the length of a rectangle is 4 times the width. if the area of the rectangle is 324 square feet, the dimensions of the rectangle are ?

Answers

Answer 1

If the area of the rectangle is 324 square feet, the dimensions of the rectangle are length 9 feet and width 36 feet.

A rectangle with an area of 324 square feet and a length that is 4 times the width can be described by the equation W * 4W = 324. This equation can be expanded to 4W^2 = 324.

To find the width of the rectangle, we can take the square root of both sides of this equation, which gives W^2 = 81. Taking the square root of 81 gives W = 9 feet, which is the width of the rectangle.

Since the length of the rectangle is 4 times the width, the length of the rectangle is 4 * 9 = 36 feet. So the dimensions of the rectangle are 9 feet by 36 feet.

This means that if you draw a rectangle with a width of 9 feet and a length of 36 feet, the area of this rectangle would be 324 square feet.

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Related Questions

the graph of the function f(x) = (x+2)(x-4) is shown.

Which describes all of the values for which the graph is
negative and increasing?
all real values of x where x < -2
all real values of x where -2 all real values of x where 1 all real values of x where x < 0
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Submit

Answers

The function is negative, and for values of x closer to -2, the function is increasing.

What is function?

A function is a block of code that performs a specific task. It is a self-contained unit of code that can be reused throughout a program to perform a specific task. Functions accept inputs in the form of parameters, perform a set of operations and then return an output. They allow for a code to be written once and used multiple times, making it easier to read and maintain. Functions also help to organize code into smaller, manageable pieces, making it easier to track down bugs and other errors.

The graph of f(x) is negative and increasing for all real values of x where x < -2, since the graph is a downward-opening parabola with its vertex at x=-2. For values of x less than -2, the function is negative, and for values of x closer to -2, the function is increasing.

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complete the sentence to describe the distance and ruler postulates. between every pair of distinct points, there is a positive unique number called t

Answers

Between every brace of distinct points, there's a positive unique number called t which is the distance.

The positive number between every brace of distinct points is known as the distance and it can be set up as the absolute value of the difference between the corresponding real figures.

The distance represents the space between a brace of distinct points. This is called the distance hypothetical.

In order to find the distance, you would need to break for the absolute value of the difference between the real figures that are at the two points.

The Distance Postulate Given any brace of distinct points, there corresponds a unique positive real number called the distance between the two points.

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Graph the equation shown below by transforming the given graph of the parent function. y = 2 x + 1

Answers

Graph of the function y = 2x + 1 along with its parent function is attached below.

What is function?

A function is defined as a relation between a set of inputs having one output each. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input.

Given function,

y = 2x + 1

The parent function is the simplest form of the type of function given

Parent function is y = 2x

Shifting the graph of parent function vertically up 1 unit.

We get the graph of function y = 2x + 1

Hence, following is the graph of function y = 2x + 1 transformed from parent function y = 2x

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The heights of basketball players, in inches, on two different teams is given in the data.

Champs: {66, 63, 65, 64, 58, 68, 47, 50, 65, 60, 62, 64, 60, 65, 55}

All Stars: {73, 62, 60, 63, 72, 65, 69, 68, 71, 66, 70, 67, 60, 70, 71}

Using the correct measure of center, which team typically has the tallest players?

The All Stars, with a mean of approximately 67.1 inches
The Champs, with a mean of approximately 60.8 inches
The All Stars, with a median of 68 inches
The Champs, with a median of 63 inches

Answers

Answer: is d

Step-by-step explanation:

A multipack of water contains 6 bottles of water.
A box holds 3 multipacks of water.
A shop orders 24 boxes of water.
How many bottles of water have they ordered


Answers

Answer:

They ordered 432 bottles of water

Step-by-step explanation:

1 multipack = 6 bottles

3 multipacks = 1 box

24 boxes = 24 (3 multipacks)

24 boxes = 72 multipacks

72 multipacks = 72 (6 bottles)

72 multipacks = 432 Bottles

A random sample of 300 students is selected from a large group of students who use a computer-equipped classroom on a regular basis. Occasionally, students leave their USB drive in a computer. Of the 300 students questioned, 180 said that they write their name on their USB drive. Which of the following is a 98 percent confidence interval for the population of all students using the classroom who write their name on their USB drive? 0.4 + 2.331 (0.4)(0.6) 300 (0.4)(0.6) 300 0.4 - 1.967 0.6 +2.05. (0.6)(0.4) 300 90.6. + 2.331 (0.6)(0.4) 300 0.6 I 1.96V (0.6)(0.4) 300

Answers

The 98 percent confidence interval for the population of all students using the classroom who write their name on their USB drive is B) 0.4 ± 1.967 (0.4)(0.6) / √300.

