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Let’s use the variable a to stand for amount of the 40% copper alloy in ounces.   You can write an equation for the amount of copper in each alloy and set it equal to the amount in the final mixture.   (Ounces of copper in the 40% alloy) + (Ounces of copper in the 90%...

This problem is telling you that Amy's total score needs to be above 84. We need to find a way to represent Amy's score. She's getting points from true/false and multiple choice questions, so her score is:   true/false points + multiple choice points = Amy's score   She...

You are being asked to find two variables (number of cans of popcorn and number of cans of nuts). When you have two variables, you need two equations. Let's write one for the number of cans and another for the total sales. Your Algebra teacher might call this a "system of equations."   Let...

First, I’ll show you a couple of options for checking your work.     Option 1. Translate the symbols you wrote back into words.   ~p (The temperature is not 90) v (or) ~q (The air conditioner is not working) v (or) ~r (The apartment is not hot)   You...

Probability problems are much easier to explain with diagrams and pictures, which the answer forum doesn’t permit, but here we go!   First, let’s consider how the probability of success is calculated for this word problem. You have two paths to a successful outcome Box 1 or Box...

Since this quartic can't be easily factored, you'll need to use formulas to find the roots.   We don't have the ability to type a lot of the notation this requires in this Wyzant forum, but here is a website that has a good explanation and a calculator: http://equationsolver.intemodino...

To solve this type of problem, you need two pieces of information: a point on the line and the slope of the line.   They have given you a point, and provided a clue to find the slope.   What is the slope of the line y = (3/4)x - 2  ?It's the number that is in front...

For percentage problems, the general set up is:   (part divided by whole) times 100%   In this case, the part is 13, the number of hits. The whole is 25, the number of times she was at bat.   13/25 x 100% = 52%   Hope that helps! Please vote up...

Good explanation, Michael! Another option is to use elimination to solve this system of two equations.   Let the first integer be a and the second integer be b.   a + b = 29 b = 4a – 1     Subtract the second equation from the first equation...

You could also consider the problem this way:   Jesse saved half of what he made. Zoie saved the same ratio, which means she also saved half of what she made. Zoie made \$60, and she saved half. Half of \$60 is \$30.

For percentage problems such as this, you want to divide the part by the whole and multiply by 100% to get the percentage.   In your example, you need to divide the number of "successes" (156) by the total number of "tries" (300) to get the proportion of successes...

Hi Michael,   Solving this problem requires the use of exponent rules and how to work with fractions.   First, let's take a look at the denominator: n^(3-n) We can apply our knowledge of exponent division to get: (n^3)/(n^n)   So we have 6/[(n^3)/(n^n)]...

Hi Natalie,   I see that you are posting a lot of similar problems. Here is one general formula that will help you with these sorts of economics/algebra-based problems. It's the compound interest formula.   A = P(1+r/n)^(nt)   The amount (A) is equal to...

Here is a generic way to set up this type of algebra problem.   d = total amount of dirt at the site (tons) r = rate or removal (tons/hr) t = time it takes to remove all of the dirt (hr)   d = rt The total amount of dirt equals the removal rate times hours spent...

You had a good hunch with the 30-60-90 triangle. Actually, you have a 30-60-90 triangle that is part of the unit circle! N is a point at the standard starting position of the unit circle. Remember, the unit circle has a radius of 1, and at 0 degrees you would be at (1,0).   When you...

You could start by calculating a z-score for 145   z = (145 - 132) / 9   z = 1.444   You could use a table or your graphing calculator to calculate the percentage above that z-score.   Then multiply the percentage by 862 (the number of values)...

Hi Pat,   You have a numerator of 84 x-to-the-fifths and a denominator of -7 x-to-the-fifths. The x^5 cancel, leaving 84/(-7). 84 divided by -7 is -12.