Answer:
We have two 6-sided dice.
Each one of them has 6 possible outcomes.
The total number of outcomes for the pair, will be equal to the product between the numbers of outcomes for each one of them
Then the total number of outcomes is:
C = 6*6 = 36.
The number of outcomes where the sum of the dice are 7 are:
1 and 6
6 and 1
2 and 5
5 and 2
3 and 4
4 and 3
So we have 6 outcomes where the sum of both numbers is equal to 7.
The probability of rolling a pair such that the sum is equal to 7, is equal to the quotient between the number of outcomes that meet this condition (6) and the total number of outcomes (36)
The probability is:
P = 6/36 = 1/6
Now let's do the same for 11.
The outcomes where the sum is 11 are:
5 and 6
6 and 5
So we have two outcomes.
In this case, the probability will be:
P = 2/36 = 1/18
The measure of an arc is the measure of its central angle, which is indicated as
Answer: 90°
right there in the figure.
The surface area of the box is being referred to as A
The surface area will be the sum of the four rectangular sides' areas and the base area.
Base area = x²
Rectangular side area = xh
A = x² + 4xh
Volume is, as you said,
V = x²h
Lets substitute h from the formula of A to obtain A in our final answer. Substituting x is possible, but more difficult
(A - x²)/4x = h
V = (x²) * (A - x²)/4x
V = (Ax - x³)/4
Answer:
$100
Step-by-step explanation:
If 1=$25, 2=$50, then 4*25=100 and 50*2=100
The work is equal to the line integral of
over each line segment.
Parameterize the paths
- from (0, 0, 0) to (2, 0, 0) by
with
, - from (2, 0, 0) to (2, 4, 1) by
with
, - from (2, 4, 1) to (0, 4, 1) by
with
, and - from (0, 4, 1) to (0, 0, 0) by
with 
The work done by
over each segment (call them
) is




Then the total work done by
over the particle's path is 46.