The sample proportion (p-hat) of students who write their name on their USB drive is 0.4, based on 180 out of 300 students. The sample size is large enough (n > 30) to use the normal approximation to the binomial distribution to calculate the confidence interval.

The standard error of the sample proportion is (p(1-p)/n)^0.5, where p is the population proportion and n is the sample size.

The confidence interval is calculated by adding and subtracting the critical value (1.967 for a 98 percent confidence level) multiplied by the standard error from the sample proportion. This interval provides an estimate of the true population proportion with 98 percent confidence.

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What is 10-11
What is 20x4
What is 72x12
What is 124+1234

finally what's y=3/4x-3

Answers

Answer:

Step-by-step explanation:

10-11 = -1

20x4 = 80

72x12 = 864

124+1234 = 1358

y=3/4x-3 =

y=34x−3

Slope: 3434

y-intercept: (0,−3)

5/6 divided by 1/2 in a fraction

Answers

Answer:5/3

Step-by-step explanation:

In the following intermediate step, cancel by a common factor of 2 gives 5/3

Answer:

[tex]1\dfrac{2}{3}[/tex]

Step-by-step explanation:

Fraction division:

      Use KCF method:

Keep the first fraction.Change division to multiplication.Flip the second fraction.

       [tex]\dfrac{5}{6} \ \div \dfrac{1}{2}=\dfrac{5}{6}*\dfrac{2}{1}[/tex]

                   [tex]\sf = \dfrac{5}{3}\\\\= 1\dfrac{2}{3}[/tex]

Researchers collect continuous data with values ranging from 0-100. In the analysis phase of their research they decide to categorize the values in different ways. Given the way the researchers are examining the data - determine if the data would be considered nominal, ordinal or ratio (you may use choices more than once) Ordinal Two categories (low vs. high) frequency (count) of values between 0-49 and frequency of values between 50-100 Ordinal Three categories (low, medum, high) frequency (count) of values between 0-25, 26-74.& 75-100) Analyze each number in the set individually

Answers

The 2-category data is nominal. The 3-category data is also nominal. Each number in the set is analyzed as ratio.

The 2 categories- are 0-50 and 50-100, gives nominal data. Because we data has nothing to do with the values itself, it is the frequency.

Now for second scenario here, there are 3 categories, where it is basically low, medium and high, these are the frequencies, not the values itself. This will also be considered as nominal data.

Each number is set, it should be ordered in a set of number, and it is not what it includes denominal and it will be including the 0, which is absolute 0 point. Therefore, this will be considered as ratio.

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Cam identified a point that was 4 units above the origin and
8 units to the right of the origin. What was the ordered pair?

Answers

The ordered pair that Cam identified is given as follows:

(8,4).

How to define the ordered pair?

The general format of an ordered pair is given as follows:

(x,y).

For the x-coordinate, we have that:

If it is positive, the point is x units right of the origin.If it is negative, the point is x units left of the origin.

The point in this problem was 8 units right, hence the x-coordinate is given as follows:

x = 8.

For the y-coordinate, we have that:

If it is positive, the point is y units above of the origin.If it is negative, the point is y units below of the origin.

The point in this problem is 4 units above the origin, hence the y-coordinate is given as follows:

y = 4.

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A binary digit, or "bit", is either 0 or 1. How many different ten-bit sequences containing a single 1 are possible?

Answers

Answer:

A ten-bit sequence can have one 1 and nine 0s. There are 10 positions for the 1 to be placed in, such as:

1000000000

0100000000

0010000000

0001000000

0000100000

0000010000

0000001000

0000000010

0000000001

So there are 10 different ten-bit sequences containing a single 1 are possible.

Please help me with this question.

Answers

An example of a derivative in accounting is a stock option.

The formula is Call Option Value = S * N(d1) - X * e^(-rT) * N(d2)

What is an example of derivative in accounting?

