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emmainna [20.7K]

1 year ago

10

If the first 3 terms of an infinite geometric sequence are 90, 22.5, and 5.625, then the sum of all the terms in the sequence is

______.

1 answer:

zhannawk [14.2K]1 year ago

3 0

The sum of all the terms in the sequence is 120

Step-by-step explanation:

The sum of the all terms in an infinite geometric sequence is

$S_{infinite}=\frac{a}{1-r}$ , where

a is the first term
r is the common ratio between each two consecutive terms
$r=\frac{a_{2}}{a_{1}}$ OR $r=\frac{a_{3}}{a_{2}}$

The sum of all terms in the infinite geometric sequence = $S_{infinite}$

∵ The first 3 terms of an infinite geometric sequence are 90, 22.5,

and 5.625

∴ a = 90

∵ $r=\frac{a_{2}}{a_{1}}$

∴ $r=\frac{22.5}{90}=0.25$

∵ $S_{infinite}=\frac{a}{1-r}$

∴ $S_{infinite}=\frac{90}{1-0.25}$

∴ $S_{infinite}=\frac{90}{0.75}$

∴ $S_{infinite}=120$

The sum of all the terms in the sequence is 120

Learn more:

You can learn more about sequences in brainly.com/question/3280369

#LearnwithBrainly

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Svetlanka [38]

Answer:

The standard deviation of car age is 2.17 years.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 7.5

(a) If 99.7% of the ages are between 1 year and 14 years, what is the standard deviation of car age?

This means that 1 is 3 standard deviations below the mean and 14 is 3 standard deviations above the mean.

So

$14 = 7.5 + 3\sigma$

I want to find $\sigma$

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The standard deviation of car age is 2.17 years.

8 0

2 years ago

Read 2 more answers

What is the 185th digit in the following pattern 12345678910111213141516

Delicious77 [7]

Answer:

The 185th digit following that pattern of '12345678910111213141516' would be the number '5'

Step-by-step explanation:

The reason the 185th digit is '5' is because the pattern increases it's standard number by the following number (ex, 1,2,3,4,5, etc), and eventually it reached 185 as one of it's numbers, '5' would be the digit because the '18' part of 185 would only be the 184th digit, hence you are needed to include the '5' to complete the sequence of that number to reach the 185th digit.

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2 years ago

186% of what is 56.73

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To do this problem, first you are going to want to turn 186% into a decimal which is 1.86. Now you put 56.73 over 1.86.................. 56.73/1.86.
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EXTRA.
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1 year ago

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Answer:

laptop: 14000

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Step-by-step explanation:

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phone: x

x + 3800 + x = 24200

2x + 3800 = 24200

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6 0

1 year ago

A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win $1.10; if

topjm [15]

Answer:

a) The expected value is $\frac{-1}{15}$

b) The variance is $\frac{49}{45}$

Step-by-step explanation:

We can assume that both marbles are withdrawn at the same time. We will define the probability as follows

#events of interest/total number of events.

We have 10 marbles in total. The number of different ways in which we can withdrawn 2 marbles out of 10 is $\binom{10}{2}$ .

Consider the case in which we choose two of the same color. That is, out of 5, we pick 2. The different ways of choosing 2 out of 5 is $\binom{5}{2}$ . Since we have 2 colors, we can either choose 2 of them blue or 2 of the red, so the total number of ways of choosing is just the double.

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Probability of winning: $\frac{2\binom{5}{2}}{\binom{10}{2}}= \frac{4}{9}$

Probability of losing $\frac{(\binom{5}{1})^2}{\binom{10}{2}}\frac{5}{9}$

Let X be the expected value of the amount you can win. Then,

E(X) = 1.10*probability of winning - 1 probability of losing = $1.10\cdot \frac{4}{9}-\frac{5}{9}=\frac{-1}{15}$

Consider the expected value of the square of the amount you can win, Then

E(X^2) = (1.10^2)*probability of winning + probability of losing = $1.10^2\cdot \frac{4}{9}+\frac{5}{9}=\frac{82}{75}$

We will use the following formula

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Thus

Var(X) = $\frac{82}{75}-(\frac{-1}{15})^2 = \frac{49}{45}$

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2 years ago