A square napkin is folded in half on the diagonal and placed on the diameter of a round plate
(see diagram below).
If the folded napkin spans the plate and the plate has an 18-inch diameter, what is the area of
the space on the plate that is NOT covered by the napkin? Leave your answer in terms of .

Answers

Answer 1

Answer:

The area of  the space on the plate that is not covered by the napkin is[tex]81(\pi-1)\ in^2[/tex]

Step-by-step explanation:

step 1

Find the area of the plate

The area of a circle is given by the formula

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=18/2=9\ in[/tex] ---> the radius is half the diameter

substitute

[tex]A=\pi (9)^{2}\\A=81\pi\ in^2[/tex]

step 2

Find the area of the square napkin folded (is a half of the area of the square napkin)

we know that

The diagonal of the square is the same that the diameter of the plate

Applying Pythagorean theorem

[tex]D^2=2b^2[/tex]

where

b is the length side of the square

we have

[tex]D=18\ in[/tex]

substitute

[tex]18^2=2b^2[/tex]

solve for b^2

[tex]b^2=162\ in^2[/tex] -----> is the area of the square

Divide by 2

[tex]162/2=81\ in^2[/tex]

step 3

Find the area of the space on the plate that is NOT covered by the napkin

we know that

The  area of the space on the plate that is NOT covered by the napkin, is equal to subtract the area of the square napkin folded (is a half of the area of the square napkin) from the area of the plate

so

[tex]A=(81\pi-81)\ in^2[/tex]

simplify

[tex]A=81(\pi-1)\ in^2[/tex]


Related Questions

Rylee shopped at a clothing store, where she spent $36.50 plus 8% tax. Then, she spent $25 to refuel her car at the gas station. Finally, she bought groceries worth $23.50. At the grocery checkout, she handed over a coupon for a 20% discount on her purchase.

Complete the following steps to help Rylee find the net change to her banking account balance.

Answers

Answer: The net change to her banking account balance is $83.22.

Step-by-step explanation:

Hi to answer this question we have to analyze the information given:

She spent $36.50 plus 8% tax.  ( to calculate the tax amount we have to multiply the cost by the percentage in decimal form)

36.50 x (8/100) =$2.92 (value of tax)

Adding to the original cost

36.50+2.92 = $39.42

Then, she spent $25 to refuel her car at the gas station.

39.42 +25 = $64.42

She bought groceries worth $23.50. At the grocery checkout, she handed over a coupon for a 20% discount on her purchase

23.50 x (20/100) = 4.7 (amount of discount)

Subtracting to the purchase

23.50 -4.7= $18.8

Finally, adding to the total cost.

64.42 +18.8 = $83.22

Final answer:

To find the net change in Rylee's banking account balance, calculate the tax on her clothing purchase, add the fuel cost, and then subtract the grocery discount from the grocery purchase before summing all costs to get a total of $83.22.

Explanation:

The problem of calculating the net change to Rylee's banking account balance is a typical Mathematics problem involving percentages and addition. This is commonly tackled at the High School level. To solve it, we will need to calculate the total cost of each of Rylee's expenditures, including the application of tax and discounts where applicable.

Start by calculating the tax on the clothing store purchase: $36.50 * 8% = $2.92.Add the tax to the original amount to get the total clothing cost: $36.50 + $2.92 = $39.42.Add the fuel cost directly as there is no tax mentioned: $39.42 + $25 = $64.42.Calculate the discount on groceries: $23.50 * 20% = $4.70.Subtract the discount from the grocery total to find the final cost: $23.50 - $4.70 = $18.80.Add the discounted grocery cost to the previous total: $64.42 + $18.80 = $83.22.

The net change to Rylee's banking account balance after all her purchases is $83.22.

Can someone help me do this thank you​

Answers

Answer:

d = 15

Step-by-step explanation:

6+15 = 21

A middle school has 6th, 7th, and 8th-grade students. Which of the following would be a random sample of the students
A.) Surveying all of the teachers
B.) Surveying the students who buy their lunch in the cafeteria
C.) Surveying everyone whose last name begins with a G
D.) Surveying every 10th student who is on the class rosters

Answers

the answer would probably be d.

