Answer:
Step-by-step explanation:
Given that :
population mean μ = 120
sample size n = 37
sample mean x = 111
standard deviation = 21
The null hypothesis and the alternative hypothesis can be computed as:
The null hypothesis:
![\mathbf{ H_o: \mu = 120 }](https://tex.z-dn.net/?f=%5Cmathbf%7B%20H_o%3A%20%5Cmu%20%3D%20120%20%7D)
The alternative hypothesis:
![\mathbf{ H_o: \mu \neq 120 }](https://tex.z-dn.net/?f=%5Cmathbf%7B%20H_o%3A%20%5Cmu%20%5Cneq%20120%20%7D)
Since this test is two-tailed, the value for the test statistics can be computed as:
![z = \dfrac{\overline x - \mu}{\dfrac{\sigma }{\sqrt{n}}}](https://tex.z-dn.net/?f=z%20%3D%20%5Cdfrac%7B%5Coverline%20x%20-%20%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%20%7D%7B%5Csqrt%7Bn%7D%7D%7D)
![z = \dfrac{111 - 120}{\dfrac{21}{\sqrt{37}}}](https://tex.z-dn.net/?f=z%20%3D%20%5Cdfrac%7B111%20-%20120%7D%7B%5Cdfrac%7B21%7D%7B%5Csqrt%7B37%7D%7D%7D)
![z = \dfrac{-9}{\dfrac{21}{6.08}}](https://tex.z-dn.net/?f=z%20%3D%20%5Cdfrac%7B-9%7D%7B%5Cdfrac%7B21%7D%7B6.08%7D%7D)
z = -2.605
z = -2.61
Since this is a two-tailed test
P-value = 2(z < -2.61)
From the z table;
P-value = 2(0.0045)
P -value = 0.009
Decision rule: To reject the null hypothesis if the p-value is lesser than the level of significance
Conclusion: We reject the null hypothesis since the p-value is lesser than the level of significance. Thus, there is sufficient evidence to conclude that the average breaking distance differs from 120 feet.
Answer:
12
Step-by-step explanation:
Lets c = chord inside circle
3(3 + c) = 6^2
9 + 3c = 36
3c = 27
c = 9
x = 3 + 9
x = 12
The question is incomplete:
The dot plot shows the number of hours Stan worked each week for the last 3 months.
What fraction of the total number of weeks did Stan work 15 or more hours? Express in simplest form.
A. 5/7
B. 1/6
C. 1/5
D. 5/12
The image with the dot plot is attached.
Answer:
D. 5/12
Step-by-step explanation:
The dot plot shows the number of hours Stan worked and in order to know the number of weeks that he worked 15 hours or more, you have to count the dots that are between 15 and 18 hours. So, you have 3 dots in 15 hours, 1 dot in 16 hours and 1 dot in 18 hours. If you add this numbers (3+1+1=5), this means that he worked 5 weeks 15 or more hours. This number would be the numerator in your fraction. Then, the denominator would be the total amount of weeks and to find that you can count all the dots. The total number of dots is 12.
So, the fraction that represents the total number of weeks that Stan worked 15 or more hours is: 5/12. This is the simplest form because this numbers don't have any common factors other than 1.
Let's use 304,900,000 as an example.
In scientific notation it is 3.049 x 10^8
When converting to scientific notation, just drop any zeros at the end of the number and put the decimal place after the first digit. Then for the power on the 10, count all the digits (including zeros). In our example there are 8 digits after the 3 so we raise 10 to the 8th power.
Now let's look at small numbers. For example, 0.0000718
If the number is between 0 and 1, we will raise the 10 to a negative power. In this case the answer is 7.18 x 10^-5.
What you do to find the power is move the decimal point over so that there is one digit in front. Just like we did with the first example. Count how many places the decimal moved and use it for the power.
Hopefully this helps. Let me know if you need further explanation :)
Answer:
x=63
y=27
Step-by-step explanation: