The size of a certain insect population is given by P(t) = 100e^.03t. where t is measured in days. a. How many insects were present initially? b. Give a differential equation satisfied by P(t). c. At what time will the population double?
d. At what time will the population equal 300?

Since an ellipse and a hyperbοla can intersect at mοst fοur pοints, the answer is 4.

A hyperbοla is a type οf cοnic sectiοn, which is a curve that is created when a plane intersects a dοuble cοne. A hyperbοla is fοrmed when a plane intersects bοth halves οf a dοuble cοne, resulting in twο distinct curves that mirrοr each οther.

Tο find the pοints οf intersectiοn between the graphs οf the twο hyperbοlas, we need tο sοlve the system οf equatiοns:

[tex]3x^2-5y^2+5x -7y+2=0[/tex]

[tex]3x^2-2y^2+5x-y+2=0[/tex]

We can simplify the system by subtracting the secοnd equatiοn frοm the first:

[tex]-3x^2 - (-2y^2) - 6y = -6[/tex]

Simplifying further:

[tex]3x^2 + 2y^2 + 6y = 6[/tex]

Nοw we can cοmplete the square fοr the y terms:

[tex]3x^2 + 2(y+1)^2 = 9[/tex]

Dividing by 9, we get:

[tex]x^2/3 + (y+1)^2/4 = 1[/tex]

This is the equatiοn οf an ellipse cantered at (-√3, -1) and (√3, -1), with the majοr axis alοng the x-axis and a minοr axis alοng the y-axis.

Therefοre, an ellipse and a hyperbοla can intersect at mοst fοur pοints, the answer is ο 4.

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The equivalent fraction of two ones and two hundredths is 101/50 by converting the whole number part to a fraction, then add it to the fraction part.

Two ones and two hundredths can be represented as a mixed number, which is [tex]2 \frac{2}{100}[/tex].

To convert this mixed number to an equivalent fraction, we need to first convert the whole number part to a fraction by multiplying it by the denominator of the fraction part, and then adding the numerator of the fraction part. So, we have:

2 + 2/100 = (2 * 100 + 2) / 100 = 202/100

Now, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:

202/100 = (2 * 101) / (2 * 50) = 101/50

Therefore, the equivalent fraction of two ones and two hundredths is 101/50.

In summary, to convert a mixed number to an equivalent fraction, we first convert the whole number part to a fraction, then add it to the fraction part, and finally simplify the resulting fraction if possible.

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The length of XF is equal to 13 units.

Is EG ⊥ DF: D. impossible to tell; not enough information is given.

In Mathematics and Geometry, a rhombus is a type of quadrilateral that is composed of four (4) equal sides and opposite interior angles that are congruent (equal).

Additionally, a rhombus typically has two (2) diagonals that bisect each other at right angles (90 degrees);

3x - 5 = 2x

3x - 2x = 5

x = 5

Next, we would determine the length of the diagonal DF;

Diagonal DF = 5x + 1

Diagonal DF = 5(5) + 1

Diagonal DF = 26 units.

XF = DF/2

XF = 26/2

XF = 13 units.

In conclusion, it is impossible to determine whether side EF is perpendicular to side DF because information about the side length was not provided.

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The response is: [tex]$32x^{3}-16x^{3}+4x^{3}-2x^{3}$[/tex] equals 2x (4x - x²) equals 3x²x (Option C)

An expressiοn is a grοup οf digits, variables, and mathematical οperatοrs (such as additiοn, subtractiοn, multiplicatiοn, divisiοn, expοnents, etc.) that depicts a quantity οr relatiοnship. Expressiοns can be straightfοrward οr intricate, and they can cοntain any number οf different mathematical οperatiοns and values.

Fοr instance, "3 + 5" is a straightfοrward statement that denοtes the additiοn οf 3 and 5, whereas "2x² + 5xy - 7" is a mοre intricate expressiοn that uses expοnents and variables. In algebra and οther branches οf mathematics, expressiοns are frequently emplοyed tο illustrate relatiοnships and address issues.

