Word Problems

Question 0

Relative rates
2 ppl moving toward each other
One @ 5 mph and the other @ 6 mph

Answer 0

DECREASE distance between themselves at rate of 5 + 6 = 11 mph

Question 1

Total cost equation

Answer 1

Total cost = unit price x quantity

Question 2

Relative rates
Two cars driving in opposite directions
One @ 30 mph and the other @ 46 mph

Answer 2

INCREASE distance between themselves at rate of 30 + 45 = 75 mph

Question 3

Relative rates

Person X and person Y move in the same direction @ 8 and 9 mph

Answer 3

They DECREASE the distance between them at rate of 8-5= 3 mph

Question 4

Average rate

Answer 4

If object moves same distance twice but at different rates, need to find total combined time for trips and total combined distance

Question 5

Average equations

Answer 5

A = s/n
Avrg= sum/ number of terms

(Avrg) x (number of terms) = (sum)

Question 6

How many terms are there in a set of consecutive integers from -18 to 33, inclusive?

Answer 6

Last - First + 1

33 - (-18) = 51 + 1 = 52

Question 7

How do you find the average of an evenly spaced set?

Answer 7

(First + Last) / 2

Mean and median are equal to each other

Question 8

Sum of elements in a set?

Answer 8

Mean x Number of items

Question 9

How many multiples of 7 are there between 100 and 150?

Answer 9

(Last - First)/increment + 1

(147 - 105) / 7 + 1 = 7

Question 10

What is sum of integers from 20 to 100 inclusive?

Answer 10

1) average first and last to find middle
120/2= 60

2) count terms: 100-20 + 1= 81
3) multiply middle terms by number of terms to find sum: 60 x 81 = 4870

Question 11

The average of an odd number of consecutive integers will always be:

Answer 11

An integer

Question 12

The average of an even number of consecutive integers will always be:

Answer 12

Never an integer!

Question 13

How do you double a ratio?

Double the ratio 8:5

Answer 13

To double a ratio, you just change the first number.

8:5 becomes 16:5

Question 14

Standard deviation

Answer 14

SD measures how close a set of numbers are to the mean of the set.

A low SD means numbers are relatively close to the average

Question 15

Is median is greater than mean…

Answer 15

Median splits the set in two (equal number of terms above and below the median).

So if median is greater than mean > numbers below median are FARTHER from median than numbers above; they are pulling the mean down…

Question 16

What do you know about SD if mean = median?

Answer 16

Nothing. Consider:

{1,2,50,99,100}
Terms can be far below the mean and far above it

Question 17

Composite sets: what happens to mean and median when you add two sets of numbers together?

Answer 17

When two sets are combined to form composite, the mean of composite must be between 2 means of individual sets or equal to mean of both.

Median must be between 2 medians or equal to median of one or both.

Question 18

Formula for 2 overlapping sets

Answer 18

Total = group 1 + group 2 - (people in both groups) + (people in neither)

Question 19

Formula for 3 overlapping sets

Answer 19

Total = group 1 + group 2 + group 3 - (people in two groups) - 2(people in all 3 groups) + none