Reciprocal means that the two terms, added together, equal one. Notice that the sums of pairs of inverted fractions is always one.

Reciprocal means that the two terms, added together, equal one. Notice that the sums of pairs of inverted fractions is always one.

Only the first one here is a fraction, so perhaps you copied the second one incorrectly. Nonetheless, we can certainly solve the fraction. As fractions are considered "undefined" if the denominator equals zero, the only way for a fraction to equal zero is for the numerator...

Remember that the sum of the three angles of a triangle is always 180 degrees. Also, that the measure of a right angle is always 90 degrees. Therefore, as possessing a right angle is the defining characteristic of a right triangle, we already know the measures of two angles: 90 deg...

Think of it two ways: If Brand A (10 cups) is 100%, then Brand B has 100%+30% or 130%. Simply multiply 10 cups by 130%. 10 cups x 130% = ? The other way is to find 30% of 10 cups. 10 x 30% = ? Then add that amount to 10 cups. 10 cups + (10 x 30%) cups = ? Then find...

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Maths, probability (answer)

Consider that word, "estimate." It means we do not expect our results to be absolutely true or trustworthy - only that they are the most correct results possible under the given circumstances. In this circumstance, we have a "biased" coin - meaning that the coin doesn't land...

Maths, word problems (answer)

I understand how these can be confusing, and will share some ideas to help you. First, try & decide what it is that the question is asking - what answer are we looking for? Then look for other variables that play into that answer. I'm essentially asking you to look at the problem backward. Let...

how can i construct a 90% confidence interval for the mean speed of all cars on this highway (answer)

In this scenario, the 90% confidence interval implies several specific characteristics of this data range: 1. Half of all speeds of cars on this highway will be lower than the mean & half will be above the mean. 2. 5% of all sample means will be too low to fall...

Simply substitute 13 into the equation & solve: f(13)=-3(13)+9 (substitute) f(13)=-39+9 (distribute/multiply) f(13)=-30 (add)

The first amount = 2x The second amount = x The third pollutant = 0.75x 2x + x + 0.75x = 15/1,000,000 3x + 0.75x = 15/1,000,000 (combine like terms) 3.75x = 15/1,000,000 (combine like terms) x = (15/1,000,000) divided by 3.75 (divide each...

Triple a number = 3x Increased by six = +6 Original number = x Diminished by 3 = -3 3x+6 = 2(x-3) 3x+6 = 2x-6 (distribute) 3x = 2x-12 (subtract 6 from each side) x = -12 (subtract 2x from each side) The original number is -12

One-half a number = x/2 One-ninth a number = x/9 One-twelfth a number = x/12 x/2 + x/9 + x/12 = 25 18x/36 + 4x/36 + 3x/36 = 25 (find/use the least common denominator) 25x/36 = 25 (add the fractions) 25x = 900 (multiply each side by the denominator,...

2x is "a number...doubled" & "decreased by 11" would be -11: 59 = 2x - 11 70 = 2x (add 11 to each side) 35 = x (divide each side by 2) The original number is 35.

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Remember, "range" refers not to a single number, but to a set of numbers, from lowest to highest. If Karen's & Anna's measurements had some percentage of error, that error could be lower or higher than the correct measurement (notice the words "at most"). You should assume...

Word Problem (answer)

Hello, Brenna! I would set this up as an algebraic equation with one variable. Both boys paid the same amount, but Larry paid an additional $2.30. The amount that both boys paid equally will be the variable, and, since there are two of them, the coefficient will be 2: 19...

Minimizing inventory cost (answer)

There are some unclear aspects to this scenario that make it difficult to assist you, but I will try to interpret the meaning by making some reasonable assumptions. For example, When talking about costs of doing business, we assume that "unit cost" refers to how much the business pays...

Word problem (answer)

We first make a variable out of the unknown quantity: the weight of the largest fish caught in lake B. Let's call it B. The scenario says the largest fish caught in lake A is "334.2 pounds less than eight times" our variable B: 8B-334.2=645 Now,...

You need to find 40% of 11, then subtract that amount from 11. You could use a calculator to find 40% of 11, or you could think of 40% as two-fifths (40%=40/100=4/10=2/5). 11 x 2/5 = 22/5 = 4 with 2/5 left over = 4.4 So, this comes out to more than 4 fewer cookies in...

Word problem (answer)

We know that "not one of them" is wearing the color of hat matching their name & that Ms. Red answered the lady wearing the blue hat. This should narrow it down for us - if we assume Ms. Red was not answering herself! Ms. Red is not wearing blue or red, so she must be...

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