The stage manager of a school play creates a rectangular acting area of 42 square yards. String lights will outline the acting area. To the nearest whole number, how many yards of string lights does the manager need to enclose this area?

Answers

Answer 1

Given that the stage manager of a school play creates a rectangular acting area of 42 square yards.

Let the length of the rectangular acting area be x, then the width is given by 42 / x.

The number of yards of string lights that the manager need to enclose the area is given by the perimeter of the rectangular area.

Recall that the perimeter of a rectangle is given by
P = 2(length + width) = 2(x + 42/x) = 2x + 84/x

The perimeter is minimum when the differenciation of 2x + 84/x is equal to 0.
i.e. [tex]2 - \frac{84}{x^2}=0\\ \\ \Rightarrow2x^2-84=0\\ \\ \Rightarrow x^2=42\\ \\ \Rightarrow x\approx6.48[/tex]

Therefore, the minimum number of yards of string lights the manager need to enclose this area is given by
[tex]2(6.48)+ \frac{84}{6.48} =12.96+12.96=25.92\approx26\ yards[/tex]

Related Questions

What is the domain of the inverse of a relation?

Answers

the domain is the space between the end points on the x axis
ex: D:-2(<=)x(<=)4 this means that the domain is any numbers between -2 and 4

if say a relation has a value pairs of say

(a,b),(c,d),(e,f),(g,h),(i,j)

the the value pairs for its inverse will be

(b,a),(d,c),(f,e),(h,g),(j,i)

notice, is the same pair, but flipped sideways.

and of course, the domain is the set of the x-values or the x-coordinate or the first value of each pair, as you already should know.

For each handmade greeting card jacqui sells, she makes a profit of $0.35. In one week , she made a profit of $42 .she sells the cards for $0.75 each.

Part A: About how much did she earn before paying expenses?

Answers

earn before paying expenses <---- Revenue = price * quantity

so, how many did she sell? well, we know she makes a profit of 0.35 for each, and in that week, she made a total profit of 42 bucks, so she sold 42/0.35 or 120 greeting cards.

quantity = 120
price = 0.35

Revenue = price * quantity. <---- that's how much she earned before expenses.

Answer:

$ 90

Step-by-step explanation:

Given,

The profit in each card = $ 0.35,

If she sold x cards,

Then the total profit she earned = profit in each card × number of cards

= 0.35x dollars,

According to the question,

0.35x = 42

[tex]\implies x = \frac{42}{0.35}=120[/tex]

Thus, she sold 120 cards,

Now, if the selling price of each card = $ 0.75,

Hence, total earning before paying expenses

= selling price of each card × total cards

= 0.75 × 120 = $ 90

What is 8.63 repeating as a fraction?

Answers

To write 8.63 as a fraction you have to write 8.63 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
8.63 = 8.63/1 = 86.3/10 = 863/100

Ted weighs twice as much as Julie. Mike weighs three times as much as Julie. Together, Ted, Mike, and Julie weigh 210 lbs. What is the weight of each person?

Answers

- Julie weighs 35 lbs
- Mike weighs 105 lbs
- Ted weighs 70 lbs

In this problem, Julie is the basis for figuring it out.

J = Julie's Weight

Ted = 2j
Mike = 3j

2j + 3j + j = 210 or 6j

210 ÷ 6 = 35

With this, we know Julie's weight. Also, that she might as well be skin and bones.

35 × 2 = 70

35 × 3 = 105

105 + 70 + 35 = 210

Julie's Weight = 35 lbs.
Ted's Weight = 70 lbs.
Mike's Weight = 105 lbs.

For a percentage increase of 36%, state the multiplier

Answers

if we had x and increased it by 36%, we would get

x+0.36x
1x+0.36x
if we undistribute x then
x(1+0.36)
1.36x

the multiplier is 1.36

What's the answer to 3/2(16n+3)=24n

Answers

N is equal to negative 4

3 times 2 IS 6
Take 6 times 16n then take 6 times 3
Now you have 96n plus 18 equals 24n
Subtract 96n from both sides
18 equals negative 72n
Divide both sides by 18 you get 4 now u can't have a negative n so divide each by a negative so now u have n equals -4

The number of girls, g, in a room is four more than two times the number of boys, b. Half of the number of girls in the room minus the number of boys is 2. The equations below represent the situation.

Answers

Call g the number of girls and b the number of boys.

These are the equations that represent the situation:

1) g = 4 + 2b

2) g/2 - b = 2

To solve it you can multiply the second by 2:

=> 2 { g/2 - b = 2 }

=> g - 2b = 4

As you can see this equation is equivalent to the first equation, so this system is not determined (it has infinite solutions).

