a freeway with two northbound lanes is shut down because of an accident. at the time of the accident, the traffic flow rate is 1200 vehicles per hour per lane and the flow remains at this level. the capacity of the freeway is 2200 vehicles per hour per lane when not impacted by an accident. the freeway is shut down completely for 20 minutes after the accident and then one lane is open for 20 minutes and finally both lanes are opened (40 minutes after the accident). what is the average delay per

Answers

Answer 1

vehicle?

The average delay per vehicle would be 20 minutes. This is calculated by taking the total time the freeway was shut down (40 minutes) and dividing it by the total number of vehicles that would have been on the freeway during that time (2400 vehicles).


Related Questions

The solid below is dilated by a scale factor of 1/2. Find the volume of the
solid created upon dilation.
24
26
10
34

Answers

Answer: 4080

Step-by-step explanation:

First you have to find the area of the triangle. 24*10 = 240. 240/2 = 120. Then you multiply the area of the triangle and multiply it by 34. 120 * 34 = 4080. This means the answer is 4080

You roll a six sided die 30 times. A 5 is rolled 8 times. What is the theoretical probability of rolling a 5? What is the experimental probability of rolling a 5?

Answers

The theoretical and experimental probability of rolling a 5 are 1/6 and 4/15 respectively.

How do we derive the probability?

We will calculate the theoretical probability by substituting 30 for the number of favorable outcomes as the die is rolled 30 times with one option each for 30 rolls and 180 for total number of outcomes in theoretical probability formula.

P(Theoretical probability of rolling a 5) = 30/180

P(Theoretical probability of rolling a 5) = 1/6.

The experimental probability is calculated by substituting 8 for the number of time the event occurs and 30 for the total number of trials.

P(Experimental probability of rolling a 5)= 8/30

P(Experimental probability of rolling a 5) =4/15

Read more about probability

brainly.com/question/24756209

#SPJ1

A container built for transatlantic shipping is constructed in the shape of a right
rectangular prism. Its dimensions are 4 ft by 9.5 ft by 13 ft. If the container is entirely
full and, on average, its contents weigh 0.05 pounds per cubic foot, find the total
weight of the contents. Round your answer to the nearest pound if necessary

Answers

Thus, the on average the contents weight for the transatlantic shipping is found as  24.7  pounds.

Explain about the rectangular prism:a solid, three-dimensional object with six rectangular faces.It is a prism due to its uniform cross-section along its whole length.Volume is a unit of measurement for the amount of 3-dimensional space a thing occupies. Cubic units are used to measure volume.

Given dimension of rectangular prism

Length l = 4ft

width w = 9.5 ft

height h = 13 ft

Volume of rectangular prism = l*w*h

V = 4*9.5*13

V = 494 ft³

Now,

1  ft³ = 0.05 pounds

So,

weight of  494 ft³ =  494*0.05 pounds

weight of 494 ft³ =  24.7  pounds

Thus, the on average the contents weigh for the transatlantic shipping is found as  24.7  pounds.

know more about the rectangular prism

https://brainly.com/question/24284033

#SPJ1

1. suppose we know that the average weight of coyotes is 14.5kg with a standard deviation of 4kg. what is the probability of trapping a coyote that is 17kg or larger?

Answers

The probability of trapping a coyote that is 17kg or larger, given an average weight of 14.5kg and a standard deviation of 4kg is approximately 0.2743 or 27.43%.

To solve the problem, we first need to standardize the weight of the coyote using the formula:

z = (x - μ) / σ

Where:

x = the weight of the coyote we want to find the probability for (17kg in this case)

μ = the population mean (14.5kg in this case)

σ = the population standard deviation (4kg in this case)

z = the standardized score

Substituting the given values in the formula, we get:

z = (17 - 14.5) / 4

z = 0.625

Next, we need to find the probability of getting a coyote weighing 17kg or more, which is equivalent to finding the area under the normal distribution curve to the right of z = 0.625. We can use a standard normal distribution table or a calculator to find this probability.

Using a calculator, we can use the cumulative distribution function (CDF) of the standard normal distribution. The CDF gives the area under the curve to the left of a specified z-score. Since we want the area to the right of z = 0.625, we can subtract the CDF from 1 to get the area to the right.