Answer:

c

Step-by-step explanation:

because you wount have a good esstimite you would only have the kids that start with G please mark as brainliest

Find the surface area of a sphere with radius of 1.5 and slant height of 6.​

Answers

Answer:

about 28.27

Step-by-step explanation:

A=4πr2

What is the median of the following numbers

Answers

Answer: You did not give me any numbers...

Step-by-step explanation:

just to say, The median is the value separating the higher half of a data sample, a population, or a probability distribution, from the lower half. In simple terms, it may be thought of as the "middle" value of a data set.

The median of a set of numbers is the middle number in the set (after the numbers have been arranged from least to greatest) or, if there are an even number of data, the median is the average of the middle two numbers.

3/5 * (t + 26) = −3(2 − t)

t =

Answers

Answer:

t=9

Step-by-step explanation:

The area of a square garden is 36 square feet. What is the side length of the garden

Answers

Answer:

6

Step-by-step explanation:

because 6 times 6 =36 so the answer is 6

Answer:

6 ft

Step-by-step explanation:

We know that side * side equals area, and that squares have all sides the same length. So therefore, A = [tex]s^{2}[/tex].

If we know the area, then we can do [tex]\sqrt{36}[/tex] which equals 6

A museum groundskeeper is creating a semicircular statuary garden with a diameter of 23 feet. There will

be a fence around the garden. The fencing costs $7.50 per linear foot. About how much will the fencing

cost altogether? Round to the nearest hundredth. Use 3.14 for pi

Answers

Answer: $443.32

Step-by-step explanation:

Hi, to answer this question we have to calculate perimeter of a semicircle:

P = π (d/2) + d

Where d is the diameter

Replacing with the values given:

P = 3.14 (23/2) + 23 = 59.11 feet  

Since each linear foot cost $7.50, we have to multiply that cost by the perimeter.

59.11 x 7.50 = $443.32

Feel free to ask for more if needed or if you did not understand something.

Simplify:
X(3.8 - 2.6) +3+3.2 (x + 2)

Answers

Answer:

4.4x+9.4

Step-by-step explanation:

x(3.8)-x(2.6)+3+3.2(x)+3.2(2)

3.8x-2.6x+3+3.2x+6.4

Combine all of x's with the blanks

4.4x+9.4

What is the length of Line segment B C? Round to the nearest tenth.

Triangle A B C is shown. Angle B C A is a right angle and angle C A B is 65 degrees. The length of hypotenuse B A is 16 centimeters and the length of B C is x.

6.8 cm
7.5 cm
14.5 cm
17.7

Answers

The length of segment B C is 6.8cm

Answer:

14.5

Step-by-step explanation:

since the hypotenuse is 16 you multiply that by (sin(65)) and 14.5 is the answer.

The Johnson family is moving and they need a truck with at least 55 cubic meters of space. The moving trucks they have to choose from are shown in the table below. Which is the smallest truck they can use?
PLEASE I WILL MARK AS BRAINLIEST!

Answers

Answer:

Medium

Step-by-step explanation:

Cause that what it is.

So what you have to do is find the area of each truck and find the one that is only a little bit higher than 55 or exactly 55. In this case, that should be the large truck, because the medium truck is too small (approx. 40 cubic meters)

Justin is skeet shooting. The height of the skeet is modeled by the equation h= -5t^2 +32t + 2, where h represents the height in meters and t seconds after the skeet is released. The path of Justin's bullet is modeled by the equation h= 31.5t + 1, with the same units. How long will it take for the bullet to hit the skeet? How high off the ground will the skeet be?

Answers

Final answer:

By solving the system of equations representing the paths of the bullet and the skeet, we find that the bullet will reach the skeet 3.79 seconds after the skeet's release, at a height of approximately 120 meters.

