Mathematics College

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.

Answers

Answer 1

Answer:

52.78% probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X greater than x is given by the following formula.

[tex]P(X > x) = \frac{b-x}{b-a}[/tex]

Uniformly distributed between 0 and 9 minutes.

This means that [tex]a = 0, b = 9[/tex]

Find the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.

[tex]P(X > 4.25) = \frac{9 - 4.25}{9 - 0} = 0.5278[/tex]

52.78% probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.

Related Questions

differentiate 1_x² over 1+x²

Answers

Answer:

Dy/Dx=-4x/(1+x²)²

Step-by-step explanation:

The differential of 1_x² over 1+x²

First of all

1_x² over 1+x² = (1_x²) / (1+x²)

Let (1_x²) = u

Let (1+x²) = v

Differential = Dy/Dx

Dy/Dx of (1_x²) / (1+x²)

= (VDu/Dx -UDv/Dx)V²

u = (1-x²)

Du/Dx = -2x

(VDu/Dx) =(1+x²)(-2x)

V = 1+x²

Dv/Dx = 2x

UDv/Dx= (1-x²)(2x)

v² = (1+x²)²

Dy/Dx = ((1+x²)(-2x) - (1-x²)(2x))/(1+x²)²

Dy/Dx= ((-2x -2x³)-(2x-2x³))/(1+x²)²

Dy/Dx=( -2x -2x - 2x³ +2x³)/(1+x²)²

Dy/Dx=-4x/(1+x²)²

Find the distance from the point (9, –2) to the line y = 3∕2x + 4. Choices are in the attachment...

Answers

Answer: Choice B) [tex]\sqrt{117} \text{ units}[/tex]

===================================================

Work Shown:

y = (3/2)x + 4

2y = 3x + 8 .... multiply both sides by 2

0 = 3x + 8 - 2y

3x-2y+8 = 0

The original equation transforms to 3x-2y+8 = 0. It is in the form Ax+By+C = 0. We see that A = 3, B = -2, C = 8. This form is very useful to help find the distance from a point to this line.

The formula we will use is

[tex]d = \frac{|A*p+B*q+C|}{\sqrt{A^2+B^2}}\\\\[/tex]

where A,B,C were the values mentioned earlier. The p,q are the x and y coordinates of the point given. So p = 9 and q = -2

Plugging all that in gives...

[tex]d = \frac{|A*p+B*q+C|}{\sqrt{A^2+B^2}}\\\\d = \frac{|3*9+(-2)*(-2)+8|}{\sqrt{3^2+(-2)^2}}\\\\d = \frac{|27+4+8|}{\sqrt{9+4}}\\\\d = \frac{|39|}{\sqrt{13}}\\\\d = \frac{39}{\sqrt{13}}\\\\d = \frac{39\sqrt{13}}{\sqrt{13}\sqrt{13}} \ \text{ rationalizing denominator}\\\\d = \frac{39\sqrt{13}}{13}\\\\d = 3\sqrt{13}\\\\d = \sqrt{9}*\sqrt{13}\\\\d = \sqrt{9*13}\\\\d = \sqrt{117}\\\\[/tex]

In a circle, diameter AB¯¯¯¯¯¯¯¯ is perpendicular to chord CD¯¯¯¯¯¯¯¯ at point L. Which statement will always be true about this circle?

Answers

Answer:

CL = LD

Step-by-step explanation:

In a circle, diameter AB is perpendicular to chord CD at point L. Which statement will always be true about this circle?

1) (CL)(LD)=AB

2) AL > LB

3) CL = LD

4) BL > AB

Answer: The chord is CD and the diameter AD of the circle are perpendicular to each other at point L. According to the perpendicular bisector theorem, if the diameter of a circle is perpendicular to a chord then the diameter bisects the chord and its arc. This means that chord CD is bisected by the diameter of the circle at point L.

Since CD is bisected at point L, CL = LD

Also CD = 2CL = 2LD

A baby’s t-shirt requires 2/9 yards of fabric. How many t-shirts can be made from 38 yards?