Using a standard normal distribution table or calculator, we find that the CDF for z = 0.625 is approximately 0.734. Therefore, the area to the right of z = 0.625 is 1 - 0.734 = 0.266 or 26.6%.

Thus, the probability of trapping a coyote that is 17kg or larger is approximately 0.266 or 26.6%.

For more questions like Probability click the link below:

https://brainly.com/question/30034780

#SPJ11

Using a standard normal distribution table or a calculator, the probability of trapping a coyote that is 17kg or larger is approximately 0.266 or 26.6%.

What exactly is a standard normal distribution?

The standard normal distribution is a probability distribution that is used to calculate probabilities associated with a random variable that has a normal distribution with mean 0 and standard deviation 1. Any normally distributed random variable can be standardized by subtracting its mean and dividing by its standard deviation to obtain a new variable with mean 0 and standard deviation 1.

In this case, we are given that the weight of coyotes has a normal distribution with a mean of 14.5kg and a standard deviation of 4kg. We want to find the probability of trapping a coyote that is 17kg or larger.

To calculate this probability, we need to standardize the weight of a 17kg coyote using the formula:

z = (× - μ) / σ

where:

x is the value we want to standardize (in this case, 17kg),

μ is the mean of the distribution (14.5kg),

σ is the standard deviation of the distribution (4kg).

Substituting the values we have:

[tex]z =\frac{(17 - 14.5)}{4} = 0.625[/tex]

This value of 0.625 is the z-score for a coyote weighing 17kg. The z-score represents the number of standard deviations that a particular value is above or below the mean.

Next, we need to find the probability of a randomly selected coyote weighing 17kg or larger, which can be calculated using the standard normal distribution table or a calculator.

The standard normal distribution table gives the probability associated with a given z-score. However, since the table only gives probabilities for z-scores less than 0, we need to use the fact that the standard normal distribution is symmetric about the mean (0) to find the probability of a z-score greater than 0.625.

Specifically, we can use the property that:

P(Z > z) = 1 - P(Z < z)

where Z is a standard normal random variable and z is a z-score. This formula tells us that the probability of a z-score greater than a certain value is equal to 1 minus the probability of a z-score less than that value.

Using this formula, we can calculate:

P(Z > 0.625) = 1 - P(Z < 0.625)

We can look up the value of P(Z < 0.625) in a standard normal distribution table or calculate it using a calculator. For example, using a standard normal distribution table, we can find that P(Z < 0.625) = 0.734.

Substituting this value into the formula, we get:

P(Z > 0.625) = 1 - 0.734 = 0.266

Therefore, the probability of trapping a coyote that is 17kg or larger is approximately 0.266 or 26.6%.

Learn more about probability here:

https://brainly.com/question/13604758

#SPJ11

2. Find the area of the circle. Use 3.14 for r. Round to the nearest unit.
18 cm
01,017 cm²
0254 cm²
057 cm²
028 cm²
(1 point)

Answers

The area of the circle for given problem will be approx. 254 [tex]cm^2[/tex].

How to find the area of circle?

The formula for finding the area of a circle is given by:

Area =[tex]\pi* r^2[/tex]

where "π" (pi) is a mathematical constant approximately equal to 3.14159, and "r" represents the radius of the circle.

Measure the radius (r) of the circleSquare the radius: (r * r)Multiply the squared radius by π (pi):[tex]\pi* r^2[/tex].The result is the area of the circle.

Given,

Find the radius (r) of the circle. The radius is half of the diameter, so divide the diameter by 2:

Radius (r) = Diameter / 2 = 18 cm / 2 = 9 cm

Area = [tex]\pi * r^2[/tex] = [tex]3.14*(9 \;cm)^2[/tex] = [tex]254.34 \;cm^2[/tex] (rounded to two decimal places)

Learn more about Area of Circle here:

https://brainly.com/question/28642423

#SPJ1

Correct Question: Find the area of the circle with Diameter =18 cm(refer to image). Use 3.14 for π.( Round to the nearest unit).

what is the answer of this question (please i need help)

Answers

First I’m assuming you take the shapes with the numbers and variable in it to make a number. So that would be

5x+4=10 (not sure if it’s adding lmk if it’s subtraction if you can tell which one it is.)

Then solve.

Subtract 4 from each side. You get

5x=6

Get x by itself, so divide by 5

x= 6/5

The answer is B.

That should be your answer if I read it correctly. Lmk if you have extra questions. I hope it’s not wrong but it helps you understand the concept.

