b. What is the final velocity of a runner who is accelerating at 1.5 feet per second squared for 5
seconds with an initial velocity of 2 feet per second?

Answer:

  30 miles per hour

Step-by-step explanation:

We want to know the average speed over a course with one leg run at one speed, and another leg run at a different speed.

To find the average speed, we need to know the total time and the total distance. The relation ...

  time = distance/speed   ⇔   distance = speed × time

can be used to fill in the blanks.

The first leg is a distance of 140 miles. The time for that leg is ...

  t1 = (140 mi)/(28 mi/h) = 5 h

The second leg takes 2 hours at a speed of 35 mph. The distance covered is ...

  d2 = (35 mi/h)(2 h) = 70 mi

The total distance is ...

  d = d1 +d2 = 140 mi +70 mi = 210 mi

The total time is ...

  t = t1 +t2 = 5 h + 2 h = 7 h

The average speed is the ratio of total distance to total time:

  d/t = (210 mi)/(7 h) = 30 mi/h

Susan's average speed for the trip was 30 mph.

Answer:

rational number

Step-by-step explanation:

it doesnt keep going ,it stops unlike pi were pi continues to go on forever

Answer:

Its rational

Step-by-step explanation:

Rational numbers can be made by dividing 2 integers. And it's a either a termination or repeating decimal.

And 15.625 is a terminating decimal.

The function that provides the height of the stack of cups based on any number of cups is height(n) = 7.5 + 1.5(n-1)

Let's assume that the height of one cup is 7.5 inches.

When we add the second cup, the bottom of the second cup rests on the top of the first cup, including the 1.5" lip.

Therefore, the height of the second cup is 7.5 inches plus 1.5 inches, or 9 inches.

When we add the third cup, the bottom of the third cup rests on the top of the second cup, including the 1.5" lip.

Therefore, the height of the third cup is the height of the first two cups plus 1.5 inches, or 16.5 inches.

The function we get by continuing this pattern for any number of cups n by using the formula:

height(n) = 7.5 + 1.5(n-1)

Therefore, the function that provides the height of the stack of cups based on any number of cups is height(n) = 7.5 + 1.5(n-1)

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Answer:

1,647.75

Step-by-step explanation:

Well 25,340 times the interest rate .065 which equals 1647.75

The maximum monthly profit Mt. Nittany is  $23,100 and, for Happy Valley Rentals,  monthly profits will be approximately $23,100.

(a) To find the number of apartments Mt. Nittany should rent out each month to maximize profits, we need to find the vertex of the quadratic function P(x) = -7x^2 + 980x - 10900.

The x-coordinate of the vertex is given by -b/2a, where a = -7 and b = 980. So, x = -b/2a = -980/(2*(-7)) ≈ 70.

The maximum monthly profit is obtained by plugging this value of x into P(x), giving P(70) = -7(70)^2 + 980(70) - 10900 ≈ $23,100.

(b) Similarly, for Happy Valley Rentals, we need to find the vertex of the quadratic function P(x) = -7x^2 + 980x - 10900 when they manage 50 apartments.

The x-coordinate of the vertex is again given by

b/2a, where a = -7 and b = 980, but now we have x = -b/2a = -980/(2*(-7)) ≈ 70.

The maximum monthly profit is obtained by plugging this value of x into P(x), giving P(70) = -7(70)^2 + 980(70) - 10900 ≈ $23,100.

Therefore, both companies should rent out 70 apartments each month to maximize their profits, and their maximum monthly profits will be approximately $23,100.

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Answer:

3/4

Step-by-step explanation:

the numerator of slope (in this case 3) is always y because y rises. in this case, in order to get to the other plot you need to rise three times then run 4. "run" is how many it takes to get to the plot but in the x direction. for example in this case it took 3 rise and 4 run.

Answer: The zero of a function is the value of y when x equals zero.

