Evaluate the iterated integral. The first integral is 0 to 2 and the second integral is 2 to 3. xy^2 dx dy. Please show step by step with detail. Thanks
\int \int xy^2 dx dy

According to the information, it can be inferred that the bees must travel a distance of 4,803,620.82 km to complete the 30 kg of honey that a hive produces.

To calculate the distance that bees register to produce honey we must perform the following operation.

1. Calculate how many kilometers are equal to the circumference of the earth with the following formula 2*pi*R. In this case we replace the R, by the radius of the earth and we will obtain the distance of the circumference of the earth.

[tex]2\pi r[/tex]

[tex]2\pi 6,371 km = 40,030.1736[/tex]

2. Once we have identified the circumference of the earth, we must multiply it by four to know how much distance the bee will recover to produce one kg of honey.

40,030.1736 * 4 = 160,120.694

3. Finally we must multiply the distance it takes to produce 1kg by 30 to find the distance it takes to produce 30kg of honey.

160,120,694 * 30 = 4,803,620.82

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Answer:

1/(2p4)1/3

Step-by-step explanation:

From P10,000 in full pesos and with no spare change, each person receives P4,000, P,3000, and P3,000, respectively.

$10,000 has been given in total as an allowance.

This idea came about due to the fact that the eldest and the youngest siblings are not meant to receive an equal amount of anything when it is shared among them.

3 individuals should share it.

2 younger siblings and 1 older sibling

Let

the younger sibling receives P4,000

Every younger sibling would receive P3,000

There is no residual in the overall allowance supplied; each person receives the full value of their pesos.

So, from a total of P10,000, each person receives P4,000, P,3000, and P3,000.

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Answer: 1/5 is shaded becaus e there are 5 sides the second one is 50

Step-by-step explanation:

24 quarts of green paint should be mixed with 4 cups of black paint. This can be solved by using the concept of cross- multiplication.

Fractions are multiplied by multiplying the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction.

In order to get the second fraction's numerator, multiply the first fraction's denominator by it. Cross multiply is another name for the butterfly technique of multiplication. The cross-multiply technique is used to find one or more variables in a fraction.

Jasper Green mix 4 quarts of green paint with 2/3 cups of black paint.

Let's convert 4 quarts into cups.

1 quart = 4 cups

4 quarts = 16 cups

Here mix 16 cups of green paint with 2/3 cups of black paint.

Let's use the proportion

Green paint            Black paint

  16                                  2/3

   x                                     4

16/x =2/3 divided by 4

Cross multiplying, we get

16 × 4 = (2/3) x

64 = (2/3) x

x = 64 ÷ (2/3)

x = 64 × (3/2)

x = 192/2

x = 96 cups

96 cups of green paint should be mixed with 4 cups of black paint.

We can covert 96 cups into quarts by dividing by 4

96/4 = 24 quarts

24 quarts of green paint should be mixed with 4 cups of black paint.

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The correct variations for the formula for speed, given the formulas , are :

The formula for speed shows how fast an object is going and it is based on the distance covered by the object, and the time it takes to cover this distance.

The formula for speed is therefore :

Speed = Distance / time

This can therefore be written in another variation of :

Speed = Distance / time

Distance = Speed x Time

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Answer:

the answer A, B, and E

If we multiply both numerator and denominator of the first ratio by 3, we will get the second ratio, thus, these are equivalent.

For any ratio:

a/b

If we multiply both numerator and denominator by the same real number, we will get an equivalent ratio.

In this case, we can start with the smaller of the two ratios:

1/6.

Now we can multiply both numerator and denominator by 3, then we will get:

(3*1)/(3*6) = 3/18

So yes, the ratios 1/6 and 3/18 are equivalent.

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Answer: y = -4.5x

Step-by-step explanation:

        To see if there is a direct variation, we will check to see if there is a direct proportionality constant (usually represented by k). We will find this by dividing the y by x for each row.

