How much should Roman invest today in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly?

Answers

Answer 1

Roman should invest $18,223.97 in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly.

First, convert R as a percent to r as a decimal

r = R/100

r = 5.65/100

r = 0.0565 per year,

Then, solve the equation for P

P = A / (1 + r/n)^(nt)

P = 22,450.15 / (1 + 0.0565/12)^{(12)(3.7)}

P = 22,450.15 / (1 + 0.0047)(44.4)

P = $18,223.97

The principal investment required to get a total amount of $22,450.15 from compound interest at a rate of 5.65% per year compounded 12 times per year over 3.7 years is $18,223.97.

Therefore, Roman should invest $18,223.97 in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly.

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Related Questions

A small class has 9 students, 4 of whom are girls and 5 of whom are boys. The teacher is going to choose two of the students at random. What is the probability that the first student chosen will be a boy and the second will be a girl? Write your answer as a fraction in simplest form.

Answers

The probability that the first student chosen will be a boy and the second will be a girl is 0.28.

What is probability?

Probability is also called the chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

Total students = 9

Number of girls = 4

Number of boys = 5

Probability of choosing first boy = Number of boys / total students

⇒ 5/9

Now since 1 boy extract so remaining students = 9 - 1 = 8

Probability of choosing second girl = Number of girls / Total students

⇒ 4//8

Probability of A and B = P(A) × P(B)

Therefore,

The probability that the first student chosen will be a boy and the second will be a girl = (5/9) × (4/8) = 0.28

Hence "The probability that the first student chosen will be a boy and the second will be a girl is 0.28".

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Write the following in terms of sin x and cos x ; then simplify if possible. sec x csc x cot x =

Answers

The expression sec x csc x cot x  in terms of sin x and cos x is

1/ (sin x)^2.

According to the given question.

We have an expression sec x csc x cot x.

Here, we have to write the above expression in terms of sinx and cosx.

As we know that,

sec x = 1/cos x

csc x = 1/sin x

cot x = cos x/ sin x

Thereofore, the expression sec x csc x cot x  in terms of sin x and cos x is given by

sec x csc x cot x

= (1/cos x) (1/sinx) (cosx/ sinx)

= 1/ (sin x)^2

Hence, the expression sec x csc x cot x  in terms of sin x and cos x is

1/ (sin x)^2.

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Which of the following equations represents a linear function?

Question 8 options:

y =[tex]\sqrt4{x}[/tex]


y =6/x



2x – 4y = 6


x3 – y = –2

Answers

Answer:

2x – 4y = 6

x3 – y = –2

Step-by-step explanation:

When graphing these two are linear.

Answer:

2x - 4y = –2

x3 – y = –2

Step-by-step explanation:

'cause they both have two unknown digits and this can be worked out with 3 methods;

1. substitution method

2. elimination method

3. grahical method

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Question
The following data set represents the dollar amounts of donations collected at the entrance to a free museum during one hour.

Donation Amount ($) Frequency
1 1
5 5
10 3
15 1
600 1


Is the median a reasonably good measure of central tendency for this data set? What if the outlier were removed from consideration?

Select the correct answer below:


The median is a good measure regardless of whether the outlier is included.

The median is a very poor measure regardless of whether the outlier is included.

The median is a good measure when the outlier is included, but it would be a very poor measure if the outlier were removed from consideration.

The median is a very poor measure when the outlier is included, but it would be a good measure if the outlier were removed from consideration.

Answers

In the given situation (A) the median is a good measure regardless of whether the outlier is included.

What do we mean by media?The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution in statistics and probability theory. It is sometimes referred to as "the middle" value in a data set. The basic difference between the median and the mean in describing data is that the median is not skewed by a small proportion of extremely large or small values, and thus provides a better representation of a "typical" value.

To find the median:

1, 5, 5, 5, 5, 5, 10, 10, 10, 15, 600The number of terms is 11, so the middle number will be the 5th term from both ends.The 5th term is 5.So, regardless of whether the outlier is included, the median is a good measure in the given situation.

Therefore, in the given situation (A) the median is a good measure regardless of whether the outlier is included.

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The correct question is given below:

The following dataset represents the dollar amounts of donations collected at the entrance to a free museum for one hour.

