A footbridge is in the shape of an arc of a circle. the bridge is 10 ft tall and 27 ft long, horizontally. what is the radius of the circle that contains the bridge? round your answer to the nearest tenth.

Answers

Answer 1

Final answer:

The radius of the circle that includes the footbridge, given the bridge's arc length and height, is 14.1 ft.

Explanation:

The problem relates to the geometry of a circle, specifically the concept of the arc length and radius. Given the arc length (L) and the height of the arc (h), we can use these to find the radius (r) of the circle using the formula r = L²/(8h) + h/2.

Here, the arc length is the horizontal length of the footbridge, which is 27 ft and the height h is the height of the bridge, 10 ft.

Substituting these values into the formula we get:

r = (27² ft)/(8*10 ft) + 10 ft/2 = 729/80 + 5 = 14.1 ft

So, to the nearest tenth of a foot, the radius of the circle that includes the footbridge is 14.1 ft.

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Related Questions

A toy manufacturer makes a toy truck, a toy car, and a toy boat. The production spreadsheet is:
Toy Time to Produce Cost to Produce Profit for Each Truck 10 minutes $1.00 $1.00 Car 12 minutes $0.75 $1.50 Boat 8 minutes $0.80 $0.60
After accounting for breaks, a worker actually works 400 minutes each day. The manufacturer needs each worker to generate a potential profit of $35 each day. Write a system of inequalities that expresses these constraints.

Answers

Let x be the number of toy truck, y is the number of toy car, and z is the number of toy boat.

The constraint for the time
[tex]10x+12y+8z\le 400[/tex]

The constraint for the profit
[tex]x+1.50y+0.6z\ge 35[/tex]

Answer:

[tex]\left\{\begin{array}{l}10x+12y+8z\le 400\\x+1.5y+0.6z\ge 35\end{array}\right.[/tex]

Step-by-step explanation:

Let x be the number of toy trucks, y be the number of toy cars and z be the number of toy boats a worker makes each day.

1. If a worker spends 10 minutes to make one toy truck, then he spends 10x minutes to make x toy trucks. If a worker spends 12 minutes to make one toy car, then he spends 12y minutes to make y toy cars. If a worker spends 8 minutes to make one toy boat, then he spends 8z minutes to make z toy boats. In total he can spend at most 400 minutes each day, then

[tex]10x+12y+8z\le 400.[/tex]

2. If a worker generates profit of $1.00 per one toy truck, then he generates profit of $x per x toy trucks. If a worker generates profit of $1.50 per one toy car, then he generates profit of $1.50y per y toy cars. If a worker generates profit of $0.60 per one toy boat, then he generates profit of $0.60z per z toy boats. The manufacturer needs each worker to generate a potential profit of $35 each day, then

[tex]x+1.5y+0.6z\ge 35.[/tex]

Thus, the system of two inequalities is

[tex]\left\{\begin{array}{l}10x+12y+8z\le 400\\x+1.5y+0.6z\ge 35\end{array}\right.[/tex]

Please help asap xx

The picture below shows a container that Jeff uses to freeze water:

What is the minimum number of identical containers that Jeff would need to make 2000 cm3 of ice? (Use π = 3.14.)

A. 8
B. 4
C. 2
D. 16

Answers

Hey! This is very long overdue!

The diameter is 8 and we'll reduce that to 4 so we can use [tex] \pi [/tex]R2.
3.14*16 is 50.24. Then we'll multiply that by the height which is 10 to get 502.4cm3.

Now we'll divide 2000/502.4 to see how many containers Jeff would need to make to make 2000 cm3 of ice.

This comes out to 3.98 but we can round it up to 4.

B. 4

(should I explain?)

Hey there!

We are looking for cm[tex]^{3}[/tex], so therefore we will be dealing with volume.

The formula for the volume of a cylinder is shown below.

V= h([tex]\pi[/tex]r²)

Our base has a diameter of 8. The radius is half of the diameter, so our radius is 4. Our height is also 10, so will plug that in for h.

We can plug our values into the equation.

V= 10([tex]\pi[/tex]4²)

V=10(16[tex]\pi[/tex])

We simplify further, using 3.14 for pi.

V=10(50.24)

V=502.4

Therefore, the volume of one cylinder is 502.4.

Now, we need to see how many of these cylinders we need to get 2,000 cm³ of ice. We will divide below.

