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sesenic [268]
2 years ago
12

What is the sum of the infinite geometric series? mc010-1.jpg

Mathematics
1 answer:
ra1l [238]2 years ago
4 0
You haven't provided the series, therefore, I can only help with the concept.

<u><em>For an infinite geometric series, we have two possibilities for the common ratio (r):</em></u>
for r > 1, the terms in the series will keep increasing infinitely and the only possible logic summation of the series would be infinity
for r < 1, the terms will decrease, therefore, we can formulate a rule to get the sum of the infinite series

<u><em>In an infinite series with r < 1, the summation can be found using the following rule:</em></u>
sum = \frac{a_{1} }{1-r}
where:
a₁ is the first term in the series
r is the common ratio

<u>Example:</u>
For the series:
2 , 1, 0.5 , 0.25 , ....
we have:
a₁ = 2
r = 0.5
Therefre:
sum = \frac{2}{1-0.5} = 4

Hope this helps :)
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A library buys 36 English books, 48 Science books and 72 Mathematics books. The thickness of each book is the same. Now, the lib
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Answer:

13

Step-by-step explanation:

The GCF of 36, 48, and 72 is 12 so there will be 36 / 12 = 3 stacks of English books, 48 / 12 = 4 stacks of science books and 72 / 12 = 6 stacks of math books for a total of 3 + 4 + 6 = 13 stacks.

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2 years ago
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Given a normal distribution with u = 75 and o = 40, if you select a sample of n = 16, a) what is the probability that the sample
Volgvan

Answer:

a) 0.0228

b) 94.6

Step-by-step explanation:

The formula for calculating a z-score when you are given a random.number of samples is z = (x-μ)/σ/√n

where x is the raw score

μ is the population mean

σ is the population standard deviation

n = random number of samples

Given a normal distribution with u = 75 and o = 40, if you select a sample of n = 16,

a) what is the probability that the sample mean is above 95? (4 d.p.) b)

= x = 95

Hence:

z = 95 - 75/40/√16

= 20/40/4

= 20/10

= 2

Probability value from Z-Table:

P(x<95) = 0.97725

P(x>95) = 1 - P(x<95) = 0.02275

The probability that the sample mean is above 95 to 4 decimal places = 0.0228

b) What is the value, of which there is 97.5% chance that a sample mean is less than that value?

97.5% chance = z score for the confidence interval = 1.96

Hence:

z = (x-μ)/σ/√n

1.96 = x - 75/40/√16

1.96 = x - 75/ 40/4

1.96 = x - 75/10

Cross Multiply

1.96 × 10 = x - 75

19.6 = x - 75

x = 19.6 + 75

x = 94.6

The value, of which there is 97.5% chance that a sample mean is less than that value is 94.6

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2 years ago
Let x = a + bi and y = c + di and z = f + gi Which statements are true? Check all of the boxes that apply. x + y = y + x (x × y)
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The usual rules of addition and multiplication apply to complex numbers as well as to real numbers. The true statements are ...

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2 years ago
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The table below shows the population of a town over x years. A 2-column table with 5 rows. The first column is labeled years wit
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Answer:

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Step-by-step explanation:

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8 0
2 years ago
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Which expression is equivalent to Negative 2 and one-fourth divided by negative two-thirds? StartFraction 9 over 4 EndFraction d
Tanzania [10]

Answer:

The correct answer is:

Negative StartFraction 9 over 4 EndFraction divided by two-thirds

i.e.

-\dfrac{9}{4} \div \dfrac{2}{3}

Step-by-step explanation:

We have to find equivalent expression to :

Negative 2 and one-fourth divided by negative two-thirds

i.e.

-2\dfrac{1}{4} \div \dfrac{2}{3} = ?

We have to convert the the mixed fraction form -2\frac{1}{4} to simpler \frac{p}{q} fraction form.

Let us learn the concept first.

Mixed fraction is combination of a whole number and a fraction.

Expression of the form a\frac{b}{c} have the following understanding:

c is the divider

b is the remainder and

a is the quotient.

To convert mixed fraction to fraction we can use the following:

a\dfrac{b}{c} = \dfrac{a \times c+b}{c}

\therefore -2\dfrac{1}{4} = -\dfrac{(2 \times 4+1)}{4} = -\dfrac{9}{4}

Hence

-2\dfrac{1}{4} \div \dfrac{2}{3} = -\dfrac{9}{4} \div \dfrac{2}{3}

i.e. the given expression is equivalent to :

Negative StartFraction 9 over 4 EndFraction divided by two-thirds

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