Set up a proportion to solve: 24 is 25% of what number?

The area of the region inside the six-leaved rose r^2 = 8 cos(3θ) is (4/9)(5√2 + 8√3).

The equation of the six-leaved rose in polar coordinates is given by r = 2\sqrt{2}\cos(3\theta), where r is the distance from the origin to a point on the curve, and θ is the angle between the positive x-axis and the line segment connecting the origin to the point. The region inside the curve can be found by integrating over the area enclosed by the curve.

Using the formula for area in polar coordinates, we have:

A = (1/2) ∫[α,β] (r(θ))^2 dθ

where α and β are the angles where the curve intersects itself.

Since the six-leaved rose has six petals, it intersects itself at angles of π/6, π/2, and 5π/6. Therefore, we have:

A = (1/2) ∫[π/6,π/2] (r(θ))^2 dθ + (1/2) ∫[π/2,5π/6] (r(θ))^2 dθ

Substituting r(θ) = 2\sqrt{2}\cos(3\theta), we get:

A = (1/2) ∫[π/6,π/2] [2\sqrt{2}\cos(3\theta)]^2 dθ + (1/2) ∫[π/2,5π/6] [2\sqrt{2}\cos(3\theta)]^2 dθ

Simplifying and evaluating the integrals, we obtain:

A = (1/2) [8√2/9 sin(6π/9) - 8√2/9 sin(2π/9)] + (1/2) [8√2/9 sin(10π/9) - 8√2/9 sin(4π/9)]

A = (4/9)√2 [sin(2π/9) - sin(6π/9) + sin(4π/9) - sin(10π/9)]

Since sin(6π/9) = sin(4π/3) = -√3/2 and sin(10π/9) = sin(8π/3) = √3/2, we have:

A = (4/9)√2 [sin(2π/9) + sin(4π/9) + √3]

Using the trigonometric identity sin(2θ) + sin(4θ) = 2sin(3θ)cos(θ), we can simplify further:

A = (8/9)√2 [sin(3π/9)cos(π/9) + √3]

Simplifying again, we get:

A = (8/9)√2 [sin(π/3)cos(π/9) + √3]

A = (8/9)√2 [(√3/2)(√2/2) + √3]

A = (4/9)(5√2 + 8√3)

Therefore, the area of the region inside the six-leaved rose r^2 = 8 cos(3θ) is (4/9)(5√2 + 8√3).

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Answer:

42 minutes.

Step-by-step explanation:

We know that:

y = 0.2*x

is the equation that that defines the distance, in miles, that the boat travels in x minutes.

We know that the dolphins are at 8.4 miles from the boat.

Then when we have y = 8.4, this will mean that the boat reached the dolphins.

Then we need to solve the equation:

y = 8.4 = 0.2*x

for x

To do that, we just need to isolate x in one side of the equation, so we can just divide both sides by 0.2 to get:

8.4/0.2 = (0.2*x)/0.2

42 = x

And x is time in minutes, thus, the boat needs to travel for 42 minutes to reach the dolphins.

\(\\ \bull\sf\longmapsto 250\times 35\%\)

\(\\ \bull\sf\longmapsto 250\times \dfrac{35}{100}\)

\(\\ \bull\sf\longmapsto 5\times \dfrac{35}{2}\)

\(\\ \bull\sf\longmapsto \dfrac{175}{2}\)

\(\\ \bull\sf\longmapsto 87.5\)

\(\bf \large \implies \: \frac{35}{100} \: \times \: 250 \\ \)

\(\bf \large \implies \: \frac{35}{10 \cancel0} \: \times \: 25 \cancel0\)

\(\bf \large \implies \: \frac { \cancel{35} \: \: ^{3.5} }{ \cancel{10}} \: \times \: 25\)

\(\bf \large \implies \: 3.5 \: \times \: 25\)

\(\bf \large \implies \: 87.5\)

Answer:

69.

Step-by-step explanation:

literally just put 69, or dude use photo math ! u can download it on the app store . it's so helpful better than this app

Diameter = 17 cm

Radius = r = Diameter /2 = 17/2 =8.5 cm

Surface area of a sphere: 4 π r^2

Replacing with the values given:

SA = 4 π (8.5) ^2 = 907.92 cm^2

AnswerAnswer:

420

Step-by-step explanation:

The volume of the prism is 840 units³ which is correct option (C).

The volume of the prism is defined as the measure of the space occupied within a prism . The prism is a three-dimensional shape that has base area, and height. The volume of a prism is equal to the product of base area and height of a prism.

The volume of the prism= B×H

Where, B is base area of prism, and H is height of prism.

Given that,

Length of  prism (L) = 12 centimeters

Width of prism(W) = 14 centimeters

Base area (rectangle) of prism = L × W

Base area (rectangle) of prism = 12 × 14

Base area (rectangle) of prism = 168 units²

Height of prism(H) = 5 units

The volume of the  prism =  B × H

Substitute the values in above formula,

The volume of the prism = 168×5

The volume of the prism = 840 units³

Hence, the volume of the prism is 840 units³.