Let's first simplify each phrase that appears after the square rοοt:

√32x^3 = √(16x²) * √(2x) = 4x√2x √16x³ = √(16x²) * √x = 4x√x 4√x³ = 4√(x²) * √x = 4x√x √2x³ = √(2x²) * √x = √2x * x√x

Cοmbining the οriginal statement with these simplificatiοns results in:

32x³ - 16x³ + 4x³ - 2x³ = 4x²x - 4xx + 4xx - xx = 4x²x - xx = 2x (4x - x²).

As 4x and x2 are bοth nοn-negative because x 0, their difference is alsο

non-negative.

Hence, the response is: [tex]$32x^{3}-16x^{3}+4x^{3}-2x^{3}$[/tex] equals 2x (4x - x²) equals 3x²x (Option C) .

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Answer:

19

Step-by-step explanation:

r = 32.5 cm

C = 2πr = 2(3.14159)(32.5 cm) = 204.20 cm

40 m = 40 m × (100 cm)/m = 4000 cm

4000 cm / 204.2 cm = 19.588

Answer: 19

Answer:

a. x

b. 1/s^2

c. z^2

Step-by-step explanation:

Answer:

(x,y) ——-> ( - x ,  y )

Step-by-step explanation:

When reflected across the y-axis, the sign of the x will change. So, the answer to this is (x,y) ——-> ( - x ,  y )

The requires algebraic expression is (12 + 4)

An algebraic expression is a mathematical phrase that consists of variables, constants, and mathematical operations.

Algebraic expressions can represent a wide range of mathematical concepts and can be used to solve problems in various fields such as physics, engineering, economics, and more.

Here we have

the sum of 12 and 4

Here the sum of 12 and 4 implies the addition of 12 and 4

Hence, we need to use the symbol '+' to write the expression

Hence,

The requires algebraic expression is (12 + 4)

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Diego will ride 21 miles in 2.5 hours as a result, which is answer option C as 8.4 miles per hour divided by 2.5 hours equals 21 miles.

Mathematicians use the unitary technique to address proportional relationship issues involving two or more quantities. To answer problems involving rates, ratios, and proportions, it is frequently employed in academics and everyday life. With the unitary technique, the value with one unit is first determined, and the value of the desired amount of units is then determined using this value. The unitary technique can be used, for instance, to determine the price of 1 pen if the price of 4 pens is $8. Cost of 1 pen equals the sum of the costs of 4 other pens. One pen costs $8 plus $4. One pen costs $2.

given

Diego will cover 2.5 miles in that time, according to the following formula:

Rate times distance

Diego's bicycle travels at an average speed of:

Rate: Distance x Time

Hence, we may determine his rate as:

12.6 miles divided by 1.5 hours equals 8.4 miles per hour.

Now that we know this rate, we can calculate how far Diego will travel in 2.5 hours:

8.4 miles per hour divided by 2.5 hours equals 21 miles in the formula for distance.

Diego will ride 21 miles in 2.5 hours as a result, which is answer option C as 8.4 miles per hour divided by 2.5 hours equals 21 miles.

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The visitor should run 1.2 miles to minimize the time it takes to reach the island.

Consider the following figure.

Let us assume that x (CD) represents the distance covered when visitor runs at a rate of 5 mph

So, the time taken by visitor would be:

t₁ = x/5

Let the distance covered 10 - x when visitor swims at a rate of 3 mph

From figure consider right triangle ABC.

Using Pythagoras theorem,

BC² = 7² + (10 - x)²

BC = [tex]\sqrt{49 + (10-x)^2}[/tex]

Now the times taken by visitor when he swims at a rate of 3 mph,

t₂ =  [tex]\frac{ \sqrt{49 + (10-x)^2}}{3}[/tex]

so, the total time would be:

t = t₁ + t₂  

[tex]t=\frac{x}{6}+\frac{ \sqrt{49 + (10-x)^2}}{3}[/tex]

Differentiating with respect to x we get,

[tex]\frac{dt}{dx}=\frac{1}{6} -\frac{(10-x)}{ \sqrt{49 + (10-x)^2}}[/tex]

consider dt/dx = 0

[tex]\frac{1}{6} -\frac{(10-x)}{ \sqrt{49 + (10-x)^2}}=0[/tex]

If we solve above equation for x we get, x = 11.2 and x = 8.8

The distance the visitor should run to minimize the time would be:

10 - 8.8 = 1.2 miles

Therefore, the required distance is 1.2 miles

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Answer:x = 4

Step-by-step explanation:

220 squares would be shaded on 10 x 10 grids to represent an increase of 120%.

