You would need to do this with a graphing calculator
Lets factor first to see if we can make the problem simple
2(4x^2-25)
now we see that in parenthesis we have 2 square numbers
4x^2=(2x)^2
25=(5)^2
our expression is now
2(2x+5)(2x-5)
Answer:
a) ![P(X = 1) = 0.38742](https://tex.z-dn.net/?f=P%28X%20%3D%201%29%20%3D%200.38742)
b) ![P(X = 3) = 0.05740](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%200.05740)
c) ![P(X = 9) = 0.00000](https://tex.z-dn.net/?f=P%28X%20%3D%209%29%20%3D%200.00000)
d) ![P(X \geq 5) = 0.00163](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%205%29%20%3D%200.00163)
Step-by-step explanation:
For each container, there are only two possible outcomes. Either it is undefilled, or it is not. This means that we can solve this problem using the binomial probability distribution.
Binomial probability distribution:
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
In which
is the number of different combinatios of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
And p is the probability of X happening.
In this problem
There are 10 containers, so
.
A food-packaging apparatus underfills 10% of the containers, so
.
a) This is P(X = 1)
![P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742](https://tex.z-dn.net/?f=P%28X%20%3D%201%29%20%3D%20C_%7B10%2C1%7D.%280.1%29%5E%7B1%7D.%280.9%29%5E%7B9%7D%20%3D%200.38742)
b) This is P(X = 3)
![P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%20C_%7B10%2C3%7D.%280.1%29%5E%7B3%7D.%280.9%29%5E%7B7%7D%20%3D%200.05740)
c) This is P(X = 9)
![P(X = 9) = C_{10,9}.(0.1)^{9}.(0.9)^{1} = 0.00000](https://tex.z-dn.net/?f=P%28X%20%3D%209%29%20%3D%20C_%7B10%2C9%7D.%280.1%29%5E%7B9%7D.%280.9%29%5E%7B1%7D%20%3D%200.00000)
d) This is
.
Either the number is lesser than five, or it is five or larger. The sum of the probabilities of each event is decimal 1. So:
![P(X < 5) + P(X \geq 5) = 1](https://tex.z-dn.net/?f=P%28X%20%3C%205%29%20%2B%20P%28X%20%5Cgeq%205%29%20%3D%201)
![P(X \geq 5) = 1 - P(X < 5)](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%205%29%20%3D%201%20-%20P%28X%20%3C%205%29)
In which
![P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)](https://tex.z-dn.net/?f=P%28X%20%3C%205%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29%20%2B%20P%28X%20%3D%202%29%20%2B%20P%28X%20%3D%203%29%20%2B%20P%28X%20%3D%204%29)
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 0) = C_{10,0}.(0.1)^{0}.(0.9)^{10} = 0.34868](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20C_%7B10%2C0%7D.%280.1%29%5E%7B0%7D.%280.9%29%5E%7B10%7D%20%3D%200.34868)
![P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742](https://tex.z-dn.net/?f=P%28X%20%3D%201%29%20%3D%20C_%7B10%2C1%7D.%280.1%29%5E%7B1%7D.%280.9%29%5E%7B9%7D%20%3D%200.38742)
![P(X = 2) = C_{10,2}.(0.1)^{2}.(0.9)^{8} = 0.1937](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20C_%7B10%2C2%7D.%280.1%29%5E%7B2%7D.%280.9%29%5E%7B8%7D%20%3D%200.1937)
![P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%20C_%7B10%2C3%7D.%280.1%29%5E%7B3%7D.%280.9%29%5E%7B7%7D%20%3D%200.05740)
![P(X = 4) = C_{10,4}.(0.1)^{1}.(0.9)^{9} = 0.38742](https://tex.z-dn.net/?f=P%28X%20%3D%204%29%20%3D%20C_%7B10%2C4%7D.%280.1%29%5E%7B1%7D.%280.9%29%5E%7B9%7D%20%3D%200.38742)
So
![P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.34868 + 0.38742 + 0.19371 + 0.05740 + 0.01116 = 0.99837](https://tex.z-dn.net/?f=P%28X%20%3C%205%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29%20%2B%20P%28X%20%3D%202%29%20%2B%20P%28X%20%3D%203%29%20%2B%20P%28X%20%3D%204%29%20%3D%200.34868%20%2B%200.38742%20%2B%200.19371%20%2B%200.05740%20%2B%200.01116%20%3D%200.99837)
Finally
![P(X \geq 5) = 1 - P(X < 5) = 1 - 0.99837 = 0.00163](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%205%29%20%3D%201%20-%20P%28X%20%3C%205%29%20%3D%201%20-%200.99837%20%3D%200.00163)
Answer:
c. 14
Step-by-step explanation:
Let the missing y value be y2.
If the data represent a linear function, then:
![\frac{6 - 2}{2 - 1} = \frac{y_2 - 6}{4 - 2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B6%20-%202%7D%7B2%20-%201%7D%20%3D%20%5Cfrac%7By_2%20-%206%7D%7B4%20-%202%7D%20)
![\frac{4}{1} = \frac{y_2 - 6}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B4%7D%7B1%7D%20%3D%20%5Cfrac%7By_2%20-%206%7D%7B2%7D%20)
![4 = \frac{y_2 - 6}{2}](https://tex.z-dn.net/?f=%204%20%3D%20%5Cfrac%7By_2%20-%206%7D%7B2%7D%20)
Multiply both sides by 2
![4 \times 2 = \frac{y_2 - 6}{2} \times 2](https://tex.z-dn.net/?f=%204%20%5Ctimes%202%20%3D%20%5Cfrac%7By_2%20-%206%7D%7B2%7D%20%5Ctimes%202%20)
![8 = y_2 - 6](https://tex.z-dn.net/?f=%208%20%3D%20y_2%20-%206%20)
Add 6 to both sides
![8 + 6 = y_2 - 6 + 6](https://tex.z-dn.net/?f=%208%20%2B%206%20%3D%20y_2%20-%206%20%2B%206%20)
![14 = y_2](https://tex.z-dn.net/?f=%2014%20%3D%20y_2%20)
The missing value is 14
Answer:
1.18 is the answer but if u want to round u have the answer as 1.20=1.2