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2 years ago

The nth term of an AP is 12-4n. Find the first term and the common difference.

Mathematics

1 answer:

Virty [35]2 years ago

4 0

Answer:

the first term is 8 and common difference d is -4.

Step-by-step explanation:

We are given nth term of an arithmetic sequence is: aₙ=12-4n

We need to find first term and common difference of given arithmetic sequence

First term can be found by putting n=1:

$a_n=12-4n\\a_1=12-4(1)\\a_1=12-4\\a_1=8$

So, first term is a₁= 8

Now to find common difference we need to find second term

Second term can be found by putting n=2

$a_n=12-4n\\a_2=12-4(2)\\a_2=12-8\\a_2=4$

So, second term is: 4

The common difference is found by subtracting second term with first term: a₂-a₁= 4-8 = -4

So, first term is 8 and common difference d is -4

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The telephone company charges $1.35 fir the first 3 minutes of a phone call and $0.35 for each additional minute. i talk on the

irinina [24]

Answer:

$5.20

Step-by-step explanation:

Talked on the phone for 14 minutes .

14 - 3 = 11

11 x .35 = 3.85

3.85 + 1.35 = 5.2

8 0

2 years ago

Suppose that, in the past, 40% of all adults favored capital punishment. Do we have reason to believe that the proportion of adu

Alex_Xolod [135]

Answer:

The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.

Step-by-step explanation:

Suppose that, in the past, 40% of all adults favored capital punishment. Test if the proportion has increased:

At the null hypothesis, we test if the proportion is still of 40%, that is:

$H_0: p = 0.4$

At the alternative hypothesis, we test if the proportion has increased, that is, is greater than 40%, so:

$H_1: p > 0.4$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.4 is tested at the null hypothesis:

This means that $\mu = 0.4, \sigma = \sqrt{0.4*0.6}$

Random sample of 15 adults, 8 favor capital punishment.

This means that $n = 15, X = \frac{8}{15} = 0.5333$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.5333 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{15}}}$

$z = 1.05$

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion of 0.5333 or more, which is 1 subtracted by the p-value of z = 1.05.

Looking at the z-table, z = 1.05 has a p-value of 0.8531.

1 - 0.8531 = 0.1469.

3 0

2 years ago

What is the solution of 2|2x-1|-8=18?

Maurinko [17]

Solve for $|2x-1|$ :

$2|2x-1|-8=18\implies2|2x-1|=26\implies|2x-1|=13$

Now if $2x-1\ge0$ , we have $|2x-1|=2x-1$ and

$2x-1=13\implies2x=14\implies x=7$

On the other hand, if $2x-1$ , then $|2x-1|=-(2x-1)=1-2x$ and

$1-2x=13\implies-2x=12\implies x=-6$

4 0

2 years ago

Read 2 more answers

Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Dovator [93]

Answer:

1) yes 2) no 3) yes

Step-by-step explanation:

The lengths of the two shorter sides must be greater than the length of the longest side.

1) 8 + 9 > 10 yes

2) 1 + 1 = 2 no

3) 6 + 8 > 9 yes

8 0

2 years ago

Is 27/51 equal to 18/34

Nata [24]

Yes.
27/51-18/34=0
if something minus something is zero, then the 2 numbers subtracting each other are equal. :)

7 0

2 years ago

Read 2 more answers