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2 years ago

What’s the 38th term of the arithmetic sequence 31,40,49,58?

Mathematics

1 answer:

Trava [24]2 years ago

3 0

Answer:

$a_3_8=364$

Step-by-step explanation:

we know that

In an <u><em>Arithmetic Sequence</em></u> the difference between one term and the next is a constant, and this constant is called the common difference

we have

$31,40,49,58,...$

Let

$a_1=31\\a_2=40\\a_3=49\\a_4=58$

we have that

$a_2-a_1=40-31=9$

$a_3-a_2=49-40=9$

$a_4-a_3=58-49=9$

The common difference is equal to 9

We can write an Arithmetic Sequence as a rule:

$a_n=a_1+d(n-1)$

where

a_n is the nth term

a_1 is the first term

d is the common difference

n is the number of terms

Find the 38th term of the arithmetic sequence

we have

$a_1=31\\d=9\\n=38$

substitute the values

$a_3_8=31+9(38-1)$

$a_3_8=31+9(37)$

$a_3_8=364$

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1.17 A study of the effects of smoking on sleep patterns is conducted. The measure observed is the time, in minutes, that it tak

bearhunter [10]

Answer:

$\bar X_F=43.7$

$\bar X_{NF}=30.32$

$S_F=16.9278$

$S_{NF}=7.12783$

Attached file

Apparently the practice of smoking reduces the ability to fall asleep, demanding much more time in individuals who smoke, than in those who do not smoke.

Step-by-step explanation:

a, b) For the group of smoking individuals, the average time it takes to fall asleep and the standard deviation of those times is:

$\bar X_F={\frac{1}{n} \sum_{i=1}^n x_i = 43.7$

$S_F=\sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i-\bar{x})^2}=16.9278$

a, b) For the group of non-smoking individuals, the average time it takes to fall asleep and the standard deviation of those times is:

$\bar X_{NF}={\frac{1}{n} \sum_{i=1}^n x_i = 30.32$

$S_{NF}=\sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i-\bar{x})^2}=7.12783$

c. In the attached file you can see the diagram of points for the times, in the smoking and non-smoking groups.

d. Apparently the practice of smoking reduces the ability to fall asleep, demanding much more time in individuals who smoke, than in those who do not smoke.

Download pdf

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2 years ago

How many solutions does the following equation have? 60z+50-97z=-37z+4960z+50−97z=−37z+49

Tpy6a [65]

Copy question and paste it and it will show up trust

8 0

2 years ago

Most US adults have social ties with a large number of people, including friends, family, co-workers, and other acquaintances. I

xxTIMURxx [149]

Answer:

$t=\frac{669-634}{\frac{732}{\sqrt{1700}}}=1.971$

$p_v =2*P(t_{(1699)}>1.971)=0.049$

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is different from 634 at 10% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=669$ represent the sample mean

$s=732$ represent the sample standard deviation

$n=1700$ sample size

$\mu_o =68$ represent the value that we want to test

$\alpha=0.$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is different from 634, the system of hypothesis would be:

Null hypothesis: $\mu = 634$

Alternative hypothesis: $\mu \neq 634$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{669-634}{\frac{732}{\sqrt{1700}}}=1.971$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=1700-1=1699$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(1699)}>1.971)=0.049$

Conclusion

3 0

2 years ago

Jackie bought a 3-pack of tubes of glue. She used 0.27 ounce of the glue from the 3-pack

adell [148]

This question is not correct because one of its options was not written correctly.

Correct question:

Jackie bought a 3-pack of tubes of glue. She used 0.27 ounce of the glue from the 3-pack

and had 1.35 ounces left in total. Which describes a way to determine the number of ounces

sold in each tube of glue?

a) Solve for x in the equation 3x - 0.27 = 1.35.

b) Divide 1.35 by 3 and then subtract 0.27 from the quotient.

c) Subtract 0.27 from 1.35 and the divide the difference by 3.

d) Solve for w in the equation 3 (x - 0.27) = 1.35.

Answer:

a) Solve for x in the equation 3x - 0.27 = 1.35.

Step-by-step explanation:

From the question we are told that 0.27 ounces of glue was sold from a 3 pack glue and we have 1.35 ounces of glue left in total.

The first step would be represent the 3 pack of glue as 3x where x represents each pack of the glue.

Therefore, mathematically, we have the Algebraic equation:

3x - 0.27 = 1.35..... Equation 1

This is because when we solve for x, we would be able to find the number of ounces sold in each tube.

Solving for x in the equation 3x - 0.27 = 1.35.

3x - 0.27 = 1.35.

3x = 1.35 + 0.27

3x = 1.62 ...... Equation 2

3x = The three pack tube containing the glue.

Where x represents each of the tubes.

This means, the three pack tube contained 1.62 ounces of glue.

To find out he amount of glue sold from each pack, we go back to our equation 2

3x = 1.62

x = 1.62 ÷ 3

x = 0.54 ounces.

This means from each tubes, 0.54 ounces of glue was sold.

Therefore, Option a) "Solve for x in the equation 3x - 0.27 = 1.35" is correct.

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2 years ago

What is the completely factored form 8x2-50y2?

lorasvet [3.4K]

Remember
a²-b²=(a-b)(a+b)

8x²-50y²
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2 years ago