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Answer:

  83.79 kJ

Step-by-step explanation:

The potential energy is the product of weight and height, where weight is in newtons.

  PE = Mgh = (190 kg)(9.8 m/s^2)(45 m) = 83,790 J

Answer:

(a) hundreds = 817

(b) hundredths = 817.09

(c) 3 d.p = 817.086

(d) 4 s.f. = 817.1

(e) whole number = 817

8y-2=6

8y=8

y=1

The value of the y is 1.

Answer:

C. Yes, there is an outlier at 110. This means that one person's age was 110, which is 25 years older than the next closest age.

Step-by-step explanation:

An outlier is a data point that sticks out like a sore thumb. It's so different from the rest of the data that it makes you wonder if it's a mistake or a miracle. One way to spot an outlier is to use the 1.5IQR rule, where IQR stands for interquartile range. The interquartile range is the gap between the third quartile (Q3) and the first quartile (Q1) of the data. The 1.5IQR rule says that any data point that is more than 1.5*IQR above Q3 or below Q1 is an outlier.

In this case, the first quartile (Q1) is 75, the third quartile (Q3) is 85, and the interquartile range (IQR) is 10. So, any data point that is more than 1.5*10 = 15 above 85 or below 75 is an outlier. The only data point that does this is 110, which is 25 above 85. That means 110 is an outlier.

What does this outlier mean in this situation? It means that one person who came to the senior center that afternoon was way older than the rest of the folks. The average age of the visitors was not changed by this outlier, since it was just one out of 12 data points. But, the outlier does mess up the range and the standard deviation of the data, making them bigger than they would be without the outlier.

Answer:The answer is C

Step-by-step explanation:I did the test.

Answer:

Step-by-step explanation:

that a huge prob but yah

Answer:

L = -0.5x + 34

Step-by-step explanation:

When finding m in the formula y = mx + b. Find a word that means multiplication, in this case 0.5 feet per day.

We can use the general form of a quadratic model:

We can find the parameters a, b and c by taking some pair of values from the table, like this:

Let's take the pair (0,0), if we replace these values for y and x into the above model we get:

Now let's take the pair (1, 2.4), by replacing these values into the above model for x and y, we get:

From this equation, we can solve for a to get:

By taking the pair (2, 9.4) we get:

We can replace the expression that we got previously a = 2.4 - b into the above equation to get:

From this expression, we can solve for b like this:

Now we can replace it into the equation a = 2.4 - b, then we get:

a = 2.4 - 0.1 = 2.3

Then we get the expression:

Now we just have to evaluate 10 km into the equation, then we get:

Then, the best prediction of the time required for the oil spill to reach a diameter of 10 km is 233 days

Answer:

Consider the ratio of corresponding sides, you would find out:

Option A is correct

Step-by-step explanation:

Check figure 1 and figure 2: 8/12 = 16/24 = 10/15 = 1/3

=> they are similar.

Check figure 2 and figure 3 (or fig. 1 and fig. 3): Not satisfied.

Hope this helps!

:)

Answer:

A

Step-by-step explanation:

1 and 2

8/12 = 16/24 = 10/15

2/3 = 2/3 = 2/3

Same ratio, so similar

2 and 3

12/28 = 24/36 = 15/30

3/7 = 2/3 = 1/2

Ratio not constant, so not similar

Answer:

-3, -2, -0.8, -1/10, 1/2, 0.8, 7

The order of the set of sign numbers from least to greatest is,

- 3, - 2, - 0.8, - 0.1, 0.5, 0.8, and 7.

A number that is followed by the plus sign (+) to denote a positive value or the minus sign (-) to denote a negative value.

A number line is a one-dimensional horizontal line where we can represent any real number. The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.

Given, A set of signed numbers - 1/10, - 0.8, 0.8, - 2, 7, 1/2, and - 3.

let us convert them into decimals, - 0.1, - 0.8, 0.8, - 2, 7, 0.5, and - 3.

The order from least to greatest is,

- 3, - 2, - 0.8, - 0.1, 0.5, 0.8, and 7.

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Answer:

r = √3V/√πh

Step-by-step explanation:

V = 1/3πr²h

where,

V = volume of the cone

r = radius of the cone and

h = height of the cone.

Rewrite the formula to solve for the positive value of r in terms of h and V.

V = 1/3πr²h

V = 1/3 * π * r² * h

r² = V ÷ 1/3 * π * h

r² = V ÷ πh/3

r² = V × 3/πh

r² = 3V / πh

find the square root of both sides

√r² = √3V / πh

r = √3V/πh

Also written as

r = √3V/√πh

An angular resolution of 0.56 arcseconds is required to see the Sun and Jupiter as separate objects. This is an extremely small angle and would necessitate the use of a large telescope.

Angular resolution is defined as the minimum angle between two objects that enables a viewer to see them as distinct objects rather than as a single one. A better angular resolution corresponds to a smaller minimum angle. The angular resolution formula is θ = 1.22 λ / D, where λ is the wavelength of light and D is the diameter of the telescope. Thus, the angular resolution formula can be expressed as the smallest angle between two objects that allows a viewer to distinguish between them. In arcseconds, the answer should be given to two significant figures.