Answer:

The answer is B ([tex]x=\frac{6}{5}[/tex])

Step-by-step explanation:

We start with creating labels for the shapes that represent what they value -at first I tried multiplying the 5x by 4 but there wasn't an answer for that.

[tex]5x+4=10[/tex]

First we just simplify,

[tex]5x (-4)=10(-4)[/tex]

[tex]5x=6[/tex]

then divide,

[tex]\frac{5x}{5} =\frac{6}{5}[/tex]

and we end up with:

[tex]x=\frac{6}{5}[/tex]

or

B

During a flood, there were 6000 acres of land under water. After 2 days, only 3375 acres of land were under water. Assume that the water receded at an exponential rate. Write a function to model this situation that has a B-value of 1.

Answers

where t is measured in days, and A(t) represents the amount of flooded land at time t. This function has a B-value of -0.3118.

To model the situation of the flood, we can use an exponential decay function, which represents the decreasing amount of flooded land over time. The function can be written as:

[tex]A(t) = A0 * e^{(-kt)}[/tex]

where A(t) is the amount of flooded land at time t, A0 is the initial amount of flooded land, k is a constant representing the rate of decay, and e is the mathematical constant approximately equal to 2.718.

To determine the value of k, we can use the given information that after 2 days, only 3375 acres of land were under water. Substituting t = 2 and A(t) = 3375 into the equation above, we get:

[tex]3375 = A0 * e^{(-2k)[/tex]

We also know that initially, there were 6000 acres of land under water. Substituting A0 = 6000 into the equation above, we get:

Dividing both sides by 6000, we get:

ln(0.5625) = -2k[tex]ln(0.5625) = -2k[/tex]

Taking the natural logarithm of both sides, we get:

[tex]ln(0.5625) = -2k[/tex]

Solving for k, we get:

[tex]k = -ln(0.5625)/2[/tex]

k ≈ 0.3118

Therefore, the function to model the situation of the flood is:

[tex]A(t) = 6000 * e^{(-0.3118t)}[/tex]

To learn more about function, visit

https://brainly.com/question/12431044

#SPJ1

find the average rate of change of the car's position on the interval . include units on your answer.

Answers

The average rate of change of the car's position on the interval is ∆P/∆t.

To find the average rate of change of the car's position on the interval, follow these steps:

Identify the interval: First, determine the specific interval for which you need to find the average rate of change (e.g.,

between times t1 and t2).

Calculate the change in position:

Determine the car's position at both the beginning and end of the interval (e.g., positions P1 and P2).

Then, subtract the initial position (P1) from the final position (P2) to find the change in position (∆P).

Calculate the change in time: Subtract the initial time (t1) from the final time (t2) to find the change in time (∆t).

Calculate the average rate of change: Divide the change in position (∆P) by the change in time (∆t) to find the average

rate of change.

The average rate of change of the car's position on the interval is ∆P/∆t. Include units in your answer (e.g., meters per

second or miles per hour) to indicate the car's rate of change in position.

for such more question on average

https://brainly.com/question/20118982

#SPJ11

Write the functions in standard form:
h(x)=2(x-3)²-9
h(x)=
p(x) = -5(x + 2)² + 15
p(x)=

Answers

Answer:

[tex]h(x)=2x^2-12x+9[/tex],  [tex]p(x)=-5x^2-20x-5[/tex]

Step-by-step explanation:

To get to the standard form of a quadratic equation, we need to expand and simplify. Recall that standard form is written like so:

[tex]ax^2+bx+c[/tex]

Where a, b, and c are constants.

Let's expand and simplify h(x).

[tex]2(x-3)^2-9=\\2(x^2+9-6x)-9=\\2x^2+18-12x-9=\\2x^2+9-12x=\\2x^2-12x+9[/tex]

Thus, [tex]h(x)=2x^2-12x+9[/tex]

Let's do the same for p(x).

[tex]-5(x+2)^2+15=\\-5(x^2+4+4x)+15=\\-5x^2-20-20x+15=\\-5x^2-5-20x=\\-5x^2-20x-5[/tex]

Thus, [tex]p(x)=-5x^2-20x-5[/tex]

a random sample of n equal to 64 scores is selected from a normally distributed population with mu equal to 77 and sigma equal to 21. what is the probability that the sample mean will be less than 79? hint: this is a z-score for a sample.

