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OLEGan [10]
3 years ago
12

Use the distributive property to find an expression that is equivalent to 2x(x + 7)-(3x +1)

Mathematics
1 answer:
zaharov [31]3 years ago
7 0

Given expression:

     2x(x + 7)-(3x +1);

To distribute implies to spread a process equally in an expression. Often times, the distributive property is used for expressions inside parentheses;

  2x(x + 7)-(3x +1)  

  Distribute 2x over the first parentheses;

   the negative sign distributes over the second part

    = (2x² + 14x)  - 3x -1

    = 2x² + 14x -3x -1

    Add like terms;

    = 2x² + 11x -1

This expression  2x² + 11x -1 is equal to the given one

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In 2014, the CDC estimated that the mean height for adult women in the U.S. was 64 inches with a standard deviation of 4 inches.
Vladimir79 [104]

Answer:

A. 16%

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 64, \sigma = 4

Which of the following gives the probability that a randomly selected woman has a height of greater than 68 inches?

This is 1 subtracted by the pvalue of Z when X = 68. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{68 - 64}{4}

Z = 1

Z = 1 has a pvalue of 0.84.

1 - 0.84 = 0.16

So the correct answer is:

A. 16%

6 0
3 years ago
If a cube has a volume of 13,824 cubic meters what is the edge length
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3 years ago
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777dan777 [17]

Answer:

\begin{array}{ccc}\text{Radius}&\text{Volume of sphere}&\text{Volume of cylinder}\\&&\\1&\dfrac{4}{3}\pi &2\pi \\&&\\2&\dfrac{32}{3}\pi &16\pi \\&&\\3&36\pi &54\pi \\&&\\4&\dfrac{256}{3}\pi &128\pi \\&&\\5&\dfrac{500}{3}\pi &250\pi\end{array}

Step-by-step explanation:

Use formulas for the volumes:

V_{sphere}=\dfrac{4}{3}\pi r^3,\\ \\V_{cylinder}=\pi r^2h=\pi r^2\cdot 2r=2\pi r^3.

1. When r=1,

V_{sphere}=\dfrac{4}{3}\pi\cdot 1^3=\dfrac{4}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 1^3=2\pi.

2. When r=2,

V_{sphere}=\dfrac{4}{3}\pi\cdot 2^3=\dfrac{32}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 2^3=16\pi.

3. When r=3,

V_{sphere}=\dfrac{4}{3}\pi\cdot 3^3=36\pi,\\ \\V_{cylinder}=2\pi \cdot 3^3=54\pi.

4. When r=4,

V_{sphere}=\dfrac{4}{3}\pi\cdot 4^3=\dfrac{256}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 4^3=128\pi.

5. When r=5,

V_{sphere}=\dfrac{4}{3}\pi\cdot 5^3=\dfrac{500}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 5^3=250\pi.

Note that for all r,

\dfrac{V_{sphere}}{V_{cylinder}}=\dfrac{\frac{4}{3}\pi r^3}{2\pi r^3}=\dfrac{2}{3}.

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3 years ago
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