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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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Answer:

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Step-by-step explanation:

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2 years ago
If f'(0) = 5 and F(x) = f(3x), what is F'(0)?
Llana [10]

Answer:

\displaystyle F'(0) = 15

Step-by-step explanation:

We are given that:

f'(0) = 5 \text{ and } F(x) = f(3x)

And we want to find F'(0).

First, find F(x):

\displaystyle F'(x) = \frac{d}{dx}\left[ f(3x)]

From the chain rule:

\displaystyle \begin{aligned} F'(x) &= f'(3x) \cdot \frac{d}{dx} \left[ 3x\right] \\ \\ &= 3f'(3x)\end{aligned}

Then:

\displaystyle \begin{aligned} F'(0) & = 3f'(3(0)) \\ \\ & = 3f'(0) \\ \\ & = 3(5) \\ \\ & = 15\end{aligned}

In conclusion, F'(0) = 15.

7 0
2 years ago
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Westkost [7]

Answer: b

Step-by-step explanation: 19 x 3 = 57 & 12 x 3= 36 so subtract 57 and 36 that’s going to give you 21 & 21 plus 6 is 27

7 0
2 years ago
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Solnce55 [7]

Answer:

11 ft

Step-by-step explanation:

Given the two lengths of a triangle as

AB = 6ft

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This is an isosceles triangle because only 2 sides are equal.

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Therefore the range of values for BC =

0 < BC < 12

Since BC must be bigger than one of the lengths and it must also be less than the sum of the 2 sides. The length of BC could be 11 because it is less than (6+6) 12 and greater than 6.

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