Find the surface area of the figure

• Concept: Exponents

• Solution:

You want to simplify the expression 4⁰×4².

We will use basic exponent properties for this.

First bear in mind that anything to the power of 0 is 1.

So that means that 4⁰ = 1.

We're not done yet because we still need to simplify the other part:

4².

Don't forget that:

Because

4² = 4×4 which is 16

So we have 1 times 16 or just 16.

Answer: choice "c": 16

Answer:

To solve the expression 2 + 7 • (-3)^2, we follow the order of operations, also known as PEMDAS/BODMAS, which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

First, we evaluate the exponent: (-3)^2 = 9 (because squaring a number means multiplying it by itself).

Next, we perform multiplication: 7 • 9 = 63.

Finally, we perform addition: 2 + 63 = 65.

So, the value of the expression 2 + 7 • (-3)^2 is 65.

Five points on the inverse function g(x) = log₄(x) are: (1, 0), (4, 1), (16, 2), (1/4, -1/2), and (2, 0.5).

Given that

f(x) = 4^x.

To find the inverse of the function f(x) = 4^x,

We need to interchange the positions of x and y and solve for y. So, we have:

x = 4^y

Taking the logarithm base 4 of both sides, we get:

y = log₄(x)

Therefore, the inverse of the function f(x) = 4^x is g(x) = log₄(x)

To find five points on the inverse function g(x), we can choose five x-values and find the corresponding y-values:

If x = 1, then g(x) = log₄(1) = 0, so the point is (1, 0).

If x = 4, then g(x) = log₄(4) = 1, so the point is (4, 1).

If x = 16, then g(x) = log₄(16) = 2, so the point is (16, 2).

If x = 1/4, then g(x) = log₄(1/4) = -1/2, so the point is (1/4, -1/2).

If x = 2, then g(x) = log₄(2) ≈ 0.5, so the point is (2, 0.5).

Therefore, five points on the inverse function g(x) = log₄(x) are: (1, 0), (4, 1), (16, 2), (1/4, -1/2), and (2, 0.5).

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we can see that the growth rate increases as x increases. However, since we are only interested in the average growth rate over the interval [1, 3], we can calculate it using the formula mentioned above.

How to solve the question?

To determine the average growth rate of each sample over the interval [1, 3], we need to calculate the ratio of the change in bacteria population to the change in time for each sample, and then take the average of these ratios over the given interval.

For Sample A, the change in bacteria population over the interval [1, 3] is 480 - 120 = 360, and the change in time is 3 - 1 = 2. So the average growth rate of Sample A over this interval is 360/2 = 180 bacteria per hour.

For Sample B, the change in bacteria population over the interval [1, 3] is 480 - 240 = 240, and the change in time is 3 - 1 = 2. So the average growth rate of Sample B over this interval is 240/2 = 120 bacteria per hour.

For Sample C, the change in bacteria population over the interval [1, 3] is (1.2600)(1.2*1.2 - 1) = 345.6, and the change in time is 3 - 1 = 2. So the average growth rate of Sample C over this interval is 345.6/2 = 172.8 bacteria per hour.

For Sample A, the growth rate is the highest, followed by Sample C and then Sample B. Therefore, the order of the samples by their average growth rate over the interval [1, 3] from least to greatest is Sample C, Sample A, and Sample B.

It's important to note that the growth rate of Sample C is not constant but increases over time due to the 20% increase in the initial bacteria population. The exponential function f(x) = 200(3/2)in power x represents this growth, and we can see that the growth rate increases as x increases. However, since we are only interested in the average growth rate over the interval [1, 3], we can calculate it using the formula mentioned above.

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Your complete question is :-A scientist is studying the growth rates of three samples of bacteria in different conditions. The following three functions represent the number of bacteria in the three samples after x hours.

Sample A Sample B Sample C

x g(x)

0 60

1 120

2 240

3 480

On solving the provided question we can say that Manny would thus require 160 yards of fencing to surround the rectangular plot.