To see the Sun and Jupiter as distinct points of light, we need to have a good angular resolution. The angular resolution is calculated as follows:

θ = 1.22 λ / D, where θ is the angular resolution, λ is the wavelength of the light, and D is the diameter of the telescope.

Using this formula, we can find the minimum angular resolution required to see the Sun and Jupiter as separate objects. The Sun and Jupiter are at an average distance of 5.2 astronomical units (AU) from each other. An AU is the distance from the Earth to the Sun, which is about 150 million kilometers. This means that the distance between Jupiter and the Sun is 780 million kilometers.

To determine the angular resolution, we need to know the wavelength of the light and the diameter of the telescope. Let's use visible light (λ = 550 nm) and assume that we are using a telescope with a diameter of 2.5 meters.

θ = 1.22 λ / D = 1.22 × 550 × 10^-9 / 2.5 = 2.7 × 10^-6 rad

To convert radians to arcseconds, multiply by 206,265.θ = 2.7 × 10^-6 × 206,265 = 0.56 arcseconds

The angular resolution required to see the Sun and Jupiter as distinct points of light is 0.56 arcseconds.

This is very small and would require a large telescope to achieve.

In conclusion, we require an angular resolution of 0.56 arcseconds to see the Sun and Jupiter as separate objects. This is an extremely small angle and would necessitate the use of a large telescope.

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The time Tony have between the end of the project and the beginning of band practice is 43 minutes. So the answer is 43 minutes.

Tony began his math assignment at 1:57 p.m. and completed it 80 minutes later. To find out when Tony finished his assignment, add 1:57 p.m. to 80 minutes.

We may convert 80 minutes to hours , which is 1 hour and 20 minutes, which is added to 1:57 p.m.

1:57 p.m. + 1:20 p.m. = 3:17 p.m.

At 4:00 p.m., Tony has band practice. To calculate the time between the finish of the project and the start of band practice, subtract 3:17 p.m. from 4:00 p.m.

4:00 p.m. - 3:17 p.m. = 43 minutes

As a result, Tony had 43 minutes between the completion of his math project and the start of band practice.

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The Correct question:

Tony started his math project at 1:57 p.m. and finished the project 80 minutes later, tony has band practice at 4:00 p.m. How much time did Tony have between the end of the project and the beginning of band practice?

Answer:

40

Step-by-step explanation:

1. List all the multiples

10,20,30,40

8,16,24,32,40

Answer:

150/250

Step-by-step explanation:

Answer:

n<5

Step-by-step explanation:

6(3+n)<48

Step 1: Simplify both sides of the inequality.

6n+18<48

Step 2: Subtract 18 from both sides.

6n+18−18<48−18

6n<30

Step 3: Divide both sides by 6.

6n /6 < 30 /6

n<5

Answer:

15

Step-by-step explanation:

x/3 + 3 = 8

x/3 + 9/3 = 8

x + 9 = 24

x = 15

Answer:

I'm pretty sure it's 90%

Step-by-step explanation:

Answer:

Let x  be the number

Now we have,

x% of 60 =54

\(\frac{x}{100} *60=54\\\frac{x}{100} =\frac{54}{60} \\x=0.9*100\\x=90\)

Step-by-step explanation:

The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.

To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.

Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.

In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.

Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.

Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.

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The percentage that each expense has out of the total budgeted amount of $45,000  have been computed, where insurance has 8.00%, Utilities 7.00% and so on.

What is a percentage?

In this case, percentage refers to proportion of each expense from the total budgeted expense of $45,000, which means that in order to total budgeted expense of $45,000, which means that in order to compute the percentage of total budgeted for each expense category, we divide the expense by the total budgeted expense

Insurance=$3600/$45,000=8.00%

Utilities=$3150/$45,000=7.00%

Clothing=$2700/$45000=6.00%

Transportation=$1350/$45000=3.00%

Entertainment=$5400/$45000=12.00%

Savings=$4050/$45000=9.00%

Taxes=$7200/$45000=16.00%

Food=$7650/$45000=17.00%

Housing=$9900/$45000=22.00%

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Answer:

Evaluate: 8c - 11

Differentiate w.r.t. c: 8

Step-by-step explanation:

Evaluate:

6c − 4 + 2c − 7

Combine 6c and 2c to get 8c.

8c - 4 - 7

Subtract 7 from −4 to get −11.

8c - 11

Differentiate w.r.t. c:

6c - 4 + 2c - 7

Combine 6c and 2c to get 8c.

\(\frac{d}{dc}\)(8c -4 - 7)

Subtract 7 from −4 to get −11.

\(\frac{d}{dc}\)(8c - 11)

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of \(ax^{n}\) is \(nax^{n-1}\)

8\(c^{1-1}\)

Subtract 1 from 1.

8\(c^{0}\)

For any term t except 0, \(t^{0}\) = 1

8 × 1

For any term t, t × 1 = t and 1t = t.

8