The function is graphed as shown below
Part A:
We use the formula
![- \frac{b}{2a}](https://tex.z-dn.net/?f=-%20%5Cfrac%7Bb%7D%7B2a%7D%20)
to find the vertex of the function. A quadratic function of the form of
![a x^{2} +bx+c](https://tex.z-dn.net/?f=a%20x%5E%7B2%7D%20%2Bbx%2Bc)
and equating this form to the given function
![- x^{2} +20x-75](https://tex.z-dn.net/?f=-%20x%5E%7B2%7D%20%2B20x-75)
, we have
![b=20](https://tex.z-dn.net/?f=b%3D20)
and
![a=-1](https://tex.z-dn.net/?f=a%3D-1)
.
Substituting
![a](https://tex.z-dn.net/?f=a)
and
![b](https://tex.z-dn.net/?f=b)
into the vertex formula, we have
![x=- \frac{20}{2(-1)}=10](https://tex.z-dn.net/?f=x%3D-%20%5Cfrac%7B20%7D%7B2%28-1%29%7D%3D10%20)
, as shown in the graph
This calculation means that the highest profit is achieved when the number of photo printed equals to ten photos
Part B:
We can find solution to this equation by factorising
![- x^{2} +20x-75=0](https://tex.z-dn.net/?f=-%20x%5E%7B2%7D%20%2B20x-75%3D0)
![-( x^{2} -20x+75)=0](https://tex.z-dn.net/?f=-%28%20x%5E%7B2%7D%20-20x%2B75%29%3D0)
![x^{2} -20x+75=0](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20-20x%2B75%3D0)
![(x-5)(x-15)=0](https://tex.z-dn.net/?f=%28x-5%29%28x-15%29%3D0)
![x=5](https://tex.z-dn.net/?f=x%3D5)
and
![x=15](https://tex.z-dn.net/?f=x%3D15)
, as shown in the graph
The two values means that the company makes no profit when they either produce 5 or 15 photos
Answer:
what do you need help with
Step-by-step explanation:
Yes. 1/5 is equal to .2. All you need to do to solve this is to put 1 divided by 5 into a calculator.
Answer:
It is 10 quarters and 10 nickels
10 x 25 = $2.50
10 x 5 = $0.50
2.50 + 0.50 = $3.00
***I hope this helps
Step-by-step explanation:
Answer:
A sample size of 6755 or higher would be appropriate.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.
![\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=%5Cpi%20%5Cpm%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
In which
z is the zscore that has a pvalue of
.
The margin of error M is given by:
![M = z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
90% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
52% of Independents in the sample opposed the public option.
This means that ![p = 0.52](https://tex.z-dn.net/?f=p%20%3D%200.52)
If we wanted to estimate this number to within 1% with 90% confidence, what would be an appropriate sample size?
Sample size of size n or higher when
. So
![M = z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
![0.01 = 1.645\sqrt{\frac{0.52*0.48}{n}}](https://tex.z-dn.net/?f=0.01%20%3D%201.645%5Csqrt%7B%5Cfrac%7B0.52%2A0.48%7D%7Bn%7D%7D)
![0.01\sqrt{n} = 0.8218](https://tex.z-dn.net/?f=0.01%5Csqrt%7Bn%7D%20%3D%200.8218)
![\sqrt{n} = \frac{0.8218}{0.01}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%5Cfrac%7B0.8218%7D%7B0.01%7D)
![\sqrt{n} = 82.18](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%2082.18)
![\sqrt{n}^{2} = (82.18)^{2}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%5E%7B2%7D%20%3D%20%2882.18%29%5E%7B2%7D)
![n = 6754.2](https://tex.z-dn.net/?f=n%20%3D%206754.2)
A sample size of 6755 or higher would be appropriate.