All categories

3 years ago

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>

<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

You might be interested in

Consider the figure below. Find m∠ABAC.<br><br><br>will give 20 points

lesya692 [45]

Answer:

Step-by-step explanation:

3 0

3 years ago

Please tell me how much it would be for 1

Monica [59]

Answer:

small

per Oz

0.269 dollars

medium

per Oz

0.227 dollars

large

per Oz

0.1845 dollars

3 0

3 years ago

Read 2 more answers

Solve for x. Round your answer to the nearest tenth.

zlopas [31]

Answer:

By Pythagorean theorem:

$c^2=a^2+b^2$

$x=\sqrt{15^2+33^2}$

$x=36.25$

$x=36.3$

7 0

2 years ago

Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which o

myrzilka [38]

Answer:

a) 0.0000001024 probability that he will answer all questions correctly.

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

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

d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

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.

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

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.

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

And p is the probability of X happening.

Each question has five answers, of which only one is correct

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

10 questions.

This means that $n = 10$

A) What is the probability that he will answer all questions correctly?

This is $P(X = 10)$

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

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024$

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

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

In which

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

$P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264$

$P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055$

$P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008$

$P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001$

$P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0$

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328$

0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

8 0

3 years ago

I need help on 21 . Please

kupik [55]

Answer:

Air travels 6,920 meters in 20 seconds.

Step-by-step explanation:

If in one second air travels 346 meters, and you want to find out how many meters air travels in 20 seconds, then just multiply 346 by 20.

4 0

3 years ago