Answer:
Martin will get a refund of about $370.
Step-by-step explanation:
The gross pay of Martin = $30135
The federal income tax percent that is withheld from his paycheck is 15%, this becomes = ![0.15*30135=4520.25](https://tex.z-dn.net/?f=0.15%2A30135%3D4520.25)
As given, he owes the government after federal deductions is $4,150.
So, amount that exceeds this amount = ![4250.25-4150=370.25](https://tex.z-dn.net/?f=4250.25-4150%3D370.25)
Means, this $370.25 is to be refunded to Martin.
Hence, the true option is Martin will get a refund of about $370.
Answer:
35.98
Step-by-step explanation:
To find the perimeter take 1/2 of the circumference plus the length of the diameter
P = 1/2 * pi *d + d
=1/2 pi 14 +14
= 7pi +14
Letting pi = 3.14
7(3.14) + 14
21.98 +14
35.98
Answer:
80 telephones should be sampled
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 z-score that has a p-value of
.
The margin of error is of:
![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)
89% confidence level
So
, z is the value of Z that has a p-value of
, so
.
How many telephones should be sampled and checked in order to estimate the proportion defective to within 9 percentage points with 89% confidence?
n telephones should be sampled, an n is found when M = 0.09. We have no estimate for the proportion, thus we use ![\pi = 0.5](https://tex.z-dn.net/?f=%5Cpi%20%3D%200.5)
![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)
![0.09 = 1.6\sqrt{\frac{0.5*0.5}{n}}](https://tex.z-dn.net/?f=0.09%20%3D%201.6%5Csqrt%7B%5Cfrac%7B0.5%2A0.5%7D%7Bn%7D%7D)
![0.09\sqrt{n} = 1.6*0.5](https://tex.z-dn.net/?f=0.09%5Csqrt%7Bn%7D%20%3D%201.6%2A0.5)
![\sqrt{n} = \frac{1.6*0.5}{0.09}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%5Cfrac%7B1.6%2A0.5%7D%7B0.09%7D)
![(\sqrt{n})^2 = (\frac{1.6*0.5}{0.09})^2](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%5E2%20%3D%20%28%5Cfrac%7B1.6%2A0.5%7D%7B0.09%7D%29%5E2)
![n = 79.01](https://tex.z-dn.net/?f=n%20%3D%2079.01)
Rounding up(as 79 gives a margin of error slightly above the desired value).
80 telephones should be sampled
Answer:
28a³ - 5a² - 23a - 5
Step-by-step explanation:
FOIL and Distribute Parenthesis
Step 1: Write out expression
(4a + 1)(7a² - 3a - 5)
Step 2: Distribute 4a
28a³ - 12a² - 20a
Step 3: Distribute 1
7a² - 3a - 5
Step 4: Combine
28a³ - 12a² - 20a + 7a² - 3a - 5
Step 5: Combine like terms
28a³ - 5a² - 23a - 5
1/3 + 1/6 equals 1/2 so you have away half of the cake