An increase of 120% means that the new value is 100% + 120% = 220% of the previous value.

If we let the previous value be x, then the new value is 2.2x.

To represent this increase on a 10 x 10 grid, we can shade in 220 out of 100 squares, or:

The new value would be 2.2 times the previous value, since an increase of 120% means that the new value is 220% of the previous value.

If we let the previous value be x, then the new value is:

new value = x + 120% of x

220/100 x 10 x 10 = 220 squares

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Using derivative of the function  dy/dt = 6.

Differentiation involves finding the derivative of a function, which is a new function that describes the rate of change of the original function at each point.

Since we have x term and we are differentiating with respect to t, we need to apply the chain rule. This means we first differentiate with respect to x and then multiply by dx/dt. That is:

dy/dt = d[x² + 3]/dt

dy/dt = (2x) dx/dt

dy/dt = 2(1) + 4    (Since x=1 and dx/dt= 4)

dy/dt = 2 + 4

dy/dt = 6

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Answer:

The difference between the price after value added tax (VAT) and the price after discount of an article gives us the actual amount of money saved by the customer.

The price after VAT is the price of the item including the tax imposed by the government, whereas the price after discount is the price of the item after any promotional or discounted price reduction. By subtracting the price after discount from the price after VAT, we can determine the actual amount saved by the customer, which is the discount amount minus any VAT paid on the original price.

For example, if an item originally cost $100 with a 10% VAT, the price after VAT would be $110. If the item was discounted by 20%, the price after discount would be $80. The difference between the price after VAT and the price after discount would be $30, which is the actual amount saved by the customer ($20 discount minus $10 VAT paid on the original price).

Step-by-step explanation:

To calculate the actual amount saved by the customer, we need to follow these steps:

Determine the original price of the item. For example, let's say the original price of the item is $100.

Calculate the VAT amount paid on the original price. To do this, multiply the original price by the VAT rate as a decimal. For example, if the VAT rate is 10%, then the VAT amount would be:

VAT amount = original price x VAT rate

VAT amount = $100 x 0.1

VAT amount = $10

So, the VAT amount paid on the original price of $100 is $10.

Determine the discounted price of the item. For example, let's say the item is discounted by 20%, so the discounted price is:

Discounted price = original price - (original price x discount rate)

Discounted price = $100 - ($100 x 0.2)

Discounted price = $80

So, the discounted price of the item is $80.

Calculate the actual amount saved by the customer. To do this, subtract the discounted price from the price after VAT. For example:

Actual amount saved = price after VAT - discounted price

Actual amount saved = $110 - $80

Actual amount saved = $30

So, the actual amount saved by the customer is $30, which is the discount amount minus the VAT paid on the original price.

Answer: The diameter of a circle is the distance across the circle passing through the center.

To find the diameter of a circle with a radius of 100 km, we can simply double the radius, since the diameter is twice the length of the radius.

Therefore, the diameter of a circle with a radius of 100 km is:

2 x 100 km = 200 km

So the diameter is 200 km.

Step-by-step explanation:

Answer:

$5.69

Step-by-step explanation:

To find the unit price (price per pair) of the gloves, we need to divide the total cost by the number of pairs:

Unit price = Total cost / Number of pairs

In this case, the total cost is $34.14 and the number of pairs is 6, so:

Unit price = $34.14 / 6

Unit price = $5.69 (rounded to the nearest cent)

Therefore, the unit price of the pairs of insulated gloves is $5.69.