Step-by-step explanation: The zero of a function is the value of y when x equals zero. It is also known as an x-intercept. In this case, I believe there is a mistake in this question, as when x equals 0, it shows on the table that it is 6. The zero of the function should be (0,6). They say that the zero is -2, but that is not possible as that would be the y-intercept, where y is zero.

For your homework, I would ask the teacher about the question as it seems to be an error. You can use the response above, since it is correct, but make sure to check with your teacher for review.  

Answer:

x=10 L of .30 solution

x+y=30

y=20 L water

Step-by-step explanation:

The ratio of rectangle A to rectangle B is 9 to 11

The area of rectangle A is:

The area of rectangle B is:

The ratio of rectangle A to rectangle B is:

18/22

= 9/11

The area is 9 to 11

The correct statements regarding the steps Jorge could take to complete the reflection are:

1) Jorge should graph in the vertical line with values of -4 for the line of reflection.

2) Jorge could count how far each pre-image point is from the line of reflection along the perpendicular from the point to the line of reflection.

3) Jorge could count how far each vertex of the figure is from the y-axis and count the same distance on the other side.

4) Jorge will not move any point that lies on the line of reflection.

5) Jorge could check his work by seeing if each segment joining a pre-image point with its image has the midpoint on the line of reflection.

6) Jorge could check his work by making sure that the image has the same orientation as the original.

To complete the reflection of a figure across the line y = -4, Jorge can take the following steps:

1) Jorge should graph the vertical line y = -4 as the line of reflection. This line represents the axis of reflection, and all points on this line will remain fixed in their positions after the reflection.

2) Jorge could count how far each pre-image point is from the line of reflection along the perpendicular from the point to the line of reflection. This will help him determine the distance and direction each point should move to reflect across the line.

3) Jorge could count how far each vertex of the figure is from the y-axis and count the same distance on the other side. Since the line of reflection is y = -4, which is parallel to the y-axis, he can use the distance from the vertex to the y-axis as a guide to placing the reflected point on the other side of the line.

4) Jorge will not move any point that lies on the line of reflection. Points on the line of reflection will remain fixed in their positions as they are symmetric to themselves across the line.

5) Jorge could check his work by seeing if each segment joining a pre-image point with its image has the midpoint on the line of reflection. In a reflection, the midpoint of each line segment connecting a point and its reflection will lie on the line of reflection. Checking this property helps ensure the accuracy of the reflection.

6) Jorge could check his work by making sure that the image has the same orientation as the original. The orientation refers to the arrangement or direction of the figure's components (e.g., angles, lengths, shapes). If the image retains the same orientation as the original, it indicates a correct reflection.

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Question

Jorge needs to reflect a figure across the line y = negative 4. Which statements are correct regarding steps he could take to complete the reflection? Check all that apply.

1) Jorge should graph in the vertical line with values of –4 for the line of reflection.

2) Jorge could count how far each pre-image point is from the line of reflection along the perpendicular from the point to the line of reflection.

3) Jorge could count how far each vertex of the figure is from the y-axis and count the same distance on the other side.

4) Jorge will not move any point that lies on the line of reflection.

5) Jorge could check his work by seeing if each segment joining a pre-image point with its image has the midpoint on the line of reflection.

6) Jorge could check his work by making sure that the image has the same orientation as the original.

Answer:

x=5

Step-by-step explanation:

10+2x -4= 2x+1+x

6+2x=3x+1

6=x+1

5=x

Answer:

It's 10, on acellus :)

Step-by-step explanation:

Answer:

D. x=1

Step-by-step explanation:

8-2x = -8x + 14

First, add 8x to both sides.

8+6x=14

Next, subtract 8 from both sides.

6x=6

Lasty, divide 6 from both sides.

x=1

Hope this helps!

If not, I am sorry.

Answer:

Sorry if this is late but it's 11/15

Step-by-step explanation:

I did it on edg 2020 so ye

Answer:

the first one 11/15

Step-by-step explanation:

When a study's findings are highly valid, it means that they accurately reflect the genuine features, traits, and variations in the physical or social reality. The measure of frequency of drinking and driving is: reliable but not valid.

