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3 years ago

What’s a general equation of an arithmetic series

Mathematics

1 answer:

lana66690 [7]3 years ago

5 0

The general equation of an arithmetic series is $a_{n} + a_{1} + (n - 1) d$

<em>Hope this helps! :) from peachimin</em>

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Choose the graph of the function <br><br>g(x) = 2 x 4^x

dexar [7]

Answer:

its B

Step-by-step explanation:

hope it helped you

8 0

3 years ago

Solve the inequation 2x -3(3x-4)>_8

svlad2 [7]

Answer:

x≤47

Step-by-step explanation:

2x−3(3x−4)≥8

Step 1: Simplify both sides of the inequality.

−7x+12≥8

Step 2: Subtract 12 from both sides.

−7x+12−12≥8−12

−7x≥−4

Step 3: Divide both sides by -7.

−7x−7≥−4−7x≤47

Answer:x≤47

8 0

3 years ago

Solve: -8 = -7 + x X =

Amanda [17]

Answer:

Your question is not correct.

8 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

It is 90 ft between the bases of baseball diamond. A catcher throws a baseball to the shortstop who is half-way between second a

Hunter-Best [27]

Answer:

127.3 ft

Step-by-step explanation:

A baseball diamond is constructed in a square shape.

The sides are 90 ft each

If a catcher throws a baseball to the shortstop who is half-way between second and third bases, the distance between the third base and the short stop = 1/2(90)

= 45 ft

length of the throw is found using Pythagoras theorem.

Hypothenus ^2 = opposite ^2 + adjacent ^2

= 90^2 + 45^2

Hypothenus = √8100 + 2025

=√10125

= 100.62 ft (approximately)

8 0

3 years ago