Cumulative Exam — Cumulative exam Answers

Rectangle J K L M is shown. Diagonals are drawn from point J to point L and from point K to point M and intersect in the middle. All angles are right angles. The length of J M is 12 and the distance from M to the center point is 10.

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.

Triangle X Y Z is shown. Angle X Z Y is a right angle. Angle Z X Y is 60 degrees and angle X Y Z is 30 degrees. The length of hypotenuse X Y is 42 and the length of X Z is 21.

Quadrilateral W X Y Z is shown. The length of W X is (x + 8) millimeters, the length of X Y is (2 x minus 5) millimeters, the length of Z Y is 15 millimeters, and the length of W Z is (x + 2) millimeters.

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

The relative frequency table shows the results of a survey in which parents were asked how much time their children spend playing outside and how much time they spend using electronics.Given that a child spends at least 1 hour per day outside, what is the probability, rounded to the nearest hundredth if necessary, that the child spends less than 1 hour per day on electronics?

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.

On a coordinate plane, rhombus W X Y Z is shown. Point W is at (7, 2), point X is at (5, negative 1), point Y is at (3, 2), and point Z is at (5, 5).

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?

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.

One exterior angle of a regular pentagon has a measure of (2x)°. What is the value of x?

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.

The volume of a cone is 3πx3 cubic units and its height is x units.Which expression represents the radius of the cone’s base, in units?

A napkin is folded into an isosceles triangle, triangle ABC, and placed on a plate, as shown. The napkin has a perimeter of 38 centimeters.Trigonometric area formula: Area =

The area of the regular octagon is 10.15 cm2.

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

Law of sines:

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?

Rhombus L M N O is shown. Diagonals are drawn from point L to point N and from point M to point O and intersect at point P. The length of L M is 3 x minus 3 and the length of M N is x + 7.

A cone has a circular base with a diameter of 18 inches. The height of the cone is 40 inches.What is the approximate lateral area of the cone? Use 3.14 for π and round to the nearest whole number.