(Refer to the table given below)

Is the median a reasonably good measure of central tendency for this dataset? What if the outlier were removed from consideration?

Select the correct answer below:

(A) The median is a good measure regardless of whether the outlier is included.

(B) The median is a very poor measure regardless of whether the outlier is included.

(C) The median is a good measure when the outlier is included, but it would be a very poor measure if the outlier were removed from consideration.

(D) The median is a very poor measure when the outlier is included, but it would be a good measure if the outlier were removed from consideration.

two classes each with 21 students were given a physical fitness test. the result of the number of pull ups performed in 30 seconds were recorded in the table below

Answers

Based on the results of the physical fitness test, the reason why we are unable to calculate the mean number of pull-us done by the students in each class is that we don't have the exact number of pull-ups done by each student.

What is needed to calculate mean?

To calculate the simple mean of a distribution of numbers, we would need the value of all the numbers to be known. These numbers will then be summed up and divided by the number of the distribution.

In this case of the physical fitness test, the number of pull-ups is not known for all the students as there are some that either did below 5 or above 10 and we don't know the exact number of pull-ups done.

As a result, we are unable to calculate the mean.

Question is:
Explain why we are unable to calculate the mean number of pull-ups done by the students in each class.

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question is in the photos

Answers

Answer:

n(AuB)=15

n(AnB)=8 is the answer!

Find the quotient. Do not round your answer 58.543/10,000

Answers

Answer:

0.0058543

Step-by-step explanation:

58.543/10,000 = 58.543 divide 10,000

Which equations have the same value of x as Two-thirds (6 x + 12) = negative 24? Select two options.

Answers

4 x + 8 = negative 24 , 9 x + 18 = negative 24 are  equations have the same value of x .

What in mathematics is a linear equation?

There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.

A - 4 x + 8 = negative 24

E - 4 x = negative 32

ARE CORRECT ON EDGE.

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The complete question is-

Which equations have the same value of x as Two-thirds (6 x + 12) = negative 24? Select two options.

4 x + 8 = negative 24

9 x + 18 = negative 24

4 x = negative 16

StartFraction 18 x + 36 over 2 EndFraction = negative 24

4 x = negative 32

find the value of ...B​

Answers

Answer:

b=–2

Step-by-step explanation:

we've got:

(3+bx)⁵===> b⁵x⁵+15b⁴x⁴+90b³x³+720b²x²+405bx+243

and we've also got the coefficient of x³ as –720

90b³=–720===> b³=–8===> b=–2

a movie theater has a seating capacity of 329. the theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. there are half as many adults as there are children. if the total ticket sales was $ 2392, how many children, students, and adults attended?

Answers

Taking into account the definition of a system of linear equations, 178 children, 62 students and 89 adults attended to the movie theater.

System of linear equations

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be found, with which when are replaced in the equations, they must give the solution proposed.

This case

In this case, a system of linear equations must be proposed taking into account that:

C is the number of children who attended the movie theater.S is the number of students who attended the movie theater.A is the number of adults who attended the movie theater.

On the other hand, you know:

A movie theater has a seating capacity of 329. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. The total ticket sales was $ 2392.There are half as many adults as there are children.

So, the system of equations to be solved consists of the following equations:

Equation 1: C + S + A= 329

Equation 2: 5C + 7S + 12A= 2392

Equation 3: A= C÷2= 1/2C

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

Replacing equation 3 in equation 1 and isolating the variable S you get:

C + S + 1/2C= 329

3/2C + S= 329

S= 329 - 3/2C

Replacing this expression and equation 3 in equation 2 you get:

5C + 7(329 - 3/2C) + 12×1/2C= 2392

Solving:

5C + 7×329 - 7×3/2C + 12×1/2C= 2392

5C + 2303 - 21/2C + 6C= 2392

5C - 21/2C + 6C= 2392 -2303

1/2C= 89

C= 89÷ 1/2

C= 178

Remembering that S= 329 - 3/2C, you get S= 329 - 3/2×178 → S= 62

Finally, substituting the value of C in Equation 3: A= 1/2C= 1/2×178 → A=89

In summary, 178 children, 62 students and 89 adults attended to the movie theater.

