9514 1404 393
Answer:
x = 25
Step-by-step explanation:
The parallel lines divide the triangle sides proportionally.
x/40 = 15/24
x = 40(15/24) . . . . multiply by 40
x = 25
Answer:
the y intercept is -2
Step-by-step explanation:
the y intercept is always the value on the end
The teachers plan to raise 3/4 of of the 8th grade.
The 8th grade plans to raise 4/3 of the teachers.
Answer:
![Var(Y) = E(Y^2) -[E(Y)]^2 = \frac{112}{5} -[\frac{12}{5}]^2 =\frac{128}{75}](https://tex.z-dn.net/?f=%20Var%28Y%29%20%3D%20E%28Y%5E2%29%20-%5BE%28Y%29%5D%5E2%20%3D%20%5Cfrac%7B112%7D%7B5%7D%20-%5B%5Cfrac%7B12%7D%7B5%7D%5D%5E2%20%3D%5Cfrac%7B128%7D%7B75%7D)
Step-by-step explanation:
Previous concepts
The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.
The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).
Solution to the problem
Since the warranty on a machine specifies that it will be replaced at failure or age 4 and the distribution for X is defined between 0 and 5 then if we define the random variable Y ="the age of the machine at the time of replacement" we know that the values for Y needs to be between 0 and 4 or between 4 and and we can define the following density function:
![f(y) = x, 0 \leq x \leq 4](https://tex.z-dn.net/?f=f%28y%29%20%3D%20x%2C%200%20%5Cleq%20x%20%5Cleq%204)
![f(y) = 4, 4 \leq x \leq 5](https://tex.z-dn.net/?f=%20f%28y%29%20%3D%204%2C%204%20%5Cleq%20x%20%5Cleq%205)
for other case
Now we can apply the definition of expected value and we have this:
![E(Y) = \int_{0}^4 \frac{1}{5} x dx +\int_{4}^5 \frac{4}{5}dx](https://tex.z-dn.net/?f=%20E%28Y%29%20%3D%20%5Cint_%7B0%7D%5E4%20%5Cfrac%7B1%7D%7B5%7D%20x%20dx%20%2B%5Cint_%7B4%7D%5E5%20%5Cfrac%7B4%7D%7B5%7Ddx)
![E(Y) = \frac{1}{10} (4^2-0^2) +\frac{4}{5} (5-4) = \frac{16}{10}+ \frac{4}{5}=\frac{12}{5}](https://tex.z-dn.net/?f=%20E%28Y%29%20%3D%20%5Cfrac%7B1%7D%7B10%7D%20%284%5E2-0%5E2%29%20%2B%5Cfrac%7B4%7D%7B5%7D%20%285-4%29%20%3D%20%5Cfrac%7B16%7D%7B10%7D%2B%20%5Cfrac%7B4%7D%7B5%7D%3D%5Cfrac%7B12%7D%7B5%7D)
And for the second moment we have:
![E(Y) = \int_{0}^4 \frac{1}{5} x^2 dx +\int_{4}^5 \frac{16}{5}dx](https://tex.z-dn.net/?f=%20E%28Y%29%20%3D%20%5Cint_%7B0%7D%5E4%20%5Cfrac%7B1%7D%7B5%7D%20x%5E2%20dx%20%2B%5Cint_%7B4%7D%5E5%20%5Cfrac%7B16%7D%7B5%7Ddx)
![E(Y^2) = \frac{1}{15} (4^3-0^3) +\frac{16}{5} (5-4) = \frac{64}{15}+ \frac{16}{5}=\frac{112}{5}](https://tex.z-dn.net/?f=%20E%28Y%5E2%29%20%3D%20%5Cfrac%7B1%7D%7B15%7D%20%284%5E3-0%5E3%29%20%2B%5Cfrac%7B16%7D%7B5%7D%20%285-4%29%20%3D%20%5Cfrac%7B64%7D%7B15%7D%2B%20%5Cfrac%7B16%7D%7B5%7D%3D%5Cfrac%7B112%7D%7B5%7D)
And the variance would be given by:
![Var(Y) = E(Y^2) -[E(Y)]^2 = \frac{112}{5} -[\frac{12}{5}]^2 =\frac{128}{75}](https://tex.z-dn.net/?f=%20Var%28Y%29%20%3D%20E%28Y%5E2%29%20-%5BE%28Y%29%5D%5E2%20%3D%20%5Cfrac%7B112%7D%7B5%7D%20-%5B%5Cfrac%7B12%7D%7B5%7D%5D%5E2%20%3D%5Cfrac%7B128%7D%7B75%7D)
$30 + $30 = $60
$60 + $30 = $90
To pay back his sister the $80 he will to deposit money into his account for 3 weeks.
Since Steven would have $10 left over in his account from paying his sister all he needs now is $570.
You need to divide:
$570/$30 = 19
So Steven will need to deposit $30 into his bank account for 19 weeks to be able to buy the $580 bicycle.
Hope this Helps!!