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Artemon [7]
3 years ago
10

Find the sum of the first 12 terms of the sequence. Show all work for full credit. 1, -4, -9, -14, . . . (2 points)

Mathematics
2 answers:
nordsb [41]3 years ago
5 0
<h2>Answer:</h2>

<u>The sum is = </u><u>-318</u>

<h2>Step-by-step explanation:</h2>

See the attached image

My name is Ann [436]3 years ago
4 0

<u>Answer:</u>

S_n= -348

<u>Step-by-step explanation:</u>

We are given the following arithmetic sequence and we are to find the sum of its first 12 terms:

1, -4, -9, -14, . . .

For that, we will use the formula for the sum of the arithmetic mean:

S_n=\frac{n}{2} (a_1+a_n)

We know the value of the first term (a_n) but we need to find the value of a_{12}. So we will use the following formula:

a_{12}=a_1+(n-1)d

a_{12}=(-4)+(12-1)(5)

a_{12}=-59

Substituting these values in the sum formula to get:

S_n=\frac{12}{2} (1+(-59))

S_n= -348

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Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which o
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a) 0.0000001024 probability that he will answer all questions correctly.

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Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

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This means that the probability of correctly answering a question guessing is p = \frac{1}{5} = 0.2

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This means that n = 10

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This is P(X = 10)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

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0.0000001024 probability that he will answer all questions correctly.

B) What is the probability that he will answer all questions incorrectly?

None correctly, so P(X = 0)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074

0.1074 = 10.74% probability that he will answer all questions incorrectly

C) What is the probability that he will answer at least one of the questions correctly?

This is

P(X \geq 1) = 1 - P(X = 0)

Since P(X = 0) = 0.1074, from item b.

P(X \geq 1) = 1 - 0.1074 = 0.8926

0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

D) What is the probability that Richard will answer at least half the questions correctly?

This is

P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

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