A boundary is a closed route that embraces, encircles, or delimits a two-dimensional form or length in one dimension. The perimeter of a circle or an ellipse is its outermost section. The perimeter calculation is used in a variety of real-world situations. The perimeter of a form is the radius of its edge. Discover how to calculate the perimeter by adding the lengths of the sides of various shapes. The perimeter of a shape may always be calculated by multiplying the lengths of its sides. The perimeter of a thing is the region that surrounds it. At your house, one example is an enclosed garden. The distance around anything is referred to as its perimeter. A 200-foot fence will be required for a 50-foot-by-50-foot yard.

P = 2(l + w), where l is the length and w is the width, gives the perimeter of a rectangle.

The length in this example is 35 yards, while the breadth is 45 yards. So,

[tex]P = 2(35 + 45)\\= 2(80)\\= 160 yards\\[/tex]

Manny would thus require 160 yards of fencing to surround the rectangular plot.

As a result, option (b) 160 yards is the right answer.

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1. The rule states that the product of the lengths of the two segments of one chord equals the product of the lengths of the two segments of the other chord (i.e., (a1 x a2) = (b1 x b2), where a1 and a2 are segments of chord A, and b1 and b2 are segments of chord B).

2. The rule states that the product of the length of the external segment of one secant and the length of the entire secant equals the product of the length of the external segment of the other secant and the length of the entire secant (i.e., (e1 (e1 + i1)) = (e2 (e2 + i2)), where e1 and e2 are the external segments and i1 and i2 are the internal segments).

3.  The rule states that the square of the length of the tangent segment equals the product of the length of the external segment of the secant and the length of the entire secant (i.e., t^2 = e * (e + i), where t is the length of the tangent segment, e is the external segment, and i is the internal segment).

The three rules of segments are:

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a. The total quantity of employed women among the sample of 7 who are not married yet is the random variable X of interest in this situation. b) Probability = 0.2749.

The number of successes in a defined number of independent trials with two possible outcomes (success or failure) and a constant probability of success are described by a discrete probability distribution called a binomial distribution. The number of trials (n) and the likelihood that a trial will succeed (p) serve as the two parameters that define the binomial distribution.

a. The total quantity of employed women among the sample of 7 who are not married yet is the random variable X of interest in this situation.

b) The probability of 2 women who have never been married is:

P(X = 2) = (7 choose 2) * (0.2)² * (0.8)⁵

P(X = 2) = 21 * 0.04 * 0.32768

P(X = 2) = 0.2749

c) For 2 or fewer have never been married:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X ≤ 2) = (7 choose 0) * (0.2)⁰ * (0.8)⁷ + (7 choose 1) * (0.2)¹ * (0.8)⁶ + (7 choose 2) * (0.2)² * (0.8)⁵

P(X ≤ 2) = 0.0577 + 0.2013 + 0.2749

P(X ≤ 2) = 0.5339

d) The mean is given as:

μ = np

Substitute n = 7 and p = 0.2:

7 * 0.2 = 1.4

Now, the standard deviation is given as:

σ = √(np(1-p)) = √(7 * 0.2 * 0.8) = 1.0198

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Answer:

a)3.68kg

b)900g

Step-by-step explanation:

a) First off we know that he weighs 4kg now and he weighed 8% less the next week. 8% of 4kg=0.32kg. We then have to subtract 0.32 kilograms from the original weight. 4-0.32=3.68

Your answer for A is 3.68 kg

b) If the baby gains 200g every two weeks, assuming it's a constant rate, he should gain 100g every week. 100*9weeks=900g.

Answer:

Step-by-step explanation:

(3n³ + 2n)² = 9n^6 + 12n^4 + 4n^2

(4k² + 2k³) = 2k²(2 + k)

(3y²-y')' = 6y-y''

(4c+30) = 2(2c+15)

(2b² * b)² = 4b^6

(2gh²)* = 2gh^2

(6w³)² = 36w^6

Answer: direction angle of c is pi/4.