Answer:

Step-by-step explanation:

Mario purchases a prepaid phone plan for $50. Each minute he uses costs $0.13. How many minutes can Mario talk on this plan? Write an inequality that represents this problem and solve the inequality

Answers

Final answer:

Mario can talk for up to 384 minutes on his $50 prepaid phone plan. We use the inequality 0.13m ≤ 50 and solve for m to find the maximum number of whole minutes Mario can use.

Explanation:

To solve this problem, we need to set up an inequality that represents the constraints of Mario's prepaid phone plan budget. The inequality will help us determine the maximum number of minutes Mario can talk on this plan.

Let's use m to represent the number of minutes Mario can talk. We know that each minute of talk time costs $0.13, and Mario's prepaid plan is $50. Our inequality should reflect the fact that the total cost of talking m minutes cannot exceed his budget of $50.

The inequality will look like this:

0.13m ≤ 50

To solve for m, we divide both sides of the inequality by 0.13:

m ≤ 50 / 0.13

When we calculate 50 divided by 0.13, we get approximately 384.6154. Since Mario cannot talk for a partial minute on his prepaid plan, we round this number down to the nearest whole minute, which is 384 minutes.

Therefore, Mario can talk for up to 384 minutes on his prepaid phone plan.

Final answer:

To find the number of minutes Mario can talk on the prepaid phone plan, we can set up an inequality: 0.13x <= 50. Solving this inequality, we find that Mario can talk for a maximum of 384 minutes.

Explanation:

To find the number of minutes Mario can talk on the prepaid phone plan, we can set up an inequality based on the cost. Let x represent the number of minutes. The cost of the phone plan is $50, and each minute costs $0.13. So, the inequality is: 0.13x <= 50. To solve this inequality, we divide both sides by 0.13 to isolate x and find: x <= 50 / 0.13. Using long division or a calculator, we can find that x is approximately 384.61, but since we can't have a fraction of a minute, the maximum number of minutes Mario can talk on this plan is 384 minutes.

Show all work please!!!!!!

1. PB (there is a line on top) is a line segment on a number line. It has endpoints at -2 and 12. What is the coordinate of its midpoint?

2. The midpoint of CD (there is a line on top) is E(-1, 0). One endpoint is C(5,2). What are the coordinates of the other endpoint?

3. Explain the distance formula. Then use it to calculate the distance between A(1, 1) and B(7, -7).

Answers

The midpoint formula is:
(point1 + point2)/2

1) (-2 + 12)/2 = 5

2) (-1 +5)/2 = 2
    (0+2)/2 = 1
     (2,1)

3) Sqrt of (x2-x1)^2 + (y2 - y1)^2
     sqrt of (7 -1)^2 + (-7 - 1)^2
     sqrt of (6)^2 + (-8)^2
     sqrt of 36 + 64
     sqrt of 100
     10

Hope this helps!

Can the following question be considered a statistical question and why or why not? Do students at Bryan Middle School exercise?

Answers

Answer:

this is a multiple choice question with 4 answers

Yes, it specifies the population

No, it does not specify the population

Yes, it anticipates enough variability in responses

No, it does not anticipate enough variability in responses

I think the answer is.......... (Drum roll please)........... D.

Step-by-step explanation:

There is not any variability in this question it is just a yes or no question. If the question was "How long does an average person exercise for "

He sum of three consecutive integers is −369−369. find the three integers.

Answers

n + (n+1) + (n+2) = -369
3n + 3 = -369
3n = -366
n = -122

so the three consecutive integers are : -124 ; -123 ; -122

What is −20÷45 ?−25−16−116−125

Answers

-20÷45= -.4444444444 (repeating)
-25-16-116-125=-282

Its -25 i just did the test

Gabrielle's age is three times Mikhail's age. The sum of their ages is 32 . What is Mikhail's age?

Answers

g + m = 32
g = 3m

3m + m = 32
4m = 32
m = 32/4
m = 8 <=== Mikhail's age

g = 3m
g = 3(8)
g = 24 <== Gabrielle's age

g + m = 32

g = 3m

3m + m = 32

4m = 32

m = 32/4

m = 8 (Mikhail's age)

g = 3m

g = 3(8)

g = 24 (Gabrielle's age)

how can you discover a person's age by year?

:To find out a person's age, all you need is that person's 12 months of beginning. After this, all you want to do now's subtract the beginning 12 months from the continuing modern year and you will have the age. this can help you to calculate the age from the date of delivery. Age= 2020- 1966 = 54.

