Answer:
27
Step-by-step explanation:
First solve 3a - 9= 6
3a - 9 = 6 add 9
3a = 15 divide by 3
a = 5
Now that you know a is 5, put that in the other expression.
5a + 2
= 5(5) + 2
= 25 + 2
= 27
Answer:
-7 4/5 or -7.8
Step-by-step explanation:
Product means multiplication
( - 13/8 )( 24/5)
= (-13 · 24)/(8 · 5) negative · positive = negative
= - 312/40
= -7 32/ 40 = -7 4/5 or 7.8
Answer:
15 blue marbles
Step-by-step explanation:
Given that:
A bag contains 6 red marbles.
The Ratio of red to blue marbles is 2:5
Thus, the ratio of red marbles for 6 red marbles in a bag will be = 6/2 = 3
Now; the ratio of blue marbles in a bag containing 6 red marbles = 3 × 5 = 15 blue marbles
OR
Mathematically;
![\dfrac{2}{5} \times \dfrac{x}{x} = \dfrac{6}{blue}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B5%7D%20%5Ctimes%20%5Cdfrac%7Bx%7D%7Bx%7D%20%3D%20%5Cdfrac%7B6%7D%7Bblue%7D)
So, we are looking for the same number we can multiply for both the numerator and the denominator that can give us the value of 6 in the above numerator to determine the value of the denominator. If we use 3 since 2× 3 = 6
We have:
![\dfrac{2}{5} \times \dfrac{3}{3} = \dfrac{6}{blue}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B5%7D%20%5Ctimes%20%5Cdfrac%7B3%7D%7B3%7D%20%3D%20%5Cdfrac%7B6%7D%7Bblue%7D)
![\dfrac{2}{5} \times \dfrac{3}{3} = \dfrac{6}{15}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B5%7D%20%5Ctimes%20%5Cdfrac%7B3%7D%7B3%7D%20%3D%20%5Cdfrac%7B6%7D%7B15%7D)
So, there are 15 blue marbles in the bag.
Answer:
The value of the test statistic is z = -0.877.
Step-by-step explanation:
Testing the difference in mean time spent on housework between husbands and wives.
At the null hypothesis, we test if there is no difference, that is, the subtraction of the means is 0:
![H_0: \mu_H - \mu_W = 0](https://tex.z-dn.net/?f=H_0%3A%20%5Cmu_H%20-%20%5Cmu_W%20%3D%200)
At the alternate hypothesis, we test if there is a difference, that is, the subtraction of the means is different from 0.
![H_1: \mu_H - \mu_W \neq 0](https://tex.z-dn.net/?f=H_1%3A%20%5Cmu_H%20-%20%5Cmu_W%20%5Cneq%200)
The test statistic is:
![z = \frac{X - \mu}{s}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7Bs%7D)
In which X is the sample mean,
is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that ![\mu = 0](https://tex.z-dn.net/?f=%5Cmu%20%3D%200)
For the wives the mean was 7 hours/week and for the husbands the mean was 4.5 hours/week. The standard deviation of the differences in time spent on house work was 2.85.
This means that ![X = 4.5 - 7 = -2.5, s = 2.85](https://tex.z-dn.net/?f=X%20%3D%204.5%20-%207%20%3D%20-2.5%2C%20s%20%3D%202.85)
What is the value of the test statistic for testing the difference in mean time spent on housework between husbands and wives?
![z = \frac{X - \mu}{s}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7Bs%7D)
![z = \frac{-2.5 - 0}{2.85}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B-2.5%20-%200%7D%7B2.85%7D)
![z = -0.877](https://tex.z-dn.net/?f=z%20%3D%20-0.877)
The value of the test statistic is z = -0.877.
Answer:
28.26
Step-by-step explanation:
For this, we can simply use the pi times r squared because we have the radius.
simplify pi to 3.14, so we can do 3.14 times 3 squared.
we get 9x 3.14, which is 28.26.