Find the exact value of each expression. (a) cot−1(1)

Assume the blood pressures of 10 people were measured before and after sleeping for the night. What is the corresponding critica

NeX [460]

Answer:

For the critical value we need to calculate the degrees of freedom given by:

$df = n-1= 10-1=9$

And since we have a one tailed test we need to look in the t distribution with 9 degrees of freedom a quantile who accumulates 0.05 of the area on a tail and we got:

$|t_{crit}| =1.833$

Step-by-step explanation:

Previous concepts

A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.

Let put some notation

x=test value with right arm , y = test value with left arm

The system of hypothesis for this case are:

Null hypothesis: $\mu_y- \mu_x = 0$

Alternative hypothesis: $\mu_y -\mu_x \neq 0$

The first step is calculate the difference $d_i=y_i-x_i$

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{361}{5}$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}$

The 4 step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}$

For the critical value we need to calculate the degrees of freedom given by:

$df = n-1= 10-1=9$

And since we have a one tailed test we need to look in the t distribution with 9 degrees of freedom a quantile who accumulates 0.05 of the area on a tail and we got:

$|t_{crit}| =1.833$

5 0

2 years ago

Sean has 15,000 to invest she will put some of it into a fund that pays 4.5% annual interest in the rest in a certificate of dep

DENIUS [597]

Answer:$12500 was invested into the account that pays 4.5% annual interest..

$2500 was invested into the the certificate of deposit that pays 1.8% annual interest..

Step-by-step explanation:

Let x represent the amount invested into the account that pays 4.5% annual interest.

Let y represent the amount invested into the certificate of deposit that pays 1.8% annual interest.

Sean has 15,000 to invest. She will put some of it into a fund that pays 4.5% annual interest and the rest in a certificate of deposit that pays 1.8% annual interest. This means that

x = y + 15000

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

Considering the account earning 4.5% interest, the interest would be

I = (x × 4.5 × 1)/100 = 0.045x

Considering the account earning 11% interest, the interest would be

I = (x × 1.8 × 1)/100 = 0.018y

if she wants to earn 4.05% annual interest on the total amount, the amount would be

4.05/100 × 15000 = 607.5

Therefore,

0.045x + 0.018y = 607.5 - - - - - - - - - - -1

Substituting x = 15000 - y into equation 1, it becomes

0.045(15000 - y) + 0.018y = 607.5

675 - 0.045y + 0.018y = 607.5

- 0.045y + 0.018y = 607.5 - 675

- 0.027y = - 67.5

y = - 67.5/- 0.027

y = $2500

x = 15000 - y = 15000 - 2500

x = $12500

6 0

2 years ago

What inverse operation is used to solve the equation 2x=10

Jlenok [28]

It’s c multiply by 2 on both sides

5 0

2 years ago

Read 2 more answers

The diagram shows a field.<br>140 m<br>66 m<br>102 m<br>Work out the area of the field.

aalyn [17]

Answer:

7986

Step-by-step explanation:

66x0.5x(140+102)=7986

3 0

2 years ago

108 identical books have a mass of 30 kg,find the mass of 150 such books

snow_lady [41]

Answer:

150 * 0.27777777778 kg = 41.666666667 kg.

7 0

2 years ago