Solving problems like this you need to pay attention to the units you need for the solution. We want the rate in pounds per second. Luckily the information we are given is about pounds and seconds, so we don't need to covert any units.
We can divide (2/7) by...
4a + 6b = 1.56
9a + 7b = 2.60 Add these two equations together vertically!
13a + 13b = 4.16 Now divide this whole equation by 13 to see what a + b would be
(13a)/13 + (13b)/13 = (4.16)/13
It says the sum of m and 125 is 240, so the two things we are adding are m
and 125. The result is 240.
If I said the sum of 7 and 9 is 16, I could also write that 7 + 9 = 16.
If I only knew that 9 was one of the two numbers and did not know the...
These can be tricky.
Let x = ounces of 60% saline. 0.6x = ounces of saline
Let y = ounces of 20% saline. 0.2y = ounces of saline
Total solution needed is 8 oz., so x + y = 8
To get a 50% saline solution, (total ounces of saline)/(total...
You can use the same strategy for all four problems that you posted.
1. Set up variables. Usually let x represent whatever follows "as" if there is a comparison. In this case you have "Brandon owns
4 times as many soccer cards as Paul.
Let x = # of panels produced by B
Let y = # of panels produced by A
y=3x, so 3x = # of panels produced by A
Let 0.04x = # of defective panels from B
Let 0.02(3x) = # of defective panels from A
0.04x + 0.02(3x) = 1100 total defective panels
0.04x + 0.06x = 1100
The key phrase is that the ranch she wants is 7/8 the size of her current property. Think about whether 7/8 is greater or less than 1. If 7/8 is greater than 1, then the property is bigger than hers. If 7/8 is less than 1, then the property is smaller than hers.
First, we know we can't have more than 1.5 gallons in the container. Each gallon is 128 ounces, so our maximum volume in ounces is 128(1.5)=192 ounces.
We need the total solution to be a maximum of 7% alcohol.
Let w = ounces of 11% wine, 0.11w = ounces of alcohol
Let s =...
The average of two numbers a and b is (a + b)/2
If I told you the average was (a + b)/2, and the first number was a you would do the following:
((a + b)/2)*2 = (a + b) = the sum of my two numbers.
but one of the numbers is a, so my...
You need to take each quantity in the original recipe and multiply by 1/2.
(1/2 teaspoon)(1/2)= 1/4 teaspoon
(3 teaspoons)(1/2) ... just multiply 3 times 1/2 and the answer is the number of teaspoons of cinnamon.
(3 1/2 cups flour)(1/2) .... change 3...
David, thanks for your question. The two trinomials you used as examples are very similar : ax2+bx+c is the general form and x2+bx+c is the specific case where a = 1.
when c=0: ax2+bx+c --> ax2+bx
There is a common factor of x in both terms so x(ax+b)...
Let a=mass of 30% alloy
Let b= mass of 60% alloy
Since the total mass after mixing is 300 kg, a + b = 300 kg
The new mixture is a 50% alloy, so 0.3a + 0.6b = 0.5(300)
We have 2 equations with...
You should have learned something that sounds a lot like this:
Given two parallel lines and a transversal, alternate interior angles are congruent.
The key here is that you are told the two lines are parallel, and you have learned that the relationships between the...
Your formula is perfect! On the left side is your total cost and on the right side is your brothers total cost. For some value of m they are equal. Solve for m and you will have your answer in months.
P = Probability of being defective = 0.03
1-P = Probability of not being defective = 0.97
12 C 5 = the number of combinations of 5 defects out of 12
(P)5(1-P)7= the probability for a single combination of 5 defects out of 12
The probability of...
In answering each of these questions remember how a function is defined in term the of input and output.
A function is a relationship in which each input has only one output. To check for a function look at the input and its output.
Is there another piece of data that has...
Since the probability for each seed is 0.8, and there are 50 seeds, the expected value would be the individual event probability multiplied by the number of events.
(0.8)(50) = 40 expected seedlings.
Total value = 4.00, let d = number of dimes, let q= number of quarters
We have also been given that d = 2q - 5
Total value = (0.10)(d) + (0.25)(q) = 4.00
Since d = 2q - 5, substitute for d
(0.10)(2q - 5) + 0.25q = 4.00
Make sure you draw a sketch to help you set up this problem.
The border will extend beyond the rectangle above, below, left, and right by the same amount, x.
Consider the border to be four thin rectangles along the sides and four little squares outside the four corners of the rectangle...
Remember that the formula for interest problems is: A = P(1+(i/n))nt
where A = amount
P = principal (the dollars you start with)
i = annual interest rate
n = number...