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Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson’s eventual profit function is given as: , where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson’s profit start decreasing

Answers

If Wilson produces only one 1 bag, then his profit starts decreasing

How to determine the point

Given the function;

Let  f ( x ) = [tex]2x^4 - 4x^3 + 7[/tex]

Where;

x is  the number of bags of cereal produced

[tex]f'x = 2x^4 - 4x^3 + 7[/tex]

[tex]f'(x) = 8x^3 - 12x^2[/tex]

Factorize the expression

[tex]f'(x) = 4x^2(2x - 3)[/tex]

If the value of x is decreasing, we have;

f ′ ( x ) ≤ 0

4x² (2x - 3) ≤ 0

If x² ≥ 0, then;

2x - 3  ≤ 0

x ≤ 3/ 2

With x as the number of bags

x ∈ N

x = 1 is the only possibility

Thus, if Wilson produces only one 1 bag, then his profit starts decreasing

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The complete question:

Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson’s eventual profit function is given as: pi = 2x ^ 4 - 4x ^ 3 + 7,  where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson’s profit start decreasing

A traffic cone with a height of 20 in. is ideal for traffic control. Find the lateral area of a cone with a height of 20 in. and a diameter of 12 in. Round the answer to the nearest whole number.​ (Hint: The height given is not the slant​ height.)

Answers

The lateral area of the cone is 394 square inches

How to determine the value

The formula for lateral area of a cone is expressed as;

Lateral area = πr √h² + r²

Given that;

height = 20 inDiameter = 12 in, radius = 12/ 2 = 6 in

Substitute the values into the formula

Lateral area = 3. 142(6) √20² + 6²

Lateral area = 18. 85 √436

Lateral area = 18. 85 × 20. 8

Lateral area = 394 square inches

Thus, the lateral area of the cone is 394 square inches

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The upper arm length of males over 20
years old in the United States is approximately Normal with mean 39.1
centimeters (cm) and standard deviation 5.1
cm. Use the 68−95−99.7
rule to answer the following questions. (Start by making a sketch of the Normal distribution for upper arm lengths for this population.)



A normal plot shows the range of Iowa test scores for 68% of the data, 95% of the data and 99.7% of the data. About 68% of the distribution of scores ranges from 5.29 to 8.39. About 95% of the distribution of scores ranges from 3.74 to 9.94. About 99.7% of the distribution of scores ranges from 2.19 to 11.49. There is an annotation that One standard deviation is 1.55 and another annotation that 2.5% of sores are below 3.74.


What percentage of men over 20
have upper arm lengths greater than 44.2 cm?
Provide your answer to one decimal place.

Answers

Using the Empirical Rule, it is found that 16% of men over 20 have upper arm lengths greater than 44.2 cm.

What does the Empirical Rule state?

It states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of  the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.

For the distribution in this problem, we have that:

The mean is of 39.1 cm.The standard deviation is of 5.1 cm.

Hence, 44.2 is one standard deviation above the mean, as 44.2 = 39.1 + 1 x 5.1.

The normal distribution is symmetric, meaning that 50% of the measures are above the mean and 50% are below. Of those measures above the mean, 68% are less than 44.2 and 32% are more than 44.2 cm, hence:

0.5 x 32 = 16%.

16% of men over 20 have upper arm lengths greater than 44.2 cm.

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The perimeter of the figure below is 110 cm. Find the length of the missing side.

Answers

Answer:

  6.1 cm

Step-by-step explanation:

You want to know the remaining side of the irregular figure such that the perimeter is 110 cm.

Perimeter

The perimeter of a plane figure is the sum of the lengths of the sides. Working clockwise from the upper left corner, we have ...

  34.6 +8.6 +17.3 +11.6 +? +11.6 +11.6 +8.6 = 110

  103.9 +? = 110 . . . . collect terms

  ? = 6.1 . . . . . . . . . subtract 103.9

The length of the missing side is 6.1 cm.

__

Additional comment

If the angles that appear to be right angles actually were right angles, the perimeter would be 109.6 cm. The perimeter is longer than this, so at least three of the angles are not right angles.

Kaleb determined how much money he would spend if he stopped at McDonalds each day after school. His cost can be modeled using c(m)=2.3m+2.50, where m is the number of McGriddle he orders each time. What is the cost that Kaleb would spend at McDonalds if he ordered 3 McGriddles?

