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3 years ago

7

A father promises to pay his son $5.00 for each correct answer he obtains in his math homework. For each incorrect answer, the s

on must pay his father $8.00. The boy answered twenty-six math questions. At the end, no money was exchanged.

1 answer:

bogdanovich [222]3 years ago

6 0

He got 16 questions right (5x16=80) and 10 wrong (8x10=80) He got paid $80 but also had to pay $80.

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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 is 10% of 7/8 of 160

olga55 [171]

Answer:

14

7/8of 160=140

140×10=1400

1400÷100=14

4 0

2 years ago

Someone grew an average of 0.5 cm per month last year. How many inches did they grow in a year.

ivolga24 [154]

One inch is equivalent to 2.54 centimeters. if they grew .5(12)=6 cm then you would.divide six by 2.54 and get approximately 2.36inches

6 0

3 years ago

39 is 84% of what number

Sati [7]

Answer=46.43

39 84
___=____
x 100

cross multiply
84x=3900
divide both sides by 84
x=46.43

7 0

4 years ago

Read 2 more answers

How do you find an exponential function given the points are (0,13) and (2,325)

slava [35]

Answer:

y = 13 $(5)^{x}$

Step-by-step explanation:

An exponential function has the form

y = a $b^{x}$

To find a and b use the given points

Using (0, 13), then

13 = a $b^{0}$ , since $b^{0}$ = 1, then

a = 13, thus

y = 13 $b^{x}$

using (2, 325) , then

325 = 13 b² ( divide both sides by 13 )

25 = b² ( take the square root of both sides )

5 = b

y = 13 × $5^{x}$ ← is the exponential function

4 0

3 years ago