Answer:
3.5/100*8=.28
Step-by-step explanation:
Answer:
The minimum sample size that can be taken is of 14 dogs.
Step-by-step explanation:
The formula for calculating the minimum sample size to estimate a population mean is given by:
![n=\frac{z^{2}\sigma^{2}}{e^{2}}](https://tex.z-dn.net/?f=n%3D%5Cfrac%7Bz%5E%7B2%7D%5Csigma%5E%7B2%7D%7D%7Be%5E%7B2%7D%7D)
The <u>first step</u> is obtaining the values we're going to use to replace in the formula.
Since we want to be 95% confident,
.
Therefore we look for the critical value
.
Then we calculate the variance:
![\sigma = 3.7 \Rightarrow \sigma^{2}=13.69](https://tex.z-dn.net/?f=%5Csigma%20%3D%203.7%20%5CRightarrow%20%5Csigma%5E%7B2%7D%3D13.69)
And we have that:
![e=2 \Rightarrow e^{2}=4](https://tex.z-dn.net/?f=e%3D2%20%5CRightarrow%20e%5E%7B2%7D%3D4)
<u>Now</u> we replace in the formula with the values we've just obtained:
![n=\frac{1.96^{2}*13.69}{4}=13.1479\approx 14](https://tex.z-dn.net/?f=n%3D%5Cfrac%7B1.96%5E%7B2%7D%2A13.69%7D%7B4%7D%3D13.1479%5Capprox%2014)
Therefore the minimum sample size that can be taken to guarantee that the sample mean is within 2 inches of the population mean is of 14 dogs.
Answer:
10* 299.99=2999.9
2999.9/100=29.999
this would round up to 30, so Brittany saved $30. : )
Find the slope of the line passing throught the points (2, 2) and (4, 3).
The formula of a slope:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Substitute:
![m=\dfrac{3-2}{4-2}=\dfrac{1}{2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B3-2%7D%7B4-2%7D%3D%5Cdfrac%7B1%7D%7B2%7D)
If the point (x, -1) lie on the same line, then the slope of line passing through the points (2, 2) and (x, -1) the same:
Substitute:
![m=\dfrac{-1-2}{x-2}=\dfrac{-3}{x-2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B-1-2%7D%7Bx-2%7D%3D%5Cdfrac%7B-3%7D%7Bx-2%7D)
We have the equation:
<em>cross multiply</em>
![(1)(x-2)=(-3)(2)](https://tex.z-dn.net/?f=%281%29%28x-2%29%3D%28-3%29%282%29)
<em>add 2 to both sides</em>
![x=-4](https://tex.z-dn.net/?f=x%3D-4)
<h3>Answer: x = -4.</h3>
Recall the logarithm rules :
a^y = x is the same as log_a x = y
In this case,
a = 18
y = r - 10
x = 93
So,
18^ (r-10) = 93
is the same as
log_18 93 = r - 10
Solve for r to get :
10 + log_18 93 = r