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3 years ago

What is the sum of the geometric series: 3∑5(-2/3)^ii=0

1 answer:

7 0

We use the law of the sum of the 3 first terms of the geometric sequence:
$\sum_{i=0}^35\left(\dfrac{-2}{3}\right)^i=5\dfrac{1-\left(\dfrac{-2}{3}\right)^4}{1-\left(\dfrac{-2}{3}\right)}\\=5\dfrac{\left(\dfrac{3^4-2^4}{3^4}\right)}{\left(\dfrac{5}{3}\right)}\\=3\left(\dfrac{65}{81}\right)=\dfrac{65}{27}$

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(-3c+6) + (-c+8) simplify with a step by step please

mel-nik [20]

Step-by-step explanation:

$= ( - 3c + 6) + ( - c + 8)$

$= - 3c + 6 - c + 8$

$= - 3c - c + 6 + 8$

= -4c + 14

hence -4c + 14 is the answer ...

hope it helped !!

6 0

1 year ago

Gcf of 56f^3 g^2 and 70fg^3

yulyashka [42]

<span>56f^3 g^2 = 7fg^2(8f^2)
and
70fg^3 = 7fg^2(10g)

</span>Gcf of 56f^3 g^2 and 70fg^3 = 7fg^2

7 0

3 years ago

what equation is used to represent "three minus the difference of a number and one equals one-half of the difference of three ti

sesenic [268]

(n-1)-3=1/2(3n-4)
hope it hrlps

8 0

3 years ago

How many 3 letter words can be made from 4 letters “FGHI” if repetition is allowed and if repetition isn’t alllowed ?

PolarNik [594]

Answer:

1. Word: Fig

Definition: The hollow, pear-shaped false fruit of the fig tree, with sweet, pulpy flesh containing numerous tiny, seed-like true fruits.

2. Word: GIF

Definition: Is an image file that is compressed to allow it to be transferred quickly, or an animated gif which is a collection of images played in sequence to appear to move.

3. Word: Ghi

Definition: Uncountable (is also the alternative spelling of ghee)

Step-by-step explanation:

8 0

3 years ago

A company receives shipments of a component used in the manufacture of a component for a high-end acoustic speaker system. When

Tanya [424]

Answer:

$ME= 2.33*\sqrt{\frac{0.096*(1-0.096)}{250}}= 0.0434$

Step-by-step explanation:

For this case we have a sample size of n = 250 units and in this sample they found that 24 units failed one or more of the tests.

We are interested in the proportion of units that fail to meet the company's specifications, and we can estimate this with:

$\hat p = \frac{24}{250}= 0.096$

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The confidence interval for a proportion is given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 98% confidence interval the value of $\alpha=1-0.98=0.02$ and $\alpha/2=0.01$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.33$

And the margin of error would be:

$ME= 2.33*\sqrt{\frac{0.096*(1-0.096)}{250}}= 0.0434$

4 0

3 years ago