Answer:

15) surface area = 791.68, volume = 1693.32

16) surface area = 138.23, volume = 113.1

17) surface area = 650.87, volume = 1073

18) surface area = 34.87, volume = 10.52

19) surface area = 153.94, volume = 179.59

20) surface area = 314.16, volume = 523.6

Step-by-Step Explanation:

sorry I didn't add the cm or inches or km in my answers :)

0.148 is the probability that they are both democrats.

In one town, 39% of all voters are democrats.

If two voters are randomly selected for a survey, the probability that they are both democrats can be calculated as follows.

P(A) = 0.39 is the probability of selecting a democrat in the first draw.

P(B|A) = 0.38

is the probability of selecting a democrat in the second draw if the first draw selects a democrat.

P(B|A') = 0.39 is the probability of selecting a democrat in the second draw if the first draw does not select a democrat.

The probability that both voters are democrats is:

P(A) x P(B|A) = 0.39 x 0.38 = 0.1482

The result is 0.1482, which means the probability that two voters are both democrats in one town is 0.1482 to the nearest thousandth.

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Niraek will have covered 400 donut holes by the time all three workers finish their current donut holes at the same time.

The time it takes to coat a donut hole is directly proportional to the surface area of the donut hole.

The surface area of a sphere is given by the formula:

Surface Area = 4πr²

Here, r is the radius of the sphere.

Comparing the surface areas of the donut holes:

Niraek's donut hole: Surface Area = 4π(6²)

Theo's donut hole: Surface Area = 4π(8²)

Akshaj's donut hole: Surface Area = 4π(10²)

Now, let's find the LCM of the surface areas to determine the time it takes for all workers to finish:

LCM(144π, 256π, 400π) = 57600π mm²

This means that it will take the same amount of time for all three workers to finish their current donut holes when they have covered a total surface area of 57600π mm².

Number of donut holes = (Total surface area) / (Surface area of Niraek's donut hole)

= (57600π mm²) / (144π mm²)

= 57600 / 144

= 400

Therefore, Niraek will have covered 400 donut holes by the time all three workers finish their current donut holes at the same time.

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Answer:

y = x + 3

Step-by-step explanation:

The question is y is 3 more than x.

We know that "more" means addition.

and since y is the greater number here, the answer would be y = x + 3!

Simple!

:)

To find how many times larger the diameter of the Sun is than the diameter of the Earth, we need to divide the diameter of the Sun by the diameter of the Earth:

(1.3 x 10^6 km) / (1.3 x 10^4 km)

Simplifying:

= (1.3 / 1.3) x (10^6 / 10^4)

= 100

Therefore, the diameter of the Sun is 100 times larger than the diameter of the Earth.

I explained step by step I hope it was helpful

The measure of angle M in triangle KLM is approximately 47.3 degrees, to the nearest 10th of a degree.

Solving for nearest 10th of degree:

To find the measure of angle M in triangle KLM, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles. The Law of Cosines states that:

[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]

where c: length of the side opposite angle C, and a & b are the lengths of the other two sides.

In this case, we wish to find the measure of angle M, which will be opposite the side of length m. We are aware that the lengths of the other two sides, k and l, and measure of angle L. To find l, we use the Law of Cosines:

[tex]l^2 = k^2 + m^2 - 2km cos(L)[/tex]

Substituting:

[tex]l^2 = 8.3^2 + 5.2^2 - 2(8.3)(5.2) cos(162 degree)[/tex]

Solve for the l, we get:

l = 10.038 cm

We will use Law of Cosines again to find the measure of angle M:

cos(M) = [tex](k^2 + l^2 - m^2) / (2kl)[/tex]

Substituting:

cos(M) = [tex]([/tex][tex]8.3^2 + 10.038^2 - 5.2^2)[/tex] [tex]/ (2(8.3)(10.038))[/tex]

Simplifying:

cos(M) = 0.665

To get the measure of angle M, we take the inverse cosine:

M = 47.3°

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Answer:

[tex]y = -2x + 15[/tex]

Step-by-step explanation:

center of the circle C is at (0, 0).

let P be the point (6, 3),

There is a property of a circle,

line drawn from center of a circle to a point P (x, y) is perpendicular to the tangent at P.

see the attached figure

so basically we have to find the equation of line perpendicular to the line passing through (6, 3).

slope of line CP = 1/2

therefore the slope of perpendicular line = -2 (tangent at P)

It passes through (6, 3) (the point of tangency),

using the equation,

[tex]y_2 - y_1 = m(x_2 - x_1)[/tex]

[tex]y - 3 = -2(x - 6)[/tex]

[tex]y = -2x + 15[/tex]

Hopefully, this answer will help you!

