Mini Exam 36 — Timed Mini Exams

Questions in this quiz (10)

1. The maximum temperature on April 1, in degrees Fahrenheit, was recorded each year at a certain weather station for $$11$$ years. The histogram summarizes the recorded data set. The temperature of $$80^\circ F$$ is removed from this data set to create a new data set of $$10$$ temperatures. Which of the following statements must be true?I. The mean of the new data set is less than the mean of the original data set.II. The median of the new data set is less than the median of the original data set.

   • I only
   • II only
   • I and II
   • Neither I nor II

2. The manager of a gym selected a sample of $$150$$ members at random to estimate the percentage of the gym's members that would continue to pay for a membership if the price increased. From the survey, the manager estimates that $$78\%$$ of the gym's members would continue to pay for a membership if the price increased, with an associated margin of error of $$5.8\%$$. If the survey is repeated with a random sample of $$300$$ members and the results are calculated in the same way, which of the following will be the most likely effect of using the larger random sample compared to the smaller random sample?

   • The margin of error will be lower.
   • The margin of error will be higher.
   • The estimate of the percentage of the gym's members that would continue to pay for a membership if the price increased will be lower.
   • The estimate of the percentage of the gym's members that would continue to pay for a membership if the price increased will be higher.

3. In the figure shown, line $$m$$ is parallel to line $$n$$, and line $$k$$ intersects both lines. Which of the following statements is true?

   • $$q=145$$
   • $$r=145$$
   • $$s=145$$
   • $$t=145$$

4. Triangle $$T$$ has an area of $$60$$ square centimeters. Square $$S$$ has side lengths of $$6$$ centimeters. What is the total area of triangle $$T$$ and square $$S$$, in square centimeters?

   • $$36$$
   • $$72$$
   • $$96$$
   • $$108$$

5. Triangles $$TUV$$ and $$XYZ$$ are similar, where $$T$$ corresponds to $$X$$, and $$U$$ corresponds to $$Y$$. The measure of angle $$T$$ is $$32^\circ$$, and $$TU=6$$. Which of the following statements must be true?I. The measure of angle $$X$$ is $$32^\circ$$.II. $$XY=6a$$, where $$a$$ is a whole number.

   • I only
   • II only
   • I and II
   • Neither I nor II

6. In triangle $$ABC$$, the measure of angle $$A$$ is $$35^\circ$$ and the measure of angle $$B$$ is $$75^\circ$$. In triangle $$XYZ$$, the measure of angle $$X$$ is $$35^\circ$$ and the measure of angle $$Y$$ is $$75^\circ$$. Which additional pieces of information is needed to determine whether triangle $$ABC$$ is similar to triangle $$XYZ$$?

   • The measure of angle $$C$$
   • The measure of angle $$Z$$
   • The measure of angle $$C$$ and the measure of angle $$Z$$
   • No additional information is needed

7. In isosceles right triangle $$RST$$, $$RS=23$$ and $$ST=23$$. What is the length of $$RT$$?

   • $$\sqrt{23}$$
   • $$\sqrt{46}$$
   • $$23\sqrt2$$
   • $$46\sqrt2$$

8. A circular park has a radius of $$8$$ miles. What is the area, in square miles, of the park?

   • $$4\pi$$
   • $$8\pi$$
   • $$16\pi$$
   • $$64\pi$$

9. A right circular cone has a height of $$9$$ millimeters and a base with a radius of $$5$$ millimeters. What is the volume, in cubic millimeters, of this cone?

   • $$25\pi$$
   • $$45\pi$$
   • $$75\pi$$
   • $$135\pi$$

10. The length of one side of square $$Q$$ is $$5$$ times the length of one side of square $$R$$. The area of square $$R$$ is $$16$$ square centimeters. What is the area, in square centimeters, of square $$Q$$?

    • $$25$$
    • $$80$$
    • $$100$$
    • $$400$$