Which value for x makes the sentence true?

The store clerk has 21 mugs to display on shelves. She wants to display a equal number of mugs on each shelf with no mugs left o

elena55 [62]

I believe it’s C, 21 divided by 7. This one doesn’t leave any extra mugs out cause 21 divided by 7 is 3, leaving 7 mugs per 3 shelves and having none left.

8 0

3 years ago

Find the slope of a line perpendicular to 2x-y-16

Alekssandra [29.7K]

put the equation 2x - y = 16 in the form of y = mx + c

2x - y = 16

2x = 16 + y

y = 2x - 16

the slope of this line is 2. the slope of a line perpendicular to it would be the negative reciprocal of 2. in other words, it would multiply with 2 to give -1.

you can form this equation with that info

2x = -1

x = -1/2

OR

you can flip and change the sign (numerator) of 2/1

2/1

= -1/2

6 0

3 years ago

Checking the Mean Value Theorem:<br><br>Number 3

mrs_skeptik [129]

$\bf f(x)=x+\cfrac{1}{x}\qquad \left[\frac{1}{2},2 \right]\\\\
-----------------------------\\\\
\cfrac{df}{dx}=1+\left(-1x^{-2} \right)\implies \cfrac{df}{dx}=1-\cfrac{1}{x^2}
\\\\\\
f'(c)=1-\cfrac{1}{c^2}\quad \quad 1-\cfrac{1}{c^2}=\cfrac{f(2)-f\left( \frac{1}{2} \right)}{2-\frac{1}{2}}
\\\\\\
1-\cfrac{1}{c^2}=\cfrac{\frac{5}{2}-\frac{5}{2}}{\frac{3}{2}}\implies 1-\cfrac{1}{c^2}=\cfrac{0}{\frac{3}{2}}\implies 1-\cfrac{1}{c^2}=0
\\\\\\
1=\cfrac{1}{c^2}\implies c^2=1\implies c=\pm\sqrt{1}\implies c=\pm 1$

there's a quick graph below of the bounds and the tangent at "c"

not happening -2 or 2 will have a tangent parallel to a,b, needless to say -2 is out of the range [a,b] anyway, so the only value is really 1, on the positive 1st quadrant

6 0

3 years ago

Point Q' is the image of Q (4,-6) is under a translation by 1 unit to the right.

alexandr1967 [171]

Answer:

The coordinates of point Q' would be (5, -6) after being translated 1 unit to the right.

Step-by-step explanation:

4 0

3 years ago

What is the formula for a confidence interval?

ikadub [295]

Answer:

a) The formula is given by mean $\pm$ the margin of error. Where the margin of error is the product between the critical value from the normal standard distribution at the confidence level selected and the standard deviation for the sample mean.

b) $\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

If the distribution for X is normal or if the sample size is large enough we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

Part a

The formula is given by mean $\pm$ the margin of error. Where the margin of error is the product between the critical value from the normal standard distribution at the confidence level selected and the standard deviation for the sample mean.

Part b

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

5 0

4 years ago