Answers

The probability of the sample mean being less than 79 is 77.64%

In order to solve the given problem we have to take the help of Standard error mean

SEM = ∑/√(n)

here,

∑ = population standard deviation

n = sample size

hence, the z-score can be calculated as

z = ( x' - μ)/σ/√(n)

here,

x' = sample mean

μ = population mean

σ = population standard deviation

n = sample size

adding the values into the formula

SEM = σ / √(n)

= 21/√64

= 2.625

z = (x' - μ)/SEM

= (79-77)/2.625

= 0.76

now, using standard distribution table we find that probability of a z-score is less than 0.77 then converting it into percentage

0.77 x 100

= 77%

The probability of the sample mean being less than 79 is 77.64%

To learn more about probability,

https://brainly.com/question/13604758

#SPJ4

3. Technology required. Here are the data for the population f, in thousands, of a city d decades after 1960 along with the graph of the function given by f(d) = 25 - (1.19)ª. Elena thinks that shifting the graph off up by 50 will match the data. Han thinks that shifting the graph of f up by 60 and then right by 1 will match the data. a. What functions define Elena's and Han's graphs? b. Use graphing technology to graph Elena's and Han's proposed functions along with f. population (thousands) c. Which graph do you think fits the data better? Explain your reasoning.​

Answers

The relationship between the functions are indicated in the attached graph. see further explanation below.


What is the explanation for the above response?

a. Elena's graph is obtained by shifting the original function f up by 50 units, so her function is g(d) = f(d) + 50 = 75 - (1.19)ª.

Han's graph is obtained by shifting the original function f up by 60 units and then to the right by 1 unit, so his function is h(d) = f(d - 1) + 60 = 85 - (1.19)^(a-1).

b. Using graphing technology, we can graph the three functions f, g, and h to compare how well they fit the given data. Here's an example graph:

graph of f, g, and h

c. From the graph, it appears that Han's function h fits the data better than Elena's function g. The graph of h seems to align more closely with the plotted data points than the other two functions. Moreover, the shift to the right and up of the graph of f seems to better capture the overall trend of the data, as it appears that the population increased and shifted slightly to the right over time.

Learn more about graph  at:

https://brainly.com/question/17267403

#SPJ1

dora drove east at a constant rate of 75 kph. one hour later, tim started driving on the same road at a constant rate of 90 kph. for how long was tim driving, before he caught up to dora? a. 5 hours b. 4 hours c. 3 hours d. 2 hours

Answers

Tim was driving for 5 hours before he caught up to Dora.

The answer is (a) 5 hours.

To solve this problem, we can use the formula:
distance = rate × time
Let's denote the time Tim drove as t hours.

Since Dora started driving one hour earlier, her driving time would be (t + 1) hours.
Dora's distance: 75 kph × (t + 1)
Tim's distance: 90 kph × t
Since Tim catches up to Dora, their distances will be equal:
75(t + 1) = 90t
Now we can solve for t:
75t + 75 = 90t
75 = 15t
t = 5.

The answer is (a) 5 hours.

For similar question on distances.

https://brainly.com/question/29657955

#SPJ11

Find the surface area and width of a rectangular prism with height of 6 cm, length of 5 cm, and the
volume of 240 cm³.

Answers

236 cm2 is the surface area

Answer:

236 cm^2  and  8 cm

Step-by-step explanation:

width=w

240=6(5)(w)

w=8 cm

area=2[(6)(5)+(6)(8)+(5)(8)]

area=236 cm^2

A bottle of water that is 80°F is placed in a cooler full of ice. The temperature of the water decreases by 0. 5°F every minute. What is the temperature of the water, in degrees Fahrenheit, after 5 1/2
minutes? Express your answer as a decimal

Answers

After 5 and a half minutes, the temperature of the water will be 77°F.

In this scenario, we are given that the initial temperature of the water is 80°F. We also know that the temperature of the water decreases by 0.5°F every minute. We want to find out what the temperature of the water will be after 5 and a half minutes.

To solve this problem, we need to use a bit of math. We know that the temperature of the water is decreasing by 0.5°F every minute. So after 1 minute, the temperature of the water will be 80°F - 0.5°F = 79.5°F. After 2 minutes, the temperature will be 79.5°F - 0.5°F = 79°F. We can continue this pattern to find the temperature after 5 and a half minutes.

