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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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What is a derivative.

choli [55]

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2 years ago

Three less than eight times the number is equal to half of 16 times the number after it was increased by one

finlep [7]

Answer:

1) The question is aimed to determine the number that Laura is trying to come up with.

Such question is solved by stating an algebraic equation from the word statement, which is done step by step.

2) Using the name x for the unknown, the expression "three less than 8 times the number" is translated to: 8x - 3

3) The expression "half of 16 times the number after it was increased by 1" is translated to: (1/2) (16x + 1)

4) Finally, since they are equal, you can set the equation:

8x - 3 = (1/2) (16x + 1)

5) And solve for x in this way:

i) Distributive property:

8x - 3 = 8x + 1/2

ii) At this stage you can see that the both 8x terms (on the left and on the right) cancel each other, which leads to the impossibility to determine the value of the unknown:

-3 = 1/2 which is alwasy false, meaning that the equation has no solution.

Read more on Brainly.com - brainly.com/question/10888245#readmore

Step-by-step explanation:

hope it help

6 0

2 years ago

Calculate the mean given the frequency table

DaniilM [7]

Answer:

~15.55 is the mean.

Step-by-step explanation:

The class of frequency is given as 0-9, 10-19 and 20-29.

First of all, let us taken middle value of class:

$\dfrac{0+9}{2} = 4.5$

$\dfrac{10+9}{2} = 14.5$

$\dfrac{20+9}{2} = 24.5$

Formula for mean:

$\text{Mean = } \dfrac{\sum (m \times f)}{\sum f}$

where f is the frequency

and m is the mean value calculated in above step (4.5, 14.5 and 24.5)

The frequencies are given as:

4.5 - 24

14.5 - 20

24.5 - 32

Putting the values in above formula:

$Mean = \dfrac{4.5\times 24+14.5\times 20 +24.5\times 32}{24+20+32}\\\Rightarrow \dfrac{108+290+784}{76}\\\Rightarrow \dfrac{1182}{76} \\\Rightarrow 15.55$

Please refer to the attached image that contains the table for calculation of mean.

So, mean = ~15.55

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2 years ago

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kolezko [41]

Answer:

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2 years ago

Read 2 more answers

find the margin of error to use for this sample mean sushi based on a sample of 35 people he average out of pieces of sushi a pe

NNADVOKAT [17]

Answer:

{13.7756,18.2244}

Step-by-step explanation:

Given the sample size, the margin of error can be calculated with the formula $M=Z*\frac{\sigma}{\sqrt{n}}$ where Z is the critical value for the desired confidence level, σ is the population standard deviation, and n is the sample size. Therefore, our margin of error for a 90% confidence level is:

$M=Z*\frac{\sigma}{\sqrt{n}}=1.645*(\frac{8}{\sqrt{35}})=2.2244$

The formula for a confidence interval is $CI=\bar{x}+M$ where x-bar is the sample mean. Therefore, the 90% confidence interval for the mean amount of sushi pieces a person can eat is:

$CI=\bar{x}\pm[M]=16\pm2.2244={13.7756,18.2244}$

Therefore, we are 90% confident that the true mean amount of sushi pieces a person can eat is contained within the interval {13.7756,18.2244}

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2 years ago