This option contends that although the survey's measure was not valid, it was dependable. This happens when research is constructed in a consistent but ineffective manner. In this instance, a sample of young people from a small town was taken into account; however, despite its consistency and reliability, it does not accurately reflect the findings of data from police records.

How well a method measures what it is supposed to measure is known as its validity. When a study's findings exists highly valid, it indicates that they accurately reflect the genuine features, traits, and variations in the physical or social reality. High dependability exists one sign of a valid measurement.

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Answer:

75 - x - 1.25y

Step-by-step explanation:

According to the uniform distribution, there is a 0.625 = 62.5% chance that a randomly chosen passenger will have to wait longer than 2.25 minutes.

The boundaries of a uniform distribution are a and b.

The likelihood of discovering a value greater than x is:

P(X > x)=b-x/b-a

In this issue, the distribution of time is evenly spaced between 0 and 6 minutes, therefore

a=0 b=6

P(X > x)= 6-2.25/6-0

=0.625

0.625 = 62.5% probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.

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Answer:

467.36 m^2 (maybe)

Answer: About 0.2 gallons

Step-by-step explanation: 4/18=0.2 repeating, so each person gets about 0.2 gallons.

Each of her friend will get 4 and a half gallons of juice.

Division is one of the four main arithmetical operations by which we find the equal distribution of something.

Given that, At Lara's party, 4 gallon of fruit punch are shared equally among 18 friend.

To find how much each of them got, we will divide total amount of punch  by total number friends

Amount of juice each of them gets, = 18/4 = 4.5

Hence,  Each of her friend will get 4 and a half gallons of juice.

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Answer:

fewaaaaa

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Trial and error into (ABOUT/APPROXIMATELY)

y=12000(1.04)^x

The equation of a line A is y=2x+3 and the equation of a line B is y=2x-6.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

Here,

From the given graph,

Equation of a line A is

Slope = Rise/Run = 8/4 =2

Here y-intercept is 3

Substitute m=2 and c=3 in y=mx+c, we get

y=2x+3

From the given graph,

Equation of a line B is

Slope = Rise/Run = 4/2 =2

Here y-intercept is -6

Substitute m=2 and c=-6 in y=mx+c, we get

y=2x-6

Therefore, the equation of a line A is y=2x+3 and the equation of a line B is y=2x-6.

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The value of the function f(x) at x = 1.477.

f(1.477) = 32.857

The value of the function g(x) at x = 20.

g(20) = 1.729

We have,

Two functions:

f(x) = b^x

g(x) = log_b(x)

Now,

From the table,

f(0.699) = b^0.699 = 5

Taking the logarithm of both sides with base b.

log_b(5) = 0.699

b = 5^(1/0.699)

b = 8.343

Now, we can find the value of f(1.477).

f(1.477) = b^1.477 = 8.343^1.477 = 32.857

Similarly, we can find the value of g(20).

g(20) = log_b(20) = log_8.343(20) = 1.729

Thus,

The value of the function f(x) at x = 1.477.

f(1.477) = 32.857

The value of the function g(x) at x = 20.

g(20) = 1.729

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Answer:  x = 23

Step-by-step explanation:

The sum of interior angles in a triangles is equal to 180°, therefore:

(2x - 1) + 110 + 25 = 180

1. Get rid of parentheses.

 2x - 1 + 110 + 25 = 180  

2. Add the number up in the left side.

            2x  + 134 = 180

3. Subtract 134 from both sides.

                      2x = 46

4. Divide by 2 from both sides.

                      x = 23

The system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

A line process has three processing stages with the characteristics given below:

Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100%

To determine the system capacity and the bottleneck stage and utilization of Stage 3:

The system capacity is calculated by the product of the processing capacity of each stage:

1 x 1 x 2 = 2 units per minute

The bottleneck stage is the stage with the lowest capacity and it is Stage A. Therefore, Stage A has the lowest capacity and determines the system capacity.The utilization of Stage 3 can be calculated as the processing time per unit divided by the available time per unit:

Process time per unit = 1 + 2 + 3 = 6 minutes per unit

Available time per unit = 90% x 100% x 100% = 0.9 x 1 x 1 = 0.9 minutes per unit

The utilization of Stage 3 is, therefore, (6/0.9) x 100% = 666.67%.