A derivative in accounting is a financial instrument whose value is derived from the value of one or more underlying assets, such as stocks, bonds, currencies, commodities, or real estate. One common example of a derivative in accounting is a stock option.

A stock option is a contract that gives the holder the right, but not the obligation, to buy or sell a specified number of shares of a stock at a specified price (the strike price) within a specified period of time. The value of a stock option is derived from the value of the underlying stock.

One formula used to calculate the value of a call option is the Black-Scholes model. The formula is as follows:

Call Option Value = S * N(d1) - X * e^(-rT) * N(d2)

Where:

S = the current stock price

X = the strike price

r = the risk-free interest rate

T = the time until expiration (in years)

N(d1) and N(d2) are the cumulative distribution functions of the standard normal distribution

For example, if a stock is currently trading at $50 per share, and the strike price of a call option on that stock is $45, with an expiration date of 1 year and the risk-free interest rate is 2%, the value of the call option can be calculated as follows:

Call Option Value = $50 * N(d1) - $45 * e^(-0.02*1) * N(d2)

N(d1) and N(d2) can be calculated using a financial calculator or software.

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The desert temperature, H, oscillates daily between 37°F at 6am and 77°F at 6pm.
Write a possible formula for H, measured in hours from 6am, using the form
H = Kcos(Bt) + C
.
Enter your values for K, B and C below. (Hint: the letter K does not mean amplitude.)

Answers

The function of the temperature is H = 20cos(2π/12t) + 57

How to determine the function of the temperature

The temperature oscillates between 37°F at 6am and 77°F at 6pm,

So we can use the average of these two temperatures as the "midline" or "average" temperature (C).

The average temperature, C = (37+77)/2 = 57

The amplitude of the oscillation is half the difference between the maximum and minimum temperatures,

Amplitude, K = (77-37)/2 = 20

The period of the oscillation is the time it takes for the temperature to repeat, which is 24 hours.

i.e. T = 24

The angular frequency B is given by:

B= 2π/T

So we have B = 2π/24 = π/12

Finally, we can substitute these values into the formula H = Kcos(Bt) + C

H = 20cos(2π/12t) + 57

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(5-i)(5 + i) =
26
25 i
24

Answers

Answer:

[tex]-i^{2}[/tex] + 25

Step-by-step explanation:

(5-i)(5 + i)

25 + 5i - 5i - [tex]i^{2}[/tex]

25 [tex]-i^{2}[/tex]

Determine whether each function is linear or nonlinear

1. 2x(5+x)=y
2. Y=7x+15
3. X/y=8

Answers

Answer:

1.This function is linear.

2.This function is linear.

3.This function is nonlinear.

Answers

1. Is Non- linear because when you multiply you get x^2 which is a quadratic function and not linear

2. Is Linear - it is in slope intercept form which is linear

3. Is linear, it can be changed to slope intercept form which is linear, (y= 1/8x)

I graphed these to prove my assessment of which are linear and nonlinear

Of all the companies on the New York Stock Exchange, profits are normally distributed with a mean of $6.54 million and a standard deviation of $10.45 million. In a random sample of 73 companies from the NYSE, what is the probability that the mean profit for the sample was between -2.9 million and 4.5 million?

Answers

The probability that the mean profit for the sample was between -2.9 million and 4.5 million is of:

0.0475 = 4.75%.

How to obtain probabilities using the normal distribution?

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

The parameters for this problem are given as follows:

[tex]\mu = 6.54, \sigma = 10.45, n = 73, s = \frac{10.45}{\sqrt{73}} = 1.22[/tex]

The probability that the mean profit for the sample was between -2.9 million and 4.5 million is the p-value of Z when X = 4.5 subtracted by the p-value of Z when X = -2.9, hence:

X = 4.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (4.5 - 6.54)/1.22

Z = -1.67

Z = -1.67 has a p-value of 0.0475.

X = -2.9:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (-2.9 - 6.54)/1.22

Z = -7.73

Z = -7.73 has a p-value of 0.

Hence:

0.0475 - 0 = 0.0475 = 4.75%.

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You pick a card at random. 5 6 7 8 What is P(not greater than 7)? Write your answer as a fraction or whole number.

Answers

The Probability that card will not have greater than 7 number is, 3/4

What is probability?

