21. How many times larger is the volume of a cone if the height is multiplied by 3?

The product 5x^(2/3) can be written as the product of the whole number 5 and the unit fraction 1/x^(-2/3), which simplifies to x^(2/3)/1 or just x^(2/3). So, we have:

5x^(2/3) = 5 * (1/x^(-2/3)) = 5x^(2/3) = 5 * (x^(2/3) / 1) = 5x^(2/3) = 5x^(2/3)

To write the product 5x^(2/3) as the product of a whole number and a unit fraction, we need to express x^(2/3) as a unit fraction.

Recall that a unit fraction is a fraction with a numerator of 1, so we need to find a fraction that has 1 as the numerator and x^(2/3) as the denominator. We can do this by using the reciprocal property of exponents:

x^(2/3) = 1 / x^(-2/3)

Now we can substitute this expression into the original product:

5x^(2/3) = 5 * (1 / x^(-2/3))

Simplifying the right-hand side of the equation, we can write it as:

5 / x^(-2/3) = 5x^(2/3)

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Rounded to the nearest cubic centimeter, the volume of the regular hexagonal prism is approximately 82 [tex]cm^3.[/tex]

To calculate the volume of the regular hexagonal prism, we need to find the area of the base and multiply it by the height.

The base of the prism is a regular hexagon with side length 3 centimeters. The formula for the area of a regular hexagon is:

[tex]Area = (3√3/2) * (side length)^2.[/tex]

Substituting the given side length of 3 centimeters:

[tex]Area = (3√3/2) * 3^2[/tex]

= (3√3/2) * 9

= (27√3/2).

Now, let's calculate the volume by multiplying the base area by the height:

Volume = Area * height

= (27√3/2) * 7

≈ 81.729[tex]cm^3[/tex].

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Answer:

289.5

Step-by-step explanation:

200+26.25+63.25

289.5

8. Patricia uses 600 milliliters of water each time she waters her vegetable garden. The correct option is A © 600 mL.

9. 4-5 =-1

For first question:

8. A watering can holds 3 liters of water, and Patricia waters her vegetable garden 5 times a day using one full can in total. To find out how many milliliters of water she uses each time, you need to first convert the 3 liters to milliliters (1 liter = 1,000 milliliters) and then divide by 5.

3 liters × 1,000 milliliters/liter = 3,000 milliliters
3,000 milliliters ÷ 5 = 600 milliliters

So, Patricia uses 600 milliliters of water each time she waters her vegetable garden. The correct answer is 600 mL.

9. For second question, the calculation is as follows:

4 - 5 = -1

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The population density is 87.4, under the condition that a study report shows that in 2010 the population of the United States was counted to be  308,745,538 people and the land area is approximately 3,531,905 square miles.

Now to evaluate  the population density of the United States in 2010, here we have to use the principles of division
Population density = Population / Land area

Staging  the values from the study
Population density = 308,745,538 / 3,531,905
The evaluated Population density = 87.4 people per square mile

Then, the United State's population density in 2010 was  evaluated as 87.4 people per square mile.

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The complete question is
A study reports that in 2010 the population of the United States was 308,745,538 people and the land area was approximately 3,531,905 square miles. ​Based on the study, what was the population density, in people per square mile, of the United States in 2010? ​Round your answer to the nearest tenth. ​

Answer:

  20°

Step-by-step explanation:

You want the measure of angle G in triangle GPQ with side lengths GP=74, PQ=31, QG=88 meters.

The law of cosines tells you the relevant relationship is ...

  PQ² = GP² +GQ² -2·GP·GQ·cos(G)

Solving for angle G gives ...

  G = arccos((GP² +GQ² -PQ²)/(2·GP·GQ))

  G = arccos((74² +88² -31²)/(2·74·88)) = arccos(12259/13024)

  G ≈ 19.735° ≈ 20°

The golfer must play the shot within an angle of about 20°.

p and q both are equal and p=q=20.

