Answer:
Five touchdowns were made in the game
Step-by-step explanation:
Here, we want to know the number of touchdowns made during the game.
We proceed as follows;
Let the number of touch downs be x
So the total points earned through touchdowns is 6 * x = 6x
The number of scores is 10 times
Let the number of extra kick be y which means that the number of conversions will be (y-1)
So the total number of score times will be ;
x + y + y-1 = 10
x + 2y = 11 •••••••••(i)
Now let’s work with points
Touch down points = 6 * x = 6x
Points from extra kick = 1 * y = y
Points from 2-point conversions = 2(y-1) = 2y - 2
So;
6x + y + 2y -2 = 37
6x + 3y = 37 + 2
6x + 3y = 39
divide through by 3
2x + y = 13 •••••••(ii)
So now solve simultaneously
From ii, y = 13 - 2x
Put this into i
x + 2(13-2x) = 11
x + 26 - 4x = 11
x -4x = 11-26
-3x = -15
x = -15/-3
x = 5
There are five touchdowns in the game
Answer:
a) 2.9%
b) Option B is correct.
The prisoners must be independent with regard to recidivism.
Step-by-step explanation:
Probability that one prisoner goes back to prison = 17% = 0.17
a) The probability that two prisoners released both go back to prison = 0.17 × 0.17 = 0.0289 = 2.89% = 2.9% to 1 d.p
b) The only assumption taken during the calculation is that probability of one of the prisoners going back to prison has no effect whatsoever in the probability that another prisoner goes back to prison. That is the probability that theses two events occur are totally independent of each other.
If they weren't, we wouldn't be able to use 0.17 as the probability that the other prisoner goes back to prison too.
![\\ \sf{:}\implies (side)^3=14](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%7B%3A%7D%5Cimplies%20%28side%29%5E3%3D14)
![\\ \sf{:}\implies side=\sqrt[3]{14}](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%7B%3A%7D%5Cimplies%20side%3D%5Csqrt%5B3%5D%7B14%7D)
![\\ \sf{:}\implies side=2.5in](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%7B%3A%7D%5Cimplies%20side%3D2.5in)
Now
![\\ \sf{:}\implies Area=11(8)=88in^2](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%7B%3A%7D%5Cimplies%20Area%3D11%288%29%3D88in%5E2)
Cut it into 10 parts as per question(Open side means five sides hence it will be 5×2=10)
![\\ \sf{:}\implies 88/10=8.8in](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%7B%3A%7D%5Cimplies%2088%2F10%3D8.8in)
Now divide by previous side
![\\ \sf{:}\implies \dfrac{8.8}{2.5}=3.52=3.5](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%7B%3A%7D%5Cimplies%20%5Cdfrac%7B8.8%7D%7B2.5%7D%3D3.52%3D3.5)
Option D
Sometimes...
2^-3 = 1/(2^3) = 1/8
-2^-3 = 1/(-2^3) = -1/8