What is the circumference of this circle?

Find an equation of the line that passes through the point (-6,7) and is perpendicular to the line 12x-18y-72=0

madreJ [45]

Answer:

y=-1.5x-2

Step-by-step explanation:

18y=12x-72

3y=2x-12

y=2/3x-4

Slope=-1.5

7=-6(-1.5)+b

7=9-2

4 0

3 years ago

A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies. Random

Yuliya22 [10]

Answer:

b) independent samples t-test

$t=\frac{(5.92 -5.74)-(0)}{\sqrt{\frac{1.88^2}{5}}+\frac{1.81^2}{5}}=0.154$

$p_v =2*P(t_{8}>0.154) =0.881$

So with the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).

Step-by-step explanation:

The system of hypothesis on this case are:

Null hypothesis: $\mu_1 = \mu_2$

Alternative hypothesis: $\mu_1 \neq \mu_2$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 = 0$

Alternative hypothesis: $\mu_1 -\mu_2\neq 0$

Our notation on this case :

$n_1 =5$ represent the sample size for group 1

$n_2 =5$ represent the sample size for group 2

We can calculate the mean and deviation for eaach group with the following formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X_1 =5.92$ represent the sample mean for the group 1

$\bar X_2 =5.74$ represent the sample mean for the group 2

$s_1=1.88$ represent the sample standard deviation for group 1

$s_2=1.81$ represent the sample standard deviation for group 2

If we see the alternative hypothesis we see that we are conducting a bilateral test and with independnet samples t test.

b) independent samples t-test

The statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{\sqrt{\frac{s^2_1}{n_1}}+\frac{S^2_2}{n_2}}$

And now we can calculate the statistic:

$t=\frac{(5.92 -5.74)-(0)}{\sqrt{\frac{1.88^2}{5}}+\frac{1.81^2}{5}}=0.154$

The degrees of freedom are given by:

$df=5+5-2=8$

And now we can calculate the p value using the altenative hypothesis:

$p_v =2*P(t_{8}>0.154) =0.881$

So with the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).

7 0

4 years ago

4x-5y=13

love history [14]

Hello :
<span>4x-5y=13...(1)
x+5y=-3...(2)
(1)+(2) : 5x = 10
x=2
subsct in (2) : 2+5y = -3
5y =-5
y = -1

</span>

8 0

4 years ago

help At 1:00 P.M. the water level of a pool is 13 inches At 1:30 P.M. the water level is 18 inches At 2:30 the water level is 28

mamaluj [8]

The answer is 5 . because if you count the # it will go to 28

7 0

3 years ago

The value of a car decreases about 7% percent each year after it is manufactured.The 2017 Honda Civic costs $19,540

Kitty [74]

Answer: a) , where 'A' is the value of car after 't' years.

b) $12446.784

Step-by-step explanation:

Given: A new car that sells for $21,000 depreciates (decreases in value) 16% each year.

Then a function that models the value of the car will be

, where 'P' is the selling price of car, 'r' is the rate of depreciation in decimal, 't' is the time in years and 'A' is the value of car after 't' years.

Thus after substituting given value, the function becomes

To find the value after 3 years, substitute t=3 in the above function.

Hence the value of car after 3 years=$12446.784

5 0

3 years ago