Answer:

10. 8

11. 64

12. 31

13. 13

14. 1

15. 74

17. 16

18. 8

Step-by-step explanation:

:))

Step-by-step explanation:

Example 1:

Given pair: (3;2)

{2x + 3y = 12,

{x - 4y = -5;

Make x the subject from the 2nd equation:

x = -5 + 4y

Replace x in the 1st equation:

2 × (-5 + 4y) + 3y = 12

-10 + 8y + 3y = 12

11 y = 12 + 10

11y = 22 / : 11

y = 2

y = 2x = -5 + 4 × 2 = -5 + 8 = 3

The answer: (3;2)

The given pair is the solution of the system of equations

.

Example 2:

Given pair: (0; -4)

{x + y = -4,

{x - 5y = 20;

x = -4 - y

(-4 - y) - 5y = 20

-4 - y - 5y = 20

-6y = 20 + 4

-6y = 24 / : (-6)

y = -4

y = -4x = -4 - (-4) = -4 + 4 = 0

The answer: (0; -4)

The given pair is the solution

.

Example 3:

Given pair: (3;3)

{x + 2y = 9,

{4x - y = 15;

x = 9 - 2y

4(9 - 2y) - y = 15

36 - 8y - y = 15

-9y = 15 - 36

-9y = -21 / : (-9)

[tex]y = 2 \frac{1}{3} [/tex]

[tex]x = 9 - 2 \times 2 \frac{1}{3} = 9 - 2 \times \frac{7}{3} = 9 - \frac{14}{3} = \frac{13}{3} = 4 \frac{1}{3} [/tex]

The given pair is not the solution

.

Example 4:

Given pair: (1; -2)

{2x - 3y = 8,

{3x + 2y = -1;

2x = 8 + 3y / : 2

x = 4 + 1,5y

3(4+1,5y) + 2y = -1

12 + 4,5y + 2y = -1

6,5y = -1 - 12

6,5y = -13 / : 6,5

y = -2

y = -2x = 4 + 1,5 × (-2) = 4 - 3 = 1

The given pair is the solution

.

Example 5:

Given pair: (1;5)

{5x - 2y = -5,

{3x - 7y = -32;

-2y = -5 - 5x / : (-2)

y = 2,5 + 2,5x

3x - 7(2,5 + 2,5x) = -32

3x - 17,5 - 17,5x = -32

-14,5x = -32 + 17,5

-14,5x = -14,5 / : (-14,5)

x = 1

x = 1y = 2,5 + 2,5 × 1 = 5

The given pair is the solution

.

Example 6:

Given pair: (-1; -3)

{3x + y = -6,

{2x = 1 + y;

y = -6 - 3x

2x = 1 + (-6 - 3x)

2x = 1 - 6 - 3x

2x + 3x = 1 - 6

5x = -5 / : 5

x = -1

x = -1y = -6 - 3 × (-1) = -6 + 3 = -3

The given pair is the solution

The average number of samples (out of 20) that will contain the pollutant is 2.

a. Probability that 2 of the next 20 samples contain the pollutantTo calculate the probability that 2 of the next 20 samples contain the pollutant, we use the binomial distribution. We can use the formula below:P(X=k) = (nCk) pk(1-p)n-kwhere:n = 20, the number of samples; k = 2, the number of samples containing the pollutant; p = 0.10, the probability that a sample contains the pollutant; q = 1 - p = 0.90, the probability that a sample does not contain the pollutant.Using the above formula, we get:P(X=2) = (20C2) (0.10)2(0.90)18= (190) (0.01) (0.2066)≈ 0.3979Therefore, the probability that 2 of the next 20 samples contain the pollutant is approximately 0.3979.

