Please help y - (-10) = 12 y = ______

1 answer:

3 0

Subtracting a negative means that you will add the number. Convert the symbols to get the following:

y + 10 = 12

Subtract 10 from both sides.

y = 2

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Help on logarithmic equation

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$\log _{ 2 }{ \left( 3-x \right) } +\log _{ 2 }{ 5 } =2\log _{ 3 }{ 5 } \\ \\ \log _{ 2 }{ \left( 5\left( 3-x \right) \right) } =\log _{ 3 }{ \left( { 5 }^{ 2 } \right) } \\ \\ { 2 }^{ \log _{ 3 }{ 25 } }=5\left( 3-x \right) \\ \\ { 2 }^{ \log _{ 3 }{ 25 } }=15-5x\\ \\ 5x=15-{ 2 }^{ \log _{ 3 }{ 25 } }\\ \\ x=\frac { 15 }{ 5 } -\frac { { 2 }^{ \log _{ 3 }{ 25 } } }{ 5 } \\ \\ x=3-\frac { { 2 }^{ \log _{ 3 }{ 25 } } }{ 5 }$

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The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 25 customers r

jolli1 [7]

Answer:

$28-2.064\frac{10}{\sqrt{25}}=23.872$

$28+2.064\frac{10}{\sqrt{25}}=32.128$

So on this case the 95% confidence interval would be given by (23.9;32.1)

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".

$\bar X=28$ represent the sample mean

$\mu$ population mean (variable of interest)

s=10 represent the sample standard deviation

n=25 represent the sample size

Solution to the problem

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

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

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=25-1=24$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that $t_{\alpha/2}=2.064$