Given are an equation show equivalent fractions 2p/5q = 40/100

We need to find the p and q,

So

2p/5q = 40/100

2p/5q = 2×20/2×20

p/q = 20/20

p/q = 1

p = q

Therefore p and q both are equal and p=q=20.

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The constant of proportionality between y and x in the graph is 3

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following readings

(x, y) = (1, 3)

Using the above as a guide, we have the following:

The constant of proportionality between y and x in the graph is

k = y/x

substitute the known values in the above equation, so, we have the following representation

k = 3/1

Evaluate

k = 3

Hence, the constant of proportionality between y and x in the graph is 3

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To find the car's average velocity between t=4 and t=10, we need to use the formula:

average velocity = (change in displacement) / (change in time)

Since we are only given the velocity function, we need to first find the displacement function by integrating the velocity function:

displacement = ∫(1t^(1/2) + 4) dt

displacement = (2/3)t^(3/2) + 4t + C

where C is the constant of integration.

Since we are only interested in the change in displacement between t=4 and t=10, we can ignore the constant of integration.

change in displacement = [(2/3)10^(3/2) + 4(10)] - [(2/3)4^(3/2) + 4(4)]

change in displacement = 28.147 - 14.265

change in displacement = 13.882

Now we can use the formula for average velocity:

average velocity = (change in displacement) / (change in time)

average velocity = 13.882 / (10 - 4)

average velocity = 1.98 m/s

Therefore, the car's average velocity between t=4 and t=10 is 1.98 m/s.

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The total number of pounds of flour he can buy is 7 pounds of flour

Let's assume that Mikal has $1 to spend on flour. According to the problem, he can buy:

- 12 pounds of wheat flour for $1, which means that the price of wheat flour is 1/12 = $0.0833 per pound.

- 6 pounds of rice flour for $1, which means that the price of rice flour is 1/6 = $0.1667 per pound.

- 4 pounds of almond flour for $1, which means that the price of almond flour is 1/4 = $0.25 per pound.

If Mikal spends $1 on an equal amount of all three types of flour, he will spend $1/3 = $0.3333 on each type of flour. To determine how many pounds of each type of flour he can buy, we need to divide $0.3333 by the respective price per pound of each type of flour:

- Wheat flour: $0.3333 / $0.0833 per pound = 3.9996 pounds (rounded to 4 pounds)

- Rice flour: $0.3333 / $0.1667 per pound = 1.9998 pounds (rounded to 2 pounds)

- Almond flour: $0.3333 / $0.25 per pound = 1.3332 pounds (rounded to 1 pound)

Therefore, Mikal can buy 4 pounds of wheat flour, 2 pounds of rice flour, and 1 pound of almond flour with $1. The total number of pounds of flour he can buy is:

4 + 2 + 1 = 7 pounds of flour.

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The area of the sprinkled lawn is approximately 19.625 square meters.

The formula for the area of a circle is:

A = πr²

Where A is the area and r is the radius and π is constant pi ( 3.14 ).

If the sprinkler as a circle with a radius of 2.5 meters. The area that the sprinkler can cover is the area of this circle.

Here, the radius is 2.5 meters, so we can substitute that into the formula:

A = πr²

A = 3.14 × 2.5²

Area = 3.14 × 6.25

Area = 19.625 m²

Therefore, the area is 19.625 m²

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Answer:

(x + 5)^2 + (y + 5)^2 = 16.

Step-by-step explanation:

(x - a)^2 + (y - b)^2 = r^2    where (a, b) is the centre and r =- the radius.

Here (a, b) = (-5, -5) and r = 4, so:

(x - (-5))^2 + (y - (-5))^2 = 4^2

(x + 5)^2 + (y + 5)^2 = 16

Answer:

78% of sixth-graders picked a field trip to a museum.

Step-by-step explanation:

39 out of 50 kids picked the museum field trip. This is 39/50. We can change this like so:

39/50 × 2/2

= 78/100

78/100 is 78% (because percent literally means "per hundred)

Another way is to just divide. 39/50 means 39 ÷ 50.

39 ÷ 50 is .78 then times by 100 to change to a percent. This works for all kinds of fractions.

