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3 years ago

Given f(x) = -5(2x-7 )- 19, what is the value of f(-2)?

Mathematics

1 answer:

Svetlanka [38]3 years ago

6 0

Answer:

X=1.8

Step-by-step explanation:

f(X)=-2

-5(2x-7)-19=-2

-10x+35-19+2=0

-10x=-18

X=-18÷(-10)

X=1.8

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Answer:

a) Point estimate of the population mean = 4.883

b) B.There is 95% confidence that the population mean pH of rain water is between 4.646 and 5.120.

c) C.There is 99% confidence that the population mean pH of rain water is between 4.549 and 5.217.

d) As the level of confidence increases, the width of the interval increases.

This makes sense since the margin of error increases as well.

Step-by-step explanation:

We have a sample for the pH of rain.

The mean of the sample is:

$M=\dfrac{1}{12}\sum_{i=1}^{12}(5.3+5.72+4.38+4.8+5.02+...+4.56+4.68)\\\\\\ M=\dfrac{58.59}{12}=4.883$

The sample standard deviation is:

$s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{12}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{11}\cdot [(5.3-4.883)^2+(5.72-4.883)^2+...+(4.68-4.883)^2]}\\\\\\$

$s=\sqrt{\dfrac{1}{11}\cdot [(0.17)+...+(0.1)+(0.04)]}\\\\\\s=\sqrt{\dfrac{1.526625}{11}}=\sqrt{0.1387841}\\\\\\s=0.373$

a) The point estimation for the population mean is the sample mean and has a value of 4.883.

b) We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=4.883.

The sample size is N=12.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{0.373}{\sqrt{12}}=\dfrac{0.373}{3.464}=0.108$

The t-value for a 95% confidence interval is t=2.201.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=2.201 \cdot 0.108=0.237$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 4.883-0.237=4.646\\\\UL=M+t \cdot s_M = 4.883+0.237=5.12$

The 95% confidence interval for the mean is (4.646, 5.120).

B.There is 95% confidence that the population mean pH of rain water is between 4.646 and 5.120.

c) We have to calculate a 99% confidence interval for the mean.

The t-value for a 99% confidence interval is t=3.106.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=3.106 \cdot 0.108=0.334$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 4.883-0.334=4.549\\\\UL=M+t \cdot s_M = 4.883+0.334=5.217$

The 99% confidence interval for the mean is (4.549, 5.217).

C.There is 99% confidence that the population mean pH of rain water is between 4.549 and 5.217.

d) When the confidence level is increased, the width also increases as it has to include more possible values for the true mean of the population.

As the level of confidence increases, the width of the interval increases.

This makes sense since the margin of error increases as well.

5 0

3 years ago