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

Given that,

The numbers are on the cards are, 5, 6, 7, 8

Favorable Outcomes = (5, 6, 7)

Total Outcomes = (5, 6, 7, 8)

Probability = 3/4

Hence, the probability is 3/4

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what is the solution to the equation square root 2x+3 - square root x+2=2

Answers

Answer:

x = 23

Step-by-step explanation:

let's square both sides. that eliminates the individual square roots and creates one central term with square roots :

2x + 3 + x + 2 - 2 sqrt(2x + 3)×sqrt(x + 2) = 4

3x + 5 - 2×sqrt((2x + 3)(x + 2)) = 4

3x + 1 - 2×sqrt(2x² + 4x + 3x + 6) = 0

3x + 1 - 2×sqrt(2x² + 7x + 6) = 0

3x + 1 = 2×sqrt(2x² + 7x + 6)

now let's square both sides again

9x² + 6x + 1 = 4(2x² + 7x + 6) = 8x² + 28x + 24

x² - 22x - 23 = 0

a quadratic equation

ax²x+ bx + c = 0

has 2 solutions

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (22 ± sqrt((-22)² - 4×1×-23))/(2×1) =

= (22 ± sqrt(484 + 92))/2 =

= (22 ± sqrt(576))/2 = (22 ± 24)/2 =

= 11 ± 12

x1 = 11 + 12 = 23

x2 = 11 - 12 = -1

since we squared twice in the process, and every solution to a square is a ±sqrt (so, 2 solutions with alternating signs), we need to try both solutions in the original equation to see which ones really fulfill it.

sqrt(2×23 + 3) - sqrt(23 + 2) = 2

sqrt(46 + 3) - sqrt(25) = 2

sqrt(49) - 5 = 2

7 - 5 = 2

correct, x = 23 is a valid solution.

sqrt(2×-1 + 3) - sqrt(-1 + 2) = 2

sqrt(-2 + 3) - sqrt(1) = 2

sqrt(1) - 1 = 2

1 - 1 = 2

wrong. so, x = -1 is not a valid solution to the original equation.

PLS HELP WILL GIVE BRAINLIEST

Answers

I would help, I cant understand it without answers.

I suggest you watch the video for help before answering it, so you can understand the question more, and try and figure it out.

Sorry I couldn't help I was going to, I did not understand I'm so sorry, hope you get the answer right.

I do prefer to watch the video instead.

Thanks for understanding if you do. If u still want to, if u got the answer right from the video, if u want u can give me brainiest?

Anyways I like to help people. pls Make sure to figure it out on ur own sometimes, You can ask for help, if u do get stuck. I'm just telling you so you don't get in trouble ok.

I would like to help you out in the future if you have questions with the answers this time lol
.

Are the following statements true or false? Explain why or why not. (a) A vector has only one unit vector parallel to it. (b) The same line/segment can have many different parametrizations. (c) The sphere x2 + y2 + z2 = 1 is a three-dimensional surface. (d) If v and w are two vectors in R3, the magnitude of v + w is greater than both v and w.

Answers

The first statement is false, the second is true, the third is true, and the fourth is false.

(a) False. A vector has infinitely many unit vectors parallel to it. A unit vector is a vector with magnitude 1 that points in the same direction as the original vector.

(b) True. The same segment/line can have many different parametrizations. A line/segment can be described by different equations, such as different parametric equations, and each of these equations represents the same line/segment.

(c) True. The sphere x² + y² + z² = 1 is a three-dimensional surface. The equation describes a set of points in three-dimensional space that are at a fixed distance of 1 from the origin.

(d) False. The magnitude of v + w is less than or equal to the magnitude of v and w. The magnitude of the sum of two vectors is equal to the distance between the tail of the first vector and the head of the second vector, which can never be greater than the magnitude of either vector.

In some cases, such as when the vectors are orthogonal, the magnitude of their sum will be equal to the magnitude of each vector.

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According to current prices 1.7 grams of gold is worth the same amount as 130 grams of
silver. How much gold would 1000 grams of silver be worth? How much silver would 10
grams of gold be worth?

Answers

Answer:

Below

Step-by-step explanation:

1.7 / 130  go/si

1000 si  * 1.7 /130 go/si = 13.08 gm of gold

10 go  /  ( 1.7/130 go/si) = 764.7 gm of  silver  

When r is close to ____, there is either a weak linear relationship...When r is close to ____, there is either a weak linear relationship between x and y or no linear relationship between x and y.A. -1B. 0C. 1D. ±[infinity]

Answers

When r is close to 0, there is either a weak linear relationship between x and y or no linear relationship between x and y.

