Area of the base = 8^2 = 64
area of 1 traingle = 1/2 * 8 * 5.4 = 21.6
there are 4 triangular sides so their area = 4 * 21.6 = 86.4
Total surface area = 64 + 86.4 = 150.4 cm2
D
Let the amount be x.
6% for the first 160000
= 6/100 * 160000 = 9600
4% for any amount exceeding 160000.
= 4/100 * (x -160000) = 0.04(x-160000)
The sum of both commission should be equal to 10560.
9600 + 0.04(x -160000) = 10560
0.04(x -160000) = 10560 - 9600
0.04(x -160000) = 960 Divide by 0.04.
(x -160000) = 960/0.04
(x -160000) = 24000
x = 24000 + 160000 = 184000.
Selling price = 184000
In 1 gallon, we have 4 quarts, and we have 4 cups in each quart, giving us 4 x 4 = 16 cups in 1 gallon. Multiply that by 5 to get 16 x 5 = 80 cups in a 5-gallon jug.
Answer:

Step-by-step explanation:
Recall that since X is uniformly distributed over the set [1,4] we have that the pdf of X is given by
if
and 0 otherwise. In the same manner, the pdf of Y is given by
if
and 0 otherwise.
Note that if Y is in the interval (4,5] then Y>X by default. So, in this case we have that P(Y>X| y in (4,5]) = 1. We want to calculate the probability of having Y in that interval . That is
. Thus,
.
We want to proceed as follows. Using the total probability theorem, given two events A, B we have that
In this case, A is the event that Y>X and B is the event that Y is in the interval (4,5].
If we assume that X and Y are independent, then we have that the joint pdf of X,Y is given by
when
. We can draw the region were Y>X and the function h(x,y) is different from 0. (The drawing is attached). This region is described as follows:
and
, then (the specifics of the calculations of the integrals are ommitted)
Thus,

Answer:
3n-1
Step-by-step explanation:
(4n+4) - (n+5)
i sperate it to be
4n-n and 4-5
so
3n-1 should be it