Answer:

Using the binomial theorem

[tex](1 .05)^5 = 1.27628[/tex]

Step-by-step explanation:

The binomial theorem is given by

[tex](a +b)^n = \binom{n}{0} a^nb^0 + \binom{n}{1} a^{n-1}b^1....+ \binom{n}{n} a^0b^n[/tex]

For the given case, we have

[tex]a = 1 \\\\b = 0.05 \\\\n = 5 \\\\[/tex]

So,

[tex](1 +0.05)^5 = \binom{5}{0} (1)^5(0.05)^0 + \binom{5}{1} (1)^4(0.05)^1 + \binom{5}{2} (1)^3(0.05)^2 + \binom{5}{3} (1)^2(0.05)^3 + \binom{5}{4} (1)^1(0.05)^4 + \binom{5}{5} (1)^0(0.05)^5[/tex]

[tex](1 +0.05)^5 = (1)(1)^5(0.05)^0 + (5) (1)^4(0.05)^1 + (10) (1)^3(0.05)^2 + (10) (1)^2(0.05)^3 + (5) (1)^1(0.05)^4 + (1) (1)^0(0.05)^5[/tex]

[tex](1 +0.05)^5 = 1 + 0.25 + 0.025 + 0.00125 + 0.00003125 + 0.0000003125[/tex]

[tex](1 + 0.05)^5 = 1.27628[/tex]

Therefore, using the binomial theorem

[tex](1 .05)^5 = 1.27628[/tex]

please help fast ! Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the fractions with equivalent percentages.

Answers

Answer:

13/20<--->65%

21/25<--->84%

3/4<--->75%

2/5<--->40%

3/5<--->60%

To find the matching pairs, divide the fraction and move the decimal point to your answer 2 places to the right to then get a percentage.

Ex: 1/2= .50->5.0->50.->50%

The image did not show the rest of the answers, but I worked with what information I received from the current image, producing 5 sets of answers. If there are more than 5 sets, please send a second image with your question so we can help you with the rest.

Hence the correct match of fractions to their equivalent percentages are;

13/20 = 65%

21/25 = 84%

3/4 = 75%

2/5 = 40%

3/5 = 60%

Percentages and fractions

Fractions are written as a ratio of two integers. In order to convert fractions to percentage, we will simply multiply the fraction given by 100.

For the fraction 13/20

13/20 * 100 = 13 * 5

13/20 = 65%

For the fraction 21/25

21/25 * 100 = 21 * 4

21/25 = 84%

For the fraction 3/4

3/4 * 100 = 3 * 25

3/4 = 75%

For the fraction 2/5

2/5 * 100 = 2 * 20

2/5 = 40%

For the fraction 3/5

3/5 * 100 = 3* 20

3/5 = 60%

Hence the correct match of fractions to their equivalent percentages are;

13/20 = 65%

21/25 = 84%

3/4 = 75%

2/5 = 40%

3/5 = 60%
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In a clinical study of an allergy drug, 108 of the 200 subjects reported experiencing significant relief from their symptoms. Test the claim that more than half of all those using the drug experience relief. Using a 0.01 significance level, what is your decision

Answers

Answer:

The decision is to not reject the null hypothesis.

At a significance level of 0.01, there is not enough evidence to support the claim that the proportion of all those using the drug that experience relief is significantly higher than 50% (P-value = 0.1443).

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the proportion of all those using the drug that experience relief is significantly higher than 50%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]

The significance level is 0.01.

The sample has a size n=200.

The sample proportion is p=0.54.

[tex]p=X/n=108/200=0.54[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{200}}\\\\\\ \sigma_p=\sqrt{0.00125}=0.035[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.54-0.5-0.5/200}{0.035}=\dfrac{0.038}{0.035}=1.061[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>1.061)=0.1443[/tex]

As the P-value (0.1443) is greater than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.01, there is not enough evidence to support the claim that the proportion of all those using the drug that experience relief is significantly higher than 50%.

