Hi, Frankie! Notice that the cable weighs 2805.0 kilograms per kilometer. Thus, we need to convert this standard to kilograms per meter, in order to match the measurement of the 137.16 meters cable. Simply divide the standard by 1000, as a kilometer is 1000 meters, and the result is 2.805 kg/m....

Let's call the year 2000 population x, which then increased by 74% to 104,400 by the year 2010. Write this as an equation:   x + (x * 0.74) = 104,400   Now, solve for x:   1.74x = 104,400 [combine like terms - 1x + 0.74x = 1.74x] x = 104,400/1.74...

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...

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...

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...

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...