Trig
Stats
Probability
Geometry
100
The cosine of 45 degrees.
What is 1/sqrt(2)?
100
Find the mean, median, mode, and range 13, 18, 13, 14, 13, 16, 14, 21, 13
mean: 15 median: 14 mode: 13 range: 8
100
What is the probability of rolling a 2 when a fair die is rolled once?
1/6
100
Find the volume of the base of a cone with a radius of 5 cm and height of 10cm.
Area of Base (B) = (pi) x r^2 = (pi) x 5^2 B = 25 x (pi) cm^2 = 78.5 cm^2 Volume = (1/3)Bh = (1/3)(78.5cm^2 x 10cm) =261 2/3 cm^3
200
The angle of elevation of the sun when a 7.6 meter flagpole casts an 18.2 meter shadow, rounded to the nearest degree.
22.7 m
200
Find the five-number summary of the following set of numbers. 0.16, 0.08, 0.27, 0.20, 0.22, 0.32, 0.25, 0.18, 0.28, 0.27
1) Min = 0.08 2) 1st Quartile = 0.18 3) Median = 0.235 4) 3rd Quartile = 0.27 4) Max = 0.32
200
There are 20 people who work in an office together. Four of these people are selected to go to the same conference together. How many such selections are possible?
Combination nCr=20C4=4845
300
BC = 118.7, ACB = 50°. Find side AB.
ACB = AB / BC AB = BC × sin ACB = 118.7 × sin 50 = 118.7 × 0.766 = 90.9
300
Molly earned a score of 940 on a national achievement test. The mean test score was 850 with a standard deviation of 100. What proportion of students had a higher score than Molly?
z = (X - μ) / σ = (940 - 850) / 100 = 0.90 P(Z > 0.90) = 1 - P(Z < 0.90) = 1 - 0.8159 = 0.1841.
300
If a three digit number is formed from the digits 1,2,3,4,5,6, and 7, with no repetitions, tell how many of these three digit numbers will have a number value between 100 and 500.
4 · 6P2 = 120
400
BC = 125, AC = 84.9. Find angle ABC.
What is sin ABC = opposite / hypotenuse = AC / BC = 84.9 / 125 = 0.6792 ABC = sin¯¹ 0.6792 = 42.8°
400
The average salary for an employee at Acme Corporation is $30,000 per year. This year, management awards the following bonuses to every employee. A Christmas bonus of $500. An incentive bonus equal to 10 percent of the employee's salary. What is the mean bonus received by employees?
Y = mX + b = 0.10 * $30,000 + $500 =$3,500
400
Two cards are drawn at random from a standard deck of 52 cards, without replacement. What is the probability of drawing a 7 and a king in that order?
4/52 x 4/51= 4/663
500
Solve.1/sin^2(x) + Sec^2(x)/Tan^2(x)
sec^2(x) = 1/cos^2(x) tan^2(x) = sin^2(x)/cos^2(x) 1/sin^2(x) + (1/cos^2(x)/(sin^2(x)/cos^2(x) = 1/sin^2(x) + cos^2(x)/sin^2(x)cos^2(x) = 1/sin^2(x) + 1/sin^2(x) = 2/sin^2(x) = 2cosec^2(x)
500
According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that the residents of a household own 2 cars and have an income over $25,000 a year is:
P(A/B) = P(AnB)/P(B) where: P(A/B) = The probability of event A occurring given that B has occurred. P(AnB) = The probability of both events A and B occurring. P(B) = Obviously, the probability that event B occurs. P(A) = The probability that the residents of a household own 2 cars. P(B) = The probability that the annual household income is greater than $25,000. P(A/B) = 0.8 P(A) = 0.7, P(B) = 0.6. 0.6*0.8 = 0.48
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