A store buys sneakers for $20.00 and marks them up 250%. What is the selling price?

Answers

Answer:

[tex]\$45[/tex]

Step-by-step explanation:

[tex]20+(2.5*20)=45[/tex]

Marking up means that the new value is added onto the original value.

As we are increasing the original price by 250% of the price, we need to multiply it by 2.5, as that is equal to 250%

Answer:

20*2.5 = $50 Gross margin $70 Selling price

Step-by-step explanation:

WILL MARK BRAINLIEST! NEED HELP!

How does the graph of f(x) = (x + 2)4 + 6 compare to the parent function g(x) = x4?

Answers

Answer:

left 2 units and up 6 units

Step-by-step explanation:

f(x) = (x + 2)^4 + 6

y = f(x) + C C > 0 moves it up

So this moves it up 6 units

y = f(x + C) C > 0 moves it left

So this moves it to the left 2 units

The parent function g(x) is shifted to the left 2 units and up 6 units to get the function f(x).

What is a function?

Function is a type of relation, or rule, that maps one input to specific single output.

Given function;

f(x) = (x + 2)^4 + 6

y = f(x) + C

C > 0 moves it up

So, this moves it up 6 units.

y = f(x + C)

C > 0 moves it left

So, this moves it to the left 2 units.

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A store accidentally priced an item at $20 instead of $30 and honored the mispricing.
Where should the store attribute the $10 difference?
Is it considered a loss or operating expense?
Thanks

Answers

Answer:

Sales

Step-by-step explanation:

Since it is mentioned that the store mistakenly priced an item at $20 instead of $30 so there is a difference of $10 so the price of sales is increased by $10 due to mispricing the value of the item so that it would be recorded at $30 rather than $20

Therefore in the given case neither it is considered as a loss nor an operating expense but as a sales and the same is to be relevant

Hence, the given options are incorrect

PLEASE HURRY DONT HAVE MUCH TIME WILL GIVE BRAINLIEST

(SEE PICTURE)

Find the value of x for m(arc AB) = 46 and m(arc CD) = 25. (The figure is not drawn to
scale.)

Answers

35.5 is the angle angle

Suppose that P(A) = 1/3, P(B) = 1/3, and P(A ∩ Bc ) = 2/9. Are A and B independent? Why or why not?

Answers

A and B are not independent events because P(A B) = 2/9 and 2/9 is not equivalent to 1/9.

Given that are two events P(A) = 1/3, P(B) = 1/3, and P(A ∩ B) = 2/9.

We need to determine if the events are independent or not.

The chance of occurrences A and B intersecting (P(A B)) must be compared to the sum of both events' individual probabilities (P(A) × P(B)) in order to assess if events A and B are independent.

Two events A and B are independent if and only if:

P(A ∩ B) = P(A) × P(B)

Let's check if this condition holds for the given probabilities:

P(A) = 1/3

P(B) = 1/3

P(A ∩ B) = 2/9

Next, add up the odds of each separately:

P(A) × P(B) = (1/3) × (1/3) = 1/9

We can infer that A and B are not independent events because P(A B) = 2/9 and 2/9 is not equivalent to 1/9.

In other words, the likelihood that one event (A) occurs influences the likelihood that another event (B) occurs, and vice versa.

The probability of both events happening at once (P(A B)) would be equal to the product of their individual probabilities (P(A) × P(B)) if A and B were independent, but this is not the case in this situation.

Learn more about Independent Events click;

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I NEED HELP PLEASE, THANKS! :)
Makya was conducting a physics experiment. He rolled a ball down a ramp and calculated the distance covered by the ball at different times. The ball rolled a distance of 1 foot during the first second, 3 feet during the next second, and so on. If the distances the ball rolled down the ramp each second form an arithmetic sequence, determine the distance the ball rolled down during the fifteenth second. (Show work)

Answers

Hey there! :)

Answer:

f(15) = 29 ft.