After 5 minutes, the temperature of the water will be 80°F - (0.5°F x 5) = 77.5°F. And after another half minute (or 0.5 minutes), the temperature will decrease by another 0.5°F, so the temperature will be 77.5°F - 0.5°F = 77°F.

To know more about temperature here

https://brainly.com/question/11464844

#SPJ4

Using the graph, determine the coordinates of the x-intercepts of the parabola.

Answers

Answer:

x = -5, x = 1

As (x, y) coordinates, the x-intercepts are (-5, 0) and (1, 0).

Step-by-step explanation:

The x-intercepts are the x-values of the points at which the curve crosses the x-axis, so when y = 0.

From inspection of the given graph, we can see that the parabola crosses the x-axis at x = -5 and x = 1.

Therefore, the x-intercepts of the parabola are:

x = -5x = 1

As (x, y) coordinates, the x-intercepts are (-5, 0) and (1, 0).

the x intercepts are 1 and-5

19.
Solve the problem.
2
Find the critical value XR corresponding to a sample size of 5 and a confidence
level of 98%.
(1 point)
O11.143
00.297
13.277
00.484

Answers

The critical value of the chi-square distribution corresponding to a sample size of 5 and a confidence level of 98% is given as follows:

0.297 and 13.277.

How to obtain the critical value?

To obtain a critical value, we need three parameters, given as follows:

Distribution.Significance level.Degrees of freedom.

Then, with the parameters, the critical value is found using a calculator.

The parameters for this problem are given as follows:

Chi-square distribution.1 - 0.98 = 0.02 significance level.5 - 1 = 4 degrees of freedom.

Using a chi-square distribution calculator, the critical values are given as follows:

0.297 and 13.277.

More can be learned about the chi-square distribution at https://brainly.com/question/4543358

#SPJ1

Please answer the question in the pdf. I just need the values for A, B, and C. I am offering 15 points. Thanks.

Answers

Recall the equation provided in the pdf:

   (125x ^ 3 * y ^ - 12) ^ (- 2/3) = (y ^ [A])/([B] * x ^ [c])

find A B and C.

The answer will be:

A = 8/3B = 3/4C = 8/3

Checkout the calculation of the exponential

We can solve this problem using the rules of exponents and algebraic manipulation.

Starting with the left-hand side of the equation:

(125x^3 * y^-12)^(-2/3)

Using the rule that (a * b)^c = a^c * b^c, we can rewrite the expression as:

125^(-2/3) * x^(-2) * y^(8)

Simplifying further, we can use the fact that a^(-n) = 1/(a^n) to get:

1/(5^2 * x^2 * y^8/3)

Now, we can see that the denominator on the right-hand side of the equation must be 5^2 * x^2 * y^8/3. To find the numerator, we need to simplify the expression y^A. Comparing exponents, we see that:

y^A = y^(8/3)

Therefore, we need to find a value of A such that A = 8/3. Solving for A, we get:

A = 8/3

Now, we can write the equation as:

y^(8/3)/(5^2 * x^2 * y^8/3) = y^(8/3)/(25 * x^2 * y^(8/3))

Comparing exponents again, we see that we need to find values of B and C such that:

B * C = 2

and

-8/3 = -C

Solving for C, we get:

C = 8/3

Substituting this value of C into the first equation, we get:

B * 8/3 = 2

Solving for B, we get:

B = 3/4

Therefore, the solution is:

A = 8/3

B = 3/4

C = 8/3

Learn more about exponential algebra here:

https://brainly.com/question/12940982

#SPJ1

Write the equation for the following graph.

Answers

Step-by-step explanation:

the equation for the following graph os (-3,-5) & (1,1)

Solve for x to make A||B.
A = x + 12
B = x + 48

X = [?]

Answers

Answer:

Step-by-step explanation:= x+48=180 ( linier pair )

                                            = x=180-48

                                            = x=132

                                         

                                              = x+12=180 (liner pair)

                                              = x=180-12

                                              = x=168

erin is playing darts at the adventure arcade. she scores a bullseye 15% of the time, and she is about to throw 5 darts. how likely is it that she will get at least one bullseye?

Answers

the likelihood of Erin getting at least one bullseye in 5 throws is 0.5563 or 55.63%.