Explanation:

This problem involves solving systems of equations to determine the interaction between a projectile and target, something commonly addressed in physics as well as in mathematics. The solution involves equalizing the equations[tex](h = -5t^2 +32t + 2)[/tex] modeling the height of the skeet and (h = 31.5t + 1) the path of Justin's bullet. By solving this system of equations we find two potential times, t = 3.79 s and t = 0.54 s.

Since we can reason the skeet won't get hit before it is released, disregard t = 0.54 s. Therefore, the bullet will hit the skeet 3.79 seconds after the skeet is released. This is the time it takes for the bullet to reach the skeet. To find the height at which the bullet hits the skeet, substitute t = 3.79 into either of the two original equations (both should work). Using h = 31.5t + 1, for instance, yields approximately h = 120 meters.

So, the bullet hits the skeet 3.79 seconds after the skeet is released, at a height of about 120 meters from the ground.

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Whole numbers between 10.99 and 13.99

Answers

Whole numbers between those two would be 11, 12, and 13.

Answer:

11, 12 & 13

Step-by-step explanation:

Whole numbers between 10.99 and 13.99 are 11, 12 & 13

The Swaying Palms Hotel has 200 rooms. The graph shows the average number of
rooms occupied during each month of the year. During which month does the hotel
have the most empty rooms?

Answers

You need to add a picture of the graph

Answer:

Februay

Step-by-step explanation:

Select all that are measures of angles that are coterminal with a –50° angle. –770° –530° –410° 50° 310° 360° 410° 670°

Answers

Answer:

-770, -410, 310, 670

Step-by-step explanation:

-50 + 360 = 310

310 + 360 = 670

-50 - 360 = -410

-410 - 360 = -770

For the angle -50°, from the given options, the coterminal angles are: -770°,-410°, 310° and 670°.

Coterminal Angles

This classification represents angles that do not present the same value, but they present vertices and sides are identical. Also, if the angles are coterminal, then their sines, cosines and tangents are equal.

A coterminal angle can be found from the formula β = α ± 360 * w, where w is a positive integer.

You should replace w for integers numbers ≥ 1. Hence,

For w=1 and α=-50°

        β = -50± 360 * 1

         β = -50± 360

      Then, β can be -50+360=310° or -50-360= -410°

For w=2 and α=-50°

        β = -50± 360 * 2

         β = -50± 720

      Then, β can be -50+720=670° or -50-720= -770°

For w=3 and α=-50°

        β = -50± 360 * 3

         β = -50± 1080

      Then, β can be -50+1080=1030° or -50-1080= -1130°

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Which is a right triangle formed using a diagonal through the interior of the cube?




Answers

Answer:

ΔABE is correct because it is a right triangle through a diagonal

Step-by-step explanation:

Answer: A

Step-by-step explanation:

On her MP3 player, Stephanie has 36 songs shorter than three minutes and 72 songs longer than three minutes. What is the probabilty the next song will be longer than three minutes?

Answers

Step-by-step explanation:

Total songs = 36 + 72 = 108

[tex]required \: probability = \frac{72}{108} \\ \hspace{100 pt} = \frac{2}{3} \\ [/tex]

Hence, probabilty that next song will be longer than three minutes is [tex] \frac{2}{3}[/tex]

Final answer:

The probability  that the next song will be longer than three minutes is 2/3 or 66.67%.

Explanation:

The question concerns calculating the probability of selecting a song longer than three minutes from Stephanie's MP3 player. Stephanie has 36 songs shorter than three minutes and 72 songs longer than three minutes.

To find the probability that the next song will be longer than three minutes, we add the total number of short and long songs to get the total number of songs. The total is 36 + 72 = 108 songs. Since probability is the number of favorable outcomes divided by the total number of outcomes, the probability of selecting a song longer than three minutes is 72 (favorable outcomes) divided by 108 (total outcomes).

This calculation gives us 2/3 or approximately 0.6667, meaning there is a 66.67% chance the next song will be longer than three minutes.

I NEED HELP! (Tap on picture!)

Answers

The probability of selecting a card with odd number
The answer must be E and C anything else would be wrong.