2,000÷502.4≈3.98

Therefore, we cannot have 2 as it will not be enough. 3.98 is about 4, so that would be the best minimum amount.

Therefore, your answer would be B) 4.

I hope this helps!

(Financial Algebra workbook 10-3)

Under his "Household expenses" Budget category, Mark has allocated $60 per month for pet food. He can purchase "wet food" for $1.50 per can or "dry food" for $3 per bag.

E). Name a combination of bags and cans that will cause him to be over budget.

Answers

A possible answer to this question is 15 cans of "wet food" and 15 bags of "dry food". 15 cans of wet food make $1.50 * 15 = $22.50 and 15 bags of dry food make $3.00 * 15 = $45. $45 + $22.50 = $67.50, which is over budget.

The local grocery store wants to know if the shoppers prefer Crest or Colgate toothpaste. The store gives all of its shoppers a value saver card, then uses a random number generator to select 30 card numbers and surveys those shoppers. Is this sampling method representative of the entire population and explain?

A. No, some shoppers may not buy toothpaste there.

B. Yes, all shoppers have a value card and the shoppers interviewed were chosen by a random number generator.

C. No, need a bigger sample.

D. No, the store should only ask women.

Answers

a, it is a biased ample because for example I may not go there to get toothpaste. Good luck

No, some shoppers may not buy toothpaste there.

The answer is option A.

What is an example of a word problem?

Word problems normally include mathematical modeling questions, where records and information approximately a positive machine is given and a student is needed to expand a model. For example, Jane had $5.00, then spent $2.00. How much does she have now?

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Please help with geometry

Answers

It's a equilateral triangle. The area of the white region is the area of a sector minus the area of a triangle.
[tex]\dfrac{60^o}{360^o}=\dfrac{1}{6}[/tex]
The sector is 1/6 of the circle, therefore the area of the sector is 1/6 of area of the circle.
The formula of an area of the circle: [tex]A_O=\pi r^2[/tex]

The area of the sector:
[tex]A_s=\dfrac{1}{6}\cdot\pi\cdot12^2=\dfrac{1}{6}\pi\cdot144=24\pi\ m^2[/tex]
The formula of an area of the equilateral triangle: [tex]A_\Delta=\dfrac{a^2\sqrt3}{4}[/tex]
[tex]A_\Delta=\dfrac{12^2\sqrt3}{4}=\dfrac{144\sqrt3}{4}=36\sqrt3\ m^2[/tex]

The area of the segment:
[tex]A_{sg}=A_s-A_\Delta\to A_{sg}=(24\pi-36\sqrt3)m^2[/tex]

The area of the shaded region:
[tex]A=A_O-A_{sg}\to A=144\pi-(24\pi-36\sqrt3)=144\pi-24\pi+36\sqrt3\\\\=\boxed{A=(120\pi+36\sqrt3)m^2}[/tex]

TON OF FREE POINTS FOR THE SMARTEST FINANCE PERSON! EASY PEASY, JUST NEED HELP TO DO IT THE RIGHT WAY ASAP!!! WHO SHALL WIN? Do not answer incorrectly or to get free points please, or you will be reported, and not smart.

David buys a home for $278,640. His home is predicted to increase in value 4% each year. What is the predicted value of David's home in 18 years? Round your answer to the nearest dollar.

Options:
$542,638
$564,474
$576,284
$580,122

Thanks in advance, you guys truly rock.

Answers

The problem can be represented by the the exponential growth formula which is :
[tex]P(t) = A * r^{t} [/tex]
Where: t ⇒ time , A ⇒ initial amount , r ⇒ rate of increase
P(t) ⇒ predicted amount at the end of t.

For the given problem:
initial amount = A = $278,640
predicted increase in value per year = 4% =0.04

∴ r = 1 + 0.04 = 1.04

for t = 18 years

∴ [tex]P(t) = A * r^{t} =278,640 * 1.04^{18}=\framebox{564,473.5}[/tex]
Rounding to the nearest dollar ⇒ ∴ P(t) = 564,474

So, the predicted value of David's home in 18 years = $564,474

So, The correct option is $564,474

564474 is the correct answer

Hope this helps...

If you need 2 tablespoons for every 5 quarts how many would you need for 4 quarts

Answers

1.6 tablespoons is the answer

If a pizza is sliced into 6 even slices, what is the angle of rotational symmetry?

Answers

Hello!

