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fiasKO [112]
2 years ago
11

Solve the inequality for u. -3u-14>3u+16

Mathematics
1 answer:
ANTONII [103]2 years ago
3 0

Hi student, let me help you out!

..............................................................................................................................................

First of all, we need to solve this inequality for u. We can easily do it if we follow these steps:

  1. Subtract 3u from both sides.
  2. Add 14 to both sides.
  3. Solve for u.

Step 1. Subtract 3u from both sides: \mathrm{-3u-3u-14 < 16}.

Upon simplifying, we get \mathrm{-6u-14 < 16}.

Step 2. Add 14 to both sides: \mathrm{-6u < 16+14}

Upon simplifying, we get \mathrm{-6u < 30}

Step 3. Solve for u, which can be done by dividing both sides by -6:

\mathrm{-6u\div(-6)=30\div{-6)}}.

Upon simplifying, we get \mathrm{u > -5}.

Have you noticed that the sign of the inequality changed from "less than" to "greater than"? This happens every time we multiply, or divide, both sides of an inequality by  a negative number. The sign changes from less than to greater than, or the other way around.

Thus, the solution is \bigstar\underline{\boxed{\mathrm{u > -5}}}

Hope it helped you out, ask in comments if any queries arise.

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TEA [102]
30 of the divisors are multiples of 3

The factors of 2160 are 1, 2160, 2, 1080, 3, 720, 4, 540, 5, 432, 6, 360, 8, 270, 9, 240, 10, 216, 12, 180, 15, 154, 16, 135, 18, 120, 20, 108, 24, 90, 27, 80, 30, 72, 36, 60, 40, 54, 45, 48
These are all divisors of 2160 but only 30 are multiples of 3.
The ones that are NOT are 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80

You can also do this using prime factors 2x2x2x2x3x3x3x5 = 2160 but it is harder to explain.
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Answer:

The mean number of gerbils seen per day is 6.

The mean absolute deviation of the data is 2.29.

Step-by-step explanation:

The mean of a data set is the value that represents the entire data set. It is the average value.

The formula to compute the mean of a data set is:

\bar x=\frac{1}{n}\sum X

The mean absolute deviation (MAD) of a data set is the average distance amid each value and the mean. The MAD provides us with an idea about the deviation in the data set.

The formula to calculate the value of MAD is:

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The data set for the number of gerbils seen per day is:

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Compute the mean of the data as follows:

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The mean number of gerbils seen per day is 6.

Compute the mean absolute deviation of the data as follows:

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