Put your numbers in order
(27, 27, 57, 57, 59, ...)
Divide them into 4 same-sized groups.
There are 24 numbers in the dataset, so it divides into 4 groups with 6 values in each one.
Since the dividing lines between fourths (quarters) all lie between two numbers (for...
First, area is measured in square units. You're asked to find an area.
The question is then, what area is inclosed in a square area. You can find the dimensions of the square from the amount of fencing required to go around the square and to divide it into 4 sub-squares...
"Similar" means one is a scale model of the other.
If you increase all dimensions of ANY plane figure by a factor, the ratio of the areas is that factor squared!
Large dimension is 4x the small one.
The ratio is 16:1.
Try it with a couple...
A = number with $20 bonus
B = number with $50 bonus
The average bonus is the total of all bonuses divided by the number of employees.
(20A + 50B) / 20 = 38
A + 2.5B = 38
A + B = 20
A + 2.5B = 38
A + 1B...
V = x3
x = 1/4
You can just multiply fractions like this:
1/4 x 1/4 x 1/4 = (1 x 1 x 1) / (4 x 4 x 4)
or you can cube the fraction like this:
(1/4)3 = 13/43 =...
The trick to this mixture problem is to calculate the amount of chlorine in each component and in the final mixture. Then you can write the second equation that you need.
A = amount of 6% solution
B = amount of 18% solution
Total of A and B is 8 liters
The trick to this one is recognizing that consecutive odd numbers increase by 2 for each step. (Would be the same for even numbers!)
Call the first one n, the second (n+2) and the third (n+4). Now you can write an equation.
Now look for things you...
The increase in the water level is the amount of volume that the nugget added, the same as if you had just added water.
225 - 80 = 145 ml
I like to tell people to look for pieces that you can write expressions for, then re-read the problem to see how to put them together.
Arthur weighs 21 lbs more than lily.
A = L + 21
four times lily's weight
114 lb less than four times...
Pr(T) would be the probability of getting tails.
The probability of getting heads OR tails is 100%, or 1.0, so Pr(H) = 1.0 - 0.6 = 0.4.
That's 4 out of 10.
How many heads out of 85 tosses?
0.4 * 85 = 34
This is a system of equations:
3b + 4e = 12.33
4b + 3e = 14.13
Multiply the top equation by 4 and the bottom one by 3:
12b + 16e = 49.32
12b + 9e = 42.39
0 + 7e = 6.93
3 - 1 / (x-1) = 3x/(x-2)
The first step is to eliminate the denominators. To do this multiply both sides by (x-1) * (x-2)
One of these factors will cancel out in each of the fractional terms.
(3)(x-1)(x-2) - (1)(x-2) = (3x)(x-1)
Now it's a matter...
This may be easier to follow. Do the synthetic division normally, but leave it in terms of a. We know the remainder must be zero because (x-3) is a factor.
3 | 1 a -5 ...
The key to starting this one is recognizing that you can factor the difference of two squares.
Taking the first part of the relationship:
a+b = a^2 - b^2 (you goofed on the sign here!)
You can factor the difference of two squares, so:
The end of the question is missing. I'm assuming that it ask how many people earned more than $60,000.
We know how many people were surveyed: 1200. 2 1/2% of those people earn more than $60,000. The question is, "How many people is that?" Stated differently,...
I don't have time to write it all out right now, but here's how you need to approach the problem.
You have to solve absolute value equations in two parts.
When (x-3) ≥ 0 you get one line. That's when x ≥ 3.
For x ≥...
We're looking for grandfather's age at death. We'll call it A.
He married grandmother after 1/3 of his life. That would be A/3 years.
Their first daughter was born 4 years later. That would be at A/3 + 4.
I'm assuming that mother is that first...
Here's the trick that lets you solve this type of problem.
s is the boat's speed in still water.
The speed relative to the shore is s-3 going upstream and s+3 going down stream.
The time t is the same for 140 miles in one direction and 100 miles...
Here's a possibility:
y=1 + [99 / (1 + x2)]
The x2 term cannot be negative, so the "+1" in the denominator eliminates the singularity issue.
This function can never exceed 100 and it cannot reach 1. Don't know if the lower...
This will be a system of equations problem.
Here's the piece that may not be obvious:
Both runners went the same distance because they started at the same place and ran to the end of the trail.
Let the distance be d.
Let the time for the first runner be t.