Triangle Congruence: SSS and HL — Cumulative exam Answers

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

Points H and F lie on circle C.

The Venn diagram shows the number of employers who ranked skills important for careers in their field.C represents communication, T represents technical skills, and M represents the ability to handle money.

Four speed skaters, Marco, Naim, Oliver, and Pedro, compete in a relay race where they all agree that Naim will be the last skater. Then, they try to decide whether or not Oliver should be the first skater in the race.Which subset, A, of the sample space shows the complement of the event in which Oliver is the first skater in the race?

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?

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?

Law of sines:

A four-person committee is chosen from a group of eight boys and six girls.If students are chosen at random, what is the probability that the committee consists of all boys?

In circle O, radius OQ measures 9 inches and the arc length of PQ is 6π inches.

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.

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?

What is radians converted to degrees? If necessary, round your answer to the nearest degree.

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.

On a coordinate plane, a circle has a center at (negative 2, 1).

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

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.

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

Law of sines:

There are 2,100 bacteria in a circular petri dish. The dish has a radius of 40 millimeters. What is the approximate population density? (Use 3.14 for π)Area of a circle = πr2

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