Step-by-step explanation: We can find c by adding the corresponding components of a and b:

c = a + b = ⟨–7, 3⟩ + ⟨–2, –12⟩ = ⟨–9, –9⟩

To find the magnitude of c, we can use the formula:

|c| = sqrt(c1^2 + c2^2)

where c1 and c2 are the x- and y-components of c, respectively. In this case, we have:

|c| = sqrt((-9)^2 + (-9)^2) = sqrt(162) = 9sqrt(2)

To find the direction angle of c, we can use the formula:

theta = atan(c2 / c1)

where theta is the angle between the positive x-axis and the vector c. In this case, we have:

theta = atan((-9) / (-9)) = atan(1) = pi/4

So the direction angle of c is pi/4.

Therefore, the magnitude of c is 9sqrt(2) and the direction angle of c is pi/4.

Answer:

27 cubes

Step-by-step explanation:

The volume of Cube A is 1 cubic centimeter. The volume of one Cube C is 1/27 of a cubic centimeter. So 27 Cube C's will fit into Cube A.

After five years, her IRA account's net worth (after taxes) will indeed be $14,322.88 ($10,000 + $4,322.88).

Sarah will be required to file taxes just on interest received each year if she places the $10,000 inside a standard savings account, which will lower her net worth.

She will have earned $800 in pre-tax interest every year, assuming she receives nominal interest of 8% annually.

She will, however, be liable for $240 in taxes just on interest generated each year (30% of $800) since she falls into the 30% tax bracket.

Her pre-tax interest earnings after five years will total $4,000 ($800 x five years). She will still have paid $1,200 in total in taxes just on interest generated ($240 x 5)

She will therefore have a net worth of $12,800 ($10,000 + $4,000 - $1,200) in the normal savings account after five years (after taxes).

Sarah won't have to pay taxable income on the $10,000 invested in such an IRA account or the interest accrued until she starts taking distributions in retirement.

She will have earned $800 in pre-tax interest every year, assuming she receives nominal interest of 8% annually.

She will have the whole $800 to reinvest & compound each year, though, as she is not subject to income taxation on the interest gained each year.

She will have earned $4,322.88 in pre-tax interest after five years, and she won't have to pay any taxes until she starts taking withdrawals in retirement.

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Answer:

(a) To calculate how much it would cost to hire the coach to travel a distance of 42 miles, we can substitute m = 42 into the formula and solve for C:

C = (42/3) + 40

C = 14 + 40

C = 54

Therefore, it would cost £54 to hire a coach to travel 42 miles.

(b) To find how many miles the coach travels if the cost of the hire is £75, we can set the formula equal to 75 and solve for m:

75 = (m/3) + 40

35 = m/3

m = 105

Therefore, the coach travels 105 miles if the cost of the hire is £75.

The margin of error for a survey with a sample size of 6400 and a 95% confidence level is approximately 1.6%.

Confidence level is a statistical concept that measures the degree of certainty or reliability associated with an estimate, such as the mean, proportion, or regression coefficient, derived from a sample of data.

The margin of error (ME) for a survey depends on several factors, including the size of the sample, the level of confidence desired, and the population size (if applicable). Assuming a 95% confidence level, a sample size of 6400, and no information about the population size, the formula for calculating the margin of error is:

ME = 1.96 × √[(p × q) / n]

where:

1.96 is the z-score associated with a 95% confidence level

p is the estimated proportion of the population that has the characteristic of interest (this is usually unknown and is typically replaced with 0.5 to get the maximum possible margin of error)

q is 1 - p

n is the sample size

Assuming a conservative estimate of p = 0.5, we have:

ME = 1.96 × √[(0.5 × 0.5) / 6400]

≈ 0.016 or 1.6%

Therefore, the margin of error for a survey with a sample size of 6400 and a 95% confidence level is approximately 1.6%. This means that if the survey were conducted multiple times using the same sample size and methodology, the results would likely differ by no more than 1.6% in either direction (plus or minus) from the true population value.

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Answer:

There are 31 days in October, so there are 31 - 15 = 16 days left in October after October 15.

16 days is equivalent to 2 weeks and 2 days (since there are 7 days in a week), so November 11 is 2 weeks and 2 days after October 15.