To calculate the likelihood of Erin getting at least one bullseye, we need to first calculate the probability of her not getting a bullseye in a single throw. Since she scores a bullseye 15% of the time, the probability of her not getting a bullseye in a single throw is 85% (100% - 15%).

Using the probability of not getting a bullseye in a single throw, we can use the following formula to calculate the probability of not getting a bullseye in all 5 throws:

0.85 x 0.85 x 0.85 x 0.85 x 0.85 = 0.4437

Therefore, the probability of Erin not getting a bullseye in all 5 throws is 0.4437 or 44.37%.

To calculate the probability of Erin getting at least one bullseye in 5 throws, we can subtract the probability of her not getting a bullseye in all 5 throws from 1:

1 - 0.4437 = 0.5563

Therefore, the likelihood of Erin getting at least one bullseye in 5 throws is 0.5563 or 55.63%.

learn more about probability

https://brainly.com/question/30034780

#SPJ11

The probability that Erin will get at least one bullseye in her 5 throws at the adventure arcade is approximately 55.63%.

To find the probability that she will get at least one bullseye in 5 throws, we can use the complementary probability.

This means we will first find the probability of her not getting a bullseye in all 5 throws, and then subtract that from 1.

Find the probability of not getting a bullseye (1 - bullseye probability)

1 - 0.15 = 0.85

Calculate the probability of not getting a bullseye in all 5 throws

0.85^5 ≈ 0.4437

Find the complementary probability (probability of at least one bullseye)

1 - 0.4437 ≈ 0.5563

So, the probability that Erin will get at least one bullseye in her 5 throws at the adventure arcade is approximately 55.63%.

for such more question on probability

https://brainly.com/question/13604758

#SPJ11

How is the volume of the first rectangular prism with base 2m by 3m and height 5m related to the volume of the second rectangular prism with base 3m by 5m and height 2​m? Explain.

Answers

Answer:

they have the same volume

Step-by-step explanation:

in order to find the volume of a rectangular prism you have to multiply the width,height and length.

2 × 3 × 5 = 30.since both prisms have the same numbers ,they have the same volume.

hope this helps :)

Answer:

The volumes of the two rectangular prisms are the same.

Step-by-step explanation:

For the first rectangular prism, the area of the base is 6 square meters, and the height is 5 meters, so the volume is 30 cubic meters.

For the second rectangular prism, the area of the base is 15 square meters, and the height is 2 meters, so the volume is 30 cubic meters, the same volume as the first rectangular prism.

Slope-intercept (0, -2) , (9,1)

Answers

Answer:
Do you have a graph or anything?

The right triangle shown is enlarged such that each side is multiplied by the value of the hypotenuse, 3y. Find the expression that represents the perimeter of the enlarged triangle. TRIANGLE AND ANSWER CHOICES BELOW!

Answers

Answer:

c.

Step-by-step explanation:

The original triangle has two sides with length 4x each, and the hypotenuse has length 3y.

After the enlargement, each of the sides with length 4x becomes 3y × 4x = 12xy, and the hypotenuse becomes 3y × 3y = 9y^2.

Therefore, the perimeter of the enlarged triangle is the sum of the lengths of its three sides:

12xy + 12xy + 9y^2 = 24xy + 9y^2 = 9y^2 + 24xy

So the answer is (C) 9y^2 + 24xy.

Which expressions are equivalent to 27^4/3?

Select the three correct answers.

A. 4^3

B. (27^1/3)^4

C. 3^1/4

D. 81

Answers

D) 81 is equivalent to 27^(4/3).

The expression 27^4/3 can be simplified using the rule that (a^m)^n = a^(m*n). Therefore, we can write,

27^(4/3) = (3^3)^(4/3)

Using the power of a power rule, we can simplify further,

(3^3)^(4/3) = 3^(3*4/3)

Simplifying the exponent, we get,

3^(4)

To check the other answer choices,

A. 4^3 is not equivalent to 27^4/3.

B. (27^1/3)^4 is equivalent to 27^(4/3), which we already simplified to 3^4. Therefore, this expression is also equivalent to 3^4.

C. 3^1/4 is not equivalent to 27^4/3.

D. 81 is equivalent to 3^(4).

Therefore, the expression 27^4/3 is equivalent to 3^4, which is answer choice D) 81.