A pizza is in the shape of a circle

A circle is 360° around

divide this by the amount of pieces

360 / 6 = 60

The answer is 60°

Hope this helps!

Final answer:

The angle of rotational symmetry of a pizza sliced into 6 even slices is 60 degrees, which is the angle required to rotate each slice to coincide with the next, demonstrating six-fold rotational symmetry.

Explanation:

The angle of rotational symmetry for a pizza sliced into 6 even slices can be calculated based on the fact that a complete rotation is 360 degrees.

Since the pizza is divided into 6 slices, the angle to rotate each slice to coincide with the next is 360 degrees divided by 6.

Step-by-Step Explanation

Start with the full rotation angle, which is 360 degrees.Divide 360 by the number of slices, which is 6.The angle of rotational symmetry is therefore 360 ÷ 6 = 60 degrees.

Each 60-degree turn will align the pizza with itself, showing that it has rotational symmetry at this angle.

Since the pizza can be rotated 6 times and each time result in the same shape positioned identically, it demonstrates six-fold rotational symmetry.

The perimeter of a square window is 360 cm find the length of one side

Answers

Final answer:

To find the length of one side of a square window with a perimeter of 360 cm, we use the formula for the perimeter of a square, resulting in each side being 90 cm long.

Explanation:

To find the length of one side of a square window when the perimeter is 360 cm, we can use the formula for the perimeter of a square, which is P = 4s, where P represents the perimeter and s represents the length of one side. Given that the perimeter is 360 cm, we can set up the equation 360 = 4s. Dividing both sides of the equation by 4 gives us s = 90 cm.

Therefore, the length of one side of the square window is 90 cm.

I need your help here! 15 pointa and brainliest. If you cant do it, at least give me the formula to this so I can solve it.

Answers

see the attached picture for the answer. You will need to write the sentence required.

Answer:

0.40 formula x3.9 standardwise. Sorry if this doesnt help. I tried.

Step-by-step explanation:

According to Newton's Law of Cooling, if a body with temperature T 1 is placed in surroundings with temperature T 0, different from that of T 1, the body will either cool or warm to temperature T(t) after t minutes, where: T(t) = T 0 + (T 1 - T 0)e kt and k is a constant. A cup of coffee with temperature 140°F is placed in a freezer with temperature 0°F. The constant k ≈ -0.0815. Use Newton's Law of Cooling to find the coffee's temperature, to the nearest degree Fahrenheit, after 15 minutes. The temperature is about a0degrees Fahrenheit.

Answers

We can substitute the given values into the equation for T, given the surrounding temperature T0 = 0, initial temperature T1 = 140, constant k = -0.0815, and time t = 15 minutes.
T = 0 + (140 - 0)e^(-0.0815*15) = 140e^(-1.2225) = 41.23°F

Final answer:

Using Newton's Law of Cooling, the coffee's temperature after 15 minutes when placed in a freezer with a temperature of 0°F is approximately 76°F.

Explanation:

According to Newton's Law of Cooling, the temperature of an object changes at a rate proportional to the difference between its temperature and the temperature of its surroundings. In the given problem, we have a cup of coffee initially at 140°F placed in a freezer at 0°F, aimed to find the coffee's temperature after 15 minutes. The constant k is given as -0.0815.

We can plug these values into the equation T(t) = T0 + (T1 - T0)ekt. Therefore, the temperature of the coffee after 15 minutes can be calculated as T(15) = 0 + (140 - 0)e-0.0815*15.

Computing this gives us a value of approximately 76°F. Thus, after 15 minutes, the coffee's temperature, to the nearest degree Fahrenheit, is 76°F when placed in a freezer with a temperature of 0°F according to Newton's Law of Cooling.

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Explain how the discriminant b squared minus 4 ac can be used to determine the number of solutions to a quadratic equation

Answers

are there any answer choices

A circle has a circumference of 144\pi144π144, pi. what is the radius of the circle?

Answers

By definition, the circumference of a circle is given by:
C = 2πR
Where,
R: radius of the circle.
Substituting values we have:
144π = 2πR
By clearing R we have:
R = 144/2
R = 72 units
Answer:
The radius of the circle is:
R = 72 units

Please help me with a simple math problem.

What is the value of b?

A. 1.5
B. 3
C. 3.75
D. 4.5

Answers

You would take 7.5 and divide it by 2 which will give you C. 3.75

3.75 is the answer because the top and bottom line are the same and then you divide 7.5 by 2.