78% of sixth graders at Ayana's school selected the museum field trip.

Answer:

a = 3

b = 1

c = 5

d = 2

Step-by-step explanation:

To find the prime factorization of 600, we can use trial division by dividing by the smallest prime numbers until we reach a prime factor:

600 ÷ 2 = 300

300 ÷ 2 = 150

150 ÷ 2 = 75

75 ÷ 3 = 25

25 ÷ 5 = 5

Therefore, the prime factorization of 600 is:

600 = 2^3 × 3^1 × 5^2

So, a = 3, b = 1, c = 5, and d = 2.

The rotated vector is (-2,0). To see why, imagine the original vector (0,2) plotted on the coordinate plane. To rotate it 270° clockwise about the origin, we can first rotate it 90° clockwise to get (2,0), then rotate that 180° clockwise to get (-2,0).

To understand this geometrically, think of the vector (0,2) as pointing straight up on the y-axis. Rotating it 90° clockwise means it now points to the right on the x-axis. Then, rotating it another 180° clockwise means it points straight down on the negative y-axis, which corresponds to the vector (-2,0).

In general, to rotate a vector (x,y) by an angle θ about the origin, we can use the following formulas: x' = x cos θ - y sin θ. y' = x sin θ + y cos θ In this case, θ = 270°, so cos θ = 0 and sin θ = -1.

Plugging in x=0, y=2, we get: x' = 0 - 2(-1) = 2 y' = 0(270) + 2(0) = 0. So the rotated vector is (2,0), which corresponds to (-2,0) because we rotated it clockwise instead of counterclockwise.

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At the point (5, 17, 1), the partial derivatives of z with respect to x and y are -12.5 and 0.25, respectively, as calculated using implicit differentiation. At the point (5, 17, 1), the partial derivatives of z with respect to z and y are 0.16 and -1.

To find the partial derivatives, we need to use the implicit differentiation.

To find ∂z/∂x, we differentiate the equation with respect to x, treating y and z as functions of x

4z^3(dz/dx) + 2z^2x^2 - 0 - 0 = 0

Simplifying, we get

4z^3(dz/dx) = -2z^2x^2

(dz/dx) = -1/2x^2z

At the point (5, 17, 1), we have

(dz/dx) = -1/2(5)^2(1) = -12.5

To find ∂z/∂y, we differentiate the equation with respect to y, treating x and z as functions of y

4z^3(dz/dy) - 1 - 0 + 0 = 0

Simplifying, we get

4z^3(dz/dy) = 1

(dz/dy) = 1/4z^3

At the point (5, 17, 1), we have

(dz/dy) = 1/4(1)^3 = 0.25

To find ∂z and ∂y at the point (5, 17, 1), we need to take partial derivatives with respect to z and y, respectively, of the implicit equation

z^4 + z^2x^2 - y - 9 = 0

Taking the partial derivative with respect to z, we get

4z^3 + 2z^2x^2(dz/dz) - dy/dz = 0

Simplifying and solving for ∂z, we get

∂z = dy/dz = 8z^3/(2z^2x^2) = 4z/x^2

At the point (5, 17, 1), we have

z = 1, x = 5

So, ∂z at the point (5, 17, 1) is

∂z = 4z/x^2 = 4(1)/(5^2) = 0.16

To find ∂y, we take the partial derivative with respect to y, keeping x and z constant

-1 = ∂y

Therefore, ∂y at the point (5, 17, 1) is -1.

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Amount after 11 hours: 3,477,373 grams; Amount after 50 hours: 33,320 grams.

The Radioactive decay formula provided in the question for the amount A(t) of a sample of uranium-240 remaining after t hours is:

A(t) = 5600100(3[tex])^(-11/14)[/tex]

To find the amount of the sample remaining after 11 hours, we substitute t = 11 in the formula and calculate:

A(11) = 5600100(3[tex])^(-11/14)[/tex] ≈ 3477373 grams

Therefore, the amount of the sample remaining after 11 hours is approximately 3,477,373 grams (rounded to the nearest gram).

