How many numbers in the list 43, 4343, 434343, ...., are prime?

A researcher examines 27 water samples for iron concentration. The mean iron concentration for the sample data is 0.802 cc/cubic

Delvig [45]

Answer:

90% confidence interval for the population mean iron concentration is [0.771 , 0.832].

Step-by-step explanation:

We are given that a researcher examines 27 water samples for iron concentration. The mean iron concentration for the sample data is 0.802 cc/cubic meter with a standard deviation of 0.093.

Firstly, the pivotal quantity for 90% confidence interval for the population mean iron concentration is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean iron concentration = 0.802 cc/cubic meter

s = sample standard deviation = 0.093

n = number of water samples = 27

$\mu$ = population mean

Here for constructing 90% confidence interval we have used t statistics because we don't know about population standard deviation.

So, 90% confidence interval for the population mean, $\mu$ is ;

P(-1.706 < $t_2_6$ < 1.706) = 0.90 {As the critical value of t at 26 degree of

freedom are -1.706 & 1.706 with P = 5%}

P(-1.706 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 1.706) = 0.90

P( $-1.706 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $1.706 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

P( $\bar X -1.706 \times {\frac{s}{\sqrt{n} }$ < $\mu$ < $\bar X +1.706 \times {\frac{s}{\sqrt{n} }$ ) = 0.90

90% confidence interval for $\mu$ = [ $\bar X -1.706 \times {\frac{s}{\sqrt{n} }$ , $\bar X +1.706 \times {\frac{s}{\sqrt{n} }$ ]

= [ $0.802 -1.706 \times {\frac{0.093}{\sqrt{27} }$ , $0.802 +1.706 \times {\frac{0.093}{\sqrt{27} }$ ]

= [0.771 , 0.832]

Therefore, 90% confidence interval for the population mean iron concentration is [0.771 , 0.832].

4 0

3 years ago

Estimate the area of Alberta in square miles. Show your reasoning

ella [17]

Answer: About $278,250\ mi^2$

Step-by-step explanation:

The missing figure is attached.

Notice in the first picture that Alberta has a complex shape.

You can calculate the area of a complex shape by decomposing it into polygons whose areas can be calculated easily.

Observe the second picture. Notice that it can be descompose into two polygons: A trapezoid and a rectangle.

The area of the trapezoid can be calcualted with the formula:

$A_t=\frac{h}{2}(B+b)$

Where "h" is the height, "B" is the long base and "b" is short base.

And the area of the rectangle can be found with the formula:

$A_r=lw$

Wkere "l" is the lenght and "w" is the width.

Then, the apprximate area of Alberta is:

$A=\frac{h}{2}(B+b)+lw$

Substituting vallues, you get:

$A=(\frac{(410\ mi-180\ mi)}{2})(760\ mi+470\ mi)+(180\ mi)(760\ im)\\\\A=141,450\ mi^2+136,800\ mi^2\\\\A=278,250\ mi^2$

Therefore, the area of of Alberta is about $278,250\ mi^2$ .

5 0

3 years ago

What is the answer and why is it correct explain

Colt1911 [192]

Top left is you answer

7 0

3 years ago

It is based on ratios

12345 [234]

Answer:

Gianna makes $18 per hour.

Step-by-step explanation:

Given Gianna makes 90$ for 5 hours. That means she should make $\frac{90}{5}$ $ = 18$ every hour.

Therefore we have:

a.

HOURS DOLLARS

1 18

2 36

3 54

4 72

5 90

6 108

7 126

b.

For the tabular column mark Hours on the x - axis and Dollars on the Y - axis. It can be plotted from the above table easily.

c.

If Gianna works for 8 hours she would have made 8 X 18 = 144$.

So, she will earn 144$ in 8 hours.

d.

To make 60$ she would have to work $\frac{60}{18}$ hours = 3.33 hours.

3 0

3 years ago

Simplify 4y (2y-7) and find it's value if y= 1/2 ANSWER FASTT!!!

Vinvika [58]

Step-by-step explanation:

This the solution

the answer is one

3 0

3 years ago