What is the sector with a central angle of 185 degrees and a diameter of 6.4 m? Round to the nearest tenth.
66.1m^2
5.3m^2
16.5m^2
21.0m^2

Answers

The area of a sector is
[tex]A=\frac{1}{2}r^2\theta =\frac{1}{2}\left(3.2\:m\right)^2\left(185\cdot \frac{\pi }{180}\right)=16.5\:m^2[/tex]

The answer is 16.5 square meters.

Geometry B Unit 5: Area - Lesson 10: Area Unit Test

1. What is the area of the trapezoid? The diagram is not drawn to scale.

72 cm^2

2. Given the regular polygon, what is the measure of each numbered angle?

m∡1 = 36°; m∡2 = 72°

3. What are a) the ratio of the perimeters and b) the ratio of the areas of the larger figure to the smaller figure? The figures are not drawn to scale.

5/2 and 25/4

4. What is the area of a regular pentagon with a side of 12 in.? Round the answer to the nearest tenth.

247.7 in.2

5. Name the minor arc and find its measure.

AB; 162°

6. What is the circumference of the given circle in terms of pi_symbol?

28pi in.

7. What is the area of the given circle in terms of pi?

10.89pi m^2

8. What is the area of a sector with a central angle of 185° and a diameter of 6.4 m? Round the answer to the nearest tenth.

16.5 m^2

9. What is the area of the shaded region in the given circle in terms of pi_symbol and in simplest form?

(270 pi + 81 Root 3) m^2

Which story problems could be solved using the given equation? 6 divided by 1/2 = ? Choose exactly two answers that are correct.

A.
Mike spends a hour reading every night before bed. How many hours does Mike spend reading before bed in 6 days?

B.
Alice has 6 yards of ribbon. She uses yard of ribbon for each package she’s wrapping. How many packages can Alice wrap?

C.
A cup of milk is used for every serving in a recipe. How many servings can be made with 6 cups of milk?

D.
Charlie spent of his savings on 6 equally priced admission tickets to the zoo. What fraction of his savings did Charlie spend on each ticket?

Answers

Most likely D, the first three you don’t divide by 1/2.

Select the factors of x2 − 14x + 49.

(x + 49)(x + 1)
(x + 7)(x + 7)
(x − 7)(x − 7)
(x − 49)(x − 1)

Answers

[tex]x^2-14x+49=x^2-7x-7x+49=x(x-7)-7(x-7)=(x-7)(x-7)[/tex]

Other method:

[tex]x^2-14x+49=x^2-2\cdot x\cdot7+7^2=(x-7)^2=(x-7)(x-7)[/tex]

Used: (a - b)² = a² - 2ab + b²

Answer: (x - 7)(x - 7)

Answer:

The factors of the expression x² - 14x + 49 are (x - 7) (x - 7) .

Step-by-step explanation:

As given the expression in the question be as follow .

= x² - 14x + 49

This is also written as

= x² - 7x - 7x + 49

= x (x - 7)-7 (x - 7)

= (x - 7) (x - 7)

Therefore the factors of the expression x² - 14x + 49 are (x - 7) (x - 7) .

which of the points satisfy the linear inequality graphed here?

a)(0,0)
b)(10,0)
c)(-10,0)
d)(10,10)

Answers

For this case, the first thing to do is observe the shaded region of the graph.
The shaded region represents the set of points that satisfy the inequality.
We note that the point (-10, 0) is within the shaded region.
Therefore, this point satisfies the inequality.
Answer:
c)(-10,0)

What is the answer? (384 ft is wrong)

Answers

Because the question is asking you what is 8√48.The calculator says 55.4256258422So, I would say the answer is D.

The age of a father is 2 less than 7 times the age of his son. In 3 years, the sum of their ages will be 52. If the son’s present age is s years, which equation models this situation?

Answers

The father is 40 which is 2 less than 7x6=42 Therefore the son is 6. In 3 years the the father will be 43 and the son will be 9. 43+9=52

Answer:

Son’s present age, s = 6 years.

Step-by-step explanation:

Let the son’s present age is s years and father's be f.

We have age of a father is 2 less than 7 times the age of his son.

f = 7s -2

7s - f = 2 -------------------eqn 1

In 3 years, the sum of their ages will be 52.

s + 3 + f + 3 = 52

s + f = 46 -------------------eqn 2

eqn 1 + eqn 2

8s = 48

s = 6

Son’s present age, s = 6 years.