Similarly, to find the amount of the sample remaining after 50 hours, we substitute t = 50 in the formula and calculate:

A(50) = 5600100(3[tex])^(-50/14)[/tex] ≈ 33320 grams

Therefore, the amount of the sample remaining after 50 hours is approximately 33,320 grams (rounded to the nearest gram).

The exponential formula for radioactive decay describes the behavior of a radioactive substance, where the amount of the substance decreases over time as it decays. In this case, uranium-240 has a half-life of 14 hours, which means that half of the initial amount of the substance will decay in 14 hours. After another 14 hours, half of the remaining amount will decay, and so on.

As time goes on, the amount of uranium-240 remaining decreases exponentially, and the rate of decay is determined by the half-life of the substance. The formula provided in the question allows us to calculate the amount of uranium-240 remaining after any given amount of time, based on its initial amount and half-life.

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The radioactive substance uranium-240 has a half-life of 14 hours.  The amount of the sample remaining after 11 hours is approximately 2265 grams, and the amount of the sample remaining after 50 hours is approximately 95 grams.

The formula for the amount of uranium-240 remaining after t hours is given by: A(t) = 5600 * (1/2)^(t/14).
Find the amount of the sample remaining after 11 hours, we substitute t = 11 into the formula and evaluate:
A(11) = 5600 * (1/2)^(11/14)
A(11) ≈ 2265 grams (rounded to the nearest gram)
Find the amount of the sample remaining after 50 hours, we substitute t = 50 into the formula and evaluate:
A(50) = 5600 * (1/2)^(50/14)
A(50) ≈ 95 grams (rounded to the nearest gram)
Therefore, the amount of the sample remaining after 11 hours is approximately 2265 grams, and the amount of the sample remaining after 50 hours is approximately 95 grams.

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The height of the triangle is 2 meters.

Para encontrar la altura del triángulo, podemos utilizar la fórmula para calcular el área de un triángulo:

Área = (base x altura) / 2

Sabemos que el área es de 1.5 m² y que la base mide 1.5 m, por lo que podemos despejar la altura de la siguiente manera:

1.5 m² = (1.5 m x altura) / 2

Multiplicando ambos lados por 2:

3 m² = 1.5 m x altura

Despejando la altura:

altura = 3 m² / 1.5 m

altura = 2 m

Por lo tanto, la altura del triángulo que representa al pino en el periódico mural es de 2 metros.

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1) If Amy deposits $2,300 in an account that pays 8.5% interest, after 4 years, the future value will be $3,187.48.

2) If Andres deposits $10,000 in an account that pays 8% interest, after 4 years, the future value will be A. $13,604.89.

3) If Kara deposits $500 in an account that pays 5% interest, after 2 years, the future value will be C. $551.25.

The future values represent the present investment compounded at an interest rate.

The future values can be determined using an online finance calculator as follows:

1) N (# of periods) = 4 years

I/Y (Interest per year) = =8.5%

PV (Present Value) = $2,300

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $3,187.48

Total Interest = $887.48

2) N (# of periods) = 4 years

I/Y (Interest per year) = =8%

PV (Present Value) = $10,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $13,604.89

Total Interest = $3,604.89

3) N (# of periods) = 2 years

I/Y (Interest per year) = 5%

PV (Present Value) = $500

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $551.25

Total Interest = $51.25

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The difference between the amount of potassium called for in the experiment (0.227 grams) and 1 gram is 0.773 grams.

The amount of potassium called for in the experiment is 227 milligrams. To convert milligrams to grams, we divide by 1000: 227/1000 = 0.227 grams.

The amount of 1 gram is larger than 0.227 grams. To find the difference between the two amounts, we subtract the smaller amount from the larger amount:

1 gram - 0.227 grams = 0.773 grams

Therefore, the difference between the amount of potassium called for in the experiment (0.227 grams) and 1 gram is 0.773 grams.

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The solution of the system of equations is given by the ordered pair (-2, 2).

Based on the table, a x-value that is a solution to the equation is -2.

The solution to the equations are (-6, 3) and (-4, -5).

