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lara [203]
3 years ago
15

The quotient of 20 and 3 more than x is 4. Find x.

Mathematics
2 answers:
tigry1 [53]3 years ago
4 0

Answer:

x=2

Step-by-step explanation:

Quotient means division

20/(x+3) =4

Multiply each side by (x+3)

(x+3)*20/(x+3) =4(x+3)

20 = 4(x+3)

Divide each side by 4

20/4 = 4(x+3)/4

5 = x+3

Subtract 3 from each side

5-3 = x+3-3

2 =x

Lemur [1.5K]3 years ago
4 0

Answer:

x=2

Step-by-step explanation:

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The life of a red bulb used in a traffic signal can be modeled using an exponential distribution with an average life of 24 mont
BartSMP [9]

Answer:

See steps below

Step-by-step explanation:

Let X be the random variable that measures the lifespan of a bulb.

If the random variable X is exponentially distributed and X has an average value of 24 month, then its probability density function is

\bf f(x)=\frac{1}{24}e^{-x/24}\;(x\geq 0)

and its cumulative distribution function (CDF) is

\bf P(X\leq t)=\int_{0}^{t} f(x)dx=1-e^{-t/24}

• What is probability that the red bulb will need to be replaced at the first inspection?

The probability that the bulb fails the first year is

\bf P(X\leq 12)=1-e^{-12/24}=1-e^{-0.5}=0.39347

• If the bulb is in good condition at the end of 18 months, what is the probability that the bulb will be in good condition at the end of 24 months?

Let A and B be the events,

A = “The bulb will last at least 24 months”

B = “The bulb will last at least 18 months”

We want to find P(A | B).

By definition P(A | B) = P(A∩B)P(B)

but B⊂A, so  A∩B = B and  

\bf P(A | B) = P(B)P(B) = (P(B))^2

We have  

\bf P(B)=P(X>18)=1-P(X\leq 18)=1-(1-e^{-18/24})=e^{-3/4}=0.47237

hence,

\bf P(A | B)=(P(B))^2=(0.47237)^2=0.22313

• If the signal has six red bulbs, what is the probability that at least one of them needs replacement at the first inspection? Assume distribution of lifetime of each bulb is independent

If the distribution of lifetime of each bulb is independent, then we have here a binomial distribution of six trials with probability of “success” (one bulb needs replacement at the first inspection) p = 0.39347

Now the probability that exactly k bulbs need replacement is

\bf \binom{6}{k}(0.39347)^k(1-0.39347)^{6-k}

<em>Probability that at least one of them needs replacement at the first inspection = 1- probability that none of them needs replacement at the first inspection. </em>

This means that,

<em>Probability that at least one of them needs replacement at the first inspection =  </em>

\bf 1-\binom{6}{0}(0.39347)^0(1-0.39347)^{6}=1-(0.60653)^6=0.95021

5 0
3 years ago
Mr .Cruz is the director of an after school program. He says that 170 or 85%of the students went on to attend collage. A parent
Nimfa-mama [501]

Answer:

  200 students were in the program

Step-by-step explanation:

The parent should know how to figure ...

  170/85% = total/100%

This is the same as ...

  total = 170/0.85 = 200

200 students were in the program.

_____

<em>Critical Thinking</em>

There are three declarative statements here. <em>There is no question</em>. We have made up a question to answer.

Another possible answer to the non-question could be, "The parent can ask his student how many students were in the program."

3 0
3 years ago
X+3y=23<br> x-2y=-17 <br> elimaiton
VMariaS [17]
<h2><u>ANSWER</u></h2>

y = 8

x= -1

Step-by-step explanation:

hope it helps ✌️✌️

6 0
2 years ago
Given that the expression 2x^3 + mx^2 + nx + c leaves the same remainder when divided by x -2 or by x+1 I prove that m+n =-6
Alla [95]

Given:

The expression is:

2x^3+mx^2+nx+c

It leaves the same remainder when divided by x -2 or by x+1.

To prove:

m+n=-6

Solution:

Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).

Let the given polynomial is:

P(x)=2x^3+mx^2+nx+c

It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that

P(2)=P(-1)              ...(i)

Substituting x=-1 in the given polynomial.

P(-1)=2(-1)^3+m(-1)^2+n(-1)+c

P(-1)=-2+m-n+c

Substituting x=2 in the given polynomial.

P(2)=2(2)^3+m(2)^2+n(2)+c

P(2)=2(8)+m(4)+2n+c

P(2)=16+4m+2n+c

Now, substitute the values of P(2) and P(-1) in (i), we get

16+4m+2n+c=-2+m-n+c

16+4m+2n+c+2-m+n-c=0

18+3m+3n=0

3m+3n=-18

Divide both sides by 3.

\dfrac{3m+3n}{3}=\dfrac{-18}{3}

m+n=-6

Hence proved.

7 0
3 years ago
Billy Found The Slope of the line through the points (2,5) and (-2, -5) using the equation shown in the picture below. What mist
Nady [450]

Answer: the numbers were negative so he needed to add the positive numbers to that equation (I think sorry if I’m wrong)

Step-by-step explanation:

7 0
2 years ago
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