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A girl throws a paper airplane from her treehouse. The height of the plane is a function of time and can be modeled by the equation \(h(t)=25+2.5t-\frac12 t^2\). Height is measured in feet, and time is measured in seconds after the airplane is thrown.
What does the model say about the airplane 2.5 seconds after the girl throws it if each of these statements is true?
\(h(2)=28\)
\(h(2.5)=28.125\)
\(h(3)=28\)
A square picture has a frame that is 3 inches thick all the way around. The total side length of the picture and frame is \(x\) inches.
Which expression represents the area of the square picture, without the frame? If you get stuck, try sketching a diagram.
\((2x+3)(2x+3)\)
\((x+6)(x+6)\)
\((2x-3)(2x-3)\)
\((x-6)(x-6)\)
The revenue from a youth league baseball game depends on the price per ticket, \(x\).
Here is a graph that represents the revenue function, \(R\).
Select all the true statements.
\(R(5)\) is a little more than 600.
\(R(600)\) is a little less than 5.
The maximum possible ticket price is \$15.
The maximum possible revenue is about \$1,125.
If tickets cost \$10, the predicted revenue is \$1,000.
If tickets cost \$20, the predicted revenue is \$1,000.
A garden designer designed a square decorative pool. The pool is surrounded by a walkway.
On two opposite sides of the pool, the walkway is 8 feet. On the other two opposite sides, the walkway is 10 feet.
Here is a diagram of the design.
The final design for the pool and walkway covers a total area of 1,440 square feet.
The side length of the square pool is \(x\). Write an expression that represents:
Suppose \(m\) and \(c\) each represent the position number of a letter in the alphabet, but \(m\) represents the letters in the original message, and \(c\) represents the letters in a secret code. The equation \(c=m+2\) is used to encode a message.
An American traveler who is heading to Europe is exchanging some US dollars for euros. At the time of his travel, 1 dollar can be exchanged for 0.91 euros.
A random sample of people are asked to give a taste score—either "low" or "high"—to two different types of ice cream. The two types of ice cream have identical formulas, except they differ in the percentage of sugar in the ice cream.
What values could be used to complete the table so that it suggests there is an association between taste score and percentage of sugar? Explain your reasoning.
| 12% sugar | 15% sugar | |
|---|---|---|
| low taste score | 239 | |
| high taste score | 126 |