Answers

Answer:
The cost that Kaleb would spend at McDonalds if he ordered 3 McGriddles would be 11.50.

Step-by-step explanation:

We know this is the answer because, when solving for c(3), we would get c(3)=2.3(3)+2.50=11.50.


Find the greatest common factor of the expressions.
12y1329, -16y6z9

Answers

Answer:

2 and 3 and y

Step-by-step explanation:

2x2x4x y x 1x2x3x3x3

-2x7x y x 2x3x z x3x3

I have 6 quarts of paint. How many shelves can be painted if each one takes one third of a quart.

Answers

6 divided by 1/3 =
6 multiplied by 3 =
28 shelves

the quotient of 10 and a number in math terms

Answers

The answer
N= number
The quotient means you would take 10 and divide it by n.

Answer—> 10/n

i need the scientific notation of 0.0000018(430,000,000) over 0.00008(0.0075)

Answers

Answer:

1.29 x [tex]10^{9}[/tex]

Step-by-step explanation:

{(1.8 x 10^-6) x (4.3 x 10^8)}  / [(8 x 10^-5) x (7.5 x 10^-3)]

[(1.8 x 4.3)x(10^-6 x 8)] / [(8 x 7.5) x(10^-5 x 10^ -3)]

(.129 x 10^[2-(-8)]

.129 x 10^10

1.29 x 10^-1 x 10^10

1.29 10^9

Absolute value of 4 is

Answers

Answer: -4

Step-by-step explanation:

it is -4 because we are looking for like the opposite so the opposite of 4 is -4

Answer:

Absolute value of |4| = 4

Step-by-step explanation:

The absolute value of a number is always positive


Determine whether the quadratic function shown below has a minimum or
maximum, then determine the minimum or maximum value of the functio
ƒ(x) = x² + 6x + 7

Answers

Answer:

Minimum = (-3, -2)

Step-by-step explanation:

Standard form of a quadratic function:

[tex]f(x)=ax^2+bx+c[/tex]

If a > 0 the parabola opens upwards and the curve has a minimum point.

If a < 0 the parabola opens downwards and curve has a maximum point.

Given function:

[tex]f(x)=x^2+6x+7[/tex]

As a > 0, the parabola opens upwards and so the curve has a minimum point.

The minimum/maximum point of a quadratic function is its vertex.

Vertex form of a quadratic function:

[tex]f(x)=(x-h)^2+k[/tex]

Where (h, k) is the vertex.

To rewrite the given function in vertex form, complete the square.

Add and subtract the square of half the coefficient of the term in x:

[tex]\implies f(x)=x^2+6x+7 +\left(\dfrac{6}{2}\right)^2-\left(\dfrac{6}{2}\right)^2[/tex]

[tex]\implies f(x)=x^2+6x+7 +9-9[/tex]

[tex]\implies f(x)=x^2+6x+9+(7 -9)[/tex]

[tex]\implies f(x)=x^2+6x+9-2[/tex]

Factor the perfect square trinomial formed by x²+6x+9:

[tex]\implies f(x)=(x+3)^2-2[/tex]

Compare with the vertex form:

h = -3k = -2

Therefore, the vertex is (-3, -2) and so the minimum value of the given function is (-3, -2).

true or false???????

Answers

Answer:

False

Step-by-step explanation:

3 x 1/3

3/1 x 1/3 = 1

Answer:false

Step-by-step explanation: i did the test

A jar contains 100 marbles. There are 21 blue marbles, 19 green marbles, 37 red marbles, and 23 yellow marbles. What is the probability of randomly selecting a yellow marble? Enter the correct answer​

Answers

Answer:

23% or 23/100

Step-by-step explanation:

Since there are 23 in 100 is is 23/100 or 23%

Answer:

4.348%

Step-by-step explanation:

blue marbles = 19

yellow marbles = 23

probably of getting yellow = 23/100

= 4.34782608696

then you round then number to three decimal places and there you go

How do you express without exponents [tex](3a^3)^2[/tex]

Answers

__________________________________________________________

Hello! In this question, we were given an expression and would have to express it without the use of exponents.

__________________________________________________________

Explanation:

In the question, we were given:

(3a³)²

In order to express the expression without the exponents, we would have to first simplify it and then expand the expression.

