A drone is flying at kilometers per hour at a constant altitude of km above a straight road. The drone pilot uses radar to determine that an oncoming motorcycle is at a distance of exactly kilometers from the drone, and that this distance is decreasing at kph. Find the speed of the motorcycle. Note: Round to the nearest hundredth. Hint: At the end, remember to consider that the drone is moving towards the motorcycle at kph. Speed cannot be negative. Note: Round to the nearest tenth.

a) The cumulative distribution function F of X is: F(x) = P(X ≤ x) = 1

b) The mean E(X) is: E(X) = 0.5 hours.

c) The variance Var(X) is: the variance of X is approximately 0.0833 hours².

To find the cumulative distribution function (CDF) of X, we need to consider two cases: when the boy comes back inside before 45 minutes and when the boy is brought inside by his mother after 45 minutes.

(a) Cumulative Distribution Function (CDF) F of X:

For 0 ≤ x < 0.75 (when the boy comes back inside before 45 minutes):

Since the boy comes back inside uniformly distributed on the interval [0, 1], the CDF is simply the probability that the boy comes back inside before time x.

The probability of the boy coming back inside before x is equal to x, as it is a uniform distribution.

F(x) = P(X ≤ x) = x

For 0.75 ≤ x ≤ 1 (when the mother brings the boy inside after 45 minutes):

If the boy is not back inside at 45 minutes (0.75 hours), his mother brings him inside.

Therefore, the probability of the boy coming back inside before x in this case is 1.

F(x) = P(X ≤ x) = 1

(b) Mean (Expected Value) E(X):

The expected value of X, denoted by E(X), is the average time the boy spends outside before coming back inside.

For a uniform distribution on the interval [0, 1], the expected value is the midpoint of the interval.

Therefore, E(X) = (1 + 0) / 2 = 0.5 hours.

(c) Variance Var(X):

The variance of X, denoted by Var(X), measures the spread or variability of the random variable X around its mean.

For a uniform distribution on the interval [0, 1], the variance is given by:

Var(X) = (1² - 0²) / 12 = 1 / 12 ≈ 0.0833 hours²

So, the variance of X is approximately 0.0833 hours².

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Answer:

Kindly check explanation

Step-by-step explanation:

Verbal:

Score, x = 560

Mean, m = 460

Standard deviation, s = 132

Quantitative :

Score, x = 740

Mean, m = 452

Standard deviation, s = 140

a)

Verbal :

X ~ N(460, 132)

Quantitative :

X ~ N(452, 140)

(b)

What is her Z score on the Verbal Reasoning section? On the Quantitative Reasoning section? Draw a standard normal distribution curve and mark these two Z scores.

Zscore = (x - m) / s

Verbal :

Zscore = (560 - 460) / 132 = 0.758

Quantitative :

Zscore = (740 - 452) /140 = 2.057

(c.)

He has a higher standardized score in the quantitative than the verbal score.

(d.)

The Zscore shows that he performed better in the quantitative reasoning than verbal.

(e) Find her percentile scores for the two exams.

(f) What percent of the test takers did better than her on the Verbal Reasoning section? On the Quantitative Reasoning section?

Verbal :

Score greater than 560

P(x > 560) :

Z = (560 - 460) / 132 = 0.758

P(Z > 0.758) = 0.22423 = 22.4%

Quantitative :

Score greater than 740

P(x > 740) :

Z = (740 - 452) / 140 = 2.057

P(Z > 0.758) = 0.0198 = 1.98%

Answer: y=4x-2 and y=4x+3

Answer:

430/ 7

Step-by-step explanation:

yess this is the correct answer

Answer:

2(2x+5)=8x-18

2x+5=4x-9

2x=14

x=7

MN=2*7+5=19

Step-by-step explanation:

Answer:

So.

The correct is (C, D, E and F)

And (A and B) isn't correct

Step-by-step explanation:

I hope that is useful for you :)

Answer:

Domain is all real numbers.

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

A coefficient is the number that is attached to the variable.

In this case, the number attached to the variable is 20.

Therefore, the coefficient is 20

hope this helps :)

Answer:

4.9

Step-by-step explanation:

100% of 2.45 is 2.45.

We add 2.45 + 2.45 which is 4.9.

Can I get brainliest?

Answer:

19.60

Step-by-step explanation:

Answer:

I am not sure honestly, but I think you should

Step-by-step explanation:

add 2,200 and 3,000 then see your answer, and divide it by 125. I'm sorry if this doesn't help......

Answer:

y=18

Step-by-step explanation:

54 divided by 3 = 18

Hope this helps :)

(Brainliest?)

