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3 years ago

Write an explicit formula for an the nth term of the sequence 8, 48, 288

Mathematics

1 answer:

ira [324]3 years ago

5 0

Answer:

Step-by-step explanation:

a₁ = 8

a₂ = 48

Common ratio r = a₂/a₁ =6

nth term = a₁rⁿ⁻¹

= 8×6ⁿ⁻¹

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A cylinder has a base of a radius of 10in and a height of 10in. What is its volume in cubic in, to the nearest tenths place?

pantera1 [17]

Answer:

3141.6 in^3

Step-by-step explanation:

The formula for volume of a right cylinder is v=πr²h. So, when you plug everything in and multiply, you get 3141.6 in^3 as your volume. Hope this helps, and stay safe! ;p

7 0

3 years ago

The probability that your call to a service line is answered in less than 30 seconds is 0.75. Assume that your calls are indepen

vfiekz [6]

Answer:

a) 0.2581

b) 0.4148

c) 17

Step-by-step explanation:

For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$p = 0.75$

a. If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X = 9)$ when $n = 12$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{12,9}.(0.75)^{9}.(0.25)^{3} = 0.2581$

b. If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X \geq 16)$ when $n = 20$

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 16) = C_{20,16}.(0.75)^{16}.(0.25)^{4} = 0.1897$

$P(X = 17) = C_{20,17}.(0.75)^{17}.(0.25)^{3} = 0.1339$

$P(X = 18) = C_{20,18}.(0.75)^{18}.(0.25)^{2} = 0.0669$

$P(X = 19) = C_{20,19}.(0.75)^{19}.(0.25)^{1} = 0.0211$

$P(X = 20) = C_{20,20}.(0.75)^{20}.(0.25)^{0} = 0.0032$

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1897 + 0.1339 + 0.0669 + 0.0211 + 0.0032 = 0.4148$

c. If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.

The expected value of the binomial distribution is:

$E(X) = np$

In this question, we have $n = 22$

$E(X) = 22*0.75 = 16.5$

The closest integer to 16.5 is 17.

7 0

3 years ago

Reciprocal of. 0×7/11

Tpy6a [65]

Answer:

it doesn't exist

Step-by-step explanation:

the expression 0×7/11 is equivalent to 0. 1/0 isn't possible, so its reciprocal doesn't exist.

8 0

3 years ago

You bought a used truck for $15,000. The value of the truck will decrease each year because of depreciation. The truck depreciat

Vesna [10]

Answer: $9886.22

Step-by-step explanation:

6 0

3 years ago

The distance around a meteor crater is 9,033ft. Find the diameter of the crater. Use 22/7 for pi. Round to the nearest tenth

Aleonysh [2.5K]

<span>We know that the circumference of a circle is equal to pi times the diameter of the circle. Therefore, assuming this crater to be circular in shape, we can divide the circumference by pi, in this case 9033*7/22, yielding an answer of 2874.1 feet after rounding.</span>

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3 years ago