Every Wednesday Carla runs 2.5 miles how many feet did she run

Which institution informs individuals and businesses about their rights and responsibilities?

Mama L [17]

Answer:

A. The Federal Trade Commission

Step-by-step explanation:

The FTC inaugurated its doors in March 1915. The FTC's purpose is to protect consumers and encourage contestants. The FTC cannot solve individual grievances, but it can present knowledge about what steps to exercise. The FTC states that accusations can improve it and its law implementation partners identify patterns of fraud and exploitation, which may direct to examinations and preventing unfair marketing practices.

4 0

2 years ago

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What are the x and y intercepts of f(x) = x2-x-12/x2+5x+6 and is there a hole?

stiv31 [10]

Answer:

There are no holes. The VAs are x=4 & x=-4 the HA is x=2 the x intercepts are (-3,0) & (3,0) and the y intercept is (0,9/8).

Step-by-step explanation:

Given f ( x ) =2 x ^2 − 18/x^2-16

find all asymptotes, holes and intercepts.

Factor the numerator and denominator.

f ( x ) =2 ( x ^2 − 9 )/( x + 4 ) ( x − 4 )

f ( x ) =2 ( x +3 ) ( x − 3 )/( x + 4 ) ( x − 4 )

A hole exists when the numerator and denominator contain the same factor (a factor "cancels out"). This function has no holes.

To find the vertical asymptote(s) (VA), find the values of x

which make the denominator equal zero. The function is undefined at these values of x

because you cannot divide by zero.

Set each factor of the denominator equal to zero and solve.

x + 4 = 0 and x − 4 = 0

x = − 4 and x = 4

These are the VAs.

To find the horizontal asymptote(HA), compare the degree of the numerator and denominator. If the degrees are the same, the HA is the ratio of the leading coefficients.

For f ( x) =2 x ^2 − 18/x^2-16

the degree in both numerator and denominator is 2

and the ratio of the leading coefficients is 2/1=1

The HA is x = 2

The x intercept is the value at which the function (or "y") equals zero. If the numerator is zero, the function equals zero.

2 ( x + 3 ) ( x − 3 ) = 0

x + 3 = 0 x − 3 = 0

x = − 3 and x = − 3

The x intercepts are ( − 3 , 0 ) and ( 3 , 0 ) .

The y intercepts are found by setting x = 0 .

f ( 0 ) = 2 ( 0 ) ^2 − 18/( 0 )^2 − 16 = 9 /8

The y intercept is ( 0 , 9/ 8 ) .

graph{(2x^2-18)/(x^2-16) [-10.04, 9.96, -3.56, 6.44]}

HOPE THIS HELPS YOU!!!!

=)

4 0

3 years ago

Surface area is always measured in square units.

lozanna [386]

This statement is true

3 0

3 years ago

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An archaeologist uses an accelerator mass spectrometer to find the age of a buried branch. At the 68\%68%68, percent confidence

Komok [63]

Answer:

B. 10000 years old, with a margin of error of 400 years

Step-by-step explanation:

Assuming this complete problem: "12. An archaeologist uses an accelerator mass spectrometer to find the age of a buried branch. At the 68% confidence level, the spectrometer estimates that the branch was 10,000 years old with a following could the spectrometer estimate as the age of the branch at the 95% confidence level?"

The possible options are:

A. 9500 years old, with a margin of error of 500 years

B. 10000 years old, with a margin of error of 400 years

C. 9500 years olds, with a margin of error of 50 years

D. 10000 years old, with a margin of error of 40 year

Solution to the problem

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

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

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The margin of error for this case is given by this formula:

$ME= z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

For the first case the confidence was 68% so then $\alpha =1-0.68 =0.32$ and $\alpha/2 =0.16$ we can find a critical value on the normal standard distribution that accumulates 0.16 of the area on each tail and this value is $z=\pm 0.994$ , because P(z<-0.944) = 0.16 and P(Z>.944) = 0.16

The margin of error can be expressed like this:

$ME = z_{\alpha/2} SE$

We can solve for the standard error on this case and we got:

$SE = \frac{ME}{z_{\alpha/2}} =\frac{200}{0.994}=201.207$

And then for the new confidence interval we need to calculate the new $z_{\alpha}$ . For the first case the confidence was 95% so then $\alpha =1-0.95 =0.05$ and $\alpha/2 =0.025$ we can find a critical value on the normal standard distribution that accumulates 0.025 of the area on each tail and this value is $z=\pm 1.96$ , because P(z<-1.96) = 0.025 and P(Z>1.96) = 0.025. So then the new margin of error would be: