Write and evaluate the definite integral that represents the volume of the solid formed by revolving the region about the x-axis. y= -x+2

Answers

Answer 1

The definite integral of the given function will be \(\pi(\dfrac{1304}{27})\).

What is integration?

Integration is defined as the summing up of the small parts to find the total value.The given function y = -x +2 will be integrated as follows:-

The limits are given as a = 0 and b = 2.

The integration will be done as:-

\(V = \pi\int_0^2\pi(y^2)dx\\\\\\V = \pi\int _0^2(\pi(-x+2)^2dx\\\\\\V = \pi\int _0^2(x^2+16+8x)dx\\\\\\V=\pi [ (\dfrac{x^3}{3}+16x+\dfrac{8x^2}{2}]_0^2\\\\\\V = \pi[(\dfrac{2^3}{3^3}+(16\times 2) + 8\dfrac{2)^2}{2}]-0\\\\\\V = \dfrac{1304}{27}\pi\)

Therefore definite integral of the given function will be \(\pi(\dfrac{1304}{27})\).

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Related Questions

Helppp!! Malcolm is training for a marathon. He runs 3 miles in
hour. What is Malcolm's rate in miles per hour?


A)5.85
B)4.75
C)6.23
D)5.42

Answers

Answer:

Malcolm would logically be running at 4.75 and since he is running at 3, it would be the lowest possible therefore its B

Step-by-step explanation:

two marbles are randomly selected without replacement from a bag containing blue and green marbles. the probability they are both blue is . if three marbles are randomly selected without replacement, the probability that all three are blue is . what is the fewest number of marbles that must have been in the bag before any were drawn? (2000 mathcounts national target)

Answers

The probability of selecting two blue marbles without replacement is 1/6, and the probability of selecting three blue marbles without replacement is 1/35. The fewest number of marbles that must have been in the bag before any were drawn is 36.

Let's assume there are x marbles in the bag. The probability of selecting two blue marbles without replacement can be calculated using the following equation: (x - 1)/(x) * (x - 2)/(x - 1) = 1/6. Simplifying this equation gives (x - 2)/(x) = 1/6. Solving for x, we find x = 12.

Similarly, the probability of selecting three blue marbles without replacement can be calculated using the equation: (x - 1)/(x) * (x - 2)/(x - 1) * (x - 3)/(x - 2) = 1/35. Simplifying this equation gives (x - 3)/(x) = 1/35. Solving for x, we find x = 36.

Therefore, the fewest number of marbles that must have been in the bag before any were drawn is 36.

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During the month of January George worked a total of 21 days, 8 hours each day. He did not work any overtime hours during October. Henry earns $29 per hour. What was his earned wages for the month of January ?

A) $232.00
B) $4,872.00
C) $4,640.00
D) $609.00

Answers

Answer:

B

Step-by-step explanation:

21*8=168

29*168=$4,872.00

A series of formulas that describe technical aspects of a system is a(n) _______ model.
a) textual
b) descriptive
c) graphical
d) mathematical

Answers

The correct option is d) mathematical

What is a technical system model?

A mathematical model is a set of equations or algorithms that represent technical aspects of a system. These equations or algorithms are used to predict or simulate system behavior and performance. Mathematical models are often used in engineering, science, economics, and other fields where complex systems need to be analyzed and optimized. For example, a mathematical model could be used to analyze how a communication network would perform with different levels of traffic or to predict how a chemical reaction would proceed under various conditions. Mathematical models are often represented graphically to provide a clear visualization of the complex relationships between variables within a system. Overall, mathematical models are an essential tool for designing, optimizing, and managing complex systems.

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Monique is planning the locations for three exhibit areas at the festival. She drew a model of one of the exhibit areas as shown on the coordinate grid below. To determine the location of the second exhibit area, she will reflect the first area across the dashed line. To determine the location of the third exhibit area, she will translate the second area (x,y)→(x+1,y+6)

Answers

The second area was translated 1 unit right and 6 units down to form the third exhibit area.

Transformation

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, dilation and rotation.

Translation is the movement of a point either up, down, left or right.