Step-by-step explanation:

We can write an arithmatic equation for this pattern:

Where:

[tex]n_{1}[/tex] = 1, [tex]n_{2}[/tex] = 3

Find the rate of change. This is constant because this is an arithmatic sequence.

3 - 1 = 2.

We can begin to write an explicit function for this situation:

f(n) = [tex]n_{1}[/tex] + d(n-1) where d is the rate of change:

f(n) = 1 + 2(n-1)

Substitute 15 for n to solve for the distance traveled after 15 seconds:

f(15) = 1 + 2(15-1)

f(15) = 1 + 2(14)

f(15) = 1 + 28

f(15) = 29 ft.

Therefore, the distance traveled after 15 seconds is 29 ft.

Name the major arc and find its measure.

Answers

Answer:

ADB = Major Arc

arc measure = 310

Step-by-step explanation:

major arc measure = 360 - 50 = 310

Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the answer is an interval, enter your answer using interval notation. If the answer is a finite set of values, enter your answers as a comma separated list of values.)

Answers

Answer:

(0, 16]

Step-by-step explanation:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

According to the ratio test, if we define L such that:

L = lim(n→∞) |aₙ₊₁ / aₙ|

then the series will converge if L < 1.

aₙ = (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

aₙ₊₁ = (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹)

Plugging into the ratio test:

L = lim(n→∞) | (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹) × n 8ⁿ / ((-1)ⁿ⁺¹ (x−8)ⁿ) |

L = lim(n→∞) | -n (x−8) / (8 (n+1)) |

L = (|x−8| / 8) lim(n→∞) | n / (n+1) |

L = |x−8| / 8

For the series to converge:

L < 1

|x−8| / 8 < 1

|x−8| < 8

-8 < x−8 < 8

0 < x < 16

Now we check the endpoints. If x = 0:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (0−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(-1)ⁿ (-8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -1 / n

This is a harmonic series, and diverges.

If x = 16:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (16−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ (8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ / n

This is an alternating series, and converges.

Therefore, the interval of convergence is:

0 < x ≤ 16

Or, in interval notation, (0, 16].

What is the inverse of f(x) = 2x − 8?

Answers

Step-by-step explanation:

firstly firstly we have to suppose f(X) as y and then solve it by interchanging X and y.

hope this is helpful

Answer:

Step-by-step explanation:

To find inverse you switch f(x) and x use y for f(x) then solve for y.

1. x = 2y - 8

2. x + 8 = 2y

3. (x + 8) / 2 = y

4. 1/2x + 4 = y

Does anyone mind explaining? I have been stuck on this for a while.

The base of the pyramid is a regular hexagon. Find the volume of the pyramid. Round your answer to the nearest tenth.

Answers

Answer:

vol = 62 in³

Step-by-step explanation:

First determine r (see attached image) by using pythagorean theorem.

a² = b² + c²

a = 3 in

b = 3/2 = 1.5 in

c = r

3² = 1.5² + r²

r = [tex]\sqrt{3^{2}-1.5^{2} }[/tex]

r = 2.598 in

Get the area = n/2 * a * r

n = number of sides = 6

r = 2.598 in

Area = 6/2 * 3 * 2.598

Area = 23.38 in²

get the volume = 1/3 * Area * h

Area = 23.38 in²

h = 8 in (as given)

vol = 1/3 * 23.38 * 8

vol = 62 in³

all my points!!!!!!!!!!!!!! Brainleist will be given

Answers

Answer:

18-22 = 1

23-27 = 3

28-32 = 3

33-37 = 3

Answer:

18-22 = 1

23-27 = 3

28-32 = 3

33-37 = 3

Help me answer this question for 5.b)

Answers

Answer:

The provement is below

Step-by-step explanation:

z^(1/2)=x^(1/2)+y^(1/2) => (z^(1/2))^2= (x^(1/2)+y^(1/2))^2

=> z=x+y+2*x^(1/2)*y^(1/2) => z-x-y= 2*x^(1/2)*y^(1/2)

