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Alekssandra [29.7K]

4 years ago

10

Consider the sequence 130, 143, 156, 169, ... Write an explicit formula to represent the arithmetic sequence and use it to find

the 13th term.

1 answer:

pantera1 [17]4 years ago

4 0

<u>Answer:</u>

a(n) = 130 + (n-1) 13

13th term = 286

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

We are given a sequence of numbers: 130, 143, 156, 169, ... and we are to write an explicit formula to represent the arithmetic sequence and use it to find the 13th term.

We know that the arithmetic sequence can be defined by:

$a_n=d(n-1)+c$

where $d$ = the common difference between consecutive terms ; and

$c$ = $a_1$

<u>13th term:</u>

$a_{13}=130+(12)13 = 286$

Therefore, the formula for this sequence will be a(n) = 130 + (n-1) 13 and 13th term is 286.

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4 0

3 years ago

Read 2 more answers

12. Use these functions to answer this question.

stira [4]

$p(x)=x^2-x-6$

$q(x)=x-3$

$p(x)-q(x)=x^2-x-6-(x-3)=x^2-x-6-x+3=\boxed{x^2-2x-3}$

The answer is C.

Hope this helps.

6 0

3 years ago

FURNITURE A modern table is constructed with four legs made

Troyanec [42]

The volume of a shape is the amount of space in it.

The expression that represents the volume of one table leg is: $V = l^3 + n^3$
The sides of the legs is 14.37 inches long

<u>(a) The volume of one table leg</u>

Represent the side length of the leg with l, and the side length of the notch with n.

So, the expression that represents the volume of one table leg is:

$V = l^3 + n^3$

<u>(b) The length of the sides</u>

From the question, we have:

$n = 40\% \times l$

Express 40% as decimal

$n = 0.40 \times l$

$n = 0.4l$

Substitute 0.4l for n in $V = l^3 + n^3$

$V =l^3 + (0.4l)^3$

$V =l^3 + 0.064l^3$

$V =1.064l^3$

The volume of the 4 legs is given as: 12636

So, the volume of one leg would be 12636/4

So, we have:

$1.064l^3 = \frac{12636}{4}$

$1.064l^3 = 3159$

Divide both sides by 1.064

$l^3 = 2968.985$

Take cube roots of both sides

$l = 14.37$

Hence, the sides of the legs is 14.37 inches long

Read more about volumes at:

brainly.com/question/1972490

7 0

2 years ago

An aptitude test is designed to measure leadership abilities of the test subjects. Suppose that the scores on the test are norma

Komok [63]

Using the normal distribution, it is found that 0.0329 = 3.29% of the population are considered to be potential leaders.

In a <em>normal distribution</em> with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.

After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

The mean is of 550, hence $\mu = 550$ .

The standard deviation is of 125, hence $\sigma = 125$ .

The proportion of the population considered to be potential leaders is <u>1 subtracted by the p-value of Z when X = 780</u>, hence:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{780 - 550}{125}$

$Z = 1.84$

$Z = 1.84$ has a p-value of 0.9671.

1 - 0.9671 = 0.0329

0.0329 = 3.29% of the population are considered to be potential leaders.

To learn more about the normal distribution, you can take a look at brainly.com/question/24663213

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2 years ago

HELP PLEASE I WILL GIVE YOU BRAINLESS

Svetllana [295]

Answer:

Step-by-step explanation:

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5 0

3 years ago