Given the translation (x,y)→(x+1,y+6). Hence:

The second area was translated 1 unit right and 6 units down to form the third exhibit area.

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Rearrange the formula m² = 5n³ + 4k to make n the subject.

Answers

Answer:

3√2-4k/5 = n

Step-by-step explanation:

m2-4k=5n^3

2-4k/5 = n^3

3√2-4k/5 = n

how many different functions are there from a set with 10elements to sets with the following numbers of elements?

Answers

Using the same logic, we can find the number of different functions from A to B2, B3, and so on. The number of possible mappings for each element in A remains the same, but the number of elements in B changes.

Let's denote the set with 10 elements as A, and the sets we are mapping to as B1, B2, B3, and so on.
To determine the number of different functions from set A to set B1, we need to consider that each element in A has to be mapped to an element in B1. There are no restrictions on which element can be mapped to which, so for each of the 10 elements in A, we have |B1| possible choices. Therefore, the total number of different functions from A to B1 is |B1|^10.

So, the total number of different functions from A to B2 is |B2|^10, and so on.
In summary, the number of different functions from A to sets with the following numbers of elements are:

- B1: |B1|^10
- B2: |B2|^10
- B3: |B3|^10
- and so on.
To determine the number of different functions from a set with 10 elements (the domain) to sets with varying numbers of elements (the range), we'll use the formula:



Number of functions = range size ^ domain size
For example, let's assume the range has 'n' elements. Then, the number of different functions from a set with 10 elements to a set with 'n' elements would be:
Number of functions = n^10
To find the number of functions for a specific range size, replace 'n' with the number of elements in that set.

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If something was sold for $270 after it was reduced by 1/3 of the original price, what was the original price

Answers

Answer:

$810

Step-by-step explanation:

you can multiply 210 by 3

How do I know how to determine whether a relation is a function? What is a function?
Input: Output:
-3 11

0 5

3 -1

6 -7

9 -13​

Answers

Answer:

all are functions

Step-by-step explanation:

a function is when each x has a y

a relation is when 1 x has more than 1 y which makes it invalid therefore not a function

it’s a function is every single input has their own output. for example, if there were 2 -3’a on the input side, the relation wouldn’t be a function because each input has to have their OWN output, and can’t share outputs.

Simplify The Following - c^5xc

Answers

if a + b is equal to 2 find the value of a cube plus b cube + 6ab

Multiply.
2x^4 (3x³ − x² + 4x)

Multiply.2x^4 (3x x + 4x)

Answers

Answer:  A

Step-by-step explanation:

When multiplying: Numbers multiply with numbers and for the x's, add the exponents

If there is no exponent, you can assume an imaginary 1 is the exponent

2x⁴ (3x³ − x² + 4x)

= 6x⁷ -2x⁶ + 8x⁵

Answer:

A. \(6x^{7} - 2x^{6} + 8x^{5}\)

Step-by-Step

Label the parts of the expression:

Outside the parentheses = \(2x^{4}\)

Inside parentheses = \(3x^{3} -x^{2} + 4x\)

You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses

\(2x^{4}\) × \(3x^{3}\)

\(2x^{4}\) × \(-x^{2}\)

\(2x^{4}\) × \(4x\)

First, multiply the whole numbers of each value before the variables

2 x 3 = 6

2 x -1 = -2

2 x 4 = 8

Now you have:

6\(x^{4}x^{3}\)

-2\(x^{4}x^{2}\)

8\(x^{4} x\)

When you multiply exponents together, you multiply the bases as normal and add the exponents together

\(6x^{4+3}\) = \(6x^{7}\)

\(-2x^{4+2}\) = \(-2x^{6}\)

\(8x^{4+1}\) = \(8x^{5}\)

Put the numbers given above into an expression:

\(6x^{7} -2x^{6} +8x^{5}\)

Key Words

distribution

variable

like exponents

Who is in more debt a person with a balance of $-30 or a person with $-40? why

Answers

Answer:

A person with $-40 is in more debt

Step-by-step explanation:

The person with $-40 has borrowed or spent money from their credit card more than the person who is in debt for $-30.

