Answer: A car dealership conducted a survey to learn the preferences of their customers. The survey data is shown in the table. Given that a survey participant is female, which is the probability that she prefers a sports utility vehicle (SUV)?
Step-by-step explanation: :)
Answer:
![\sqrt[3]{3140^2\pi}\approx 146.41\ ft^2](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B3140%5E2%5Cpi%7D%5Capprox%20146.41%5C%20ft%5E2)
Step-by-step explanation:
The volume of the cylinder is
where r is the base radius and H is the height.
Since 
and V=1570 cubic feet, then
![1570=\pi r^2\cdot \dfrac{r}{2},\\ \\1570=\dfrac{\pi r^3}{2},\\ \\r^3=\dfrac{3140}{\pi},\\ \\r=\sqrt[3]{\dfrac{3140}{\pi}}\ ft.](https://tex.z-dn.net/?f=1570%3D%5Cpi%20r%5E2%5Ccdot%20%5Cdfrac%7Br%7D%7B2%7D%2C%5C%5C%20%5C%5C1570%3D%5Cdfrac%7B%5Cpi%20r%5E3%7D%7B2%7D%2C%5C%5C%20%5C%5Cr%5E3%3D%5Cdfrac%7B3140%7D%7B%5Cpi%7D%2C%5C%5C%20%5C%5Cr%3D%5Csqrt%5B3%5D%7B%5Cdfrac%7B3140%7D%7B%5Cpi%7D%7D%5C%20ft.)
The area of its bottom floor is
![A_{floor}=\pi r^2=\pi\cdot \left(\sqrt[3]{\dfrac{3140}{\pi}}\right)^2= \sqrt[3]{3140^2\pi}\approx 146.41\ ft^2.](https://tex.z-dn.net/?f=A_%7Bfloor%7D%3D%5Cpi%20r%5E2%3D%5Cpi%5Ccdot%20%5Cleft%28%5Csqrt%5B3%5D%7B%5Cdfrac%7B3140%7D%7B%5Cpi%7D%7D%5Cright%29%5E2%3D%20%5Csqrt%5B3%5D%7B3140%5E2%5Cpi%7D%5Capprox%20146.41%5C%20ft%5E2.)
Answer:
(78, 80)
Step-by-step explanation:
Given a normal distribution :
Mean = 79 seconds
Standard deviation = 0.5 seconds
Using the empirical rule :
95% of her finishing times :
According to the empirical rule, 95% represents 2 standard deviations from the mean that is ± 2 standard deviations from the mean score or value.
Hence ;
The interval will be defined as ;
Mean ± 2(standard deviation)
79 ± 2(0.5)
79 ± 1
(79 - 1) ; (79 + 1)
78 ; 80
Answer:
cot . (x- π/2)= - tanx
Step-by-step explanation:
cot . (x- π/2)= - tanx
cot .x - cot π/2= - tanx
cot π/2= 1/tanπ/2
But tan π/2= ∞
cot π/2 = 1/∞= 0
cotx - 0= - tanx
cot x = - tanx
cosx/sinx= - sinx/cosx Putting values of cot and tan
cosx/ sinx ( sinx/cos x) = -sinx/cos x (sinx/cos x )
Multiplying both sides with sinx/cos x
1= - sin²x/cos²x
cos²x= - sin²x as cosx = -sinx
