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Alexeev081 [22]
3 years ago
11

HELP PLEASE ASAP! Tell how you found 2k + 10! 20 points!

Mathematics
1 answer:
Ivan3 years ago
8 0

Answer:

2(k+5)

Step-by-step explanation:

Factor 2k+10

2k+10

=2(k+5)

Answer:

2(k+5)

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A particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls invol
bagirrra123 [75]

Answer:

a) 0.214 = 21.4% probability that at most 4 of the calls involve a fax message

b) 0.118 = 11.8% probability that exactly 4 of the calls involve a fax message

c) 0.904 = 90.4% probability that at least 4 of the calls involve a fax message

d) 0.786 = 78.6% probability that more than 4 of the calls involve a fax message

Step-by-step explanation:

For each call, there are only two possible outcomes. Either it involves a fax message, or it does not. The probability of a call involving a fax message is independent of other calls. 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.

25% of the incoming calls involve fax messages

This means that p = 0.25

25 incoming calls.

This means that n = 25

a. What is the probability that at most 4 of the calls involve a fax message?

P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).

In which

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

P(X = 0) = C_{25,0}.(0.25)^{0}.(0.75)^{25} = 0.001

P(X = 1) = C_{25,1}.(0.25)^{1}.(0.75)^{24} = 0.006

P(X = 2) = C_{25,2}.(0.25)^{2}.(0.75)^{23} = 0.025

P(X = 3) = C_{25,3}.(0.25)^{3}.(0.75)^{22} = 0.064

P(X = 4) = C_{25,4}.(0.25)^{4}.(0.75)^{21} = 0.118

P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.001 + 0.006 + 0.025 + 0.064 + 0.118 = 0.214

0.214 = 21.4% probability that at most 4 of the calls involve a fax message

b. What is the probability that exactly 4 of the calls involve a fax message?

P(X = 4) = C_{25,4}.(0.25)^{4}.(0.75)^{21} = 0.118

0.118 = 11.8% probability that exactly 4 of the calls involve a fax message.

c. What is the probability that at least 4 of the calls involve a fax message?

Either less than 4 calls involve fax messages, or at least 4 do. The sum of the probabilities of these events is 1. So

P(X < 4) + P(X \geq 4) = 1

We want P(X \geq 4). Then

P(X \geq 4) = 1 - P(X < 4)

In which

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

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

P(X = 0) = C_{25,0}.(0.25)^{0}.(0.75)^{25} = 0.001

P(X = 1) = C_{25,1}.(0.25)^{1}.(0.75)^{24} = 0.006

P(X = 2) = C_{25,2}.(0.25)^{2}.(0.75)^{23} = 0.025

P(X = 3) = C_{25,3}.(0.25)^{3}.(0.75)^{22} = 0.064

P(X

P(X \geq 4) = 1 - P(X < 4) = 1 - 0.096 = 0.904

0.904 = 90.4% probability that at least 4 of the calls involve a fax message.

d. What is the probability that more than 4 of the calls involve a fax message?

Very similar to c.

P(X \leq 4) + P(X > 4) = 1

From a), P(X \leq 4) = 0.214)

Then

P(X > 4) = 1 - 0.214 = 0.786

0.786 = 78.6% probability that more than 4 of the calls involve a fax message

8 0
3 years ago
Find the distance between (-1,-2) and (8,9)
Rom4ik [11]

Answer:

\sqrt{202} units or 14.2 units (rounded to the nearest tenth)

Step-by-step explanation:

To find the distance between a pair of two points, use the distance formula  d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}. Substitute the x and y values of (-1,-2) and (8,9) into the formula and simplify:

d = \sqrt{(-1-8)^2+(-2-9)^2} \\d = \sqrt{(-9)^2+(-11)^2} \\d = \sqrt{81+121} \\d= \sqrt{202}  

So, as an exact answer, the distance is \sqrt{202} units.

(To find the decimal approximate of that answer, enter it into a calculator. This would make the decimal approximate 14.2 units, when rounded to the nearest tenth.)  

7 0
3 years ago
Read 2 more answers
Write an equation of the line passing through the points (4,10) and (-1,-15)
KATRIN_1 [288]

Answer:

Step-by-step explanation:

3 0
3 years ago
HELP I FORGOT TO PUT THE FILE IN SO HERE IT IS :)
xeze [42]

Answer:

0.525

21/40 as a decimal is 0.525.

3 0
3 years ago
Read 2 more answers
XYZ Software employed three different salespeople last year. Person 1
faltersainse [42]

Answer:

Total FUTA : $669.6

Step-by-step explanation:

Given the information

  • Person 1 earned $3900 in the first quarter  
  • Person 2 earned $20100 in the first quarter  
  • Person 3 earned $6900 in the first quarter

As we know, FUTA is short for Federal Unemployment Tax Act, and the FUTA tax rate is 6.2% applied to a maximum cumulative earnings of $7,000.

So in this situation, only person 1 and 2 must pay FUTA tax because ther earning are lower than $7,000.

  • Person 1: 3900 x 6.2% = $241.8
  • Person 3: 6,900 x 6.2% = $427.8

=> Total FUTA : $669.6

7 0
3 years ago
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