                 45/-10 =  -4.5

                 -4.5/1 = -4.5

                 -27/6 =  -4.5

        We see that this direct proportionality constant value is -4.5. This means the equation is;

           y = -4.5x

        We can also check our answer by graphing. I have graphed y = -4.5x and plotted all the given points. See attached. All of the given points do, and should if we are correct, fall on the line.

The side MN have the value of x = 4, and for the side LM have the value x = 5 for the similar polygons ABCD and LMNP.

The polygons ABCD and LMNP are similar so:

angle A is equal to angle L

angle B is equal to angle M

angle C is equal to angle N

angle D is equal to angle P

side MN = side BC

x + 6 = 10

x = 10 - 6 {subtract 6 from both sides}

x = 4

side LM = side AB

x + 9 = 14

x = 14 - 9 {subtract 9 from both sides}

x = 5

Therefore, the x = 4 for the side MN and x = 5 for the side LM for the similar polygons ABCD and LMNP.

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Answer: 17.

Step-by-step explanation: 429 divided by 25 = 17.16 so rounding that would just be 17.

Answer:

B.25.............. uhjii

Answer:

C

Step-by-step explanation:

1+3=4

1>0

3>0

so C is correct

Answer:

congruent

Step-by-step explanation:

two polygons are similar if their corresponding sides are congruent and their corresponding angle measures are equal

As x approaches positive infinity, the function m approaches 0.

To determine this:

In both cases, as x becomes very large in either the positive or negative direction, the value of the function m approaches 0. This is because the function m has been transformed in such a way that it approaches 0 as x becomes very large. This could be due to factors such as the presence of a constant or a coefficient that causes the function to approach 0 as x becomes very large, or due to the presence of a term in the function that cancels out other terms as x becomes very large. Regardless of the specific reason, the result is that the function m approaches 0 as x approaches both positive and negative infinity.

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Serenity's age is 13 and Grayson's age is 14

Consecutive integers are whole numbers that follow each other without gaps. For example, 15, 16, 17 are consecutive integers.

Given that, Serenity is younger than Grayson, their ages are consecutive integers, the sum of the square of Serenity's age and 4 times Grayson's age is 225.

Let the age of Serenity be x, that of Grayson (x+1)

Therefore,

x² + 4(x+1) = 225

x² + 4x + 4 = 225

x² + 4x -221 = 0

Factorizing, we get,

x = 13, -17

Since, age can not be negative therefore, neglecting -17,

Thus, Serenity's age is x = 13 and Grayson's age is x+1 = 14

Hence, Serenity's age is 13 and Grayson's age is 14

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The following number 8546 can be written in scientific notation as: 8.546*10^3.

Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as 6.5 ✕ 10^8 in scientific notation.

Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation.

We were given the value,  8546 by following the explanation above we have 8.546*10^3

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Answer: 4/12 = 8/24

Step-by-step explanation:

okay so these are fractions so it’s like 4/12 or 8/24 because smaller over longer but you can also do longer over shorter the fractions have to equal each other so you could also do 12/4 = 24/8

The equations that show the properties of the exponents are a, c and d.

The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.

We know that there are few properties that are common to the numbers that appear in the exponential form. We shall look at some of those properties.

1) when we have

[tex](ab)^x[/tex], it is the same as [tex]a^x b^x[/tex]

2) When we have [tex]b^2 \times b^x[/tex], it is the same as b² + x

3) When we have; x^-2, it is the same as 1/x²

These are the basics of the properties of the exponents as we can conclude in the question and these obey the properties of the exponents.

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For the exponential function, y increases by a factor of 3.

To determine this we take:

The linear equation is y = 3*x

when x = 1

y = 3*1 = 3

when x = 2

y = 3*2 = 6

Then as x increases by one unit, y increases by 3 units.

Then the correct statement would be something like:

"For the linear function, y increases by a sum of 3 each time x increases 1"

The exponential function is:

[tex]y = 3^x[/tex]

When x = 1

[tex]y = 3^1 = 3[/tex]

When x = 2

[tex]y = 3^2 = 3*3[/tex]

when x = 3

[tex]y = 3^3 = 3*3*3[/tex]

So when x increases by 1, we multiply the previous value of y by 3.