Determine whether the polynomial is a difference of squares and if it is, factor it. y2 – 16

Answers

I think it’s not a different of squares because when u factor it =2(y-8)

(y – 4)(y + 4) it is a difference this is it. I did the test just a second ago.

Iridium -192 has a half life of 74 days after 148 days, how many milligrams of 900 mg sample will remain?

Answers

[tex]\bf \textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &900\\ t=\textit{elapsed time}\to &148\\ h=\textit{half-life}\to &74 \end{cases} \\\\\\ A=900\left( \frac{1}{2} \right)^{\frac{148}{74}}\implies A=900\left( \frac{1}{2} \right)^2\implies A=225[/tex]

The amount that remained out of the 900 mg sample after 148 days is 225 milligrams.

Given,

Iridium -192 has a half-life of 74 days.

We need to find out after 148 days how many milligrams of the 900 mg sample will remain.

Here the initial amount is 900mg.

What is half life?

It is the time at which the initial amount of a substance is reduced to half its amount.

The formula used with half-life:

[tex]N_{t} =N_{0} (\frac{1}{2})^\frac{t}{t_\frac{1}{2} }[/tex]

Where

N_t = Amount after time t

N_0 = initial amount

t_1/2 = half-life value of the substance.

t = time.

We have,

N_0 = 900 mg

t_1/2 = 74 days.

t = 148 days.

Substituting the values in the formula,

We get,

N_t = 900 ( 1/2 ) ^148/74

N_t = 900 ( 1/2 )^2

N_t = 900/4

N_t = 225 mg

We see that the amount that remains after 148 days is 225 milligrams.

Thus the amount that remained out of the 900 mg sample after 148 days is 225 milligrams.

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If line t is perpendicular to both line l and line m, then ∠1 and ∠2 are both ____ angles. Question acute right obtuse complementary

Answers

They are both right angles.

Answer:

∠1 and ∠2 both are right angles.

Step-by-step explanation:

Given that if line t is perpendicular to both line l and line m, then

we have to find about the angle ∠1 and ∠2

As given line l is perpendicular to both line l and line m,

Therefore the point at which the ;line intersect the two lines l and m at 90° i.e

∠1 and ∠2 both angles are formed at the intersection points of line t with l and m.

Hence, ∠1 and ∠2 both are right angles.

Find the area of the shaded portion in the square.
(assuming the central point of each arc is the corresponding corner

Answers

Hello,
Please, see the attached file.
Thanks.

The diameter of a circular table top is 2.6 metres. What is it’s circumference to the nearest metre?

Answers

Hoi!

To calculate the circumference, we use the formula [tex]C = \pi d[/tex]

Plug in the values.

[tex]C = \pi * 2.6[/tex]
[tex]8.2 = \pi * 2.6[/tex]

Your answer to the nearest meter is 8.

The circumference of a circular table top with a diameter of 2.6 meters is approximately 8 meters when using the formula C = \\πd and rounding to the nearest meter.

The question is asking for the circumference of a circular table top given its diameter. To calculate the circumference, we use the formula C = \\(π)d, where d is the diameter. The diameter given is 2.6 meters, so the circumference C = \\(pi)(2.6 meters).

Using the approximation \\(π \\approx 3.14, we calculate C \\approx 3.14 \\times 2.6 = 8.164 meters. When rounding this to the nearest meter, we obtain 8 meters as the circumference of the table top.

A 15 sector in a circle has an area of 11.9 m2 What is the area of the circle?

Answers

Given that the area of a 15° secant has an area of 11.9 m2, then the area of the circle will be given by:
(Total measure in degrees of the circle)/(measure in degrees of the secant)*(area of secant)
=360/15*11.9
=24*11.9
=285.6 m^2

Answer: 285.6 m^2

Elly buys 75 shares of stock in a mutual fund for a total investment of $450. She sells 50 shares of her stock for total proceeds of $400. Determine if Elly made a profit or loss, and how much per share.
a.
loss of $0.67 per share
b.
loss of $2 per share
c.
profit of $0.67 per share
d.
profit of $2 per share

Answers

We have been given that Elly buys 75 shares of stock in a mutual fund for a total investment of $450.

It means the cost of 1 share is given by

[tex]\frac{450}{75}\\ \\ =\$6[/tex]

Now, we have been given that she sells 50 shares of her stock for total proceeds of $400.