An ordered pair which is the best estimate for the solution of the system is: A. (-0.5, -1.75).

In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

8x - 4y = -24    ......equation 1.

4x - 12y = -32  ......equation 2.

Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant II, and it is given by the ordered pairs (-2, 2).

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The probability of Karmen picking a car with a belge interior and an automatic transmission is 1/6

To find the probability, we need to start by identifying the event or situation for which we want to calculate the probability.

Since Karmen has three choices for the exterior color, two choices for the interior color, and two choices for the transmission, the total number of possible car configurations is:

3 x 2 x 2 = 12

This means there are 12 different cars to choose from.

To find the probability of picking a car that has a black exterior and a belge interior, we need to determine how many cars meet these criteria. There is only one car that has a black exterior and a belge interior, so the probability of picking this car is:

1/12

Therefore, the probability of Karmen picking a car with a black exterior and a belge interior is 1/12.

To find the probability of picking a car with a belge interior and an automatic transmission, we need to determine how many cars meet these criteria. There are two cars that have a belge interior and an automatic transmission, so the probability of picking one of these cars is:

2/12

Simplifying this fraction gives:

1/6

Therefore, the probability of Karmen picking a car with a belge interior and an automatic transmission is 1/6.

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The length of BC rounded to 3 significant figures is 6.98.

Since ∠cab = 90°, we can use the Pythagorean Theorem to find the length of AB.

Let's call BC = x, then we have:

sin(65°) = AB/BC

AB = sin(65°) * BC

In right triangle ABC, we have:

AB^2 + BC^2 = AC^2

(sin(65°) * BC)^2 + BC^2 = 8.9^2

Solving for BC, we get:

BC = 8.9 / sqrt(sin^2(65°) + 1)

BC ≈ 6.98

Therefore, the length of BC rounded to 3 significant figures is 6.98.

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Mrs. Lane's average gross monthly income would be $3,135.

To find the monthly income of  Mrs. Lane's,

First, we need to find Mrs. Lane's commission for her bi-weekly commercial sales:

Commission = 22% of $5,625 = 0.22 x $5,625 = $1,237.50

Next, we need to find her hourly wage for a week:

Hourly wage = $8.25 x 40 = $330

Her gross bi-weekly income is the sum of her commission and hourly wage:

Gross bi-weekly income = Commission + Hourly wage

= $1,237.50 + $330

= $1,567.50

To find her gross monthly income, we can multiply her gross bi-weekly income by the number of bi-weekly pay periods in a month:

Gross monthly income = Gross bi-weekly income x Number of bi-weekly pay periods in a month

= $1,567.50 x 2

= $3,135

Therefore, Mrs. Lane's average gross monthly income would be $3,135.

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the answer is Q1 = 27.5

The price of the item increases by approximately 3.93% each year.

The initial price of the item is the value of p(0), which can be obtained by setting r=0 in the given function. Therefore:

p(0) = 2000(1.039)^0 = 2000

So the initial price of the item is $2000.

To determine whether the function represents growth or decay, we need to look at the value of the base of the exponential function, which is 1.039 in this case. Since this value is greater than 1, the function represents growth.

To find the percentage change in price each year, we can calculate the percentage increase from the initial price to the price after one year (r=1):

p(1) = 2000(1.039)^1 = 2078.60

The percentage increase from $2000 to $2078.60 is:

((2078.60 - 2000)/2000) x 100% ≈ 3.93%

Therefore, the price of the item increases by approximately 3.93% each year.

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Answer:

250

Step-by-step explanation:

5 x 2= 10

25 x 10= 250

The initial number of video views was fewer than the initial number of site visits, and the number of video views grew by a larger factor than the number of site visits. The difference between the total number of site visits and the video views after 5 weeks is 20,825.

During their team meeting, both managers shared their findings. Complete the statement describing their combined results.

The initial number of video views was fewer than the initial number of site visits, and the number of video views grew by a larger factor than the number of site visits.

The difference between the total number of site visits and the video views after 5 weeks is 20,825.

Therefore the correct answer are fewer, larger factor than and 20,825.

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