To learn more about equivalent here:

https://brainly.com/question/31532746

#SPJ4

past data shows that the standard deviation of apartments for rent in the area is $200. suppose we want a 98% confidence interval with margin of error of 50. what sample size do we need?

Answers

A sample size of 87 is required to obtain a 98% confidence interval with a margin of error of 50.

How to calculate sample size?

To calculate the sample size required for a 98% confidence interval with a margin of error of 50, we need to use the following formula:

n = [Z*(σ/ME)]^2

where:

n = the sample size needed

Z = the Z-score for the desired confidence level (98% or 2.33)

σ = the standard deviation of apartments for rent in the area ($200)

ME = the margin of error ($50)

Plugging in the given values, we get:

n = [2.33*(200/50)]^2

n = [9.32]^2

n ≈ 86.7

Since we cannot have a fractional sample size, we round up to the nearest whole number to get the final answer.

Therefore, a sample size of 87 is required to obtain a 98% confidence interval with a margin of error of 50, given that the standard deviation of apartments for rent in the area is $200.

Learn more about sample size

brainly.com/question/30885988

#SPJ11

9) Given f-¹(x)=-3x+2, write an equation
that represents f(x).

Answers

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so for this inverse, since finding the inverse of the inverse, will give us the original function :)

[tex]f^{-1}(x)=-3x+2\implies y~~ = ~~-3x+2\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~-3y+2} \\\\\\ x-2=-3y\implies \cfrac{x-2}{-3}=y\implies \cfrac{2-x}{3}=y=f(x)[/tex]

Emmy went to play miniature golf on Monday, when it cost $1 to rent the club and ball, plus $2 per game. Liam went Thursday, paying $1 per game, plus rental fees of $5. By coincidence, they played the same number of games for the same total cost. How many games did each one play?

Answers

Emmy and Liam each played 4 games according to the given statement.

What is an equation?

An equation is a claim that two expressions are equal, typically indicated by the equals symbol (=). In mathematics, equations are used to simulate real-world scenarios, solve problems, and depict relationships between variables.

Exponents, logarithms, and trigonometric functions can all be used in equations, in addition to basic operations like addition, subtraction, multiplication, and division.

Let us suppose the number of games played = x.

Thus, for Emmy we have:

E = 1 + 2x

For Liam the equation is:

L = 5 + 1x

Equating the two equations we have:

1 + 2x = 5 + 1x

x = 4

Hence, Emmy and Liam each played 4 games according to the given statement.

Learn more about equation here:

https://brainly.com/question/10413253

#SPJ1

true or false: a linear programming problem can have an optimal solution that is not a corner point. select one: true false

Answers

It is true that a linear programming problem can have an optimal solution that is not a corner point.

How given statement is true? Explain further?

In linear programming, the optimal solution represents the point where the objective function is optimized while still satisfying all the constraints.

In some cases, the optimal solution may occur at a corner point of the feasible region, where two or more of the constraints intersect.

However, it is possible for the optimal solution to occur at a point that is not a corner point, but rather lies on an edge or a line segment of the feasible region.

This can occur when the objective function is parallel to one of the constraint lines or when there are redundant constraints that limit the feasible region.

Therefore, it is true that a linear programming problem can have an optimal solution that is not a corner point.

Learn more about linear programming.

brainly.com/question/15417573

#SPJ11

Help please? I just need an answer. A clear explanation earns brainliest.

Answers

the simplified  form  of expression is: -(x² + 2x - 2)/((x+2)*(x+4))

what is expression  ?

In mathematics, an expression is a combination of numbers, variables, operators, and/or functions that represents a mathematical quantity or relationship. Expressions can be simple or complex

In the given question,

To evaluate the expression 1/(x+2) - (x+1)/(x+4), we need to find a common denominator for the two terms. The least common multiple of (x+2) and (x+4) is (x+2)(x+4).

So, we can rewrite the expression as:

(1*(x+4) - (x+1)(x+2))/((x+2)(x+4))

Expanding the brackets, we get:

(x+4 - x² - 3x - 2)/((x+2)*(x+4))

Simplifying the numerator, we get:

(-x² - 2x + 2)/((x+2)*(x+4))

Therefore, the simplified expression is:

-(x² + 2x - 2)/((x+2)*(x+4))

To know more about  Expressions , visit:

https://brainly.com/question/14083225

#SPJ1

Kiran swims z laps in the pool. Clare swims 18 laps, which is 9/5
times as many laps as Kiran. How many laps did Kiran swim?
Equation:
Solution: z=

Answers

we use linear equation in one variable to solve the problem. Kiran swam 10 laps in the pool.

