Answer:
all work pictured and shown
It is easier to understand the problem if you create a number based on the criteria and then perform the computations. I am going to choose: 111 22 33 4
There are 10 options for the first "1" and only 1 option for the other two 1's
There are 9 remaining options for the first "2" and only 1 option for the other 2
There are 8 remaining options for the first "3" and only 1 option for the other 3
There are 7 remaining options for the "4"
10 x 1 x 1 x 9 x 1 x 8 x 1 x 7
10 x 9 x 8 x 7 = 5,040
Answer: 5,040
Answer:
24) x = 9.2
25) x = 30.8
Step-by-step explanation:
Given
See attachment for triangles
Solving (24)
To solve for x, we make use of cosine formula
i.e.
cos(40) = adjacent ÷ hypotenuse
So, we have:
cos(40) = x ÷ 12
Multiply both sides by 12
12 cos(40) = x
12 * 0.7660 = x
x = 9.2
Solving (25)
To solve for x, we make use of sine formula
i.e.
sin(25) = opposite ÷ hypotenuse
So, we have:
sin(25) = 13 ÷ x
Multiply both sides by
x sin(25) = 13
Divide by sin(25)
x = 13 ÷ sin(25)
Using a calculator
x = 30.8
Answer:
The probability that they purchased a green or a gray sweater is 
Step-by-step explanation:
Probability is the greater or lesser possibility of a certain event occurring. In other words, probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

The addition rule is used when you want to know the probability that 2 or more events will occur. The addition rule or addition rule states that if we have an event A and an event B, the probability of event A or event B occurring is calculated as follows:
P(A∪B)= P(A) + P(B) - P(A∩B)
Where:
P (A): probability of event A occurring.
P (B): probability that event B occurs.
P (A⋃B): probability that event A or event B occurs.
P (A⋂B): probability of event A and event B occurring at the same time.
Mutually exclusive events are things that cannot happen at the same time. Then P (A⋂B) = 0. So, P(A∪B)= P(A) + P(B)
In this case, being:
- P(A)= the probability that they purchased a green sweater
- P(B)= the probability that they purchased a gray sweater
- Mutually exclusive events
You know:
- 8 purchased green sweaters
- 4 purchased gray sweaters
- number of possible cases= 12 + 8 + 4+ 7= 21
So:
Then:
P(A∪B)= P(A) + P(B)
P(A∪B)= 
P(A∪B)= 
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