Then the correct sentence is something like:

"For the exponential function, y increases by a factor of 3".

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"For the linear function, y increases by a sum of 3 each time x increases 1"

"For the exponential function, y increases by a factor of 3".

Now, According to the question:

Let's Know:

What is Exponential Function?

An exponential function is a Mathematical function in the form f (x) = [tex]a^x[/tex], where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Now, For the linear function:

y = 3x

when x = 1

y = 3×1 = 3

when x = 2

y = 3×2 = 6

Then as x increases one unit, y increases 3 units.

"For the linear function, y increases by a sum of 3 each time x increases 1"

Now, For the exponential function:

[tex]y = 3^x[/tex]

When x = 1

[tex]y = 3^1[/tex] = 3

When x = 2

[tex]y = 3^2[/tex] = 3×3

when x = 3

[tex]y = 3^3[/tex] = 3×3×3

So when x increases by 1, we multiply the previous value of y by 3.

"For the exponential function, y increases by a factor of 3".

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From the given circle image, we can say that the two lengths that must form the ratio of 1:2 is; d. AH:HI

From the image attached, we are given that Point A is the center of the circle.

Let us access each of the options to find out which one of the two lengths must form a ratio of 1:2;

Option a. HI:EF

We see that both HI and EF are diameters of the circle. Thus, their ratio cannot be equal to 1:2.

Option b. EF:AD

We see that EF is the diameter while s the radius, we can say that;

Diameter = 2 × Radius

Thus;

EF : AD = 2:1

Option c: AD : AH

We see that both D and AH are radius and as such their ratio can never be 1:2.

Option d : AH:HI

We see that AH is the radius while HI is the diameter. Thus, their ratio will be; AH:HI = 1:2

Option e; BC:HI

We see that BC is a chord and we are not given its' length and so we can't ascertain if it forms a ratio of 1:2 with HI

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You would need to order 28.21 gallons of milk each week.

To determine how many gallons of milk your business needs to order each week, you need to first calculate the total number of ounces of milk your business uses in a day. To do this, you can multiply the number of ounces of milk used per shake by the number of shakes served per day:

6 ounces/shake * 86 shakes/day = 516 ounces/day

Next, you can divide the number of ounces of milk used per day by the number of ounces per gallon to determine the number of gallons of milk your business uses per day:

516 ounces/day / 128 ounces/gallon = 4.03 gallons/day

Finally, you can multiply the number of gallons of milk your business uses per day by the number of days in a week to determine the number of gallons you need to order each week:

4.03 gallons/day * 7 days/week = 28.21 gallons/week

So, you would need to order approximately 28.21 gallons of milk each week.

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28.21 gallons of milk you need to order each week.

The formula for calculating the amount of milk needed each week would be: (ounces of milk per shake) multiplied by (number of shakes served per day) multiplied by (number of days in the week).

For this example, the formula is:

6 ounces of milk per shake x 86 shakes per day x 7 days in the week = 3,492 ounces of milk per week.

To convert this number to gallons, we need to divide 3,492 ounces of milk by 128 ounces per gallon.

3,492 ounces of milk / 128 ounces per gallon = 28.21 gallons of milk per week.

Therefore, the answer to the question is to order 28.21 gallons of milk each week.

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The only option that represents a fraction not equivalent to 4/8 is; C: 12/32

To get the ratio that is not equivalent to 4/8, we need to first of all reduce 4/8 to the barest minimum. Thus;

Let us divide both numerator and denominator by 4 to get;1/2

Let us access each of the options;

A) 1/2 is same as the simplified form of 4/8 as seen above and so it is equivalent to 4/8

B) 9/18;

Divide numerator and denominator by 9 to get 1/2 which is same as the simplified form of 4/8 as seen above and so it is equivalent to 4/8

C) 12/32;

Divide numerator and denominator by 4 to get 3/8 which is not the same as the simplified form of 4/8 as seen above and so it is not equivalent to 4/8

D) 18/36;

Divide numerator and denominator by 18 to get 1/2 which is same as the simplified form of 4/8 as seen above and so it is equivalent to 4/8.

