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2 years ago

How many ways can 6 people sit on a bench if 3 of them have to sit side by side

Mathematics

1 answer:

pickupchik [31]2 years ago

4 0

Answer:

144 ways

Step-by-step explanation:

Let's think of the 3 persons sitting together as "one". So essentially we have 3 + "1" = "4" persons to arrange.

THey can be arranged in 4! ways, which is:

4! = 4 * 3 * 2 * 1 = 24 ways

Now, the 3 persons themselves can be arranged in 3! ways, which is:

3! = 3 * 2 * 1 = 6 ways

Total ways = 4! * 3! = 24 * 6 = 144 ways

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Nikki and Jonathan both solve this system of equations: y=−2.7x+3.2 y = - 2 . 7 x + 3 . 2 y=1.3x+1.6 y = 1 . 3 x + 1 . 6 Jonatha

N76 [4]

We have two equations that were solved by Nikki and Jonathon:

y=−2.7x+3.2
y=1.3x+1.6

Equating the above two:

⇒ 1.3x + 1.6 = -2.7x + 3.2

⇒ 4x = 1.6

⇒ x = 0.4

Hence, substituting the value of x in one of the equations we get:

y = 1.3×0.4 + 1.6 = 2.12

So the solution is (0.4, 2.12)

Jonathon's solution was (0.4, 2.12) and Nikki's was (2.25, 0.5). Hence Jonathon gave the correct solution.

7 0

2 years ago

Read 2 more answers

If the trapezoid below is reflected across the x-axis, what are the coordinates of B'?

Grace [21]

The x-coordinate remains the same as the x-coordinate of point B.
The y-coordinate becomes the additive inverse of the y-coordinate of point B.

Answer: B. (3, -8)

9 0

2 years ago

Read 2 more answers

A used bookstore will trade 2 of its books for three of yours. If Val brings in 18 books to trade, how many books can she get fr

Ainat [17]

Answer:

she can get 12 books

Step-by-step explanation:

if you divide 18 by 3 you get 6

and if you times that my 2 get 12

so your answer is 12 books

7 0

2 years ago

A thumbtack that is tossed can land point up or point down. The probability of a tack landing point up is 0.2. A simulation was

sweet-ann [11.9K]

Answer:

Option C: 0.28

Step-by-step explanation:

This is a binomial probability distribution problem.

Now, we want to find the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed. This is written as;

P(X ≥ 2) = P(2) + P(3) + P(4) + P(5)

From the histogram;

P(5) = 0.02

P(4) = 0.02

P(3) = 0.05

P(2) = 0.19

Thus;

P(X ≥ 2) = 0.19 + 0.05 + 0.02 + 0.02

P(X ≥ 2) = 0.28

8 0

2 years ago

Read 2 more answers

An online furniture store sells chairs for $200 each and tables for $600 each. Every day, the store can ship a maximum of 32 pie

wolverine [178]

Answer:

If the minimum 13 chair were sold , then the minimum number of Table sold is 14

Step-by-step explanation:

Given as :

The cost of each chair = $ 200

The cost of each table = $ 600

The total number of furniture sold per day = 32

The minimum amount of selling per day = $ 12000

Let the total number of chair = C

The total number of table = T

So , according to question

C + T = 32 .......1

200 C + 600 T = 12000 .......2

Solving eq 1 and 2

200 C + 600 T = 12000

200 × ( C + T ) = 32 × 200

I.e 200 C + 200 T = 6400

or, ( 200 C + 600 T ) - ( 200 C + 200 T ) = 12,000 - 6400

Or, 400 T = 5600

∴ T = $\frac{5600}{400}$

I.e T = 14

Put The value of T in eq 2

So, 200 C + 600 × 14 = 12000

or , 200 C + 8400 = 12,000

Or, 200 C = 12000 - 8400

Or, 200 C = 3600

∴ C = $\frac{3600}{200}$

I.e C = 18

The number of chair sold is 18

If the number of chair sold is 13 ,

Then the min number of table sold = 200 × 18 + 600 T = 12000

i.e 600 T = 12000 - 3600

or, 600 T = 8400

∴ T = $\frac{8400}{600}$

I.e T = 14

Hence if the minimum 13 chair were sold , then the minimum number of Table sold is 14 . Answer

5 0

2 years ago