Answer:
She would leave a $7.59 tip.
Step-by-step explanation:
18/100=0.18
42.15*0.18=7.587
Round up if more than 5, leave if less than 5. Since it is more than 5 you round up to 9, so the answer is $7.59.
Since <span> sin(α) > 0 and cos(α) > 0
so </span><span>α is IN THE FIRST QUADRANT (I)</span>
Answer:
V = 1184ft³
Step-by-step explanation:
Volume for Cube
we multiple l*w*h
4x4x4 = 64ft*3 area
Volume for rectangle
we multiple length of the rectangle side first with h
Surface area rectangle = 16 x 7 = 112ft ^2 (=70+42)
Then we multiply it with width 112 x 10 = 1120ft^3
Then we add together the cube V total + Rectangle V total.
64 + 1120= 1184ft^3
![\log_7(x^2+4x-11)=\dfrac52](https://tex.z-dn.net/?f=%5Clog_7%28x%5E2%2B4x-11%29%3D%5Cdfrac52)
![7^{\log_7(x^2+4x-11)}=7^{\frac52}](https://tex.z-dn.net/?f=7%5E%7B%5Clog_7%28x%5E2%2B4x-11%29%7D%3D7%5E%7B%5Cfrac52%7D)
![x^2+4x-11=7^{\frac52}](https://tex.z-dn.net/?f=x%5E2%2B4x-11%3D7%5E%7B%5Cfrac52%7D)
![x^2+4x-\left(11+7^{\frac52}\right)=0](https://tex.z-dn.net/?f=x%5E2%2B4x-%5Cleft%2811%2B7%5E%7B%5Cfrac52%7D%5Cright%29%3D0)
Now you can use the quadratic formula to solve for
.
![x=-2\pm\sqrt{15+7^{\frac52}}](https://tex.z-dn.net/?f=x%3D-2%5Cpm%5Csqrt%7B15%2B7%5E%7B%5Cfrac52%7D%7D)
Answer:
The 80% confidence interval for the mean usage of water is between 18.4 and 18.6 gallons per day.
Step-by-step explanation:
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
![\alpha = \frac{1-0.8}{2} = 0.1](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7B1-0.8%7D%7B2%7D%20%3D%200.1)
Now, we have to find z in the Ztable as such z has a pvalue of
.
So it is z with a pvalue of
, so ![z = 1.28](https://tex.z-dn.net/?f=z%20%3D%201.28)
Now, find the margin of error M as such
![M = z*\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%2A%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In which
is the standard deviation of the population and n is the size of the sample.
![M = 1.28*\frac{2.3}{\sqrt{717}} = 0.1](https://tex.z-dn.net/?f=M%20%3D%201.28%2A%5Cfrac%7B2.3%7D%7B%5Csqrt%7B717%7D%7D%20%3D%200.1)
The lower end of the interval is the sample mean subtracted by M. So it is 18.5 - 0.1 = 18.4 gallons per day.
The upper end of the interval is the sample mean added to M. So it is 18.5 + 0.1 = 18.6 gallons per day.
The 80% confidence interval for the mean usage of water is between 18.4 and 18.6 gallons per day.