Given that the measurement is in centimeters, find the circumference of the circle to the nearest tenth. (Use 3.14 for π)
A) 15.7 cm
B) 31.4 cm
C) 62.8 cm
D) 78.5 cm

Answers

Answer:

Step-by-step explanation:

The formula for the circumference of a circle of radius r is C = 2πr.  That for a circle of diameter d is C = πd.  

If we assume that the measurements below are of radius, not diameter, then in A, 15.7 cm = 2(3.14)(r), so that r must be 2.5 cm.

Please be sure to share ALL of the instructions for each problem.

Circumference of the circle is 31.4 cm

Given that;

Value of π = 3.14

Assume;

Radius of circle = 5 cm (Approx.)

Computation:

Circumference of the circle = 2πr

Circumference of the circle = 2(3.14)(5)

Circumference of the circle = (10)(3.14)

Circumference of the circle = 31.4 cm

So, option "B" is the correct answer to the following question.

Learn more:

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You go to the store and find some books that are 35% off regular price. If a book costs $20, what would you pay?

Answers

Answer: 13 dollars

Step-by-step explanation:

Answer:

13 dollars.

Step-by-step explanation:

Hope this helps!

Multiply 20 dollars by 0.65.

What type of object is pictured below?

Answers

Answer:

ray

Step-by-step explanation:

Answer:

C, a ray

Step-by-step explanation

need help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

2

Step-by-step explanation:

a=4 so plug 4 in for a 4+(-b) now we know b=2 but it has to in for b so we would get 4+(-2) now solve 4+-2 or if you think about 4-2 is easier it's going to be 2.

What is the least common multiple (LCM) of 7 and 9?

Answers

Answer:

63

Step-by-step explanation:

7*9=63

9*7-63

Answer:

63

Step-by-step explanation:

7 and 9 multiply to 63 at the least

Can anybody help? Exponential Functions

Answers

................................................................................................

What is the equation of the line through the points (-3, 4) and (5, 4)?

Answers

Answer:

The correct equation (in slope intercept form) is [tex]y=-4x+8[/tex]

       

The equation of the line through the points (-3, 4) and (5, 4) is y=4.

What is the equation of a line?

The standard form of the line is;

[tex]\rm y=mx+c[/tex]

The slope of the line is;

[tex]\rm m=\dfrac{x_2-x_1}{y_2-y_2}\\\\m =\dfrac{5-(-3)}{4-4}\\\\m =\dfrac{8}{0}\\\\m=0[/tex]

The equation of the line through the points (-3, 4) and (5, 4) is;

[tex]\rm y-y_1=m(x-x_1)\\\\y-4=0(x-(-3))\\\\y-4=0\\\\y=4[/tex]

Hence, the equation of the line through the points (-3, 4) and (5, 4) is y=4.

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The degree for 6g²h³k?

Answers

Answer:

the degree for this monomial is 7

Step-by-step explanation:

g^2 = 2

h^3= 3

k = 1

add the exponents- 2+3+1= 7

when Quinn got home he turned the air conditioner on. T represents the temperature in Quinn's home (in degrees celsius) after t minutes. T=42-0.7t how fast did the temperature drop ??​

Answers

Answer:

0.7 per minute

Step-by-step explanation:

0.7 in the equation represents how much the tempeture was dropping per minute.

Answer:

Step-by-step explanation:

T=42-0.7T

T=42-0.7(0)

T=42-0

T=42

Which sequence are geometric?

Answers

Answer:

The second one

The third one.

The last one.

Step-by-step explanation:

Hope this helps!

What type of lines are layered directly on top of each other?

Answers

Parallel lines
Explanation:

Ten cards numbered 1 through 10 are mixed together and then one card is drawn. Find the probability of each event. Write the answer in percent.
P(greater than 3)=
P(not 5, 6,7,or 8)=

Answers

Answer

probability of greater than 3 is 60%

not 5,6,7 or 8 is 60%

Answer:7/10

Step-by-step explanation: multiple of 4 is: 1,2,4. So that's 3 number which would leave you with 7 more which is 70% and 7/10 as a fraction

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