Answer:$-40

Step-by-step explanation:

A person with negative 40 dollars has 40 dollars missing, a person with -30 dollars only has 30 dollars missing. So the person with -$40 is missing more money and therefore, is in more debt.

Help Fast. Choose the system of inequalities that best matches the graph below.

Help Fast. Choose the system of inequalities that best matches the graph below.

Answers

Answer:

D

Step-by-step explanation:

Solve through logic and brain rather than lengthy calculations

Trick to be used

See

the red line is solid and that denotes to the fact that the symbol must be ≤ or ≥ .It is parallel to x axis at y=4Rest values of y are less than 4 So y≤4

Only option D contains y≤4

Option D is correct

PLS HELP, WILL GIVE BRAINLIEST!!

PLS HELP, WILL GIVE BRAINLIEST!!

Answers

Answer: D = (- ∞, -1) ∪ (-1,  ∞) R = (- ∞,3) U [5,5]

Step-by-step explanation:

Charles is going to purchase a new car that has a list price of $21,450. He is planning on trading in his good-condition 2004 Dodge Neon and financing the rest of the cost over three years, paying monthly. His finance plan has an interest rate of 12. 28%, compounded monthly. Charles will also be responsible for 6. 88% sales tax, a $1,089 vehicle registration fee, and a $124 documentation fee. If the dealer gives Charles 80% of the listed trade-in price on his car, once the financing is paid off, what percent of the total amount paid will the interest be? (Consider the trade-in to be a reduction in the amount paid. ) Dodge Cars in Good Condition Model/Year 2004 2005 2006 2007 2008 Viper $7,068 $7,225 $7,626 $7,901 $8,116 Neon $6,591 $6,777 $6,822 $7,191 $7,440 Intrepid $8,285 $8,579 $8,699 $9,030 $9,121 Dakota $7,578 $7,763 $7,945 $8,313 $8,581 a. 17. 64% b. 15. 67% c. 16. 70% d. 12. 86% Please select the best answer from the choices provided A B C D

Answers

Percent of the total amount a per the given list price, documentation fee , registration fee and other payment paid by Charles is given by :

Option c. 16.70%

Cost of his old 2004 Dodge Neon = $6591

Sales tax = 6.88%

Dealer gives 80% trade in price on hos car

After tax selling price of the car

= 6,591 × (80/100) × [ 1 - (6.88/100) ]

= $4910.03

= $4,910

Vehicle registration amount = $1,089

List price of car = $21,450

Documentation fee = $124

Total cost of the car

= $21,450 + $1,089 + $124

= $22,663

Net amount Charles needs to pay

= $22,663 - $4,910

= $17,753

Monthly payment at the rate of 12.28% compounded monthly for 3 years

= 17753 [ 12.28%( 1+ 12.28%)^3 / [( 1+ 12.28%)^3 -1 ]

= $592

Total amount paid by Charles

= $592 × 36

= $21,312

Total interest paid by Charles

= $21,312 - $17,753

= $3,559

Percent of the total amount

= ( $3,559 / $21,312 ) × 100

= 16.699%

= 16.70%

Therefore, the percent of the total amount paid by Charles is equal to Option c. 16.70%.

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to find the height of a pole, a surveyor moves 150 feet away from The base of the pole and then, with a transit 4 feet tall, measures the angle of elevation to the top of the pool to be 42°. To the nearest foot, what is the height of the pole?

to find the height of a pole, a surveyor moves 150 feet away from The base of the pole and then, with

Answers

ANSWER :

139 feet

EXPLANATION :

The surveyor is 150 feet away from the base of the pole.

The transit is 4 feet tall and the angle of elevation to the top of the pole is 42 degrees.

The illustration will be :

We have a right triangle with an angle of 42 degrees.

The side opposite to the angle is x and the side adjacent to the angle is 150

Using Tangent function :

\(\begin{gathered} \tan\theta=\frac{\text{ opposite}}{\text{ adjacent}} \\ \\ \tan42=\frac{x}{150} \\ x=150\tan42 \\ x=135.06\sim135\text{ ft} \end{gathered}\)

The height of the pole is x + 4

That will be 135 + 4 = 139 ft

to find the height of a pole, a surveyor moves 150 feet away from The base of the pole and then, with

from year to year, monthly data on the number of flu cases seen in a hospital emergency department would likely show consistent increases during certain months, and decreases during others. this is an example of group of answer choices exponential smoothing seasonality holt's method none of the above

Answers

The given scenario of monthly data on the number of flu cases seen in a hospital emergency department that shows consistent increases during certain months and decreases during others is an example of seasonality.

Seasonality refers to the predictable pattern of fluctuations in a time series data that occurs at regular intervals over a period of time. In this case, the seasonal pattern is related to the occurrence of the flu virus, which typically peaks during the winter months and decreases in the summer months.

Exponential smoothing is a statistical method used to forecast time series data, which involves assigning weights to past observations that decline exponentially over time. Holt's method is an extension of exponential smoothing that includes a trend component in addition to the level and seasonality components.

However, neither exponential smoothing nor Holt's method directly address seasonality in time series data. Therefore, the correct answer to the given question is "seasonality".

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A recent conference had 875 people in attendance. In one exhibit room of 60 people, there were 46 teachers and 14 principals. What prediction can you make about the number of principals in attendance at the conference?

There were about 204 principals in attendance.
There were about 266 principals in attendance.
There were about 671 principals in attendance.
There were about 815 principals in attendance.

Answers

There were about 204 principals in attendance.

The correct option is (A).

What is Arithmetic?

The mathematical branch known as arithmetic deals with the study and application of numbers, their relationships, and mathematical observations.

As per the given data:

The total number of people in the recent conference = 875

The total number of people in one exhibit room = 60

Number of teachers in one exhibit room = 46

Number of principals in one exhibit room = 14

To find out the total number of exhibit rooms:

= Total number of people in the conference / total people in one room

= 875 ÷ 60

= 14.58 = 15 {rounding off to the nearest integer}

Number of principals in one exhibit room = 14

Total number of principals in the conference:

= Number of rooms × Principals in one room

= 15 × 14 = 210 which is equal to 204 {approximate answer}

There were about 204 principals in attendance.

Hence, There were about 204 principals in attendance.

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anyone know the answer? its algrebra
Does the equation represent an exponential function?

y = 4 • 5x

Yes
No

Answers

Answer:

yes is rhe anwers that was that i put

Carlos bought 6.5 pounds of bananas for $5.20.

● What is the price per pound of the bananas that Carlos bought?


What quantity of bananas would one dollar buy?

Answers

Answer:

Each banana cost $0.80.

Step-by-step explanation:

5.20 divided by 6.5 is 0.80

)A spinner is divided into sections of equal size, of which some are red, some are blue, and the remaining are green. The probability of the arrow landing on a section colored red is 50%. The probability of the arrow landing on a section colored blue is 10%. What is the probability of the arrow landing on a section colored green? I need help

Answers

Answer:

40%

Step-by-step explanation:

The probability of the arrow landing on the green section is a 40% chance

This is because there are only 3 sections where one is 50 and the other is 10

To find the green we can create an equation, where x = green section

50 + 10 + x = 100

The equation equals 100 because that's the highest the percentage will go in probability, unless we were told otherwise

60 + x = 100

x = 100 - 60

x = 40

The diameter of Jacob's circular tabletop is 6 feet. What is the area, in square feet, of Jacob's tabletop? A 6 B. 9 С. 12 D 36​

Answers

Answer:

B. 9

Step-by-step explanation:

the area = π × 3² = 9π ft²

Area of a circle = pi x R^2

R is the radius which is 1/2 the diameter.

R = 6/2 = 3 feet

Area = pi x3^2

Area = 9pi

The answer is B

For the standard normal random variable z, find z for each situation. If required, round your answers to two decimal places. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300)'
a. The area to the left of z is 0.1827. z =
b. The area between −z and z is 0.9830. z =
c. The area between −z and z is 0.2148. z =
d. The area to the left of z is 0.9997. z =
e. The area to the right of z is 0.6847. z=

Answers

The z-values for the given situations are approximate:

a. The area to the left of z is 0.1827. z = -0.90

b. The area between −z and z is 0.9830. z = 2.17

c. The area between −z and z is 0.2148. z = 0.85

d. The area to the left of z is 0.9997. z = 3.49

e. The area to the right of z is 0.6847. z= -0.48

a. For an area of 0.1827 to the left of z, the corresponding z-value can be found using a standard normal distribution table or a statistical calculator. The z-value is approximately -0.90.

b. To find the z-value for an area between -z and z equal to 0.9830, we need to find the value that corresponds to (1 - 0.9830)/2 = 0.0085 in the upper tail of the standard normal distribution. Using the table or calculator, the z-value is approximately 2.17.

c. Similarly, for an area between -z and z equal to 0.2148, we find the value that corresponds to (1 - 0.2148)/2 = 0.3926 in the upper tail. The z-value is approximately 0.85.

d. For an area of 0.9997 to the left of z, we find the value that corresponds to 0.9997 in the upper tail. The z-value is approximately 3.49.

e. To find the z-value for an area to the right of z equal to 0.6847, we find the value that corresponds to 1 - 0.6847 = 0.3153 in the upper tail. The z-value is approximately -0.48.

In summary, the z-values for the given situations are approximate:

a. -0.90

b. 2.17

c. 0.85

d. 3.49

e. -0.48

These values can be used to determine the corresponding percentiles or probabilities for the standard normal distribution. The values are typically found using standard normal distribution tables or statistical calculators that provide the cumulative probability distribution function (CDF) for the standard normal distribution.

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Bonds that do not have any assets of the issuer pledged as collateral, sometimes named junk bonds, are known as: Select one: a. Secured bonds b. Callable bonds c. Convertible bonds d. Unsecured bonds

Answers

Bonds that do not have any assets of the issuer pledged as collateral and are often referred to as junk bonds are known as unsecured bonds.

Unsecured bonds, also known as non-collateralized bonds or debentures, are debt securities issued by companies or governments that do not have any specific assets pledged as collateral. These bonds rely solely on the creditworthiness and reputation of the issuer for repayment. They are considered riskier investments compared to secured bonds because in the event of default, there are no specific assets backing the bondholders' claims.

The term "junk bonds" is often used to describe high-yield bonds that carry a higher risk of default. These bonds are typically issued by companies with below-price-grade credit ratings. The term "junk" refers to the perceived low quality or higher risk associated with these bonds.

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Scores on an exam follow an approximately normal distribution with a mean of 76. 4 and a standard deviation of 6. 1 points. What is the minimum score you would need to be in the top 7%?.

Answers

If the scores on an exam follow an approximately normal distribution with a mean of 76.4 and a standard deviation of 6.1 points, then the minimum score needed to be in the top 7% is calculated to be 85.404.

This type of normal distribution problem can be solved by using the z-score.

Considering Z to be the standard score, μ to be the mean, and σ to be the standard deviation, the z-score formula to find the minimum score to be in the top 7% can be given as,

Z = x - μ / σ

z-score can be determined using a standard table if the p-value is known.

As the minimum score to be in the top 7% is required to be found, p-value = 0.07

In the standard table, the z-score corresponding to the p-value of 0.07 is found to be 1.476

Therefore,

1.476 = x - 76.4 / 6.1

1.476 (6.1) = x - 76.4

9.004 = x - 76.4

x = 9.004 + 76.4

x = 85.404

Hence, the minimum score required to be in the top 7% is equal to 85.404

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anemia for the study of jordanian children in exercise 4, the sample mean hemoglobin level was 11.3 g/dl and the sample standard deviation was 1.6 g/dl. a significance test yields a p-value of 0.0016. (a) interpret the p-value in context. (b) what conclusion would you make if a 0.05? a 0.01? justify your answer.

Answers

(a) The interpret the p-value in context of 0.0016 indicates that the probability of obtaining a sample mean hemoglobin level of 11.3 g/dl or lower.

(b) The conclusion would make if a 0.05 is rejected because the p-value (0.0016) is less than the significance level.

If using a significance level of 0.01, the null hypothesis would still be rejected because the p-value is less than 0.01.

