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MrRissso [65]
3 years ago
6

An equation is shown below: 5(2x-8) +15 = -15 write the steps you will use to solve the equation and explain each step

Mathematics
2 answers:
faust18 [17]3 years ago
6 0

Answer:

5(2x-8)+15=-15

10x-40+15=-15

10x-25=-15

    +25   +25 (add 25 to both sides)

____________

10x=10

divide by 10 on both sides

x=1

lorasvet [3.4K]3 years ago
4 0

Answer:

x=1

Step-by-step explanation:

First youd distribute the 5 to the 2x-8 so that way you can combine like terms and make the equation smaller

10x - 40 + 15 = -15

combine the -40 and 15

10x - 25 = -15

add 25 to both sides to get 10x by itself on the one side. you have to add 25 to the -15 because the two sides must stay balanced

10x = 10

divide by 10 to get x by itself. you must divide since x is being multiplied by 10

x=1

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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

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Answer:

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Step-by-step explanation:

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so 4=2k+n and 0=-2k+n

now 4=2n so n=2

now k=1

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OLEGan [10]

Answer:

C and D

Step-by-step explanation:

Mathematically, a unit circle is one in which the value of the radius is 1 unit

Generally, for a unit circle we have it that;

r^2 = x^2 + y^2

where (x,y) represents the coordinates of a point on the unit circle

But from above, r = 1

Thus:

x^2 + y^2 = 1

Looking at option C, by squaring each coordinate, we have

(6/7)^2 = 36/49 and the second as 13/49

by adding both, we have

36/49 + 13/49 = 49/49 = 1

Thus, we have this as a coordinate on the unit circle

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(5/13)^2 = 25/169 and (12/13)^2 = 144/169

Adding both, we have;

25/169 + 144/169 = 169/169 = 1

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