Answer:
Fast ball challenge
Step-by-step explanation:
Given
Slow Ball Challenge
![Pitches = 7](https://tex.z-dn.net/?f=Pitches%20%3D%207)
![P(Hit) = 80\%](https://tex.z-dn.net/?f=P%28Hit%29%20%3D%2080%5C%25)
![Win = \$60](https://tex.z-dn.net/?f=Win%20%3D%20%5C%2460)
![Lost = \$10](https://tex.z-dn.net/?f=Lost%20%3D%20%5C%2410)
Fast Ball Challenge
![Pitches = 3](https://tex.z-dn.net/?f=Pitches%20%3D%203)
![P(Hit) = 70\%](https://tex.z-dn.net/?f=P%28Hit%29%20%3D%2070%5C%25)
![Win = \$60](https://tex.z-dn.net/?f=Win%20%3D%20%5C%2460)
![Lost = \$10](https://tex.z-dn.net/?f=Lost%20%3D%20%5C%2410)
Required
Which should he choose?
To do this, we simply calculate the expected earnings of both.
Considering the slow ball challenge
First, we calculate the binomial probability that he hits all 7 pitches
![P(x) =^nC_x * p^x * (1 - p)^{n - x}](https://tex.z-dn.net/?f=P%28x%29%20%3D%5EnC_x%20%2A%20p%5Ex%20%2A%20%281%20-%20p%29%5E%7Bn%20-%20x%7D)
Where
--- pitches
--- all hits
--- probability of hit
So, we have:
![P(x) =^nC_x * p^x * (1 - p)^{n - x}](https://tex.z-dn.net/?f=P%28x%29%20%3D%5EnC_x%20%2A%20p%5Ex%20%2A%20%281%20-%20p%29%5E%7Bn%20-%20x%7D)
![P(7) =^7C_7 * 0.80^7 * (1 - 0.80)^{7 - 7}](https://tex.z-dn.net/?f=P%287%29%20%3D%5E7C_7%20%2A%200.80%5E7%20%2A%20%281%20-%200.80%29%5E%7B7%20-%207%7D)
![P(7) =1 * 0.80^7 * (1 - 0.80)^0](https://tex.z-dn.net/?f=P%287%29%20%3D1%20%2A%200.80%5E7%20%2A%20%281%20-%200.80%29%5E0)
![P(7) =1 * 0.80^7 * 0.20^0](https://tex.z-dn.net/?f=P%287%29%20%3D1%20%2A%200.80%5E7%20%2A%200.20%5E0)
Using a calculator:
--- This is the probability that he wins
i.e.
![P(Win) =0.2097152](https://tex.z-dn.net/?f=P%28Win%29%20%3D0.2097152)
The probability that he lose is:
---- Complement rule
![P(Lose) = 1 -0.2097152](https://tex.z-dn.net/?f=P%28Lose%29%20%3D%201%20-0.2097152)
![P(Lose) = 0.7902848](https://tex.z-dn.net/?f=P%28Lose%29%20%3D%200.7902848)
The expected value is then calculated as:
![Expected = P(Win) * Win + P(Lose) * Lose](https://tex.z-dn.net/?f=Expected%20%3D%20P%28Win%29%20%2A%20Win%20%2B%20P%28Lose%29%20%2A%20Lose)
![Expected = 0.2097152 * \$60 + 0.7902848 * \$10](https://tex.z-dn.net/?f=Expected%20%3D%200.2097152%20%2A%20%5C%2460%20%2B%200.7902848%20%2A%20%5C%2410)
Using a calculator, we have:
Considering the fast ball challenge
First, we calculate the binomial probability that he hits all 3 pitches
![P(x) =^nC_x * p^x * (1 - p)^{n - x}](https://tex.z-dn.net/?f=P%28x%29%20%3D%5EnC_x%20%2A%20p%5Ex%20%2A%20%281%20-%20p%29%5E%7Bn%20-%20x%7D)
Where
--- pitches
--- all hits
--- probability of hit
So, we have:
![P(3) =^3C_3 * 0.70^3 * (1 - 0.70)^{3 - 3}](https://tex.z-dn.net/?f=P%283%29%20%3D%5E3C_3%20%2A%200.70%5E3%20%2A%20%281%20-%200.70%29%5E%7B3%20-%203%7D)
![P(3) =1 * 0.70^3 * (1 - 0.70)^0](https://tex.z-dn.net/?f=P%283%29%20%3D1%20%2A%200.70%5E3%20%2A%20%281%20-%200.70%29%5E0)
![P(3) =1 * 0.70^3 * 0.30^0](https://tex.z-dn.net/?f=P%283%29%20%3D1%20%2A%200.70%5E3%20%2A%200.30%5E0)
Using a calculator:
--- This is the probability that he wins
i.e.
![P(Win) =0.343](https://tex.z-dn.net/?f=P%28Win%29%20%3D0.343)
The probability that he lose is:
---- Complement rule
![P(Lose) = 1 - 0.343](https://tex.z-dn.net/?f=P%28Lose%29%20%3D%201%20-%200.343)
![P(Lose) = 0.657](https://tex.z-dn.net/?f=P%28Lose%29%20%3D%200.657)
The expected value is then calculated as:
![Expected = P(Win) * Win + P(Lose) * Lose](https://tex.z-dn.net/?f=Expected%20%3D%20P%28Win%29%20%2A%20Win%20%2B%20P%28Lose%29%20%2A%20Lose)
![Expected = 0.343 * \$60 + 0.657 * \$10](https://tex.z-dn.net/?f=Expected%20%3D%200.343%20%2A%20%5C%2460%20%2B%200.657%20%2A%20%5C%2410)
Using a calculator, we have:
![Expected = \$27.15](https://tex.z-dn.net/?f=Expected%20%3D%20%5C%2427.15)
So, we have:
-- Slow ball
--- Fast ball
<em>The expected earnings of the fast ball challenge is greater than that of the slow ball. Hence, he should choose the fast ball challenge.</em>
Answer:
225
Step-by-step explanation:
So we know that 20% of the social workers he surveyed was 45 people. The easiest way to find all 100% of the social workers is to do 45 x 5 because 20% x 5 = 100%. So 45 x 5 = 225.
Hope this helped! :)
Okay so this is going to be confusing but work from right to left. since you can’t do 0-5, borrow from the one next to the zero on the top, cross out the one and put zero and add a one on top of the zero which makes it 10. now you can do 10-5 to get 5. put the five down below the line. next solve the second column of numbers ( second to the right). since you cannot do 0- 3, like the last one, you have to borrow from the 7 over to the left. take one from there and cross the seven out and put a six. now you have 10-3 which is 7. put the 7 down. now do move to the next column and do 6-2 to get 4. put the four down below the line. move to the next column and do 2-2 to get 0. put the zero down below the line. lastly, we know the answer has to be negative so we are going to do 2-7 to get -5. put -5 down below the line and together to get the answer -502,275. i know that was very confusing but i hope it helped a little bit. i added a picture to clarify a little
Answer:
you would transfer 15 to the other side
Step-by-step explanation:
-19=15-6x
-34=6x