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vichka [17]
3 years ago
15

A survey company asks all respondents for demographic information. There are 8 age and 7 income groups, 5 gender choices, and 6

choices for ethnicity. How many people would this company have to poll so it’s inevitable that at least three people in the sample have identical demographic information? Give the number and explain.
Mathematics
1 answer:
IgorC [24]3 years ago
6 0

Answer:

3361 people should poll so it's inevitable that at least three people in the sample have identical demographic information.

Step-by-step explanation:

Consider the provided information.

There are 8 age and 7 income groups, 5 gender choices, and 6 choices for ethnicity.

For age we have 8 choices.

For Income groups we have 7 choices.

For gender groups we have 5 choices.

For ethnicity we have 5 choices.

Therefore, the total number of groups is: 8×7×5×6=1680

That means 1680 distinct group.

According to Pigeons holes principal: If m pigeons are in n holes and m > n, then at least 2 pigeons are in the  same hole.

So to select at least 2 people in the sample have identical demographic information 1681 people needs to poll.

In order to at least 3 people (2 × 1680+1) people should need to poll.

2 × 1680 + 1 = 3361

Hence, 3361 people should poll so it's inevitable that at least three people in the sample have identical demographic information.

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1.
11 16
— X — = 44
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Answer to number 1. —- 44 cups.

2.
880 yards is half of 1,760. So, if 1,760 yards is 1 mile then 880 yards (1/2) is .5 mile.

Answer to number 2. —- 0.5 mile.

3.
36 7
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Answer to number 3. —- 84 inches.



ANSWER:
1. 44 cups
2. 0.5 mile
3.84 inches

Hope this helped you understand you how to do this. Have a great day. A thank you and (or) brainliest is always appreciated. (Optional....) Goodbye!
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Olivia is making scarves each scarf will have 5 rextangles and 2/5 of the rectangles will be purple .How many purple rectangles
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3 years ago
Jillian is trying to save water, so she reduces the size of her square grass lawn by 8 feet on each side the area of the smaller
horsena [70]

Answer: 20 feet by 20 feet.


Step-by-step explanation:

1. You know that x is the original measure of one side. Since it is a square, all its sides are equal.

2. Therefore, to solve the problem you only need to solve for x, as you can see below:

- You have that:

(a-b)^{2}=a^{2}-2ab+b^{2}

- Then, you obtain the following quadratic equation:

(x-8)^{2} =144\\x^{2}-2(x)(8)+8^{2}=144\\x^{2}-16x-80=0

- Apply the Quadratic formula to solve it:

x=\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}\\a=1\\b=-16\\c=-80

- Then, you obtain:

x_1=20\\x_2=-4

3. The dimensions cannot be negative, therefore, the answer is: 20 feet by 20 feet.


3 0
3 years ago
Read 2 more answers
How to solve and answer using elimination
grin007 [14]

Answer:

the answer is:

x=6

y=7


4 0
3 years ago
If 90 percent of automobiles in Orange County have both headlights working, what is the probability that in a sample of eight au
Alex17521 [72]

Answer:

P(X \geq 7) = P(X=7) +P(X=8)

And we can find the individual probabilities using the probability mass function

P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826  

P(X=8)=(8C8)(0.9)^8 (1-0.9)^{8-8}=0.4305  

And replacing we got:

P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131

Step-by-step explanation:

Previous concepts  

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

Solution to the problem

Let X the random variable of interest "number of automobiles with both headligths working", on this case we now that:  

X \sim Binom(n=8, p=0.9)  

The probability mass function for the Binomial distribution is given as:  

P(X)=(nCx)(p)^x (1-p)^{n-x}  

Where (nCx) means combinatory and it's given by this formula:  

nCx=\frac{n!}{(n-x)! x!}  

And for this case we want to find this probability:

P(X \geq 7) = P(X=7) +P(X=8)

And we can find the individual probabilities using the probability mass function

P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826  

P(X=8)=(8C8)(0.9)^8 (1-0.9)^{8-8}=0.4305  

And replacing we got:

P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131

3 0
2 years ago
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