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Complete question is;

Which of the following ratios is NOT equivalent to 4/8?

A) 1/2

B) 9/18

C) 12/32

D) 18/36

The four types of rigid transformations are translation, rotation, reflection, and glide reflection.

A rigid transformation, also known as an isometry or congruence transformation, is a type of transformation that preserves the distances and angles between the points in a figure. This means that a rigid transformation does not change the shape or size of a figure, but only its position and orientation in the coordinate plane.

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The given fraction can be rewritten as the sum of three smaller fractions. The first small fraction has a numerator of "8x² + 115" and a denominator of "3(x² - 10)". The second small fraction has a numerator of "3x^2 + 39" and a denominator of "3x(x² - 10)". The third small fraction has a numerator of "200" and a denominator of "3x(x² - 10)".

The given fraction can be rewritten as the sum of three smaller fractions.

The first small fraction is made up of a numerator that consists of the expression,

= 8x² + 115

divided by a denominator that consists of the expression,

= 3(x² - 10)

The second small fraction has a numerator of

= 3x² + 39

and a denominator of "3x(x² - 10)".

The third small fraction has a numerator of "200" and a denominator of = 3x(x² - 10)

When these three small fractions are added together, they equal the original fraction.

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Answer:

1. The sum of all the three interior angles of a triangle is 180 degrees.

2. The base angles of an isosceles triangle are congruent.

3. The measure of the exterior angle of a triangle is equal to the sum of the corresponding interior angles.

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The number of possible outcomes in the sample space is 3 and the list is {CN, NN, NC}.

A sample space is the set of all possible outcomes in a random experiment. Sample space is usually denoted as S.

Given that, three chocolates remain in a a box of chocolates. one has cherry filling and the other two have nuts inside. you randomly pick a piece for yourself. then you pick a piece for your friend.

Let C be the cherry filled chocolate and N be the nut filled chocolate.

The possible outcomes if the first picked chocolate is not placed back are :

{CN, NN, NC}

The possible outcomes if the first picked chocolate is placed back are :

{CC, CN, NC, NN}

Hence the number of outcomes are 3 and the set is {CN, NN, NC}

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Answer: 1/4 and 4

Step-by-step explanation:

Let √x = u

2u^2 - 5u + 2 = 0

Solve for u

(2u-1)(x-2)=0

u = 1/2 and 2

Since you want x, square u to cancel the square root.

(1/2)^2 = 1/4

(2)^2 = 4

Your answers are 1/4 and 4

Answer:Fido  ate   -723 more pies  then the winner  

Step-by-step explanation:

[tex]$47\\-$712= -665\\-665\\- 58= -723[/tex]

Hope this helps

Answer:

[tex]\huge\boxed{\sf n = -1}[/tex]

Step-by-step explanation:

2(2n - 1) = -(n + 7)

4n - 2 = -n - 7

4n + n - 2 = -7

5n - 2 = -7

5n = -7 + 2

5n = -5

n = -5/5

n = -1

[tex]\rule[225]{225}{2}[/tex]

Rodas will be exactly twice as old as her brother after 15 years.

We are trying to find the number of years until Rodas is exactly twice as old as her brother. Let's call this number of years "x".

Currently, Rodas is 25 years old and her brother is 10 years old. We know that Rodas' age in x years will be 25 + x, and her brother's age will be 10 + x. We want to find the value of x such that:

25 + x = 2(10 + x)

Simplifying the equation and solving for x, we get:

25 + x = 20 + 2x

x = 15

So Rodas will be exactly twice as old as her brother after 15 years.

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The question is -

Rodas is 25 years old and her brother is 10 years old. After how many years will Rodas be exactly twice as old as her brother?