Probability
Events A and B are independent. If P(A) = 0.4 and P(B) = 0.5, find the probability that both events occur, P(A∩B)
0.2 or 20%
An angle θ in a right triangle measures 28 degrees. If the hypotenuse is 17 units long, find the length of the side opposite θ to the nearest tenth.
State the converse of the statement: "If a triangle is equilateral, then it is equiangular."
If a triangle is equiangular, then it is equilateral.
A 45-45-90 triangle has a leg length of 7√2 units. What is the exact length of its hypotenuse?
14 units
Simplify the radical expression completely: √50
5√2
A standard six-sided die is rolled. What is the probability that the outcome is a prime number, given that the rolled number is odd?
2/3 or 66.7%
In a right triangle, an acute angle θ measures 67.4 degrees. If the side adjacent to θ is 5 units long, find the length of the opposite side to the nearest whole number.
12 units
Complete the missing reason:
1. ∠1 and ∠2 form a linear pair. (Given)
2. ∠1 and ∠2 are supplementary. (Reason?)
Linear Pair Postulate
Longer Leg = 6√3 cm
Hyp = 12 cm
Simplify the expression completely: √9/16
3/4
Out of 100 students, 60 take math, 45 take science, and 20 take both. What is the probability that a randomly chosen student takes math or science?
0.85 or 85%
In a right triangle, an acute angle θ measures 73.7 degrees. If the hypotenuse is 25 units long, find the length of the adjacent side to the nearest whole number.
7 units
Given that ray BD bisects ∠ABC, say a statement expressing the algebraic relationship between m∠ABD and m∠DBC.
m∠ABD = m∠DBC
The hypotenuse of a 45-45-90 triangle measures 10 inches. Find the exact length of each leg in simplest radical form.
5√2 inches
Multiply and simplify the expression: √6 x √2
2√3
A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles (10 total). If you draw two marbles sequentially without replacement, what is the probability that both are red?
2/9 or 22.2%
A 12-foot ladder leans against a vertical wall, reaching a height of 10.9 feet up the wall. To the nearest degree, what angle does the ladder make with the ground?
65 degrees
If line m is parallel to line n and both are cut by a transversal t, which geometric theorem proves that alternate interior angles are congruent?
Alternate Interior Angles Theorem
The longer leg of a 30-60-90 triangle is 9 units long. What is the exact length of the shorter leg?
3√3 units
Perform the operation and simplify: 5√7 + 2√7 - 3√7
4√7
A password consists of 4 distinct letters followed by 2 distinct digits. How many unique password combinations can be created?
32,292,000
A surveyor stands 50 meters away from the base of a building that is 39 meters tall. Calculate the angle of elevation from the surveyor to the top of the building to the nearest degree.
38 degrees
Given that ΔABC = ΔDEF, what specific theorem or rule allows you to state that BC is equal in length to side EF?
CPCTC
An equilateral triangle has a side length of 12 inches. Find the exact altitude (height) of the triangle.
6√3 inches
Solve the radical equation for x: √(x-5) = 4