Anemia Study Results

(a) The p-value of 0.0016 indicates that the probability of obtaining a sample mean hemoglobin level of 11.3 g/dl or lower, assuming that the true population mean is 12 g/dl (or higher), is only 0.0016. This suggests that the observed difference between the sample mean and the hypothesized population mean is statistically significant and unlikely to be due to chance alone.

(b) If using a significance level of 0.05, the null hypothesis (that the true population mean is 12 g/dl or higher) would be rejected because the p-value (0.0016) is less than the significance level. Therefore, it can be concluded that the sample provides evidence that the true population mean hemoglobin level is lower than 12 g/dl.

If using a significance level of 0.01, the null hypothesis would still be rejected because the p-value is less than 0.01. In this case, the evidence is even stronger, and the conclusion that the true population mean is lower than 12 g/dl would be even more robust.

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What is the scale factor applied to Figure A to produce Figure B.
O
A 9
B 6
C 3
D 12

What is the scale factor applied to Figure A to produce Figure B.OA 9B 6C 3D 12

Answers

The scale factor applied to Figure A with one side's length of 6 inches to produce Figure B with one side's length of 18 inches is C. 3.

What is the scale factor?

The scale factor refers to the ratio of one scale or object compared to another.

The scale factor can increase or decrease the measurement of the object.

The first side length of Figure A = 3 inches

The second side length of Figure A = 6 inches

The first side length of Figure B = 9 inches (3 x 3)

The second side length of Figure B = 18 inches (6 x 3)

Thus, the scale factor used on Figure A to produce Figure B is C. 3.

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A culture of bacteria triples by the end of each hour. If there were initially 40 bacteria in a culture, how many bacteria should be there after 3 hours.

Answers

40x3=120, so anwser is it

Answer: 360 bacteria

Step-by-step explanation: if it triples every hour, you would need to triple the amount of hours, and multiply that by 40 since 40 was the initial bacterial count. Hope this helps:)

The critical value, or z*, that is used to construct a confidence interval for a proportion depends upon? A. the confidence level. B. the sample size.C. the confidence level and the sample size. D. the sample size and the sample proportion. E. the confidence level, the sample size, and the sample proportion.

Answers

The critical value that is used to construct a confidence interval for a proportion depends upon C. the confidence level and the sample size.

The critical value used to construct the confidence interval for proportion depends on:

1) The sample size:

The probability changes as the sample size changes as the distribution of the test statistics is dependent on sample size, thus the critical value will depend on sample size.

2) The confidence level:

The critical value is always calculated by using the confidence level, so it is dependent on it.

The sample proportion is the observed value which is used to perform the test, but not to construct the critical value.

Thus the correct option is:

Option C: The confidence level and sample size.

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The
The table shows the average daily number of hours sleep of 10 children.
Age (years)
6 1 3 8 4 5 2 7 9 7
Number of hours sleep 12.5 15 13.2 11 14 12 14 11.69.8 11
The first eight results have been plotted.
a) Plot the next two points.
x
Number of hours sleep
b) What type of correlation is shown
by the graph? Negative
10
c) Draw a line of best fit.
2
4
6
8
10
Age (years)
Please help.

TheThe table shows the average daily number of hours sleep of 10 children.Age (years)6 1 3 8 4 5 2 7

Answers

Answer:

C: about 10 Hours

Step-by-step explanation:

i was on the assignment and i got C correct  

The missing points are (7, 11), and (9, 9.8) and the type of correlation is negative.

What is the line of best fit?

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

\(\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\\\\\\\rm c = \dfrac{\sum y -m \sum x}{n}\)

Let the line of best fit is:

y = mx + c

The missing points are:

(7, 11), and (9, 9.8)

The correlation will be negative.

The line of best fit is shown in the picture.

Thus, the missing points are (7, 11), and (9, 9.8) and the type of correlation is negative.