b. Probability that at least four of the next 20 samples contain the pollutantTo calculate the probability that at least four of the next 20 samples contain the pollutant, we need to calculate the probability of P(X ≥ 4).We can use the complement of P(X < 4) and use the binomial distribution formula to calculate this. We get:P(X ≥ 4) = 1 - P(X < 4)P(X < 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3)P(X=0) = (20C0) (0.10)0(0.90)20= (1) (1) (0.1216)≈ 0.1216P(X=1) = (20C1) (0.10)1(0.90)19= (20) (0.10) (0.2296)≈ 0.4593P(X=2) = (20C2) (0.10)2(0.90)18= (190) (0.01) (0.2066)≈ 0.3979P(X=3) = (20C3) (0.10)3(0.90)17= (1140) (0.001) (0.2753)≈ 0.2059Therefore, P(X < 4) ≈ 0.1216 + 0.4593 + 0.3979 + 0.2059 ≈ 1.185P(X ≥ 4) = 1 - P(X < 4)≈ 1 - 1.185= -0.185This is not a valid probability. Therefore, we have made an error in our calculations, and the probability cannot be calculated using this method.

c. Probability that more than 2 and less than 7 of the next 20 samples contain the pollutant. To calculate the probability that more than 2 and less than 7 of the next 20 samples contain the pollutant, we can use the binomial distribution formula again. We need to calculate P(3 ≤ X ≤ 6).We can use the formula:P(3 ≤ X ≤ 6) = P(X=3) + P(X=4) + P(X=5) + P(X=6)P(X=3) = (20C3) (0.10)3(0.90)17= (1140) (0.001) (0.2753)≈ 0.2059P(X=4) = (20C4) (0.10)4(0.90)16= (4845) (0.0001) (0.3112)≈ 0.1516P(X=5) = (20C5) (0.10)5(0.90)15= (15504) (0.00001) (0.3544)≈ 0.0583P(X=6) = (20C6) (0.10)6(0.90)14= (38760) (0.000001) (0.3919)≈ 0.0121Therefore,P(3 ≤ X ≤ 6) ≈ 0.2059 + 0.1516 + 0.0583 + 0.0121 ≈ 0.4279Therefore, the probability that more than 2 and less than 7 of the next 20 samples contain the pollutant is approximately 0.4279.

d. Average number of samples (out of 20) that will contain the pollutantThe expected value or average number of samples that will contain the pollutant can be calculated using the following formula:E(X) = npwhere:n = 20, the number of samples; p = 0.10, the probability that a sample contains the pollutant.Using the above formula,E(X) = np= 20 (0.10)= 2.

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The value of x that makes the shape a kite is determined as 4.

One special property of a kite shape is that it has two pairs of adjacent sides that are congruent (i.e., they have the same length). In other words, the two shorter sides are equal in length, and the two longer sides are equal in length, but the shorter and longer sides are not equal to each other.

The value of x is calculated by applying this special property of kite;

6x - 3 = 21 --- (1)

4x + 1 = 17 --- (2)

Solving equation (1)

6x = 24

x = 24/6

x = 4

Solving equation (2);

4x = 17 - 1

4x = 16

x = 16/4

x = 4

So the shape is kite if the value of x is 4.

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you know that i have gave wrong Ans  

explanation: because i need points

Answer:

Step-by-step explanation:

where’s the figure ?

The parallelogram and rectangle have the same base and height, they have the same area of 72 in2.

The parallelogram and the rectangle are related because they both have the same base and height. The area of the parallelogram is calculated by multiplying the base of the parallelogram (b) by the height (h): Area = b × h. In this case, the area of the parallelogram is 12 in × 6 in = 72 in2. The area of the rectangle is also calculated by multiplying the base of the rectangle (b) by the height (h): Area = b × h. In this case, the area of the rectangle is 12 in × 6 in = 72 in2. Since both figures have the same base and height, they have the same area.

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