Answer: 10th Percentile
Step-by-step explanation:
The percentile of a variable in a dataset is the percentage position of the variable in the dataset such that the variables before this variable are below this percentage.
There are 20 variables in this data set and Biff scored a 65 which occupies the second and third positions on this dataset.
Picking the first position, 65 is the second variable in the data set so Biff's percentile is;
= Position on dataset/ No. of variables in data set
= 2/20
= 10%
= 10th percentile
Given:
The function is
To find:
The derivative of the given function.
Solution:
Chain rule of differentiation:
![[f(g(x))]'=f'(g(x))g'(x)](https://tex.z-dn.net/?f=%5Bf%28g%28x%29%29%5D%27%3Df%27%28g%28x%29%29g%27%28x%29)
Product rule of differentiation:
![[f(x)g(x)]'=f(x)g'(x)+g(x)f'(x)](https://tex.z-dn.net/?f=%5Bf%28x%29g%28x%29%5D%27%3Df%28x%29g%27%28x%29%2Bg%28x%29f%27%28x%29)
We have,
Differentiate with respect to x.
![f'(x)=(x-5)^2[2(3-x)(0-1)]+(3-x)^2[2(x-5)(1-0)]](https://tex.z-dn.net/?f=f%27%28x%29%3D%28x-5%29%5E2%5B2%283-x%29%280-1%29%5D%2B%283-x%29%5E2%5B2%28x-5%29%281-0%29%5D)
On further simplification, we get
Therefore, the derivative of the given function is .
Answer:
138 cm³
Step-by-step explanation:
Given in the question that base of the rectangular prism = 36 cm²
Height of the prism = 3 5/6 cm = 23/6
We know that the volume of a rectangular prism with base area B and height H is given by
<h3>Volume = B(H)</h3><h3 />
Plug values in the formula above to find the volume of the prism
Volume = 36(23/6)
= 6(23)
= 138 cm³
So the volume of prism = 138 cm³
<h3>
</h3>
Options:
H0 :
H0 : µ =12
H0 > 12> H1
None of these
Answer:
None of these
Step-by-step explanation:
The answer is
H0 : µ ≧ 12
Ha : µ<12
We formulate the null and alternative hypothesis here to state that battery life of the laptop lasts at least 12 hours(more than but not less, null hypothesis) or that it lasts less than 12 hours(alternative hypothesis).
The null hypothesis is the one being tested to know whether we would reject it or not in which case we choose the alternative hypothesis. To test the hypotheses, we do a t test using a significance level of say 0.05(95% confidence interval) and find our p value in order to compare and decide if the null hypothesis would be rejected or not based on statistical significance.
Answer:
Step-by-step explanation:
So we multiply 7 by 4, and get 28. Then we multiply 2 by 12, and get 24. Next we give both terms new denominators 12 × 4 = 48.
