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3 years ago

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In how many ways can a gymnastics team of 4 be chosen from 9 gymnasts? Type a numerical answer in the space provided. Do not typ

e spaces in your answer.

1 answer:

vovangra [49]3 years ago

4 0

There are 126 ways to choose a team of 4 gymnasts from a set of 9 gymnasts.

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Find the distance between the pair of parallel lines, y = x-11 & y = x-7

kenny6666 [7]

$k:\ y = x-11\ \ \ \Leftrightarrow\ \ \ x-y-11=0\\ and\\ l:\ y = x-7\ \ \ \Leftrightarrow\ \ \ x-y-7=0\\\\the\ distance:\\\\ d(k;l)= \frac{\big{|-11-(-7)|}}{\big{ \sqrt{1^2+1^2} }} =\frac{\big{|-11+7|}}{\big{ \sqrt{2} }} =\frac{\big{|-4|}}{\big{ \sqrt{2} }} =\frac{\big{4\cdot \sqrt{2} }}{\big{ \sqrt{2}\cdot \sqrt{2} }} =\frac{\big{4 \sqrt{2} }}{\big{2 }} =2 \sqrt{2}$

6 0

3 years ago

Read 2 more answers

What is the result of adding these two equations?

arsen [322]

Answer:

-2x-7y=-4

Step-by-step explanation:

5x+-7x=-2x

-9y+2y=-7y

1+-5=-4

So -2x-7y=-4

6 0

2 years ago

What equation would you use to find the measure of

PIT_PIT [208]

The figure is a parallelogram, and in a parallelogram, the lower side and the upper side have the same length. Also, the left side and the right side have the same length. This is shown in the following image:

The red sides are equal, and the blue sides are equal.

Thus, since the blue sides are equal, we can use the following equation to find x:

$7x=3x+14$

And since, once we know x, we can know the length of JK, this is the equation that we can use to find JK.

Answer:

7x=3x+14

6 0

1 year ago

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the e

Korolek [52]

Answer:

A sample of 499 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is given by:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

In this question, we have that:

$\pi = 0.21$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 90% confidence level with an error of at most 0.03

We need a sample of n, which is found when $M = 0.03$ . So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.03 = 1.645\sqrt{\frac{0.21*0.79}{n}}$

$0.03\sqrt{n} = 1.645\sqrt{0.21*0.79}$

$\sqrt{n} = \frac{1.645\sqrt{0.21*0.79}}{0.03}$

$(\sqrt{n})^2 = (\frac{1.645\sqrt{0.21*0.79}}{0.03})^2$

$n = 498.81$

Rounding up

A sample of 499 is needed.

8 0

2 years ago

MUST ANSWER ALL PARTS!!!!

dsp73

Hello there,

The outlier of the data set is 92. Lets first find everything with the outlier.
Mean: 60.08
Median: 57
Mode: 52
Range:46

Now let's take out the outlier of the set and see the difference.
Mean: 54.27
Median:56
Mode: 52
Range: 15

So as we can see without the outlier everything is closer together. The outlier shouldn't be included because that makes the entire set screwed up. The data is more accurate without the outlier.

Hope this helps!

6 0

2 years ago