Answer:
![P(M4\ n\ V) = 2.083\%](https://tex.z-dn.net/?f=P%28M4%5C%20n%5C%20V%29%20%3D%202.083%5C%25)
Step-by-step explanation:
Given
Paper = 20 slips
Word: PENNSYLVANIA
Required
Determine P(Multiple of 4 and V)
The sample size of the 20 slips is:
![n(S) = 20](https://tex.z-dn.net/?f=n%28S%29%20%3D%2020)
The outcomes of multiples of 4 is:
![M4= \{4,8,12,16,20\}](https://tex.z-dn.net/?f=M4%3D%20%5C%7B4%2C8%2C12%2C16%2C20%5C%7D)
![n(M4) = 5](https://tex.z-dn.net/?f=n%28M4%29%20%3D%205)
So, the probability of multiples of 4 is:
![Pr(M4) = \frac{5}{20}](https://tex.z-dn.net/?f=Pr%28M4%29%20%3D%20%5Cfrac%7B5%7D%7B20%7D)
![Pr(M4) = \frac{1}{4}](https://tex.z-dn.net/?f=Pr%28M4%29%20%3D%20%5Cfrac%7B1%7D%7B4%7D)
The sample size of PENNSYLVANIA is:
![n(S) = 12](https://tex.z-dn.net/?f=n%28S%29%20%3D%2012)
The outcome of V is:
![n(V) = 1](https://tex.z-dn.net/?f=n%28V%29%20%3D%201)
So, the probability of V is:
![P(V) = \frac{1}{12}](https://tex.z-dn.net/?f=P%28V%29%20%3D%20%5Cfrac%7B1%7D%7B12%7D)
So, the required probability is: P(Multiple of 4 and V)
![P(M4\ n\ V) = P(M4) * P(V)](https://tex.z-dn.net/?f=P%28M4%5C%20n%5C%20V%29%20%3D%20P%28M4%29%20%2A%20P%28V%29)
![P(M4\ n\ V) = \frac{1}{4} * \frac{1}{12}](https://tex.z-dn.net/?f=P%28M4%5C%20n%5C%20V%29%20%3D%20%5Cfrac%7B1%7D%7B4%7D%20%2A%20%5Cfrac%7B1%7D%7B12%7D)
![P(M4\ n\ V) = \frac{1}{48}](https://tex.z-dn.net/?f=P%28M4%5C%20n%5C%20V%29%20%3D%20%5Cfrac%7B1%7D%7B48%7D)
![P(M4\ n\ V) = 0.02083](https://tex.z-dn.net/?f=P%28M4%5C%20n%5C%20V%29%20%3D%200.02083)
Express as percentage
![P(M4\ n\ V) = 0.02083 * 100\%](https://tex.z-dn.net/?f=P%28M4%5C%20n%5C%20V%29%20%3D%200.02083%20%2A%20100%5C%25)
![P(M4\ n\ V) = 2.083\%](https://tex.z-dn.net/?f=P%28M4%5C%20n%5C%20V%29%20%3D%202.083%5C%25)
Answer:
The probability that the proportion of books checked out in a sample of 412 books would differ from the population proportion by less than 4% is P=0.9255.
Step-by-step explanation:
The population's proportion is ![\pi=0.29](https://tex.z-dn.net/?f=%5Cpi%3D0.29)
If we take a sample of 412 books (n=412), we have a standard deviation of the sampling distribution of:
![\sigma_M=\sqrt{\frac{\pi(1-\pi)}{n}}=\sqrt{\frac{0.29*0.71}{412}}=\sqrt{0.0005} =0.0224](https://tex.z-dn.net/?f=%5Csigma_M%3D%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%3D%5Csqrt%7B%5Cfrac%7B0.29%2A0.71%7D%7B412%7D%7D%3D%5Csqrt%7B0.0005%7D%20%3D0.0224)
We have to calculate the probabilty that the sample proportion will be between 0.25 and 0.33.
![z_1=(0.25-0.29)/0.0224=-0.04/0.0224=-1.7857\\\\z_2=1.7857\\\\\\P(0.25](https://tex.z-dn.net/?f=z_1%3D%280.25-0.29%29%2F0.0224%3D-0.04%2F0.0224%3D-1.7857%5C%5C%5C%5Cz_2%3D1.7857%5C%5C%5C%5C%5C%5CP%280.25%3C%5Chat%7Bp%7D%3C0.33%29%3DP%28-1.7857%3Cz%3C1.7857%29%5C%5C%5C%5CP%280.25%3C%5Chat%7Bp%7D%3C0.33%29%3DP%28z%3C1.7857%29-P%28z%3C-1.7857%29%5C%5C%5C%5CP%280.25%3C%5Chat%7Bp%7D%3C0.33%29%3D0.9629-0.0371%3D0.9255)
Answer: 2 minutes
Step-by-step explanation:
Given the following :
Plane A's descent :
y = -2,500x + 14,000
Plane B's Ascent :
y = 4,000x + 1,000
where y = altitude x = minute
Time to be at the same altitude :
Being at the same altitude means ;
Plane A's descent = Plane B's Ascent
-2,500x + 14,000 = 4,000x + 1,000
-2500x - 4000x = 1000 - 14000
-6500x = - 13000
x = 13000 / 6500
x = 2
x = 2minutes.
You have a good day and good luck on that question
Answer: First top box is 2400, 2nd top box is 120
423x6 = 2400 + 120 +18 = 2538
Step-by-step explanation: