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4 years ago

How many different ways can six people be arranged in a line?

1 answer:

8 0

There are six people which means that each person can be arranged in 6 various arrangements

6×6=36

Answer: There can be 36 different ways for 6 people to be arranged

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K/5 = 9/15 plz help mee

Molodets [167]

Answer:

k = 3

Step-by-step explanation:

Reduce the right side of the equation by 3 to get 3/5. Since both denominators now are even you should get 3 which is k as your answer.

5 0

3 years ago

PLEASEE HELP!! I WILL MARK BRAINLIEST!

ycow [4]

The expression in scientific notation is given as follows:

3.5 x 10³.

<h3>What is scientific notation?</h3>

A number in scientific notation is given by:

$a \times 10^b$

With the base being $a \in [1, 10)$ .

For this problem, the expression is given by:

$\frac{5 \times 10^2 \times 4.2 \times 10^4}{6 \times 10^3}$

When two factors of a multiplication have the same base and different exponent, we keep the base and add the exponents, hence:

$10^2 \times 10^4 = 10^6$

5 x 4.2 = 21, hence the expression is:

$\frac{5 \times 10^2 \times 4.2 \times 10^4}{6 \times 10^3} = \frac{21 \times 10^6}{6 \times 10^3}$

When we divide two terms with the same base and different exponents, we keep the base and subtract the exponents, hence:

$\frac{21 \times 10^6}{6 \times 10^3} = 3.5 \times 10^3$

Which is the simplified expression.

More can be learned about scientific notation at brainly.com/question/16394306

#SPJ1

6 0

1 year ago

A company must select 4 candidates to interview from a list of 12, which consist of 8 men and 4 women.

Radda [10]

Part A

If 4 candidates were to be selected regardless of gender, that means that 4 candidates is to be selected from 12.

The number of possible selections of 4 candidates from 12 is given by

$^{12}C_4= \frac{12!}{4!(12-4)!}= \frac{12!}{4!\times8!} =11\times5\times9=495$

Therefore, the number of selections of 4 candidates regardless of gender is 495.

Part B:


If 4 candidates were to be selected such that 2 women must be selected, that means that 2 men candidates is to be selected from 8 and 2 women candidates is to be selected from 4.

The number of possible selections of 2 men candidates from 8 and 2 women candidates from 4 is given by

 $^{8}C_2\times ^{4}C_2= \frac{8!}{2!(8-2)!}\times 
\frac{4!}{2!(4-2)!} \\ \\ = 
\frac{8!}{2!\times6!}\times\frac{4!}{2!\times2!} 
=4\times7\times2\times3=168$

Therefore, the number of selections of 4 candidates such that 2 women must be selected is 168.

Part 3:

If 4 candidates were to be selected such that at least 2 women must be selected, that means that 2 men candidates is to be selected from 8 and 2 women candidates is to be selected from 4 or 1 man candidates is to be selected from 8 and 3 women candidates is to be selected from 4 of no man candidates is to be selected from 8 and 4 women candidates is to be selected from 4.

The number of possible selections of 2 men candidates from 8 and 2 women candidates from 4 of 1 man candidates from 8 and 3 women candidates from 4 of no man candidates from 8 and 4 women candidates from 4 is given by

$^{8}C_2\times ^{4}C_2+ ^{8}C_1\times ^{4}C_3+ ^{8}C_0\times ^{4}C_4 \\ \\ = \frac{8!}{2!(8-2)!}\times \frac{4!}{2!(4-2)!}+\frac{8!}{1!(8-1)!}\times \frac{4!}{3!(4-3)!}+\frac{8!}{0!(8-0)!}\times \frac{4!}{4!(4-4)!} \\ \\ = \frac{8!}{2!\times6!}\times\frac{4!}{2!\times2!}+\frac{8!}{1!\times7!}\times\frac{4!}{3!\times1!}+\frac{8!}{0!\times8!}\times\frac{4!}{4!\times0!} \\ \\ =4\times7\times2\times3+8\times4+1\times1=168+32+1=201$

Therefore, the number of selections of 4 candidates such that at least 2 women must be selected is 201.

7 0

3 years ago

Read 2 more answers

You need to haul a load of patio bricks to a job site. Each brick weighs 4 pounds 14 ounces. Truck can carry a 3/4 - ton load. H

Olin [163]

Answer:

339 bricks.

Step-by-step explanation:

We have the weight of each brick and what the truck can support. Therefore what we must do is pass all to the same unit of measurement to calculate the quantity of bricks.

In this case we will pass everything to pounds.

We have that a 1 pound is 16 ounces, therefore 14 would be:

14 ounces * 1 pound / 16 ounces = 0.875 pounds

In addition we have that 1 ton is 2204.62 pounds, therefore 3/4 would be:

3/4 ton * 2204.62 pounds / 1 ton = 1653.467 pounds

Therefore, in total the brick weighs 4,875 pounds (4 + 0.875) and the truck can support 1653,467 pounds, the number of bricks would be:

1653.467 / 4.875 = 339.17

In other words, it can support about 339 bricks.

6 0

3 years ago

The sum of two numbers is 136. One number is 51. What is other? What are the common factors of these two numbers?

Vsevolod [243]

75 // common factor is 3

8 0

3 years ago