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larisa [96]
3 years ago
9

What are the zeros of g(x)=(3x-1)(2x+5)(7x-14)^2

Mathematics
1 answer:
EastWind [94]3 years ago
6 0

The zeros are x= 1/3, 5/2, 2

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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
Which number line best represents the solutions to 7 &lt; -2x + 3?
OleMash [197]

Answer:

we need a number line for this question...

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
How can I solve this? 10+x = 5(1/5x + 2)
pshichka [43]
You use PEMDAS. Start by distributing the terms in the parentheses. The isolate the variables. To do that you subtract x from one side of the equation to the other side. You always do the other operation. If it is adding you subtract, if your multiplying your dividing and the other way around. Then you subtract 10 from each side. This equation has many solution because all the terms cancel out.
5 0
3 years ago
Whats the answer tell me please
ANEK [815]
For y=3x+4, you would put 4 on the y-intercept and from that point you go up 3 and right 1 and then plot the second point.

For y=-x-4, you would put -4 on the y-intercept and from that point go down 1 and right 1 and then plot the second point.
6 0
3 years ago
What is the intersection of the given lines?
Sophie [7]
Point D that is the intersection of the the given lines
8 0
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