=> (z-x-y)^2= (2*x^(1/2)*y^(1/2) )^2 => (z-x-y)^2=4*x*y (1)

Pls note that (z-x-y)^2= ((-1)*(-1)*(z-x-y))^2= ((-1)*(x+y-z))^2= (-1)^2*(x+y-z)^2=

=(x+y-z)^2

So (z-x-y)^2= (x+y-z)^2 !!! Substitute in (1) (z-x-y)^2 by (x+y-z)^2 and will get

the required equality (x+y-z)^2=4*x*y

Two fair dies are rolled. What is the conditional probability thatat least one lands on 6 given that the dies land on different numbers?

Answers

Answer:

33.33% conditional probability thatat least one lands on 6 given that the dies land on different numbers

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

All outcoms of the dices:

Format(Dice A, Dice B)

(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)

(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)

(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)

(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)

(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)

(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)

36 in all

Total outcomes:

In this question, we want all with no repetition.

There are 6 repetitions, they are (1,1), (2,2), ..., (6,6). So 36 = 6 = 30 outcomes.

Desired outcomes:

One landing on six:

(6,1), (6,2), (6,3), (6,4), (6,5), (1,6), (2,6), (3,6), (4,6), (5,6).

10 desired outcomes.

Probability:

10/30 = 0.3333

33.33% conditional probability thatat least one lands on 6 given that the dies land on different numbers

Find the first four iterates of the function f(z)=z^2-2-2i with an initial value of z0=2+i

Answers

Obtain the next iterate by plugging the previous iterate into the function.

First iterate:

[tex]z_0=2+i\implies z_1=f(z_0)=(2+i)^2-2-2i=1+2i[/tex]

Second iterate:

[tex]z_2=f(z_1)=(1+2i)^2-2-2i=-5+2i[/tex]

Third iterate:

[tex]z_3=f(z_2)=(-5+2i)^2-2-2i=19-22i[/tex]

Fourth iterate:

[tex]z_4=f(z_3)=(19-22i)^2-2-2i=-125-838i[/tex]

In 4 days, the price of a share of stock rose 3/4 of a point. On a average, what was the change in stock each day?

Answers

Answer:

0.15 or 15%

Step-by-step explanation:

If the price of a stock rose 3/4 on a point, it means that 1x became 1,75x (x + 3/4x). X is the price of the stock here.

To calculate how much the price went up each day on average, we will create exponential equation.

x = price of the stock

y = average daily change

[tex]x*y^{4} =1.75x[/tex] divide by x

[tex]y^{4} = 1.75[/tex]

We will calculate it using logarithms.

y = 1.15016, rounded to 1.15

We see that the stock goes up 0.15 points every day.If we multiply it by 100%, we get 15%

Use an iterated integral to find the area of the region bounded by the graphs of the equations.
y = 16 − x2 y = x + 4

Answers

Answer:

use photomath and it will solve ur problem

If you were to draw samples of size 47 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?

Answers

Answer:

The range of middle 98% of most averages for the lengths of pregnancies in the sample is, (261, 273).

Step-by-step explanation:

The complete question is:

The lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 17 days. If you were to draw samples of size 47 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?

Solution:

As the sample size is large, i.e. n = 47 > 30, the central limit theorem can be used to approximate the sampling distribution of sample mean by the normal distribution.

So,[tex]\bar X\sim N(\mu,\ \frac{\sigma^{2}}{{n}})[/tex]

The range of the middle 98% of most averages for the lengths of pregnancies in the sample is the 98% confidence interval.

The critical value of z for 98% confidence level is,

z = 2.33

Compute the 98% confidence interval as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}[/tex]

[tex]=267\pm 2.33\cdot\frac{17}{\sqrt{47}}\\\\=267\pm5.78\\\\=(261.22, 272.78)\\\\\approx (261, 273)[/tex]

Thus, the range of middle 98% of most averages for the lengths of pregnancies in the sample is, (261, 273).

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