Math

Question 0

Four right triangles

Answer 0

3:4:5
5:12:13
30/60/90 1:sqrt(3):2
45/45/90 1:1:sqrt(2)

Question 1

Standard deviation

Answer 1

Calculate avg
Diff of each to avg
Square diffs
Add squared diffs, divide by number of terms for avg2
Square root of avg2

Question 2

Numer of internal degrees in a polygon, N sides

Answer 2

(N-2) * 180

Question 3

Mixture/Balance

How many liters of soln 10% alcohol must be added to 2 liters soln 50% alcohol to create soln 15% alcohol

Answer 3

X=10, Y=50, Z=15%, N=2 liters, A = added liters

A(Z-X) = N(Y-Z)

A(15-10) = 2(50-15)

Question 4

Group, Both, Neither

120 students, 65 study French, 51 study Spanish, 53 neither, how many studying both

Answer 4

Group1 + Group2 + Neither - Both = total
65+51+53-Both = 120
Both = 49

Question 5

How many ways are there to choose 3 delegates from 8 possible candidates? General solution to Combination problem.

Answer 5

Order/arrangement does not matter
N = # in larger group, K = number you are choosing
N! / (K! * (N-K)!)
So 8! / (3! * 5!)

Question 6

Permutation: 5 runners in a race, top 3 win Gold/Silver/Bronze. How many possible outcomes for Gold, Silver, and Bronze medal winners?

Answer 6

N = number in larger group, K = number you are arranging
N! / (N-K)!
So 5! / 2! = 60