When the correlation coefficient (r) is close to 0, it means there is either a weak linear relationship or no linear relationship between the two variables (x and y).

The correlation coefficient ranges from -1 to 1, with -1 indicating a perfect negative linear relationship, 0 indicating no linear relationship, and 1 indicating a perfect positive linear relationship.

So, when r is close to 0, it suggests that there is either a weak linear relationship or no linear relationship between the variables.

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or
Sebastian uses his phone primarily to take a lot of selfies. The storage space on his phone is limited, so Sebastian needs to keep track of how many selfies he takes.
There is a proportional relationship between the number of selfies Sebastian takes, x, and the amount of storage (in megabytes) he uses taking selfies, y.

Answers

The statement suggests that there is a proportional relationship between the number of selfies Sebastian takes, x, and the amount of storage (in megabytes) he uses taking selfies, y. This means that if we were to graph the number of selfies taken, x, on the x-axis and the amount of storage used, y, on the y-axis, the points would fall on a straight line and the slope of the line would be a constant.

In mathematical terms, we can represent this proportional relationship as y = kx, where k is the proportionality constant, or the constant of proportionality. This equation states that the amount of storage used, y, is directly proportional to the number of selfies taken, x.

A sample of 200 high school students were asked how many hours per week they spend watching television.The following frequency distribution presents the results.Construct a relative frequency ogive for the frequency distribution.

Answers

The ogive curve for the data has to be obtained by first converting the data into a continuous class one and then plotting the less than cumulative frequency table obtained.

Here we have the data

0-3.9    4.0-7.9    8.0-11.9    12.0-15.9    16.0-19.9    20.0-23.9    24.0-27.9

  63          26          24              37                23               11                  16

Now first we need to convert this to a continuous distribution

We will get

Classes                  Frequency

-0.95-3.95                   63  

3.95-7.95                     26

7.95-11.95                     24

11.95-15.95                    37

15.95-19.95                   23

19.95-23.95                    11

24.0-27.95                     16

Now we need to construct a less than table

Less than                           Cumulative frequency

3.95                                                    63  

7.95                                                    89

11.95                                                   113

15.95                                                 150

19.95                                                 173

23.95                                                 184

27.95                                                200

Now to make an Ogive curve we need to plot the less than column at the x-axis and the frequency on the y-axis. Then draw a free hand line to connect all the points. This will give us our ogive curve

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Complete Question

A sample of 200 high school students was asked how many hours per week they spend watching television. The following frequency distribution presents the results.

0-3.9    4.0-7.9    8.0-11.9    12.0-15.9    16.0-19.9    20.0-23.9    24.0-27.9

  63          26          24              37                23               11                  16

Construct a relative frequency ogive for the frequency distribution.

Find the angle between the vectors. (First, find an exact expression and then approximate to the nearest degree.) a=4i−3j+k, b=2i−k

Answers

Approximating to the nearest degree, θ = arccos(cosθ) ≈ 35°.

The angle between two vectors can be found using the dot product formula:

cosθ = (a⋅b)/(||a|| ||b||)

where ||a|| is the magnitude of vector a, and ||b|| is the magnitude of vector b.

First, let's find the magnitude of the vectors:

||a|| = √(4^2 + (-3)^2 + 1^2) = √(16 + 9 + 1) = √26

||b|| = √(2^2 + 0^2 + (-1)^2) = √5

Next, let's find the dot product of the vectors:

a⋅b = (4i−3j+k)⋅(2i−k) = 8i + 3j - k

Finally, let's substitute into the cosine formula:

cosθ = (a⋅b)/(||a|| ||b||) = (8i + 3j - k)/(√26 * √5)

To approximate the angle to the nearest degree, we can use the inverse cosine function:

θ = arccos(cosθ)

Note: The range of arccos is [0,180], so we need to use the appropriate quadrant to find the correct angle.