__________________________________________________________

Solve:

[tex](3a^3)^2[/tex]

Simplify by "squaring" the variable inside the parenthesis, in which in this case we would multiply the "2" to the "3".

[tex]3a^6[/tex]

Now in this step, we would have to expand the expression in a different form to get rid of the exponent.

To get rid of the exponent, we would expand the " [tex]a^6[/tex] " term.

Note that the term [tex]a^6[/tex] is the same thing as a · a · a · a · a · a, it is just the expanded version of the exponent.

This means that our expressed expression without exponents, including our constant "3" would be:

3 · a · a · a · a · a · a

__________________________________________________________

Answer:

3 · a · a · a · a · a · a

__________________________________________________________

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12. If √1225 = 35 then √12.25​

Answers

[tex] \sqrt{12.25 } = 3.5[/tex]

Helpppp meeeee!!!! Ayudaaamee

Answers












It’s q 7 becaues if you add x and 6 it’s be 7 and q is the main one

Prove that:
( 1 - tan^4 A)cos^4 A = 1 - 2 sin^2 A​

Answers

Here we go ~

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (1 - \tan {}^{4} (a) ) \cos {}^{4} (a) [/tex]

[tex]\qquad \sf  \dashrightarrow \: (1 + \tan {}^{2} (a) )(1 - { \tan}^{2} (a)) \cos {}^{4}(a ) [/tex]

[ a² - b² = (a + b)(a - b) ]

[tex]\qquad \sf  \dashrightarrow \: ( \sec {}^{2} (a) )(1 - ( \sec{}^{2} (a) - 1) )\cos {}^{4} (a) [/tex]

[ sec² a = 1 + tan² a, so : tan² a = sec²a - 1 ]

[tex]\qquad \sf  \dashrightarrow \: \bigg( \dfrac{1}{{}cos^{2} (a)} \bigg)(2 - \sec{}^{2} (a) ) \cos {}^{4} (a) [/tex]

[tex]\qquad \sf  \dashrightarrow \: \bigg(2 - \dfrac{1}{ \cos {}^{2} (a) } \bigg) \cos {}^{2} (a) [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{2 \cos {}^{2} (a) - 1}{ \cos {}^{2} (a) } \times \cos {}^{2} (a) [/tex]

[tex]\qquad \sf  \dashrightarrow \: 2 \cos {}^{2} (a) - 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2(1 - \sin {}^{2} (a) ) - 1[/tex]

[ sin²a + cos² a = 1, hence sin²a = 1 - cos²a ]

[tex]\qquad \sf  \dashrightarrow \: 2 - 2 \sin {}^{2} (a) - 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: 1 - 2 \sin {}^{2} (a) [/tex]

Answer:

See proof below

Step-by-step explanation:

Prove [tex]\left(\:1\:-\:tan^4A\right)cos^4A\:=\:1\:-\:2\:sin^2A[/tex]

[tex]\left(1-\tan ^4\left(A\right)\right)\cos ^4\left(A\right)[/tex]  can be expressed in sin, cos terms

Use the trigonometric identity [tex]\tan \left(x\right)=\frac{\sin \left(x\right)}{\cos \left(x\right)}[/tex]

[tex]\left(1-\tan ^4\left(A\right)\right)\cos ^4\left(A\right) = \left(1-\left(\frac{\sin \left(A\right)}{\cos \left(A\right)}\right)^4\right)\cos ^4\left(A\right)[/tex]

[tex]\mathrm{Simplify}\:\left(1-\left(\frac{\sin \left(A\right)}{\cos \left(A\right)}\right)^4\right)\cos ^4\left(A\right)[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}[/tex]

= [tex]\left(1-\frac{\sin ^4\left(A\right)}{\cos ^4\left(A\right)}\right)\cos ^4\left(A\right)[/tex]

Multiplying the expression in parentheses by [tex]\cos ^4\left(A\right)[/tex] we get

[tex]\frac{\cos ^4\left(A\right)-\sin ^4\left(A\right)}{\cos ^4\left(A\right)}\cos ^4\left(A\right)[/tex]

Cancel the common factor [tex]\cos ^4\left(A\right)[/tex]

