Cumulative Exam — Cumulative exam Answers

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

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.

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

The base of a solid right pyramid is a square with an edge length of n units. The height of the pyramid is n − 1 units.

An oblique prism has trapezoidal bases and a vertical height of 10 units.

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?

Which expression is equivalent to cos120°?

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?

Triangle FGH is an equilateral triangle with sides measuring units.

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 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?

Circle Y is shown. Chords R T and S U intersect at a point. Arc S R is 55 degrees and the angle that intercepts that arc is 63 degrees.

In circle E, and are diameters. Angle BCA measures 53°.

If the legs of an isosceles right triangle have a length of ft, what is the length of the hypotenuse?

Circle Y is shown. Chords R T and S U intersect at point Z. Arc S R is 100 degrees and arc T U is 72 degrees.

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?

Consider the sets below.U = {x | x is a real number}A = {x | x is an odd integer}R = {x | x = 3, 7, 11, 27}Is R ⊂ A?

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.

Segment MP is a diameter of circle O.