Answer:
The slope of ladder is not within the safe range .
Step-by-step explanation:
Given as :
The height of the ladder up a wall = h = 2 meters
The distance of base of ladder from the wall = x = 0.4 meters
The estimated safety range of slope of ladder is between 6.3 and 9.5
Let The slope of the ladder = x
<u>According to question</u>
slope of the ladder = 
Or, x = 
Or, x = 5
So, The slope of the ladder = x = 5
Since The estimated range of slope between 6.3 and 9.5
And The calculate slope of ladder = 5
Hence, The slope of ladder is not within the safe range . Answer
Answer:
The expected cost is 152
Step-by-step explanation:
Recall that since Y is uniformly distributed over the interval [1,5] we have the following probability density function for Y
if 
and 0 othewise. (To check this is the pdf, check the definition of an uniform random variable)
Recall that, by definition
Also, we are given that 
. Recall the following properties of the expected value. If X,Y are random variables, then
Then, using this property we have that ![E[C] = 50+3E[Y]+ 9E[Y^2]](https://tex.z-dn.net/?f=E%5BC%5D%20%3D%2050%2B3E%5BY%5D%2B%209E%5BY%5E2%5D)
.
Thus, we must calculate E[Y] and E[Y^2].
Using the definition, we get that
![E[Y] = \int_{1}^{5}\frac{y}{4} dy =\frac{1}{4}\left\frac{y^2}{2}\right|_{1}^{5} = \frac{25}{8}-\frac{1}{8} = 3](https://tex.z-dn.net/?f=E%5BY%5D%20%3D%20%5Cint_%7B1%7D%5E%7B5%7D%5Cfrac%7By%7D%7B4%7D%20dy%20%3D%5Cfrac%7B1%7D%7B4%7D%5Cleft%5Cfrac%7By%5E2%7D%7B2%7D%5Cright%7C_%7B1%7D%5E%7B5%7D%20%3D%20%5Cfrac%7B25%7D%7B8%7D-%5Cfrac%7B1%7D%7B8%7D%20%3D%203)
![E[Y^2] = \int_{1}^{5}\frac{y^2}{4} dy =\frac{1}{4}\left\frac{y^3}{3}\right|_{1}^{5} = \frac{125}{12}-\frac{1}{12} = \frac{31}{3}](https://tex.z-dn.net/?f=E%5BY%5E2%5D%20%3D%20%5Cint_%7B1%7D%5E%7B5%7D%5Cfrac%7By%5E2%7D%7B4%7D%20dy%20%3D%5Cfrac%7B1%7D%7B4%7D%5Cleft%5Cfrac%7By%5E3%7D%7B3%7D%5Cright%7C_%7B1%7D%5E%7B5%7D%20%3D%20%5Cfrac%7B125%7D%7B12%7D-%5Cfrac%7B1%7D%7B12%7D%20%3D%20%5Cfrac%7B31%7D%7B3%7D)
Then
The option which is not a possible distance for the flight from Haiti back to Cuba is 43, because that number is far too low to be a possible option. The correct answer should be somewhere around 500km, which means that the remaining options are close to it, whereas 43 is not.
<span>Trapezoid area = ((sum of the bases) ÷ 2) • height
It seems we'll have to count the lines in the graphic to get those lengths.
top base = 5
bottom base = 10
height = 6
</span><span>Trapezoid area = (11 / 2) * 6
</span><span>Trapezoid area = 5.5 * 6
</span><span>Trapezoid area = 33
</span>
