Answer:
![P(X \geq 1) =1-P(X](https://tex.z-dn.net/?f=%20P%28X%20%5Cgeq%201%29%20%3D1-P%28X%3C1%29%20%3D1-P%28X%3D0%29%20)
And we can use the probability mass function and we got:
And replacing we got:
![P(X \geq 1) = 1-0.00615 = 0.99385](https://tex.z-dn.net/?f=%20P%28X%20%5Cgeq%201%29%20%3D%201-0.00615%20%3D%200.99385)
Step-by-step explanation:
Let X the random variable of interest "number of graduates who enroll in college", on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
We want to find the following probability:
![P(X \geq 1)](https://tex.z-dn.net/?f=%20P%28X%20%5Cgeq%201%29)
And we can use the complement rule and we got:
![P(X \geq 1) =1-P(X](https://tex.z-dn.net/?f=%20P%28X%20%5Cgeq%201%29%20%3D1-P%28X%3C1%29%20%3D1-P%28X%3D0%29%20)
And we can use the probability mass function and we got:
And replacing we got:
![P(X \geq 1) = 1-0.00615 = 0.99385](https://tex.z-dn.net/?f=%20P%28X%20%5Cgeq%201%29%20%3D%201-0.00615%20%3D%200.99385)
Answer:17
Step-by-step explanation: Multiply Steve’s hourly wage ($7.40) by the hours he worked in a week (16 Hours) that would give you your weekly earnings which would be (7.40x16=$118.40) Then subtract what he saved in the bank from your total (118.40-105=$13.40) then you would divide $13.40 (his leftover money) by $0.75 to find the total number of carnival rides he could ride (13.40/0.75=17.86 rides and because he cannot ride 17 and 86 hundredths of a ride he would be able to ride 17 carnival rides.
Percent cost of the total spent on
each equipment = 14.23%,fees=62.45% and transportation = 23.32%.
As given in the question,
Money spent on
Each equipment = $36
Fees = $158
Transportation = $59
Total money spent = $( 36 + 158 + 59)
= $253
Percent cost of the total spent on
Each equipment = (36/253) × 100
= 14.23%
Fees = (36/253) × 100
= 62.45%
Transportation =(36/253) × 100
= 23.32%
Therefore, percent cost of the total spent on
each equipment = 14.23%,fees=62.45% and transportation = 23.32%.
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Answer:
The number of trees at the begging of the 4-year period was 2560.
Step-by-step explanation:
Let’s say that x is number of trees at the begging of the first year, we know that for four years the number of trees were incised by 1/4 of the number of trees of the preceding year, so at the end of the first year the number of trees was
, and for the next three years we have that
Start End
Second year
-------------- ![\frac{5}{4}x+\frac{1}{4}(\frac{5}{4}x) =\frac{5}{4}x+ \frac{5}{16}x=\frac{25}{16}x=(\frac{5}{4} )^{2}x](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B4%7Dx%2B%5Cfrac%7B1%7D%7B4%7D%28%5Cfrac%7B5%7D%7B4%7Dx%29%20%3D%5Cfrac%7B5%7D%7B4%7Dx%2B%20%5Cfrac%7B5%7D%7B16%7Dx%3D%5Cfrac%7B25%7D%7B16%7Dx%3D%28%5Cfrac%7B5%7D%7B4%7D%20%29%5E%7B2%7Dx)
Third year
-------------![(\frac{5}{4})^{2}x+\frac{1}{4}((\frac{5}{4})^{2}x) =(\frac{5}{4})^{2}x+\frac{5^{2} }{4^{3} } x=(\frac{5}{4})^{3}x](https://tex.z-dn.net/?f=%28%5Cfrac%7B5%7D%7B4%7D%29%5E%7B2%7Dx%2B%5Cfrac%7B1%7D%7B4%7D%28%28%5Cfrac%7B5%7D%7B4%7D%29%5E%7B2%7Dx%29%20%3D%28%5Cfrac%7B5%7D%7B4%7D%29%5E%7B2%7Dx%2B%5Cfrac%7B5%5E%7B2%7D%20%7D%7B4%5E%7B3%7D%20%7D%20x%3D%28%5Cfrac%7B5%7D%7B4%7D%29%5E%7B3%7Dx)
Fourth year
--------------![(\frac{5}{4})^{3}x+\frac{1}{4}((\frac{5}{4})^{3}x) =(\frac{5}{4})^{3}x+\frac{5^{3} }{4^{4} } x=(\frac{5}{4})^{4}x.](https://tex.z-dn.net/?f=%28%5Cfrac%7B5%7D%7B4%7D%29%5E%7B3%7Dx%2B%5Cfrac%7B1%7D%7B4%7D%28%28%5Cfrac%7B5%7D%7B4%7D%29%5E%7B3%7Dx%29%20%3D%28%5Cfrac%7B5%7D%7B4%7D%29%5E%7B3%7Dx%2B%5Cfrac%7B5%5E%7B3%7D%20%7D%7B4%5E%7B4%7D%20%7D%20x%3D%28%5Cfrac%7B5%7D%7B4%7D%29%5E%7B4%7Dx.)
So the formula to calculate the number of trees in the fourth year is
we know that all of the trees thrived and there were 6250 at the end of 4 year period, then
⇒![x=\frac{6250*4^{4} }{5^{4} }= \frac{10*5^{4}*4^{4} }{5^{4} }=2560.](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B6250%2A4%5E%7B4%7D%20%7D%7B5%5E%7B4%7D%20%7D%3D%20%5Cfrac%7B10%2A5%5E%7B4%7D%2A4%5E%7B4%7D%20%7D%7B5%5E%7B4%7D%20%7D%3D2560.)
Therefore the number of trees at the begging of the 4-year period was 2560.