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TheThe table shows the average daily number of hours sleep of 10 children.Age (years)6 1 3 8 4 5 2 7
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EJH Company has a market capitalization of $1.2 billion and 30 million shares outstanding. It plans to distribute $100 million through an open market repurchase. Assuming perfect capital markets: a. What will the price per share of EJH be right before the repurchase? b. How many shares will be repurchased? c. What will the price per share of EJH be right after the repurchase? C--- a. What will the price per share of EJH be right before the repurchase? The price per share of EJH right before the repurchase is $. (Round to the nearest cent.) b. How many shares will be repurchased? The number of shares to be repurchased is million. (Round to two decimal places.) c. What will the price per share of EJH be right after the repurchase? The price per share of EJH right after the repurchase will be $. (Round to the nearest cent.) Polygon WXYZ has vertices W(2,1) , X(2,3) , Y(0,4) , and Z(0,0) . After a dilation the vertices of the image are W'(4,2) , X'(4,6) , Y'(0,8) , and Z'(0,0) . Determine the scale factor of the dilation.scale factor: which potential energy diagram reprsents the change in potential energy that ocurs when a catalyst is added to a chemical reaction Erica is participating in a road race. The first part of the race is on a 5.2-mile-long straight road oriented at an angle of 25 north of east. The road then turns due north for another 6.0 mi to the finish line.In miles, what is the straight-line distance from the starting point to the end of the race? A. 5453.200 debat Accourts Parabis, 513,200 creat to Herchandse invertory, and 5440,000 creat to Cash c. 3500000 debt in Acoouris Payasie and 5500,000 coedt to Cash 02:23:02A rectangle with an area of x2 - 4x - 12 square units isrepresented by the modelWhat side lengths should be used to model therectangle?O(x + 2) and (x-6)0 (x + 6) and (x - 2)0 (x + 2) and (x 10)o (x + 10) and (x - 2)XX--XSave and ExitNextSubmit Complete a research paper on Employment Discrimination inOrganizations with 5-6 scholarly reviewed references Before a collision, a 35-kg object is moving at +10. 0 m/s. Find the impulse that acted on the object if, after the collision, it moves at +8. 0 m/s _____ indicates that the two sides of the brain have different responsibilities. Where in the flower are pollen grains produced? A. SepalsB. OvariesC. OvulesD. StigmasE. Anthers what is the highest age group at risk for getting chlamydia or gonorrhea? The sum of the interior angles of each polygon is 360. In the diagram ABCD=HGEF find the values of x and y look at photo below 1. The derivative of a constant is zero.Explain why this is true:A. Using the limit definition of the derivative.B. Using a slope interpretation of the derivative.C. In your own words, giving your best explanation that demonstrates your understanding of derivatives. Question 1(a) For 5 marks, explain why storing passwords in plain text isa problem. In your explanation, give a detailed rundown on how thisproblem is solved. A 60-watt light bulb uses 60 watt hours of electricity in 1 hour. Suppose everyone in theUnited States left one unneeded 60 watt light bulb on for one hour every day for a year.9. Electricity is billed in kilowatt hours. So 60 watt hours is equal to sixtydivided by one thousand. Express the electricity used by a 60-watt lightbulb in one hour in kilowatt hours in scientific notation.10. Express the number of days in a year in scientific notation.11. There are about 315,000,000 people in the United States. Write thatnumber in scientific notation.12. Now find how many kilowatt hours of electricity would be wasted ifevery person in the United States left on one unneeded 60-watt lightbulb one hour a day for a whole year. Express your answer in bothscientific notation and standard notation.13. The average household uses about 15,000 kilowatt hours per year.How many households could use that wasted electricity from item 12and have light for a year? Express your answer in standard notation.the original content are the responsibility o an aqueous solution contains 0.390 m hydrofluoric acid. how many ml of 0.294 m sodium hydroxide would have to be added to 125 ml of this solution in order to prepare a buffer with a ph of 3.050? Select the frequency of light having a wavelength of 2.4 1010 nm and the wavelength of light with a frequency of 2.4 1010 Hz. Select all that apply.a. 1.3 x 10^7 nmb. 1.3 10^7 Hz For what values of K will the system be unstable:a) G = 1/(s+1) and H = (s-1)/(s+2),b) G(s) x H(s) = (s^2+2s+2)/(s^2(s-1)) what is interesting about the use of the narrator in The End of Something Write an equation in slope intercept form for the line with the point (-6,5) and has a slope of -5/2