How do you calculate age in mm dd yyyy?

Your age in the total range of days is calculated as a variety of years, x, with twelve months = 365x plus. a number of years, y, with three hundred and sixty-six days = 366y plus. a number of days in the remaining partial yr.

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Is 5.78778778 a rational or irrational number? Explain

Answers

Hello There!

It is rational as it can be written as a fraction and had a pattern to it.

Hope This Helps You!
Good Luck :)

The number 5.78778778 is a rational number because it has a repeating decimal pattern that can be expressed as the fraction 573/99.

The number 5.78778778 is a rational number. Rational numbers are those that can be expressed as a fraction where both the numerator and the denominator are integers.

In this case, the number 5.78778778 has a repeating decimal pattern, which is a hallmark of rational numbers.

We can convert this repeating decimal into a fraction by setting it equal to a variable, say x, subtracting a shifted version of x to isolate the repeating part, and then solving for x to find its fractional equivalent.

If we perform this process, we can turn 5.78778778... into a fraction. For example:

→ Let x = 5.78778778...

→ Multiply both sides of the equation by 100 to shift the decimal two places: 100x = 578.78778778...

→ Subtract the original x from this new equation: (100x - x) = (578.78778778... - 5.78778778...)

→ This simplifies to 99x = 573

→ Divide both sides by 99 to solve for x: x = 573/99

→ This fraction represents the decimal number 5.78778778..., confirming it is rational.

What is the vertex of the graph of the function below? y = x2 - 4x + 3

Answers

here's a nice hack

if you have [tex]y=ax^2+bx+c[/tex]
the x value of the vertex is [tex]\frac{-b}{2a}[/tex]

fo if we have
[tex]y=1x^2-4x+3[/tex]
b=-4
a=1

the x value of the vertex is
[tex]\frac{-(-4)}{2(1)}=\frac{4}{2}=2[/tex]
subsitutie that for x to find y value

[tex]y=1(2)^2-4(2)+3[/tex]
[tex]y=1(4)-8+3[/tex]
[tex]y=4-5[/tex]
y=-1

the vertex is (2,-1)

Final answer:

The vertex of the function y = x2 - 4x + 3 is at (2,-1). You can find this by using the formula -b/2a for the x-coordinate of the vertex and then substituting this x-value into the original equation to find the y-coordinate.

Explanation:

The function you are asking about, y = x2 - 4x + 3, is a quadratic function, and the graph of a quadratic function is a parabola.

The vertex of this parabola can be found using the formula -b/2a for the x-coordinate and then substituting this value into the original equation to find the y-coordinate. For this function, the coefficients a and b (from the general form ax2 + bx + c) are 1 and -4 respectively. Using the formula, the x-coordinate of the vertex is -(-4)/2*1 = 2. We then substitute x = 2 into the original equation to find y = (2)2 - 4*(2) + 3 = -1. Thus, the vertex of the function y = x2 - 4x + 3 is at (2,-1).

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How do you solve -2(6x+3)=-27–5x ?

Answers

Hi!

Our goal is to isolate x on one side by doing the same operation on both sides.

First let's use the distribution property.
-2 x 6 = -12
-2 x 3 = -6
-12x - 6 = -27 - 5x

Add 6 to both sides
-12x - 6 + 6 = -27 + 6 - 5x
-12x = -21 - 5x

Add 5x to both sides
-12x + 5x = -21 - 5x + 5x
-7x = -21

Divide by -7 on both sides
-7x/-7 = -21/-7
x = 3

The answer is x = 3

Hope this helps! :)

1. Find a counterexample.

If two angles are complementary, then they are not congruent.

Answers

Final answer:

Complementary angles are angles that add up to 90 degrees but may not have the same measure. A counterexample to the statement would be two angles that are complementary but not congruent.

Explanation:

Complementary angles are angles that add up to 90 degrees. Congruent angles are angles that have the same measure.

A counterexample is a situation where the statement is false. In this case, a counterexample would be two angles that are complementary but not congruent.

For example, let's consider a 45-degree angle and a 45-degree angle. These angles are complementary because their sum is 90 degrees. However, they are not congruent because they have different measures.

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3x - 24= -6 solve for x

Answers

3x-24=-6 . Add 24 to both sides, so that leaves you with 3x=18. Divide by 3 on both sides, and x=6

I need the answer Algebra question

Answers

He had 32 dollars at the beginning of the day

Answer: $32

Step-by-step explanation:

add 7+9+12+4 =32

The length of a rectangle is 3 inches less than 4 times the width. If the perimeter is 55 inches, what is the width of the rectangle?

