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3 years ago

Write in equation of the line containing the points (-8,-8) and (-9,-10

Mathematics

1 answer:

myrzilka [38]3 years ago

4 0

Answer:

y = 2x + 8

Step-by-step explanation:

Find the slope of a line between (-8,-8) and (-9,-10) using m = $\frac{y_2-y_1}{x_2-x_1}$ , which is the change in y over the change in x.

Substitute in the values of x and y into the equation to find slope.

$m= \frac{-10-(-8)}{-9(-8)}$

Simplify.

Simplify the numerator.

Multiply -1 by -8

$m=\frac{-10+8}{-9-(-8)}$

Add -10 and 8

$m=\frac{-2}{-9-(-8)}$

Simplify the denominator.

Multiply -1 by -8

$m=\frac{-2}{-9+8}$

Add -9 and 8.

$m=\frac{-2}{-1}$

Divide -2 by -1.

$m=2$

Using the point slope form $y-y_1=m(x-x_1)$ plug in m = 2, $x_1 = -8, y_1 = -8$

$y-(-8)=(2)(x-(-8))$

Solve for y.

Multiply -1 by -8

y + 8 = ( 2 ) ( x − ( − 8 ) )

Simplify ( 2 ) ( x − ( − 8 ) ) .

Multiply − 1 by − 8

y+8 = 2 ( x + 8 )

Apply the distributive property.

y + 8 = 2 x + 2 ⋅ 8

Multiply 2 by 8 .

y + 8 = 2x + 16

Move all terms not containing y to the right side of the equation.

Subtract 8 from both sides of the equation.

y = 2 x + 16 − 8

Subtract 8 from 16 .

y = 2 x + 8

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The average amount of water in randomly selected 16-ounce bottles of water is 16.15 ounces with a standard deviation of 0.45 oun

vekshin1

Answer:

0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

$\mu = 16.15, \sigma = 0.45, n = 35, s = \frac{0.45}{\sqrt{35}} = 0.0761$

What is the probability that the mean of this sample is less than 15.99 ounces of water?

This is the pvalue of Z when X = 15.99. So

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

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{15.99 - 16.15}{0.0761}$

$Z = -2.1$

$Z = -2.1$ has a pvalue of 0.0179

0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.

3 0

2 years ago

Rearrange the formula A = <br> Θr2<br> 2<br> for Θ.

Lina20 [59]

Answer:

$\theta=\frac{2A}{r^2}$

Step-by-step explanation:

Given : The formula $A=\frac{\theta r^2}{2}$

We have to rearrange the given formula for $\theta$

Consider the given formula $A=\frac{\theta r^2}{2}$

Multiply both side by 2, we have,

$2A={\theta r^2$

Divide both side by $r^2$ , we have,

$\frac{2A}{r^2}= \frac{\theta r^2}{r^2}$

Simplify, we get,

$\frac{2A}{r^2}=\theta$

Thus, $\theta=\frac{2A}{r^2}$

3 0

3 years ago

Read 2 more answers

PLSSS HELP WILL GIVE BRAINLIEST FOR FIRST CORRECT ANSWER!!!!!!!!!

Kryger [21]

Answer:

A fair die has 6 sides.

There are 3 odd numbers on a fair die so the probability would be 3/6

There are 4 numbers greater than 2 on a fair die o the probability of that would be 4/6

There is only one number that will make it square and that is 4. So the probability would be 1/6

6 0

3 years ago

What is 9.1 less than a number is less than 4.6 equals?

Brilliant_brown [7]

Answer:

n > 13.7

Step-by-step explanation:

Writing a symbolic statement, we get:

n - 9.1 < 4.6

Multiplying all three terms by 10 removes fractions:

10n - 91 > 46

Adding 91 to both sides isolates the 10n term:

10n > 46 + 91, or 10n > 137

Then n > 137/10, or n > 13.7

4 0

3 years ago

Please help i can not figure it out

Alisiya [41]

To solve this problem you need to figure out the volume of the sipping container, and the volume of the tissue box.
39*19.5*19.5=14,829.75
6.5*6.5*6.5=274.63

In order to figure out how many fits you need to divide
14,829.75/274.63=53.99

The maximum number that you can fit is the box is 53.

Hope this helps

4 0

3 years ago