Break apart the number you are subtracting write the different 73-7=

Which formula can be used to find the nth term of a geometric sequence where the fifth term is 1/6 and the common ratio is 1/4?

OlgaM077 [116]

Answer:

$a_n = 16(\frac{1}{4})^{n - 1}$

Step-by-step explanation:

Given:

Fifth term of a geometric sequence = $\frac{1}{16}$

Common ratio (r) = ¼

Required:

Formula for the nth term of the geometric sequence

Solution:

Step 1: find the first term of the sequence

Formula for nth term of a geometric sequence = $ar^{n - 1}$ , where:

a = first term

r = common ratio = ¼

Thus, we are given the 5th term to be ¹/16, so n here = 5.

Input all these values into the formula to find a, the first term.

$\frac{1}{16} = a*\frac{1}{4}^{5 - 1}$

$\frac{1}{16} = a*\frac{1}{4}^{4}$

$\frac{1}{16} = a*\frac{1}{256}$

$\frac{1}{16} = \frac{a}{256}$

Cross multiply

$1*256 = a*16$

Divide both sides by 16

$\frac{256}{16} = \frac{16a}{16}$

$16 = a$

$a = 16$

Step 2: input the value of a and r to find the nth term formula of the sequence

nth term = $ar^{n - 1}$

nth term = $16*\frac{1}{4}^{n - 1}$

$a_n = 16(\frac{1}{4})^{n - 1}$

3 0

2 years ago

Let x be the first factor in an expression in scientific notation. Describe the possible values of x.

Igoryamba

What are some problems that can occur when using overrides? Check all that apply.

The style guide may become cluttered.Text with overrides can’t be exported to other documents.Word won’t allow you to use more than 10 styles in a document.<span>Text with the override won’t respond when changes are made to its original style.</span>

6 0

3 years ago

If 3x + 6 = 213x plus 6 equals 21, what does x + 2x plus 2 equal?

Ludmilka [50]

Answer:

17

Step-by-step explanation:

PLS GIVE BRAINLIEST

5 0

3 years ago

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For parts a and bâ, use technology to estimate the following. âa) The critical value of t for a 90â% confidence interval with df

rjkz [21]

Answer:

a) For the 90% confidence interval the value of $\alpha=1-0.9=0.1$ and $\alpha/2=0.05$ , with that value we can find the quantile required for the interval in the t distribution with df =3. And we can use the folloiwng excel code: "=T.INV(0.05,3)" and we got:

$t_{\alpha/2} =\pm 2.35$

b) For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the t distribution with df =106. And we can use the folloiwng excel code: "=T.INV(0.005,106)" and we got:

$t_{\alpha/2} =\pm 2.62$

Step-by-step explanation:

Previous concepts

The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".

The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.

The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."

Solution to the problem

Part a

For the 90% confidence interval the value of $\alpha=1-0.9=0.1$ and $\alpha/2=0.05$ , with that value we can find the quantile required for the interval in the t distribution with df =3. And we can use the folloiwng excel code: "=T.INV(0.05,3)" and we got:

$t_{\alpha/2} =\pm 2.35$

Part b

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the t distribution with df =106. And we can use the folloiwng excel code: "=T.INV(0.005,106)" and we got:

$t_{\alpha/2} =\pm 2.62$

3 0

3 years ago

Twenty thousand six hundred and seven written in expanded form is

baherus [9]

Answer:

20000+600+7

Step-by-step explanation:

4 0

2 years ago

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