This gives us

[tex]\cos ^4\left(A\right)-\sin ^4\left(A\right)[/tex]

Now,

[tex]\sin ^4\left(A\right)=\left(\sin ^2\left(A\right)\right)^2[/tex]

[tex]\cos ^4\left(A\right)=\left(\cos ^2\left(A\right)\right)^2[/tex]

[tex]\:\cos ^4\left(A\right)-\sin ^4\left(A\right)[/tex] = [tex]\left(\cos ^2\left(A\right)\right)^2-\left(\sin ^2\left(A\right)\right)^2[/tex]

[tex]\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]

[tex]\left(\cos ^2\left(A\right)\right)^2-\left(\sin ^2\left(A\right)\right)^2=\left(\cos ^2\left(A\right)+\sin ^2\left(A\right)\right)\left(\cos ^2\left(A\right)-\sin ^2\left(A\right)\right)[/tex]

= [tex]\cos ^2\left(A\right)-\sin ^2\left(A\right)[/tex]   [tex]\textrm{ since }\cos ^2\left(A\right)+\sin ^2\left(A\right)[/tex] = 1

Using the fact that [tex]\cos ^2\left(A\right)=1-\sin ^2\left(A\right)[/tex]

we get

[tex]\cos ^2\left(A\right)-\sin ^2\left(A\right) = 1-\sin ^2\left(A\right)-\sin ^2\left(A\right)\\\\= 1-2\sin ^2\left(A\right)[/tex]

Proved

Let D={12,15,17), E = {12,14,15,16) and F = {11,13,14,15,17).
List the elements in the set D UE.
DUE= (Use commas to separate answers.)

Answers

The elements that will be coming in the set D∪E will be {12, 14, 15, 16, 17}.

A set may be defined as a collection of letters or numbers that are written in order to depict a certain value or entity. A set is always represented by a capital letter symbol and is always written in curly brackets { }. Union of two sets may be defined as a new set which has the collection of all the elements of the two individual sets. Union of two sets is represented by the symbol '∪'. Union of two Indvidual sets, set A and set b is written as A∪B.

Now, according to the question set D is = {12, 15, 17} and set E is = {12, 14, 15, 16}.

The union of the two sets contains all the elements of the sets D and E.

Thus, D∪E will be given by {12, 14, 15, 16, 17}.

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Are these fractions equivalent or
nonequivalent?

Answers

The two fractions are equivalent.

When two fractions have the same value, they are said to be equivalent, meaning that even though the numbers in the two fractions are different, their overall value is the same.

Fractions that are not equal to one another are referred to as nonequivalent fractions. The same cross multiplication procedure must be used to determine whether two fractions are comparable or not.

Consider these two fractions,

x = ( m / 4n ) and y = ( 2m / 8n )

Now when the fraction x is multiplying and dividing by 2.

We get,

x = ( m / 4n ) × ( 2 / 2 )

x = 2m / 8n

Therefore, x = y

Hence, the fractions are equivalent.

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Consider the relationship chart for the a fast-food restaurant,
Assume that the areas required for each department are:
Department Area Required (Square feet)
(CB) 300
(CF) 200
(PS) 200
(DD) 200
(CS) 300
Assume facility dimension of 6 (horizontal) by 8 (vertical) squares, where each square is 5 feet on a side. As a result, for example the CB department requires 12 squares. Develop a layout for the fast-food restaurant.

Answers

The layout of the fast-food restaurant of dimensions 6 by 8 5 feet squares is presented in the attached table created with Sheets.

How can the required layout be found?

The dimensions of the facility are;

Horizontal = 6 squares

Vertical = 8 squares

The side length of each square = 5 feet

Therefore;

Area of each square = 5² ft.² = 25 ft.²

Number of squares, n, required by each dependent are therefore;

CB department, n = 300 ÷ 25 = 12 squares

CF department, n = 200 ÷ 25 = 8 squares

PS department, n = 8 squares

DD department, n = 8 squares

CS department, n = 12 squares

A layout for the fast-food restaurant is therefore;

The first three vertical columns of 8 squares each are occupied by the CF, PS, and DD departments. The remaining 3 by 8 squares are occupied by the CB department, (3 by 4 squares), and the CS department, (3 by 4 squares)

Please see the attached table layout created using Sheets.

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