Answer:

18

Step-by-step explanation:

Divide each side by 3

54/3 = 18

Answer:

I'm not sure if the bridge is 44 kilometers long or just 4, but if the bridge is 44 kilometers long it will take 22 hours but if the bridge is 4 kilometers long it will take 2 hours.

Step-by-step explanation:

Since her average speed is 2 kilometers per hour you just have to divide the length of the bridge by 2. Then your quotient or answer to the division equation will be the amount of time it takes to cross the bridge.

Answer:

22 hours

Step-by-step explanation:

i dont know if that is 100% correct because you wrote 4 4 and not 44 but used 44 in my calculations. also, i worked it out like this:

distance÷speed=time

44 km ÷ 2kph = 22

Angle 4 = Angle 5 = 42⁰( alternate interrior angle)

Hope it helps u

Answer:

k= -18

Step-by-step explanation:

k/6 +8=5 (subtract 8 from both sides)

k/6= -3     (Multiply by 6 on both sides)

k=-18          

Answer:

74.4 (llllllllllll ignore this i need 20 characters to answer)

Answer:

4/420=105

Step-by-step explanation:

decompose 42 and divide by 4 is 10 and is 20 divided by 4 is 5

Answer:

50

Step-by-step explanation:

please brainalist

Answer:

x= 60

Step-by-step explanation:

brr 180 degrees total, divided by 3x would be 60

so X=60

Answer: 119 and -119

Step-by-step explanation: The absolute value of a number is its distance from 0.

Answer:

119 and -119

Step-by-step explanation:

the value of a positive number inside the absolute values, signs doesn't change the value but if a negative number is put inside the absolute values, the signs change to be positive.

Hope that helps :)

Answer:

[tex] \frac{11}{8} [/tex]

Step-by-step explanation:

[tex] \frac{1 \times 8 + 3}{8} [/tex]

Answer:

11/8

Step-by-step explanation:

Answer:8.99 cm

Step-by-step explanation:

Answer:

[tex]8.995[/tex]cm

Step-by-step explanation:

The circumference formula is: [tex]C=2\pi r[/tex]

We are given the circumference, which is 56.52cm.

The question wants us to find the radius, r.

To achieve this, we must solve for r.

Plugging in 56.52 for C we get:

[tex]56.52=2\pi r[/tex]

Dividing both sides by [tex]2\pi[/tex], we find r:[tex]8.995[/tex]

[tex]\frac{56.52}{2\pi } =r[/tex]

[tex]8.995[/tex]≈[tex]r[/tex]

If you want to round it up, you can round it to 9cm.

Answer:

4.5

Good luck!!

15.00 divided by 0.30 is 4.5

Answer:

82 .

Step-by-step explanation:

9x 10 = 90 then 90-8 = 82 that how many spaces are filled .

Answer:

y=-2/3x-1/3

Step-by-step explanation:

Plug in the point (-5,3)

3=-2/3(-5)+k

3=3.3333+k

k (y-intercept)=-0.33333, or -1/3

Answer:

A=6

B=19

C=55

D=119

E=70

Answer:

Blank A = 6

Blank B = 19

Blank C = 55

Blank D = 119

Blank E = 70

Answer:

a)13

b)F(x)=1/f(x) = 2/ x^2-3

c) 1/59

If the rainfall was recorded on 36 (instead of 9) randomly selected days throughout the year, the standard error of the mean would be equal to 0.195 inches.

The standard error measures the variability or uncertainty in an estimate or statistic based on a sample. It is often denoted as SE or SE(θ), where θ represents a population parameter of interest.

Given that

the standard error of the mean, SE = 0.39 (when sample size,n = 9).

Let s be the standard deviation around the mean, then

Since SE = [tex]\dfrac{s}{\sqrt n}[/tex]

In this sample,

0.39 = [tex]\dfrac{s}{\sqrt9}[/tex]

s = 0.39 × 3

s = 1.17.

If the sample size is increased from 9 to 36,

SE = [tex]\dfrac{1.17}{\sqrt36}[/tex]

SE = [tex]\frac{1.17}{6}[/tex]

SE = 0.195 inches.

Thus, the standard error of the mean changes from 0.39 inches to 0.195 inches.

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Answer:

2x=3

W+1.3=2.7

3y=5.1

z+1/3=1/2

Step-by-step explanation:

You just add up all on the left to equate that on the right

2x=3

W+1.3=2.7

3y=5.1

z+1/3=1/2

In case you have to solve:

x=3/2

W=2.4

y=1.7

z=1/6