Cumulative Exam Answers

Fifty-five percent of the members of the junior varsity swim team wear glasses. Of the team members who do not wear glasses, 30 percent of them are in the 10th grade.To the nearest whole percent, what is the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade?

A cone is cut out of the center of a pyramid with a rectangular base. The rectangular base has side lengths of 15 and 10 units. The cone has a diameter of 9 and a height of 12. The pyramid and cone have the same height.

The scores of an eighth-grade math test have a normal distribution with a mean = 83 and a standard deviation = 5. If Din’s test score was 92, which expression would she write to find the z-score of her test score?

People at the state fair were surveyed about which type of lemonade they preferred. The results are shown below.Pink lemonade: 156 males, 72 femalesYellow lemonade: 104 males, 48 females

A survey of pet owners found that on average, they spend $1,225 annually per pet, with a standard deviation of $275. Between which two amounts would you expect 95% of the survey’s respondents to spend annually per pet if the sample is approximately normal and comes from a normally distributed population?

The depth of the water, d, at the end of a pier changes periodically as a function of time, t, in hours as shown in the graph below. According to the model, the last low tide occurred at 5:00 a.m. When will the next low tide occur? Let t = 0 be 12:00 a.m.

Which of the following is a binomial experiment?

The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 24π cubic units.What is the height of the cylinder?

A guidance counselor reports that in a given semester, the probability that a student chooses art as an elective is 15 percent, the probability that a student chooses art or drama is 20 percent, and the probability that a student chooses both art and drama is 2 percent.What is the probability that a student chooses drama as an elective?

The two-way table shows the number of sport utility vehicles with certain features for sale at the car lot.What is the probability that a randomly selected car with no 4-wheel drive has third-row seats?

What is the equation of the graph below?

For the graphs below, for which probability distribution is the value of the median greater than the value of the mean?

A supervisor finds the mean number of miles that the employees in a department live from work. He finds and . Which mileage is within a z-score of -1.5?

The hypotenuse of right triangle ABC, line segment AC, measures 13 cm. The length of line segment BC is 5 cm.

A simple random sample of 50 adults was surveyed, and it was found that the mean amount of time that they spend surfing the Internet per day is 54.2 minutes, with a standard deviation of 14.0 minutes. What is the 99% confidence interval (z-score = 2.58) for the number of minutes that an adult spends surfing the Internet per day?Remember, the margin of error, ME, can be determined using the formula .

The area of the regular octagon is 10.15 cm2.

Right triangle XYZ has a right angle at vertex Y and a hypotenuse that measures 24 cm. Angle ZXY measures 70o.What is the length of line segment XY? Round to the nearest tenth.

The probability for event A is 0.3, the probability for event B is 0.6, and the probability of events A or B is 0.8.Why are the events not mutually exclusive?

The height of the equilateral triangle below is 15 units. What is the value of x?

Two students created a game of dice. They determined that each roll would add the value of the die if it was an odd number. If the roll was even, it would subtract the value of the die. (For example, a roll of 2 would subtract two points, but a roll of 3 would add three points.) What is the expected value for this game?

A regular pentagon has side lengths of 14.1 centimeters and an apothem with length 12 centimeters.

Which graph shows this set of transformations applied to the parent cosine function? l A reflection across the x-axis l A shift of 2 units up l A vertical compression by a factor of 0.5

A security alarm requires a four-digit code. The code can use the digits 0–9 and the digits cannot be repeated.What is the approximate probability that the code only contains odd numbers?

Omar recorded the number of hours he worked each week for a year. Below is a random sample that he took from his data.13, 17, 9, 21What is the standard deviation for the data?Standard deviation:

Researchers compare the body composition of cattle feeding on a grain diet with that of cattle feeding on a grass diet. This method of gathering data is classified as

Law of sines:

Which of the following is a valid probability distribution?

A survey was taken of children between the ages of 3 and 7. Let A be the event that the person has 2 siblings, and let B be the event that the person does not have a pet.

Triangle A B C is shown. Angle B C A is a right angle. The length of C B is 5 inches and the length of C A is 7 inches.

Which transformations are needed to change the parent sine function to ?

The College Board states that the average math SAT score is 514 with a standard deviation of 117. Colleen gathered data from 50 students in her graduating class and found the average score to be 529. She thinks that her class’s math SAT score is different from the average. Which of the following shows the correct z-statistic for this situation?

Triangles Q R S and X Y Z are shown. Angles Q S R and X Z Y are right angles. Angles Q R S and X Y Z are congruent. The length of Y Z is 9, the length of X Z is 12, and the length of hypotenuse X Y is 15.

Law of cosines: a2 = b2 + c2 – 2bccos(A)

The distance between city A and city B is 22 miles. The distance between city B and city C is 54 miles. The distance between city A and city C is 51 miles.

The displacement, d, in millimeters of a tuning fork as a function of time, t, in seconds can be modeled with the equation . What is the frequency of the tuning fork?

Helen has 48 cubic inches of clay to make a solid square right pyramid with a base edge measuring 6 inches.

Which solution finds the value of x in the triangle below?

Given that , what is the value of ?

For which value of is csc () undefined?

Iliana is painting a picture. She has green, red, yellow, purple, orange, and blue paint. She wants her painting to have four different colors.If order does not matter, in how many ways can she pick four colors if green must be one of them?

Circle R is shown. Line segments Q R and S R are radii. The length of Q R is 18. Sector Q R S is shaded.

Including Jose, there are eight people in his family.If order matters, how many ways can he arrange his family members into a row of five seats if Jose must sit in the first seat?

Triangle ABC is a right triangle and sin(53o) = . Solve for x and round to the nearest whole number.

In the triangle below, represents which ratio?

Marleny is creating a game of chance for her family. She has 5 different colored marbles in a bag: blue, red, yellow, white, and black. She decided that blue is the winning color. If a player chooses any other color, they lose 2 points. How many points should the blue marble be worth for the game to be fair?

Which survey is most likely affected by bias?

A standard deck of 52 playing cards contains 13 cards in each of four suits: hearts, diamonds, clubs, and spades. Four cards are drawn from the deck at random.What is the approximate probability that exactly three of the cards are diamonds?

The scores of a high school entrance exam are approximately normally distributed with a given mean = 82.4 and standard deviation = 3.3. What percentage of the scores are between 75.8 and 89?

A sphere with a diameter of 9 units fits exactly in the clear glass cube as shown.

A circular disc has an area that measures between 1,650 and 1,700 square inches.What could be the length of its radius? Use 3.14 for .