on the number line above, w,x,y, and z are the coordinates of the indicated points. which of the following is NOT true?

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

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

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.

This means that,

Probability that at least one of them needs replacement at the first inspection =

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

5 0

2 years ago

Use this graph of velocity vs. time for two objects to answer the question.

Lynna [10]

Using derivatives, it is found that the correct option is:

A. Object C has an acceleration that is greater than the acceleration for D.

The acceleration is the derivative of the velocity, given by change in velocity divided by change in time, that is:

$a = \frac{\Delta_v}{\Delta_t}$

In this problem:

The change in time for objects C and T is the same.
The change in velocity for object C is greater, thus, it has a greater acceleration, and the correct option is:

A. Object C has an acceleration that is greater than the acceleration for D.

A similar problem is given at brainly.com/question/14516604

6 0

2 years ago

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A 25% acid solution must be added to a 40% solution to get 240 liters of 30% acid solution. How many of each should be used ?

schepotkina [342]

Answer:

The number of liters of 25% acid solution = x = 160 liters

The number of liters of 40% acid solution = y = 80 liters

Step-by-step explanation:

Let us represent:

The number of liters of 25% acid solution = x

The number of liters of 40% acid solution = y

Our system of Equations =

x + y = 240 liters....... Equation 1

x = 240 - y

A 25% acid solution must be added to a 40% solution to get 240 liters of 30% acid solution.

25% × x + 40% × y = 240 liters × 30%

0.25x+ 0.4y = 72...... Equation 2

We substitute 240 - y for x in Equation 2

0.25(240 - y)+ 0.4y = 72

60 - 0.25y + 0.4y = 72

Collect like terms

- 0.25y + 0.4y = 72 - 60

0.15y = 12

y = 12/0.15

y = 80 Liters

Solving for x

x = 240 - y

x = 240 liters - 80 Liters

x = 160 liters

Therefore,

The number of liters of 25% acid solution = x = 160 liters

The number of liters of 40% acid solution = y = 80 liters

5 0

2 years ago

Is the statement true? explain 32 + (-17) is 17 units from 32, in the positive direction

Svetradugi [14.3K]

The equation is not true because
32-17 is not equal to 32 + 17
Hope it helps!
Plz give me brainliest answer

8 0

2 years ago

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Hi, can someone please help me? explain it, please!

alexdok [17]

Answer:

So overall its saying: to find your answer you have to divide the diameter (15 inches) by 3.14 to get your circumference ! :)

7 0

2 years ago

Read 2 more answers

on the number line above, w,x,y, and z are the coordinates of the indicated points. which of the following is NOT true? ​

on the number line above, w,x,y, and z are the coordinates of the indicated points. which of the following is NOT true?