It means the cost of 1 share is given by

[tex]\frac{400}{50} \\ \\ \$8[/tex]

She purchased per share at $6 and sold per share at $8.

It means that she made a profit of [tex]8-6=\$2[/tex] per share.

Therefore, d is the correct option.

(d) profit of $2 per share

Elly made a profit of $2 per share.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

First, we can determine the average cost per share of the 75 shares of stock that Elly bought:

Average cost per share = Total investment / Number of shares

= $450 / 75 shares

= $6 per share

Next, we can determine the total proceeds from the sale of 50 shares:

Total proceeds = Number of shares sold x Price per share

= 50 shares x ($400 / 50 shares)

= $400

Elly paid $6 per share for the 75 shares she bought, and she sold 50 shares for $8 per share.

The difference between these prices will determine whether she made a profit or loss per share:

Profit or loss per share = Selling price per share - Average cost per share

= $8 per share - $6 per share

= $2 per share

Since the profit per share is positive, Elly made a profit.

Therefore,

Elly made a profit of $2 per share.

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The ratio between the volumes of two cubes is 125 to 216. what is the ratio between their respective surface areas?

Answers

Volume of a cube is length * width * height. Because it's a cube, all of these lengths are the same measurement so rather than doing V = l*w*h, we can do one of the measurements cubed, let's call it x.

So Volume = x³. So if we are given the volume, we can the length by doing the cube root.

∛125 = 5
∛216 = 6

Surface area of a cube = 6x². So now we plug both of these measurements into the formula.

For 5:

SA = 6(5)² = 6(25) = 150

For 6:

SA = 6(6)² = 6(36) = 216

The ratio of their surface areas is 150:216 or if you simplify it by dividing both by the GCF of 6, 25:36

Compute the area of a triangle with sides. 15 × 15 × 18

Answers

You can find the area using Heron's formula.
A=√(s(s-a)(s-b)(s-c)),
where a,b,c are sides of the triangle,
and s=(a+b+c)/2 - half perimeter of a triangle.
a=15,
b=15
c=18
s=(15+15+18)/2=48/2=24
s=24
s-a=24-15=9
s-b=24-15=9
s-c=24-18=6

A=√(24*9*9*6)=√(4*6*6*9*9) = 2*6*9=108
A=108

Michelle can fold 4 baskets of clothes in 54 minutes, while Ruby can fold 4 baskets of clothes in 108 minutes. How long will it take them to fold 8 baskets of clothes if they are working together?

Answers

Michelle can fold 4/54 baskets per minute = 8/108 baskets per minute.
Ruby can fold 4/108 baskets per minute.

Each minute Michelle and Ruby work together, they can fold
8/108 +4/108 = 12/108 = 1/9
of a basket of clothes. For 8 baskets of clothes, it will take them
(8 baskets)/(1/9 baskets/minute) = 72 minutes

Working together, they fold (8) baskets in (72) minutes, averaging

[tex]$\frac{1}{9}$[/tex] of a basket per minute combined.

First, let's find out how many baskets of clothes each person can fold per minute.

Michelle can fold [tex]$ \frac{4}{54} $[/tex] baskets per minute, and Ruby can fold [tex]$ \frac{4}{108} $[/tex] baskets per minute.

Let's simplify these fractions:

Michelle's rate: [tex]$ \frac{4}{54} = \frac{2}{27} $[/tex] baskets per minute.

Ruby's rate[tex]: $ \frac{4}{108} = \frac{1}{27} $[/tex] baskets per minute.

Now, when they work together, their combined rate will be the sum of their individual rates:

Combined rate = Michelle's rate + Ruby's rate

Combined rate = [tex]$ \frac{2}{27} + \frac{1}{27} $[/tex] baskets per minute

Combined rate = [tex]$ \frac{3}{27} $[/tex] baskets per minute

Combined rate = [tex]$ \frac{1}{9} $[/tex] baskets per minute

Now, to find out how long it will take them to fold 8 baskets together, we can use the combined rate:

Let ( t) be the time it takes for them to fold 8 baskets together.

[tex]$ \frac{1}{9} $ baskets per minute * $ t $ minutes = 8 baskets\[ t = \frac{8}{\frac{1}{9}} \]\[ t = 8 \times 9 \]\[ t = 72 \] minutes[/tex]

So, it will take them 72 minutes to fold 8 baskets of clothes together.

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