Answer:
x = 10 cm
Step-by-step explanation:
(3x + 2) + (3x + 2) + (4x - 5) + (4x - 5) = 134 cm
combine like terms:
14x - 6 = 134
add 6 to each side of the equation:
14x = 140
divide both sides by 14:
x = 10
A pentagon and a abstract shape
The new length side of the perimeter, we'll call p. The original length, we'll call o. P's equation looks like this:
![p = 20 \times \frac{1}{4}](https://tex.z-dn.net/?f=p%20%3D%2020%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B4%7D%20%20)
Since 5 is the length of one side, subtract 2 from 5 to get 3. The equation looks like this:
![o = \frac{20}{4} - 2](https://tex.z-dn.net/?f=o%20%3D%20%20%5Cfrac%7B20%7D%7B4%7D%20%20-%202%20%20%20)
or simply
Answer:
Mean is 19.43
Standard deviation is 2.5322
Step-by-step explanation:
For each student who graduated from high school in 2012, there are only two possible outcomes. Either they have enrolled in college, or they have not. The probability of a student having enrolled in college is independent of other students. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
![E(X) = np](https://tex.z-dn.net/?f=E%28X%29%20%3D%20np)
The standard deviation of the binomial distribution is:
![\sqrt{V(X)} = \sqrt{np(1-p)}](https://tex.z-dn.net/?f=%5Csqrt%7BV%28X%29%7D%20%3D%20%5Csqrt%7Bnp%281-p%29%7D)
67% of students who graduated from high school in 2012 enrolled in college.
This means that ![p = 0.67](https://tex.z-dn.net/?f=p%20%3D%200.67)
Sample of 29 high school graduates
This means that ![n = 29](https://tex.z-dn.net/?f=n%20%3D%2029)
Mean
![E(X) = np = 29*0.67 = 19.43](https://tex.z-dn.net/?f=E%28X%29%20%3D%20np%20%3D%2029%2A0.67%20%3D%2019.43)
Standard deviation
![\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{29*0.67*0.33} = 2.5322](https://tex.z-dn.net/?f=%5Csqrt%7BV%28X%29%7D%20%3D%20%5Csqrt%7Bnp%281-p%29%7D%20%3D%20%5Csqrt%7B29%2A0.67%2A0.33%7D%20%3D%202.5322)