Let's represent the number of laps Kiran swam as "z".

We know that Clare swam 18 laps, which is 9/5 times as many laps as Kiran. We can represent this relationship with the following equation:

18 = (9/5)z

To solve for z, we can isolate it by multiplying both sides of the equation by the reciprocal of 9/5, which is 5/9:

18 * (5/9) = (9/5)z * (5/9)

10 = z

Therefore, Kiran swam 10 laps in the pool.

To know more about linear equation in one variable Visit:

https://brainly.com/question/31529190

#SPJ1

Other Questions
a researcher wanted to test the hypothesis that rats that had greater expression of a gene called pgc-1alpha would spend more time running around their cages. which type of graph would be best to explore a relationship between pgc-1alpha expression and time spent running?group of answer choicesline graph (with error bars)bar graphscatter plotline graph (no error bars) which term describes a policy of honoring diverse racial, ethnic, religious, linguistic, and national backgrounds? Find any solution(s) (refer to attachment) of and select the correct statement.A. The equation has no solution.B. The equation has two solutions.C. The equation has one solution.D. The equation has one solution and one extraneous solution. 16. an increase in aggregate supply could be caused by: group of answer choices businesses paying more for health insurance for their workers. an increase in oil prices. a drop in energy costs from cheaper natural gas. an increase in government purchases. g Calculating Average SpeedIf you know the total distance an object travels over a certain period of time, you cancalculate the average speed of the object.To do so, you use the formula ____________________________________________. Scrum masters help remove impediments, foster an environment for high-performing team dynamics and what else?- Relentlessly improve- Continuously deliver- Form and re-form teams- Estimate stories If you watch from ground level, a child riding on a merry-go-round will seem to be undergoing simple harmonic motion from side to side. Assume the merry-go-round is 10.6 feet across and the child completes 8 rotations in 120 seconds. Write a sine function that describes d, the child's apparent distance from the center of the merry-go-round, as a function of time t. Sulfurous acid ( H2SO3) is a diprotic acid with a1=1.39102 and a2=6.73108. Determine the pH of a 0.189M sulfurous acid ( H2SO3 ) solution. I dont know what to write for the equation. write an integral that quantifies the change in the area of the surface of a cube when its side length quadruples from s unit to 4s units. Alfred buys a car for 13960 which depreciates in value at a rate of 0.75% per year.Work out how much Alfred's car will be worth in 12 years. how does contemporary anthropology differ in scope from other disciplines concerned with humans (such as sociology, economics, and human biology)? Resources are scarce therefore the value maximizationis stretched. Discuss Describe, in detail, the four (4) ways in whichbusiness-to-business (B2B) firms segment their markets. You are considering purchasing your first home in about two years in the Durham region (Oshawa, ON) at a cost of about $800,000. You want to make sure that you will qualify for the mortgage and you have the following personal situation.Assets Value Liabilities BalanceSavings Account = $30,000 Credit Card = $0 (credit limit $10,000)Car = $10,000 Car Loan = $5,000 ($300/month)Wealthsimple TFSA = $3,000 Credit Line = $0 (credit limit $15,000)Based on your personal information, what will you need to qualify for the mortgage in about two years? Consider the following to justify your reasoning but please note that there will be other factors to consider.Down paymentIncome5CsCapacity requirementsAssume Property Taxes in Oshawa of about $6,000 per year.Assume Utilities of about $300 per month. The value of a control's property may be changed while the application is running by _______using an assignment statement using the Properties window using the Toolbox window all of the above Use the graph to answer the questionsWILL MARK BRAINLIEST!! help please without guessing ?// a hollow cylindrical copper (density 8.96 g/cm3) pipe is 0.71 m long and has an outside diameter of 3.50 cm and an inside diameter of 2.50 cm. the mass of this pipe is closest to Longbow Lumber is purchasing a new horizontal resaw at a cost of $375,000. There is an additional $10,000 delivery and installation cost. The machine has a capital cost allowance (CCA) rate of 20%. What is the incremental undepreciated capital cost (UCC) for year 2?A.) $346,500B.) $385,000c.) $337,500d.) $192,500e.) $375,000