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Simplify the following
[tex] \sqrt{96} [/tex]

Answers

Answer:

[tex]4\sqrt{6}[/tex]

Step-by-step explanation:

[tex]\sqrt{96}=\sqrt{(6)(16)}\sqrt{6}\sqrt{16}=4\sqrt{6}[/tex]

An empty 35 gallon tank begins filling with water.
i. Which of the following statements defines a variable to represent the amount of water added to the tank?
a. Let x represent the volume of water added to the tank.
b. Let x represent the number of gallons of water added to the tank.
c. Let x represent the number of gallons.
ii. Write an expression (in terms of x) to represent the number of gallons of water needed to fill the tank.

Answers

Let x represent the number of gallons of water added to the tank. The expression to represent the number of gallons of water needed to fill the tank is 34-x.

Let x represent the number of gallons of water added to the tank.

Total number of gallons that can filled in tank is total capacity of tank which is 34.

Now, x gallons of water is already filled in the tank.

Hence the tank needs to filled with the amount of water which is the difference of total capacity of tank and the gallons with which the tank is  already filled.

Number of gallons of water needed to fill the tank = Total capacity of tank - number of gallons of water added to the tank

Number of gallons of water needed to fill the tank = 34 - x.

The expression to represent the number of gallons of water needed to fill the tank is 34-x.

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There are five main roads between the cities A and B and 4 between B and C. In how many ways can a person drive from A to C and return without driving on the same road twice?​

Answers

There are 20 possible routes that a man could take to go between cities and then take a different route back.

What is meant by permutation?

In mathematics, a permutation of a set is, broadly speaking, the rearranging of its elements if the set is already sorted, or the arrangement of its members into a sequence or linear order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context.

Let the number of roads between the cities A and B = 5.

The rules of permutation must be used in this situation.

A permutation is an arrangement of all or a portion of a collection of items that takes into account the arrangement's order.

The man uses five different routes to get from A to B because there are five different routes accessible.

He can get back by 4 (5 1) methods because he needs to take a different route.

Therefore, there are 20 possible routes that a man could take to go between cities and then take a different route back.

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HOTE
TREAT
A. 17-4y√y
B. y.√√y
C. -3y√17 y
D. y √17y-4y√y
Question 1 of 10
Which choice is equivalent to the expression below when y> 0?
√3+√16³-4y
Tutucul

Answers

y√y i.e Option (B) is  equivalent to the expression below when y> 0.

What is equivalent ?

Equivalent means that two things have the same value, meaning, or measure. For example, 2 + 2 and 4 + 0 are equivalent equations because both equal 4. Another example is 1/2 and 0.5, which are equivalent because they are both equal to one-half.Equivalent in mathematics refers to two expressions that have the same value or the same outcome when evaluated.

Equivalent means having the same value, measure, or effect as something else. For example, two dollars is equivalent to two euros.

Let's start with the expression:

√[tex]y^{3}[/tex]+√[tex]16y^{3}[/tex]-[tex]4y[/tex]√[tex]y[/tex]

where y > 0. (this allow us to have y inside a square root, so we don't mess with complex numbers).

We want to find the equivalent expression to this one.

Here, we can do the next two simplifications:

√[tex]16y^{3}[/tex] = √[tex]16[/tex] √[tex]y^{3}[/tex] = [tex]4[/tex]√[tex]y^{3}[/tex]

And

[tex]y[/tex]√[tex]y[/tex] = √[tex](y^{2}. y)[/tex]= √[tex]y^{3}[/tex]

If we apply these two to our initial expression, we can rewrite it as:

√[tex]y^{3}[/tex]+√[tex]16y^{3}[/tex]-[tex]4y[/tex]√[tex]y[/tex]

√[tex]y^{3}[/tex] + [tex]4[/tex]√[tex]y^{3}[/tex]-[tex]4[/tex]√[tex]y^{3}[/tex] = √[tex]y^{3}[/tex]=[tex]y[/tex]√[tex]y[/tex]

Therefore, Option (B) is correct.

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Please help PLEASE this is the last question I’m really struggling…

Answers

Answer:

x√xy²

Step-by-step explanation:

First step is to distribute.

Change ⁴√x⁵y² to ⁴√x · x · x · x · x · y · y

If there are any, (which there are) sets of the same variable greater then or equal to 4, combine them and move them to the left of the radical (the square root sign).  When you are done it should look like this:

x√x · y · y

You will notice there is still an x on the right side.  This is because there were 5 x's and you can only move them (in this case) in sets of 4.  5 - 4 = 1

Combine your like terms and you're done!

x√xy²

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