Answer:
5/12
Step-by-step explanation:
1x5/2x6
Answer:
We conclude that there is enough evidence to claim that the van has a 31.3 miles/gallon (MPG) rating.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 31.3 miles/gallon
Sample mean,
= 31.1
Sample size, n = 140
Alpha, α = 0.02
Population standard deviation, σ = 1.3
First, we design the null and the alternate hypothesis
![H_{0}: \mu = 31.3\text{ miles/gallon}\\H_A: \mu \neq 31.3\text{ miles/gallon}](https://tex.z-dn.net/?f=H_%7B0%7D%3A%20%5Cmu%20%3D%2031.3%5Ctext%7B%20miles%2Fgallon%7D%5C%5CH_A%3A%20%5Cmu%20%5Cneq%2031.3%5Ctext%7B%20miles%2Fgallon%7D)
We use Two-tailed z test to perform this hypothesis.
Formula:
![z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }](https://tex.z-dn.net/?f=z_%7Bstat%7D%20%3D%20%5Cdisplaystyle%5Cfrac%7B%5Cbar%7Bx%7D%20-%20%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%20%7D)
Putting all the values, we have
![z_{stat} = \displaystyle\frac{31.1 - 31.3}{\frac{1.3}{\sqrt{140}} } = -1.82](https://tex.z-dn.net/?f=z_%7Bstat%7D%20%3D%20%5Cdisplaystyle%5Cfrac%7B31.1%20-%2031.3%7D%7B%5Cfrac%7B1.3%7D%7B%5Csqrt%7B140%7D%7D%20%7D%20%3D%20-1.82)
Now, ![z_{critical} \text{ at 0.02 level of significance } = \pm 2.33](https://tex.z-dn.net/?f=z_%7Bcritical%7D%20%5Ctext%7B%20at%200.02%20level%20of%20significance%20%7D%20%3D%20%5Cpm%202.33)
Since,
The calculated z-statistic lies in the acceptance region, we fail to reject the null hypothesis and accept it.
We conclude that there is enough evidence to claim that the van has a 31.3 miles/gallon (MPG) rating.
Answer:
B
Step-by-step explanation:
Answer:
theta = 180 -(A +B)
Step-by-step explanation:
The sum of the angles of a triangle is 180
theta + A + B = 180
solve for theta
Subtract ( A + B) from each side
theta +A+B -(A +B) = 180 -(A +B)
theta = 180 -(A +B)
To find the volume of a cylinder, start with the formula for the volume of a cylinder.
Volume = ![\pi](https://tex.z-dn.net/?f=%5Cpi)
![r^{2}](https://tex.z-dn.net/?f=r%5E%7B2%7D)
![^{h}](https://tex.z-dn.net/?f=%5E%7Bh%7D)
Notice that our cylinder has a radius of 7 and a height of 16. So we have
(
) (7)
(16)
Let's start by simplifying the exponents.
≈ 49
(
) (49) (16)
49 × 16 = 784![\pi](https://tex.z-dn.net/?f=%5Cpi)
![m^{3}](https://tex.z-dn.net/?f=m%5E%7B3%7D)
We can add a unit so we have 784![\pi](https://tex.z-dn.net/?f=%5Cpi)
.