However, utilization cannot be greater than 100%, so the actual utilization of Stage 3 is 100%.

Hence, the system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

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To write the power series in x for the given function \(f(x) = 3/3 - 6x\), we use the formula of geometric progression:\(a + ar + ar² + ar³ +...+ arⁿ-¹ +...= a / (1 - r)\) The formula of geometric series is \(1 / (1 - r) = 1 + r + r² + r³ +...+ rⁿ-¹ +...\)

we have: \(1 / (1 - 2x) = 1 + 2x + 4x² + 8x³ +... + 2ⁿ xⁿ +...\)

Thus, the power series in x for the given function\(f(x) = 3/3 - 6x is:1 + 2x + 4x² + 8x³ +... + 2ⁿ xⁿ +...\)

This is the required answer.Note: The formula of geometric progression is \(a + ar + ar² + ar³ +...+ arⁿ-¹ +...= a / (1 - r)\).

The formula of geometric series is \(1 / (1 - r) = 1 + r + r² + r³ +...+ rⁿ-¹ +...\)

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the y-intercept is 165.

The equation of the tangent line to the graph of f(x) at the point (2, 11) is:

y = -77x + 165

To find the equation of the tangent line to the graph of f(x) at the point (2, 11), we need to determine the slope of the tangent line and the y-intercept.

Find the slope of the tangent line:

The slope of the tangent line to the graph of f(x) at any point can be found by taking the derivative of f(x) with respect to x and evaluating it at the given point.

f(x) = 3x - 20x^2

f'(x) = 3 - 40x

To find the slope at x = 2, we substitute x = 2 into the derivative:

f'(2) = 3 - 40(2) = 3 - 80 = -77

Therefore, the slope of the tangent line is -77.

Find the y-intercept:

To find the y-intercept, we substitute the coordinates of the given point (2, 11) and the slope into the equation y = mx + b, and solve for b.

11 = -77(2) + b

11 = -154 + b

b = 165

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Answer:

$5

Step-by-step explanation:

1=$5 so 2 hours = 10 SO 4hours ×$5= $20

Answer:

$5 per hour

Step-by-step explanation:

hope this helps :D

cheers man

How to find slope:

Divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

The actual formula for this is: (y2 - y1)/(x2 - x1).

How to find Y intercept

To find the y-intercept, plug 0 in for 'x' and solve for 'y'.

Ex. 2x + 3y = 12

So you plug in 0 for x therefore it becomes:

3y = 12

so, the y intercept is 4

Let me know if this is helpful :)

Based on the given information, we know that the arrival rate is 9 customers per hour and the service rate is 14 customers per hour. Since the arrival and service distributions are not known, we cannot use the m/m/1 formulas to calculate the average waiting time and total time spent in the system.

However, we can still use the Little's Law formula to relate the average number of customers in the system to the average waiting time. Little's Law states that the average number of customers in the system (N) is equal to the product of the arrival rate (λ) and the average time spent in the system (T), or N = λT.

Since we want to find the total time spent in the system, we can rearrange the formula to solve for T. Thus, T = N / λ.

We know from the given information that the average waiting time in the line is 18 minutes. Therefore, the average time spent in the system for a customer is T = 18 minutes + (1/14 hour), which is equal to 1.9 hours.

To calculate the total time spent in the system, we need to add the waiting time to the service time. Since the service rate is 14 customers per hour, the service time per customer is 1/14 hour or approximately 4.3 minutes. Thus, the total time spent in the system is approximately 22.3 minutes or 0.37 hours.

In summary, the average time spent in the system for a customer is 1.9 hours, and the total time spent in the system is approximately 22.3 minutes or 0.37 hours.

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