was the vertical distance of his jump, rounded to the nearest tenth of a foot?

Suppose that you solve \(\frac{x}{5}-\frac{x}{2}-1\) by multiplying both sides by 20 rather than the least common denominator (namely, 10 ). Describe what happens. If you get the correct solution, why do you think we clear the equation of fractions by multiplying by the least common denominator?

What is an identity? Give an example.

What is a conditional equation? Give an example.

A basic cellphone plan costs \(\$ 20\) per month for 60 calling minutes. Additional time costs \(\$ 0.40\) per minute. The formula $$C-20+0.40(x-60)$$ gives the monthly cost for this plan, \(C\), for \(x\) calling minutes, where \(x>60 .\) How many calling minutes are possible for a monthly cost of at least \(\$ 28\) and at most \(\$ 40 ?\)

If a coin is tossed 100 times, we would expect approximately 50 of the outcomes to be heads. It can be demonstrated that a coin is unfair if \(h,\) the number of outcomes that result in heads, satisfies \(\left|\frac{h-50}{5}\right| \geq 1.645 .\) Describe the number of outcomes that determine an unfair coin that is tossed 100 times.

In a round-robin chess tournament, each player is paired with every other player once. The formula $$N-\frac{x^{2}-x}{2}$$ models the number of chess games, \(N\), that must be played in a round-robin tournament with \(x\) chess players. Use this formula to solve Exercises \(131-132\) In a round-robin chess tournament, 21 games were played. How many players were entered in the tournament?

Describe how to solve an absolute value inequality involving the symbol \(>\). Give an example.

Determine whether statement makes sense or does not make sense, and explain your reasoning. I can check inequalities by substituting 0 for the variable: When 0 belongs to the solution set. I should obtain a true statement, and when 0 does not belong to the solution set, I should obtain a false statement.

A pool measuring 10 meters by 20 meters is surrounded by a path of uniform width, as shown in the figure at the top of the next column. If the area of the pool and the path combined is 600 square meters, what is the width of the path?