Answers

length= 4x-3
width = x

P = 2(l+w)
55= 2(4x-3 +x)
55 = 2(5x-3)
27.5 = 5x-3
27.5+3 = 5x
30.5/5 = x
6.1=x

Width is 6.1 in, length (4 x 6.1 -3) = 21.4

The width of the rectangle is 6.1 in.

What is a rectangle?

That parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.

Perimeter of the rectangle = 2(L + W) unit

WE have been given that length of a rectangle is 3 inches less than 4 times the width.

Length = 4x-3

width = x

If the perimeter is 55 inches, then

Perimeter of the rectangle = 2(L + W) unit

55= 2(4x-3 +x)

55 = 2(5x-3)

27.5 = 5x-3

27.5+3 = 5x

30.5/5 = x

6.1=x

Thus, Width is 6.1 in

The length (4 x 6.1 -3) = 21.4

Hence, the width of the rectangle is 6.1 in.

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The perimeter of a parallelogram is 72 meters. The width of the parallelogram is 4 meters less than its length. Find the length and the width of the parallelogram

Answers

the length would be 26 and the width would be 16.
L = length
w = width
p = perimeter

p=72

2L+2w=72

L=w+4

2(w+4) + 2w = 72
2w + 8 + 2w = 72
4w = 64
w = 16

2L + 2(16) = 72
2L + 32 = 72
2L = 52
L = 26

w = 16
L = 26

Answer:

Length is 20 meters and width is 16 meters.

Step-by-step explanation:

Given: Perimeter of parallelogram is 72 meters.

Width of the parallelogram is 4 meters less than its length.

To find: Length and width of the parallelogram.

Solution: Let the length of the parallelogram be x meters. So, width of the parallelogram is [tex]x-4[/tex] meters.

As per question,

[tex]x+x+x-4+x-4=72[/tex]

[tex]4x-8=72[/tex]

[tex]4x=72+8[/tex]

[tex]4x=80[/tex]

[tex]x=\frac{80}{4}[/tex]

[tex]x=20[/tex]

Hence, length of the parallelogram is 20 meters, and width of the parallelogram is [tex]20-4=16[/tex] meters.

Is the number x positive? (1) on the number line, 0 is closer to x – 1 than to x. (2) on the number line, 0 is closer to x than to x + 1?

Answers

(1) on the number line, 0 is closer to x – 1 than to x

x is positive, let x = 5, then x-1 = 5-1 = 4, then zero is close to 4 than 5

-------------------------.------------------------.-----------------------

(2) on the number line, 0 is closer to x than to x + 1

x is positive, as zero is close to 5 than 5+1=6

I hope that helps!

A square piece of cloth, which is 10 meters on a side, is cut across the diagonal to form two right triangles. What is the length of the diagonal cut?

Answers

A² + B² = C²
So 10² + 10² is 200
The square root of 200 is about 14.14
10² + 10² ≈ 14.14²

Hope that helps :)

Answer:

Step-by-step

The answer is the square root of 288

Liam uses checks and a debit card, but does it not always right all the transactions and his checkbook register. He has lost track of his checkbook balance. Liam looks up the "available balance" using online banking, and write it on the next line as his new checkbook balance available to spend. What is wrong with Liam's method

Answers

The available balance online may not reflect all debit transactions or all checks that were written. Some recent debit transactions and check written may not have been posted to his account yet. The available balance would need to subtract any outstanding debit transactions and any written checks that have not cleared his account. This would yield the correct available balance.

Answer:

All of the above is the answer

Step-by-step explanation:

Amanda drove 355 miles using 17 gallons of gas. At this rate how many gallons of gas would she need to drive 284 miles?

Answers

355 miles/17 gallons ≈ 20.88 miles per gallon
284 miles ÷20.88= 13.6 gallons needed

Write the point-slope form of the equation of the horizontal line that passes through the point (2, 1). Pease show how!

Answers

check the picture below.

using a second for it, since it's a horizontal line, then say hmmm we'll use the y-intercept, or (0, 1), so the equation of a line that passes through (2,1) and (0,1)

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 2}}\quad ,&{{ 1}})\quad % (c,d) &({{ 0}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-1}{0-2}\implies \cfrac{0}{-2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=0(x-2)[/tex]

4. One-half of Heather's age two years from now plus one-third of her age three years ago is twenty years. How old is she now?

