Answer:
A 5040
B 35
Step-by-step explanation:
A There are 7 ways to put the first picture. There are 6 pictures left and 6 ways to put the 2nd picture. There are now 5 pictures left and 5 ways to put the 3rd picture. And so on
7 * 6*5*4*3*2*1
5040
B If we can only have 3 pictures and order does not matter
7 choices for the first * 6 *5
But
We have to take into account order
The first picture can go into 3 slots, the second into 2 and the third 1 so divide by 6
(7*6*5)/ (3*2*1)
35
Answer:

Step-by-step explanation:
The formula to find the error is:

Where:
is the standard deviation
n is the sample size
So
n = 80 people
= 12 movies
Then
= confidence level = 0.99


We look for the Z value: 
Looking in the normal standard tables
Therefore:

Answer:
Part A)

Part B)

Step-by-step explanation:
We know that the rectangle has a length of (x+5) and a width of 12 cm.
Part A)
Remember the formula for the perimeter of a rectangle:

We know that the perimeter is 86. Substitute that for P:

Substitute (x+5) for the length l and 17 for w. So:

We can simplify this to acquire our equation:

Part B)
To find the length, let's find our x first. We have the equation:

Divide both sides by 2:

Now, subtract 22 from both sides. Therefore, our x is:

To find the length, remember that the length is:

Since we now know the value of x, substitute 21 for x:

Add:

So, the length is 26 centimeters.
And we're done!
Answer:
0.2406 = 24.06% probability that exactly two of the selected major customers accept the plan
Step-by-step explanation:
The customers are chosen without replacement, which means that we use the hypergeometric distribution to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:

In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
50 major customers, 15 would accept the plan.
This means that 
The utility selects 10 major customers randomly (without replacement) to contact and promote the plan.
This means that 
a. What is the probability that exactly two of the selected major customers accept the plan
This is P(X = 2).


0.2406 = 24.06% probability that exactly two of the selected major customers accept the plan
Probability is represented as the number of ways for an event to happen over all possible outcomes. For the theoretical probability, there is 1 black spot and 5 total options. Therefore, the probability is 1/5, or 0.20.
For experimental probability, there were 103 times it landed on black out of 500 spins. The probability is 103/500, or 0.206.
Lastly, the multiple choice. The larger sample size you take, assuming a fair spinner, the more likely you are to see results similar to the theoretical probability. This is because the larger sample size taken, the less each individual spin effects the outcome.