Word Problems Flashcards
Relative rates
2 ppl moving toward each other
One @ 5 mph and the other @ 6 mph
DECREASE distance between themselves at rate of 5 + 6 = 11 mph
Total cost equation
Total cost = unit price x quantity
Relative rates
Two cars driving in opposite directions
One @ 30 mph and the other @ 46 mph
INCREASE distance between themselves at rate of 30 + 45 = 75 mph
Relative rates
Person X and person Y move in the same direction @ 8 and 9 mph
They DECREASE the distance between them at rate of 8-5= 3 mph
Average rate
If object moves same distance twice but at different rates, need to find total combined time for trips and total combined distance
Average equations
A = s/n Avrg= sum/ number of terms
(Avrg) x (number of terms) = (sum)
How many terms are there in a set of consecutive integers from -18 to 33, inclusive?
Last - First + 1
33 - (-18) = 51 + 1 = 52
How do you find the average of an evenly spaced set?
(First + Last) / 2
Mean and median are equal to each other
Sum of elements in a set?
Mean x Number of items
How many multiples of 7 are there between 100 and 150?
(Last - First)/increment + 1
(147 - 105) / 7 + 1 = 7
What is sum of integers from 20 to 100 inclusive?
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
The average of an odd number of consecutive integers will always be:
An integer
The average of an even number of consecutive integers will always be:
Never an integer!
How do you double a ratio?
Double the ratio 8:5
To double a ratio, you just change the first number.
8:5 becomes 16:5
Standard deviation
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
Is median is greater than mean…
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…
What do you know about SD if mean = median?
Nothing. Consider:
{1,2,50,99,100}
Terms can be far below the mean and far above it
Composite sets: what happens to mean and median when you add two sets of numbers together?
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.
Formula for 2 overlapping sets
Total = group 1 + group 2 - (people in both groups) + (people in neither)
Formula for 3 overlapping sets
Total = group 1 + group 2 + group 3 - (people in two groups) - 2(people in all 3 groups) + none
