Answer:
One robot will be powered for an eighth of a day (1/8 of a day) by one quarter (1/4) of a bag of coffee.
Answer:
x=9
Step-by-step explanation:
First we will evaluate: ( substitution: u = x² - y², du = - 2 y dy )
![\int\limits^x_0 {y \sqrt{ x^{2} - y^{2} } } \, dy= \\ \frac{-1}{2} \int\limits^x_0 { u^{1/2} } \, du =](https://tex.z-dn.net/?f=%20%5Cint%5Climits%5Ex_0%20%7By%20%5Csqrt%7B%20x%5E%7B2%7D%20-%20y%5E%7B2%7D%20%7D%20%7D%20%5C%2C%20dy%3D%20%5C%5C%20%20%20%5Cfrac%7B-1%7D%7B2%7D%20%5Cint%5Climits%5Ex_0%20%7B%20u%5E%7B1%2F2%7D%20%7D%20%5C%2C%20du%20%20%3D)
=
![\frac{-1}{3} \sqrt{ (x^{2} - y^{2} ) ^{3} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B-1%7D%7B3%7D%20%5Csqrt%7B%20%28x%5E%7B2%7D%20-%20y%5E%7B2%7D%20%29%20%5E%7B3%7D%20%7D%20%20)
( than plug in x and 0 )
=
![- \frac{1}{3} ( \sqrt{( x^{2} - x^{2}) ^{3} } - \sqrt{ (x^{2} -0 ^{2} ) ^{3} }](https://tex.z-dn.net/?f=-%20%5Cfrac%7B1%7D%7B3%7D%20%28%20%20%5Csqrt%7B%28%20x%5E%7B2%7D%20-%20x%5E%7B2%7D%29%20%5E%7B3%7D%20%20%7D%20%20-%20%20%5Csqrt%7B%20%28x%5E%7B2%7D%20-0%20%5E%7B2%7D%20%29%20%5E%7B3%7D%20%7D%20)
=
= 1/3 x³ ( then another integration )
![1/3\int\limits^1_0 { x^{3} } \, dx = 1/3 ( x^{4}/4)}= 1/3 ( 1 ^{4}/4 - 0^{4} /4 )](https://tex.z-dn.net/?f=%201%2F3%5Cint%5Climits%5E1_0%20%7B%20x%5E%7B3%7D%20%7D%20%5C%2C%20dx%20%3D%201%2F3%20%28%20%20x%5E%7B4%7D%2F4%29%7D%3D%201%2F3%20%28%201%20%5E%7B4%7D%2F4%20-%200%5E%7B4%7D%20%2F4%20%29%20%20%20)
= 1/3 * 1/4 =
1/12
Answer:
90 millimeters
Step-by-step explanation:
multiply the length value by 10
Form the confidence level (99%), we calculate the "alpha" value
alpha=1-(99/100)=0.01
Now, calculate the critical probability (p-start)
p*=1-(alpha/2)=1-(0.01/2)=0.995
z-score could be calculated from p*,,,
z-score=2.57583
Now, calculate the Margin of Error:
standard deviation = s
number of adults = n
ME=(z*s)/(sqrt n)=(2.57583*12)/(sqrt 250) = 1.955
The confidence interval = mean +or- ME
= 70+1.955 or 70-1.955
So that we can conclude that the 99% confidence interval for the mean beats per minute is 68.045 and 71.955
I hope you got the idea!