Answers

x = the age of Heather

One half of Heather's age two years from now plus one-third of her age three years ago is twenty years

(x + 2)/2 + (x - 3)/3 = 20

by solving the equation we find

x = 24 years

The function L = 0.8T2 models the relationship between L, the length in feet of a pendulum, and T, the period in seconds of the pendulum. Which value is closest to the period in seconds for a pendulum that is 30 ft long?
A) 5.4 s
B) 4.9 s
C) 6.8 s
D) 6.1 s
Please help A.S.A.P

Answers

L = (0.8) T^2

T^2 = L / 0.8

T = sqrt{ L / 0.8 }

T = sqrt{ 30 / 0.8 }

T = sqrt{ 37.5 }

T = 6.1 seconds

The correct answer is D) 6.1 seconds

Final answer:

Using the formula L = 0.8T², we find that a pendulum 30 ft long has a period of approximately 6.1 seconds, which corresponds to Option D.

Explanation:

The question is about finding the period, T, in seconds for a pendulum that is 30 ft long, using the formula L = 0.8T2. First, to solve for T given that L = 30, we rearrange the equation to T = √(L/0.8). Plugging in L = 30, we have T = √(30/0.8), which simplifies to T = √(37.5).

Calculating further, we find T ≈ 6.12 seconds. Therefore, the answer closest to the period in seconds for a pendulum that is 30 ft long is 6.1 seconds (Option D).

Plz help! Convert 6/9 into fractions with a denominater of 27 A. 6/7 B.21/27 C. 9/27 D.18/27

Answers

D. 6 x 3 = 18 and 9 x 3 = 27, hope this helps :)

How much would $400 invested at 9% interest compounded continuously be worth after 3 years? Rounded by the nearest cent

Answers

[tex]\bf \qquad \textit{Continuously Compounding Earned Amount} \\\\ A=Pe^{rt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$400\\ r=rate\to 9\%\to \frac{9}{100}\to &0.09\\ t=years\to &3 \end{cases} \\\\\\ A=400e^{0.09\cdot 3}[/tex]

notice, "e" is the Euler's constant, and yes, is on your calculator.

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People do all kinds of work from home, including research, management, marketing, and creative work. Talia took the bus from her home to the bank and then walked back to her home along the same route. The round trip took 0.9 hours total. The bus traveled at an average speed of 40 km/h and she walked at an average speed of 5 km/h. Use the table to complete these statements. How might the complaints of a peasant and a merchant compare during the revolution What's -4q-(-8q)+10 ?? also if you understand how to combine like terms can you help me with the rest? When is it necessary to use three points to name an angle? If CP bisects and DPB , what is the measure of angle CPB? Find the amount (future value) of the ordinary annuity. (round your answer to the nearest cent.) $1500/semiannual period for 8 years at 2.5%/year compounded semiannually What is the symbol of the element in group 4a 14 and period 2? The lengths of corresponding sides of 2 proportional rectangles are 20cm. and 8cm. The width of the larger rectangle is 5cm. What is the proportion used to find the width of the smaller rectangle? a reasonable estimate for 697 x 82 = 56,000. is this correct? what were some important industries along the eastern coast in the new england colonies? Select all that apply. 1.Shipping 2.Fur trade 3.Cattle farming 4.Fishing 5.Tobacco farming Pick 2 What might a psychodynamic theorist think about a person with extreme shyness? Which of the following best explains the difference between climate and weather?A. Weather refers to long term atmospheric conditions; climate refers to short term.B. Climate refers to long term atmospheric conditions; weather refers to short term.C. Weather and climate mean the same thing and can be used interchangeably.D. Weather refers to the atmospheric conditions on Earth; climate refers to the conductions in space. Find the value of x for which l is parallel to m. The diagram is not to scale.a. 31b. 62c. 93d. 149 Which of the pairs of molecular structures shown below depict enantiomers (enantiomeric forms) of the same molecule? Describe the four main spheres of Earth. 1. lithosphere: 2. hydrosphere: 3. atmosphere: 4. biosphere: A student sets up an experiment with two groups of bacteria. One group is exposed to the normal amount of mercury found in the environment. The other group gets a larger dose. Which term describes the normally treated group? A. independent group B. control group C. variable group D. experimental group .Which step comes last in the scientific method?testing a hypothesisdeveloping a theoryconducting an experimentproposing a hypothesis Josiah went to the local barber to get his hair cut. It cost $18 for the haircut. Josiah tipped the barber 15%. What was the total cost of the haircut including the tip Why might increased anger about corruption in government lead to less interest in government attempts to reconstruct the South? The processing speed of a certain computer is 10 to the power of 11 instructions per second. Another computer has a processing speed that is 10 to the 3 power times as fast. How many instructions per second can the faster computer processes Steam Workshop Downloader