Answer:
1. Benny had 266 dollars to spend on 9 books. After buying them, he had 14 dollars. How much did each book cost?
The books cost $28 dollars each.
<em>how to calculate...</em>
<em>
$266 - $14 = $252
</em>
<em>
then take $252 divided by 9 = $ 28</em>
<em />
2. Oceanside Bike Rental Shop charges 14 dolars plus 9 dollars an hour for renting a bike. Sally paid 86 dollars to rent a bike. How many hours did she pay to have the bike checked out?
8 hours
how to calculate...
take 86 - 14 = 72
then 72 divided 9 = 8 hours
3. The sum of three consecutive numbers is 132. What is the smallest of the three numbers?
43 is the smallest of the 3 numbers
<em>calculation...</em>
<em>x + (x+1) + (x+2) = 132</em>
<em>3x + 3 = 132 -3</em>
<em>3x=129
</em>
<em>x=129/3
</em>
<em>
x=43 (answer for the 1st number)</em>
<em>43+1=44 (answer for the 2nd number)</em>
<em>43+2=45 (answer for the 3rd number)</em>
add them all to make sure they equal to 132
<em>43+44+45=132
</em>
<em>132=132</em>
4. Sandy sold half of her comic books and then bought 8 more. She now has 16. How many did she begin with?
x= how many Sandy started with
<em>1/2 x + 8 = 16</em>
<em>1/2x = 16 - 8</em>
<em>1/2x = 8 * 2</em>
x = 16 comics books
Step-by-step explanation:
Answer:
I believe the answer is A
Step-by-step explanation:
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
If you mean <em>x</em> = 0.666…, then
10<em>x</em> = 6.666…
10<em>x</em> - <em>x</em> = 6.666… - 0.666…
9<em>x</em> = 6
<em>x</em> = 6/9 = 2/3
If you mean <em>x</em> = 0.060606…, then
100<em>x</em> = 6.060606…
100<em>x</em> - <em>x</em> = 6.060606… - 0.060606…
99<em>x</em> = 6
<em>x</em> = 6/99 = 2/33
