# Math

## 49 terms

### a number is divisible by 3 if

the sum of its digits is divisible by 3

### a number is divisible by 4 if

its last two digits compose a two-digit number that is itself divisible by 4

### a number is divisible by 9 if

the sum of its digits is divisible by 9

### a number is divisible by 11 if

the difference between the sum of its odd-placed digits and the sum of its even-placed digits is divisible by 11

### average value =

sum of values / number of values

### sum of values =

average value X number of values

### John travels x miles in a hours and y miles in b hours. What is is his average speed?

(x + y) miles / (a + b) hours

### How to handle complex rate problems

make a table
row labels = rate, time, and distance
column labels = a to b, b to c, and entire trip

rate X time = distance

### combined work total time formula for 2 people/machines

total time = AB / A + B

### Bob can paint a room in 3 hours, and George can paint the same room in 2 hours. How many hours does it take Bob and George to paint the room if they work together but independently?

(3 X 2) / ( 3+ 2)

### combined total work formula for more than 2 people/machines

1/total time = 1/A + 1/B + 1/C + ... + 1/N

12 minutes

### formula for overlapping sets

total = group 1 + group 2 - both + neither

venn diagram

### overlapping sets approach for complicated problems

draw a chart
row labels = in group 1, not in group 1, and total
column labels = in group 2, not in group 2, and total

### if selection is unordered, then it's a

combinations problem

### if the selection is ordered, it is a

permutations question

### the combinations formula is used when

solving for the number of k unordered selections one can make from a group of n items

nCk = n! / k!(n-k)!

### A company is selecting 4 members of its board of directions to sit on a committee. If the board has 9 members, any of whom may serve, how many different selection of members could be made?

9C4 = 9! / 4!(9-4)!

### County X holds an annual math competitions, where each county high school sends a team of 4 students. If School A has 6 boys and 7 girls whose math grades qualify them to be on their school's team, and competition rules stipulate that the team must consists of 2 boys and 2 girls, how many different teams might school A send to the competition?

6C2 and 7C2

(6! / 2!4!) X (7! / 2!5!)

n!

6!

and = multiply

6! / 3!

8! / 4!2!

### If a fair coin is flipped 3 times, what is the probability of getting at least one tail?

subtract the probability of the undesired outcomes from the total

1 - 1/2 x 1/2 x 1/2

### If a fair coin is flipped 5 times, what is the probability of getting exactly 3 heads?

solve for the probability of one possible desired outcome, then multiply by all the permutations of that outcome

HHHTT = 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/32
HHHTT = 5! / 3!2! = 10

1/32 x 10

### probability =

# of desired outcomes / total number of possible outcomes

3:4:5

5:12:13

7:24:25

8:15:17

9:40:41

1:SQRT3:2

### bisecting an equilateral triangle creates __________.

two 30-60-90 triangles

### how to find the longest side of a triangle

longest side is across from largest angle

pi d or 2 pi r

### arc length where angle opens up at center

(n/360) x circumference

### arc length where angle opens up at edge of circle

(n/180) x circumference

pi r^2

### area of sector

(n/360) x area of circle

lwh

2lw x 2lh x 2wh

### rectangular solids diagonal

diagonal^2 = l^2 + w^2 + h^2

e^3

6e^2

pi r^2 h

2 pi r h

### total SA of cylinder

2 pi r^2 2 pi r h