Hello there! The answer would be the first one, or No. At least one output results in two inputs.
When dealing with functions: you must remember that x does not repeat. So, lets look at the relation given, {(6, 1), (8, –3), (6, 7)}. You can see that x does repeat, so this is not a function. This eliminates second and fourth option choices. Out of the options A and C, A would be your choice since x is the input value and y is the output value, and there are two input values.
Hope his helps and have a great day!
Answer:
a) n = 1037.
b) n = 1026.
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 ![1 - \frac{\alpha}{2}](https://tex.z-dn.net/?f=1%20-%20%5Cfrac%7B%5Calpha%7D%7B2%7D)
The margin of error is:
![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)
99% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
(a) Assume that nothing is known about the percentage to be estimated.
We need to find n when M = 0.04.
We dont know the percentage to be estimated, so we use
, which is when we are going to need the largest sample size.
![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)
![0.04 = 2.575\sqrt{\frac{0.5*0.5}{n}}](https://tex.z-dn.net/?f=0.04%20%3D%202.575%5Csqrt%7B%5Cfrac%7B0.5%2A0.5%7D%7Bn%7D%7D)
![0.04\sqrt{n} = 2.575*0.5](https://tex.z-dn.net/?f=0.04%5Csqrt%7Bn%7D%20%3D%202.575%2A0.5)
![(\sqrt{n}) = \frac{2.575*0.5}{0.04}](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%20%3D%20%5Cfrac%7B2.575%2A0.5%7D%7B0.04%7D)
![(\sqrt{n})^{2} = (\frac{2.575*0.5}{0.04})^{2}](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%5E%7B2%7D%20%3D%20%28%5Cfrac%7B2.575%2A0.5%7D%7B0.04%7D%29%5E%7B2%7D)
![n = 1036.03](https://tex.z-dn.net/?f=n%20%3D%201036.03)
Rounding up
n = 1037.
(b) Assume prior studies have shown that about 55% of full-time students earn bachelor's degrees in four years or less.
![\pi = 0.55](https://tex.z-dn.net/?f=%5Cpi%20%3D%200.55)
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)
![0.04 = 2.575\sqrt{\frac{0.55*0.45}{n}}](https://tex.z-dn.net/?f=0.04%20%3D%202.575%5Csqrt%7B%5Cfrac%7B0.55%2A0.45%7D%7Bn%7D%7D)
![0.04\sqrt{n} = 2.575*\sqrt{0.55*0.45}](https://tex.z-dn.net/?f=0.04%5Csqrt%7Bn%7D%20%3D%202.575%2A%5Csqrt%7B0.55%2A0.45%7D)
![(\sqrt{n}) = \frac{2.575*\sqrt{0.55*0.45}}{0.04}](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%20%3D%20%5Cfrac%7B2.575%2A%5Csqrt%7B0.55%2A0.45%7D%7D%7B0.04%7D)
![(\sqrt{n})^{2} = (\frac{2.575*\sqrt{0.55*0.45}}{0.04})^{2}](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%5E%7B2%7D%20%3D%20%28%5Cfrac%7B2.575%2A%5Csqrt%7B0.55%2A0.45%7D%7D%7B0.04%7D%29%5E%7B2%7D)
![n = 1025.7](https://tex.z-dn.net/?f=n%20%3D%201025.7)
Rounding up
n = 1026.
Answer:
Yes: the variable K would equal "6"
Step-by-step explanation:
After you set you equation up, you have to isolate the given variable. To do that you have to do the recipriocal (6k-multiplying) which would be division. You would divide k = 36 ÷ 6 . that isolates the variable ,which you would then solve. k = 6 .
Answer:
$
or ≈$![563.00](https://tex.z-dn.net/?f=563.00)
Step-by-step explanation
The question states that Mrs. Hadley spent $126.97 on one month, $237.81 on the next, and $198.42 on the last. To get the total, we can add these values together.
![126.97+237.81+198.42=563.20](https://tex.z-dn.net/?f=126.97%2B237.81%2B198.42%3D563.20)
An estimation would be:
![127+238+198=563](https://tex.z-dn.net/?f=127%2B238%2B198%3D563)
We can use this estimation to determine that the total value is reasonable.
Answer: B) a + c = 10
8a + 5c = 59
Step-by-step explanation:
We know that 10 total people went, so the first equation has to be equal to 10. The total was $59, so the second equation should be set equal to $59. Now that the second equation is for cost, we must make it 8a + 5c to represent the cost of the adult and child tickets which are $8 and $5, respectively.