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3 years ago

Write a recursive rule and an explicit rule for the sequence 3,7,11,15

Mathematics

1 answer:

m_a_m_a [10]3 years ago

6 0

Answer:

The Recursive formula for the sequence is:

aₙ = aₙ₋₁ + d

The Explicit formula for the sequence is:

$a_n=4n-1$

Step-by-step explanation:

Given the sequence

3,7,11,15

Here:

a₁ = 3

computing the differences of all the adjacent terms

7 - 3 = 4, 11 - 7 = 4, 15 - 11 = 4

The difference between all the adjacent terms is the same and equal to

d = 4

We know that a recursive formula basically defines each term of a sequence using the previous term(s).

The recursive formula of the Arithmetic sequence always involves the first term.

a₁ = 3

We know that, in the Arithmetic sequence, every next term can be obtained by adding the common difference and the preceding term.

The recursive formula of the sequence is:

aₙ = aₙ₋₁ + d

substitute n = 2 to find the 2nd term

a₂ = a₂₋₁ + d

a₂ = a₁+ d

substitute a₁ = 3 and d = 4

a₂ = 3 + 4

a₂ = 7

Thus, the recursive formula for the sequence 3,7,11,15 is:

aₙ = aₙ₋₁ + d

<u>An explicit rule for the sequence</u>

Given the sequence

3,7,11,15

We already know that

a₁ = 3

d = 4

An arithmetic sequence has a constant difference 'd' and is defined by

$a_n=a_1+\left(n-1\right)d$

substituting a₁ = 3 and d = 4

$a_n=4\left(n-1\right)+3$

$a_n=4n-4+3$

$a_n=4n-1$

Therefore, an explicit rule for the sequence

$a_n=4n-1$

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Answer:

P = 0.9989

Step-by-step explanation:

In order to do this, I will use the following numbers to make the calculations easier. In this case, We'll say that we have 7 majors and 14 non majors anthopology to present a topic.

This means that in the class we have 21 students.

Now, we choose 5 of them, and we want to know the probability that 1 of them is non major.

First, we need to calculate the number of ways we can select the students in all cases, and then, the probability.

First, we'll use the combination formula, to calculate the number of ways we can select the 5 students out of the 21. We use combination, because it does not matter the order that the students are selected.

C = m! / n!(m - n)!

Where:

m: number of students

n: number of selected students out of m.

With this expression we will calculate first, how many ways we can choose the 5 students out of 21:

C1 = 21! / 5!(21-5)! = 20,349

Now let's calculate the number of ways you can get the all 5 students are non majors:

C2 = 14! / 5!(14 - 5)! = 2002

Now we need to know the number of ways we can get 4 non majors and 1 major:

C3 = C3' * C3''

C3' represents the number of ways we can get 4 non majors and the C3'' represents the number of ways we can get 1 major.

C3' = 14! / 4!(14 - 4)! = 1,001

C3'' = 7! / 1!(7 - 1)! = 7

C3 = 1001 * 7 = 7,007 ways to get 4 non majors and 1 major

Now the way to get 3 non majors and 2 majors, we do the same thing we do to get 4 non majors and 1 major, but changing the numbers. Then the way to get 2 non majors and 3 majors, and finally 1 non major and 4 majors:

3 non majors and 2 majors:

C4 = C4' * C4'' = [14! / 3!(14 - 3)!] * [7! / 2!(7 - 2)!] = 7,644

2 non majors and 3 majors:

C5 = C5' * C5'' = [14! / 2!(14 - 2)!] * [7! / 3!(7 - 3)!] = 3,185

1 non major and 4 majors:

C6 = C6' * C6'' = [14! / 1!(14 - 1)!] * [7! / 4!(7 - 4)!] = 490

Finally to know the probability of getting 1 out of the 5 to be non major, we have to sum all the previous results, and divide them by the ways we can choose the 5 students (C1):

P = 2,002 + 7,007 + 7,644 + 3,185 + 490 / 20,349

P = 0.9989

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3 years ago

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Mashutka [201]

Answer:

Option C. is the correct option.

Step-by-step explanation:

Given question is incomplete; here is the complete question.

Aubrey is making cone-shaped hats for a birthday party. She mistakenly thinks that she will need about 104 square inches of paper for each hat.

Cone with diameter six inches and slant height eight inches.

What is the correct amount of paper Aubrey will need per hat? Explain Aubrey’s mistake. Use 3.14 for π and round to the nearest inch.

A. About 70 in2; Aubrey found the surface area of the cone, but did not include the base.

B. About 70 in2; Aubrey used the diameter instead of the radius to find the surface area of a cone.

C. About 75 in2; Aubrey found the surface area of the cone and included the base.

D. About 75 in2; Aubrey found the volume of the cone instead of the surface area.

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Here r = radius of the cone

l = lateral height of the cone

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= 75.36 square inches

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= πr(r + l)

= 3.14(3)(3 + 8)

= 103.62

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AlekseyPX

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