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IrinaVladis [17]
3 years ago
8

Assume red and green are equally likely occurrences. Using Pascal’s triangle, what is the probability that you will get one gree

n light in a row of five lights? a. 3/16 b. 1/32 c. 5/16 d. 5/32
Mathematics
1 answer:
Serggg [28]3 years ago
5 0

Answer:

5/32.

Step-by-step explanation:

                     1

                  1      1

              1       2      1

           1       3      3       1

      1       4       6      4       1

  1      5      10      10     5       1

As there are 5 lights we need the last row in the above Pascals triangle.

And  there is 1 red and 4 green  ( = 5) and it can happen in 5 ways, so that gives us the second term in the last row . The total  in that last row = 1+5+10+10+5+1 = 32.

so the probability is 5/32.

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In an arithmetic sequence, if a2= 5 and a10= 19 find a6
OLEGan [10]

Answer:

a₆ = 12

Step-by-step explanation:

The nth term of an arithmetic sequence is

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₂ = 5 and a₁₀ = 19 , then

a₁ + d = 5 → (1)

a₁ + 9d = 19 → (2)

Subtract (1) from (2) term by term to eliminate a₁

8d = 14 ( divide both sides by 8 )

d = 1.75

Substitute d = 1.75 into (1)

a₁ + 1.75 = 5 ( subtract 1.75 from both sides )

a₁ = 3.25

Then

a₆ = 3.25 + 5(1.75) = 3.25 + 8.75 = 12

6 0
2 years ago
Three less than twice a number is 15.
inessss [21]

Answer:

3-2x=15

Step-by-step explanation:

add 3 to both sides makes -2x=18. divide -2 from both side gets the answer x=-9, so the answer is C, -9

5 0
3 years ago
Nancy found that x=1 is one solution to the quadratic equation (x 2)2=a. what is the value of a? -9 -3 3 9
AlladinOne [14]

The value of the <em>a, </em>in the provided quadratic equation for which Nancy found one solution as x=1 is 9.

<h3>What is the solution of equation?</h3>

The solution of the quadratic equation is the solution of the variable of the equation, for which the equation satisfies.

Nancy found that x=1 is one solution to the quadratic equation. The quadratic equation is,

(x +2)^2=a

For this equation, one solution is <em>x</em>=1. Put this value in the above equation to get the value of <em>a,</em>

(1 +2)^2=a\\(3)^2=a\\9=a\\a=9

Thus, the value of the <em>a, </em>in the provided quadratic equation for which Nancy found one solution as x=1 is 9.

Learn more about the solution of the equation here;

brainly.com/question/21283540

5 0
2 years ago
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If 8 boys are arranged in a row, what is the probability that 3 boys will sit together?
mezya [45]

Answer:

100% if you have 8 boys in a row the change that three boys will sit next to each other is 100%

Hope This Helps!!!

8 0
2 years ago
Read 2 more answers
How to solve 3 variable systems
AVprozaik [17]
<span>Pick two pairs: 4x - 3y + z = - 10. 2x + y + 3z = 0. ... Eliminate the same variable from each system: 4x - 3y + z = - 10. 2x + y + 3z = 0. ... Solve the system of the two new equations: -5y - 5z = - 10. 5y - 7z = 34. ... Substitute into one of the original equations: - x + 2y - 5z = 17. ... <span>Check: Does 2(1) + 4 + 3(- 2) = 0 ? Yes.</span></span>
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3 years ago
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