Problem 20
Assume that a scientist is able to measure the average weight of lobsters within a 50-mile radius of an island with a confidence level of \(90 \%\) by collecting data from 100 random spots around the island. If he wishes to increase the confidence level in his results to \(95 \%\), what would best help him achieve his goal? (A) Compare the results to those from another island 300 miles away. (B) Expand the radius of sampling to 100 miles and redistribute his 100 random spots within the larger range. (C) Increase the number of data samples. (D) Use a scale with \(5 \%\) more accuracy.
Problem 20
A wall's height is two-thirds that of its length. The entire wall will be painted. The paint costs \(\$ 12\) per gallon, and 1 gallon of paint covers 60 square feet. What expression gives the cost of the paint (assuming one can purchase partial and full gallons) to cover a wall that is \(\mathrm{L}\) feet long? (A) \(\quad\) Cost \(=L^{2}\) (B) \(\quad\) Cost \(=\frac{1}{5} L^{2}\) (C) \(\quad\) Cost \(=\frac{2}{15} L^{2}\) (D) \(\quad\) Cost \(=\frac{3}{64} L^{2}\)
Problem 21
Consider the function \(f(x)=2 x-3 .\) What is the range of the absolute value of this function? (A) \(y<-3\) (B) \(y \leq 0\) (C) \(y \geq 0\) (D) \(y>5\)
Problem 22
An animal shelter can house only cats and dogs. Each dog requires 2 cups of food and 3 treats a day, while each cat requires 1 cup of food a day and 2 treats a day. If the shelter has available a total of 400 cups of food and 500 treats a day, what expressions portray the full scope of the number of \(c\) cats and dogs the shelter could potentially house? (A) \(2 \mathrm{~d}-\mathrm{c} \leq 400\) and \(3 \mathrm{~d}+\mathrm{c}<500\) (B) \(2 d+c \leq 400\) and \(3 d+2 c \leq 500\) (C) \(4 \mathrm{~d}+\mathrm{c}<400\) and \(\mathrm{d}+\mathrm{c}<500\) (D) \(2 \mathrm{~d}+2 \mathrm{c} \leq 400\) and \(2 \mathrm{~d}+3 \mathrm{c} \leq 500\)
Problem 22
If a set of 20 different numbers has its smallest and largest values removed, how will that affect the standard deviation of the set? (A) The standard deviation will increase. (B) The standard deviation will decrease. (C) The standard deviation will remain the same. (D) Not enough information is provided.
Problem 23
Which of the following expressions is equivalent to the diameter of the sphere portrayed above, with a radius of \(\mathrm{r}\) and volume \(\mathrm{V}\) ? (A) \(2 \sqrt[3]{\frac{3 V}{4 \pi}}\) (B) \(\pi r 3\) (C) \(4 \sqrt{\frac{2 r^{3}}{3}}\) (D) \(\frac{4 V^{3}}{3 r^{2}}\)
Problem 23
Jay is purchasing gifts for his four friends' high school graduation. He has a budget of at most \(\$ 150 . \mathrm{He}\) is purchasing a restaurant gift card of \(\$ 25\) for one friend, a tool set that costs \(\$ 40\) for another friend, and a \(\$ 35\) college sweatshirt for a third friend. For his fourth friend, he wants to see how many \(\$ 0.25\) quarters \((Q)\) he can give for the friend to use for laundry money. What expression gives the range of quarters Jay can acquire given his budgetary restrictions? (A) \(1 \leq Q \leq 300\) (B) \(1 \leq Q \leq 200\) (C) \(10 \leq Q \leq 120\) (D) \(40 \leq Q \leq 60\)
Problem 24
A pretzel stand has fixed costs for the facility and cooking supplies of \(\$ 500\). The cost for the labor and supplies to cook one pretzel after the pretzel stand has been set up is \(\$ 2\) per pretzel. What is the graph of the cost function \(c(x)\) given \(x\) pretzels?
Problem 24
Caitlin opens a checking account that earns no interest to set aside spending money for vacations. Each month she puts the same dollar amount, \(\$ 50\), into the account. Unfortunately, she does not expect to be able to take a vacation at any point in the foreseeable future. Which of the following best describes the relationship between the number of months and the total amount of money in the account? (A) A linear relationship, with the line of the relationship having a negative slope B) A linear relationship, with the line of the relationship having a positive slope (C) An exponentially increasing relationship (D) An inverse exponential relationship
Problem 25
Which of the following could be a value of \(x\) in this equation? $$ 8 x^{2}=-16 x-2 $$ I. \(-1-\frac{\sqrt{3}}{2}\) II. \(\frac{1}{2}(-2-\sqrt{6})\) III. \(\frac{1}{2}(\sqrt{3}-2)\) (A) I only (B) II only (C) \(\mid\) and IIl only (D) \(\quad\) II and III only
