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3 years ago

If a geometric sequence has a1 = 256 and a8 = 512, find the exact value of the common ratio ????.

Mathematics

1 answer:

marusya05 [52]3 years ago

7 0

Answer:r=1.104

Step-by-step explanation:

Given

First term a_1=256

$a_8=512$

Also $a_8$ can also be written in

$a_8=ar^7$

where r=common difference

$512=256r^7$

$2=r^7$

$r=\left ( 2\right )^{\frac{1}{7}}$

r=1.104

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The estimated daily living costs for an executive traveling to various major cities follow. The estimates include a single room

Alexandra [31]

Answer:

$\bar x = 260.1615$

$\sigma = 70.69$

The confidence interval of standard deviation is: $53.76$ to $103.25$

Step-by-step explanation:

Given

$n =20$

See attachment for the formatted data

Solving (a): The mean

This is calculated as:

$\bar x = \frac{\sum x}{n}$

So, we have:

$\bar x = \frac{242.87 +212.00 +260.93 +284.08 +194.19 +139.16 +260.76 +436.72 +355.36 +.....+250.61}{20}$

$\bar x = \frac{5203.23}{20}$

$\bar x = 260.1615$

$\bar x = 260.16$

Solving (b): The standard deviation

This is calculated as:

$\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}$

$\sigma = \sqrt{\frac{(242.87 - 260.1615)^2 +(212.00- 260.1615)^2+(260.93- 260.1615)^2+(284.08- 260.1615)^2+.....+(250.61- 260.1615)^2}{20 - 1}}$ $\sigma = \sqrt{\frac{94938.80}{19}}$

$\sigma = \sqrt{4996.78}$

$\sigma = 70.69$ --- approximated

Solving (c): 95% confidence interval of standard deviation

We have:

$c =0.95$

So:

$\alpha = 1 -c$

$\alpha = 1 -0.95$

$\alpha = 0.05$

Calculate the degree of freedom (df)

$df = n -1$

$df = 20 -1$

$df = 19$

Determine the critical value at row $df = 19$ and columns $\frac{\alpha}{2}$ and $1 -\frac{\alpha}{2}$

So, we have:

$X^2_{0.025} = 32.852$ ---- at $\frac{\alpha}{2}$

$X^2_{0.975} = 8.907$ --- at $1 -\frac{\alpha}{2}$

So, the confidence interval of the standard deviation is:

$\sigma * \sqrt{\frac{n - 1}{X^2_{\alpha/2} }$ to $\sigma * \sqrt{\frac{n - 1}{X^2_{1 -\alpha/2} }$

$70.69 * \sqrt{\frac{20 - 1}{32.852}$ to $70.69 * \sqrt{\frac{20 - 1}{8.907}$

$70.69 * \sqrt{\frac{19}{32.852}$ to $70.69 * \sqrt{\frac{19}{8.907}$

$53.76$ to $103.25$

8 0

3 years ago

7 2,451 people came to watch the Easter parade. 745 of those people were adults. How many children came to the parade?

lukranit [14]

Take to total number of people attending and subtract the number of adults. The remainder are the children

2,451 - 745 = 1,706

7 0

3 years ago

Witch method can be used to find the area of the composite shape?

Setler79 [48]

No idea because there is no image

6 0

3 years ago

Joseph and Wendy were catching tadpoles. At first Wendy caught nine times three more than Joseph caught. Joseph was upset and re

Dmitriy789 [7]

Answer:

Joseph caught 7 tadpoles

Step-by-step explanation:

Let the number of tadpoles caught by Joseph be x

The number of tadpoles Wendy caught will be ;

9(x + 3)

After Joseph was upset, he released half of Wendy’s tadpole and then six times as many as Joseph caught swam away leaving Wendy with only three tadpoles left;

Hence, mathematically;

9(x + 3)/2 - 6x = 3

Multiply through be 2

9(x + 3) - 12x = 6

9x + 27 -12x = 6

9x -12x = 6-27

3x = 21

x = 21/3

x = 7

6 0

3 years ago

The enrollment for a new program is 1,500 students. the program is expected to grow at a rate of 0.03. what is the expected enro

Hatshy [7]

The expected enrolment in 7 years is 1845.

<h3>What is the expected enrolment?
</h3>

The formula for calculating future value of the number of students is an exponential equation with this form:

FV = P (1 + r) ^n

FV = Future population
P = Present population
R = rate of growth of the population
N = number of years

1500 x (1.03)^7 = 1845

To learn more about future value, please check: brainly.com/question/18760477

#SPJ1

3 0

2 years ago