Answer:
Let b be the number of branches that the shrub will have after m months, since the shrub has an initial amount of 12 branches and the shrub grows 4 new branches every month, then we can set the following equation:
![b=4m+12.](https://tex.z-dn.net/?f=b%3D4m%2B12.)
Evaluating the above equation at m=7 we get:
![b=4\cdot7+12.](https://tex.z-dn.net/?f=b%3D4%5Ccdot7%2B12.)
Simplifying the above result we get that the shrub will have
![40](https://tex.z-dn.net/?f=40)
branches after 7 months.
Use the Pythagorean Theorem: a^2 + b^2 = c^2
a and b are the measures of the legs and c is the measure of the hypotenuse
Let's solve for a (the length of the other leg)
<em>*I am hoping that m is not a variable and just an abbreviation for meters* </em>
b = 4 m
c = 6 m
a^2 + 4^2 = 6^2
a^2 + 16 = 36
a^2 = 20
a =
![\sqrt{20}](https://tex.z-dn.net/?f=%20%5Csqrt%7B20%7D%20)
<em>after simplifying...</em>
<em />a =
![2 \sqrt{5}](https://tex.z-dn.net/?f=2%20%5Csqrt%7B5%7D%20)
m
<span>F(x)=-1/2x-2 x=-4
</span>And the last one we need graph options.
Answer:
x^5+6x^4+9x^3−9x^2−27x−38/(this is where the fraction is.)x+3
Step-by-step explanation:
C is the answer
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.