I need help with 12,19, and 21

zimovet [89]

Answer:

1/4 to the 3rd power is 0.015625

Step-by-step explanation:

Im assuming that is what your asking, you worded it a little differently. When you figure out what the value of something is based on the power it is raised to, you multiply that number by itself the amount of the exponent.

1/4 x 1/4 x 1/4 = 0.015625

5 0

2 years ago

Construct a 99% confidence interval for the population mean, mu. Assume the population has a normal distribution. A group of 1

Zarrin [17]

Answer:

99% confidence interval for the population mean is [19.891 , 24.909].

Step-by-step explanation:

We are given that a group of 19 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8 years.

Assuming the population has a normal distribution.

Firstly, the pivotal quantity for 99% confidence interval for the population mean is given by;

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

where, $\bar X$ = sample mean age of selected students = 22.4 years

s = sample standard deviation = 3.8 years

n = sample of students = 19

$\mu$ = population mean

<em>Here for constructing 99% confidence interval we have used t statistics because we don't know about population standard deviation.</em>

So, 99% confidence interval for the population mean, $\mu$ is ;

P(-2.878 < $t_1_8$ < 2.878) = 0.99 {As the critical value of t at 18 degree of

freedom are -2.878 & 2.878 with P = 0.5%}

P(-2.878 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 2.878) = 0.99

P( $-2.878 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $2.878 \times {\frac{s}{\sqrt{n} } }$ ) = 0.99

P( $\bar X -2.878 \times {\frac{s}{\sqrt{n} }$ < $\mu$ < $\bar X +2.878 \times {\frac{s}{\sqrt{n} }$ ) = 0.99

<u>99% confidence interval for</u> $\mu$ = [ $\bar X -2.878 \times {\frac{s}{\sqrt{n} }$ , $\bar X +2.878 \times {\frac{s}{\sqrt{n} }$ ]

= [ $22.4 -2.878 \times {\frac{3.8}{\sqrt{19} }$ , $22.4 +2.878 \times {\frac{3.8}{\sqrt{19} }$ ]

= [19.891 , 24.909]

Therefore, 99% confidence interval for the population mean is [19.891 , 24.909].

6 0

3 years ago

Solve x2+12x=82 using completing the square. Answer the questions below.

galben [10]

Answer:

exact form : x = ± √ 118 − 6

Decimal form : x = 4.86278049 or − 16.86278049

Step-by-step explanation:

Use the formula ( b /2 ) ^2 in order to create a new term. Solve for x by using this term to complete the square.

4 0

2 years ago

The diameter of a circle is 3 meters. What is the circumference?

Gennadij [26K]

Answer:

C≈9.42m

Using any of this formulas

C=2πr

C=2πrd=2r

Solution:

C=πd=π·3≈9.42478m

3 0

2 years ago

Which situation can be modeled by the inequality 60−15x≥760-15x≥7? 1 )You borrowed $60 from your olde

aliina [53]

The answer is number 4 "You have $60 to spend on hats at the mall, but you need to save at least $7 for lunch. You plan to spend the rest on hats that cost $15 each including tax"
60-$15x refers to "you have $60 to spend on hats" and "to spend the rest on hats" while <7 for ''save at least $7 for lunch"

5 0

3 years ago