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4 years ago

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Mathematics

1 answer:

NemiM [27]4 years ago

6 0

I’m only 70% positive about my answer, but I believe the answer is A) g(x) = |x+4| - 2.

If I’m correct, the numbers on the inside of the absolute marks are an indication of a horizontal shift of the function and you go the opposite direction of the sign. In this case, it’s a shift to the left (looking at the graph, 4) Then the outside number tells you how far you shift vertically (down 2, following the negative sign this time).

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Waiting on the platform, a commuter hears an announcement that the train is running five minutes late. He assumes the arrival ti

natima [27]

Answer:

D. 91%

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Less than 15 minutes.

Event B: Less than 10 minutes.

We are given the following probability distribution:

$f(T = t) = \frac{3}{5}(\frac{5}{t})^4, t \geq 5$

Simplifying:

$f(T = t) = \frac{3*5^4}{5t^4} = \frac{375}{t^4}$

Probability of arriving in less than 15 minutes:

Integral of the distribution from 5 to 15. So

$P(A) = \int_{5}^{15} = \frac{375}{t^4}$

Integral of $\frac{1}{t^4} = t^{-4}$ is $\frac{t^{-3}}{-3} = -\frac{1}{3t^3}$

Then

$\int \frac{375}{t^4} dt = -\frac{125}{t^3}$

Applying the limits, by the Fundamental Theorem of Calculus:

At $t = 15$ , $f(15) = -\frac{125}{15^3} = -\frac{1}{27}$

At $t = 5$ , $f(5) = -\frac{125}{5^3} = -1$

Then

$P(A) = -\frac{1}{27} + 1 = -\frac{1}{27} + \frac{27}{27} = \frac{26}{27}$

Probability of arriving in less than 15 minutes and less than 10 minutes.

The intersection of these events is less than 10 minutes, so:

$P(B) = \int_{5}^{10} = \frac{375}{t^4}$

We already have the integral, so just apply the limits:

At $t = 10$ , $f(10) = -\frac{125}{10^3} = -\frac{1}{8}$

At $t = 5$ , $f(5) = -\frac{125}{5^3} = -1$

Then

$P(A \cap B) = -\frac{1}{8} + 1 = -\frac{1}{8} + \frac{8}{8} = \frac{7}{8}$

If given the train arrived in less than 15 minutes, what is the probability it arrived in less than 10 minutes?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{7}{8}}{\frac{26}{27}} = 0.9087$

Thus 90.87%, approximately 91%, and the correct answer is given by option D.

3 0

3 years ago

What are some words that relate to geometry but are difficult to precisely define

Yuki888 [10]

Answer:

the point
the line
the plane

Step-by-step explanation:

8 0

3 years ago

Every bike at a sports store is on sale for 40% off the regular price. About how much would a bike cost that regularly sells for

Neko [114]

Answer:

$140-40%= 84

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

In a survey of 1,532 former UF students, 84% said they were still in love with Tim Tebow. The survey's sampling error was 2%. Us

nalin [4]

Answer:

confidence interval for the proportion of all former UF students who are still in love with Tim Tebow.

(0.79 , 0.89)

Step-by-step explanation:

step 1:-

Given sample survey former UF students n = 1532

84% said they were still in love with Tim Tebow

p = 0.84

The survey sampling error

$= \sqrt{\frac{p(1-p)}{n} }$

Given standard error of proportion = 2% =0.02

<u>Step 2</u>:-

The 99% of z- interval is 2.57

The 99% of confidence intervals are

p ± zₐ S.E (since sampling error of proportion = $\sqrt{\frac{pq}{n} }$

$(0.84 - 2.57X0.02 , 0.84 + 2.57X0.02)$

on simplification , we get

(0.84 - 0.0514 , 0.84 + 0.0514)

(0.79 , 0.89)

<u>conclusion</u>:-

confidence interval for the proportion of all former UF students who are still in love with Tim Tebow.

(0.79 , 0.89)

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3 years ago

The volume of a cylinder is 1280pi cm cubed. The radius is 8cm. Find the missing length.

Mademuasel [1]

Look take a picture of your problem and Brainly will get the answer for u just like that within 3 seconds

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3 years ago