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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...

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...

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...

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...

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...

Antonio paid \$8 for a hat he sold for \$18, so his profit was \$10. Markup is a percentage increase from the wholesale price, so let's find the percentage of \$10 to \$8:   \$10/\$8 = 125%   Think of it this way: \$10 is more than \$8, so we know the markup is more than 100%. It...

This is actually two related problems. We should first draw representations of each scenario, so that we are in a position to visualize each situation & solve each problem. We also must make a few assumptions. The problem does not state that the post is exactly on the edge of the river, but...

First, notice that this problem says nothing about how many games these people attend. We can probably assume that, for the same amount of money spent, the season ticket holder can attend more games than the single ticket buyer. We do know how much the season ticket holder paid & can use this...

In order to answer this, you need to understand some measurements & convert them into forms you can use in an equation. As "2.0 m/s" refers to meters per second, we must find out how many seconds are in an hour - or 3.0 hours, actually. To solve this problem, you will simply multiply...

Let's first make sure we're clear on definitions of terms. Difference refers to subtraction, so we're talking about subtracting 5 from 4 times a number. That difference, the problem says, is "the same as three more than twice" the original number.   We first need an equation...