Therefore, November 11 falls on a Wednesday + 2 weeks + 2 days = Friday.

So November 11 of that same year falls on a Friday.

The point (1, 8) would then represent that the babysitter charges $8 per hour

The point (1, 8) in this situation could mean that the babysitter charges $8 for one hour of work.

In general, when working with a fee-per-hour situation, we can use the slope-intercept form of a linear equation, y = mx + b,

If we assume that the initial fee is $0, then the equation for the babysitter's fee would be y = mx, where m is the hourly rate.

The point (1, 8) would then represent that the babysitter charges $8 per hour, since when x = 1 (one hour of work), y = 8 (the fee for one hour).

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The amount of insecticide that Vivian needs to purchase

for the control of pest in the lawn would be = 198.08 ounces

To calculate the area of the rectangular lawn, the formula for the area of rectangle should be used. That is ;

Area = Length× width

Length = 123.8 feet

width = 80feet

Area = 123.8× 80 = 9,904ft²

But 0.02 ounces of insecticide = 1 ft²

X ounces = 9,904ft²

Make X the subject of formula;

X = 9904×0.02

= 198.08 ounces.

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Answer: C

Step-by-step explanation:

1/2 pound of almonds = 5/6 cup of almond butter

To find out how much almond butter 1 pound of almonds will make, we need to multiply both sides of the equation by 2:

1 pound of almonds = (2 × 1/2) pounds of almonds = 2 × 5/6 cups of almond butter

Simplifying, we get:

1 pound of almonds = 5/3 cups of almond butter

So, a reasonable estimate for the amount of almond butter the recipe makes per pound of almonds is more than 2 cups of almond butter. Therefore, the answer is (c) more than 2 cups of almond butter.

Answer: b) between 1 1/2 and 2 cups of almond butter

Step-by-step explanation:

We can create a proportion to help us solve this question.

         [tex]\displaystyle \frac{\frac{1}{2} lbs\;almonds}{\frac{5}{6}lbs\;butter } =\frac{1lbs\;almonds}{xlbs\;butter}[/tex]

Now we can cross multiply.

         [tex]\displaystyle \frac{1}{2} *x=\frac{5}{6} *1[/tex]

         [tex]\displaystyle \frac{1}{2}x =\frac{5}{6}[/tex]

Next, we will divide both sides of the equation by one-half.

         [tex]\displaystyle x =\frac{5}{6}\div \frac{1}{2}[/tex]

         [tex]\displaystyle x =\frac{5}{6}* \frac{2}{1}[/tex]

         [tex]\displaystyle x =\frac{10}{6}[/tex]

Lastly, we will find which answer option this falls under by creating an improper fraction. This leads us to answer optoin b, b) between 1 1/2 and 2 cups of almond butter.

         [tex]\displaystyle 10-6=4\text{, so } 1\frac{4}{6} =1\frac{2}{3}[/tex]

Therefore , the solution of the given problem of expression comes out to be 6.5 is the abbreviated numerical expression.

Shifting numbers, which can be expanding, variable diminishing, or blocking, should be used instead of random estimations. Only through exchanging goods like tools, expertise, or answers to problems could they assist one another. The explanation on the reality equation may include the justifications, elements, or mathematical claims for tactics like increased argumentation, falsification, and blending.

Here,

The mathematical expression is expressed as follows:

=> 42 / 7 + (3 / 6)

We can use the division operations to make the expression simpler:

=> 7 /42 = 6

=> 6 / 3 = 0.5.

The statement is thus more easily expressed as follows

=> 6 + 0.5

When we add the two numbers, we get:

=> 6.5

Therefore, 6.5 is the abbreviated numerical expression.

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Answer:

0,-1

Step-by-step explanation:

Hope this helps! =D

Brainliest! =D

Answer:

-1

Remember y=mx+b

m is your slope and b is your y-int
m = -4/3

b = -1

The circumference of a circle whose area is 20π cm² in terms of pi is 8.94π centimeters.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

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

The circumference of a circle is expressed mathematically as;

[tex]\text{C} = 2\pi \text{r}[/tex]

Given that the area of the circle is 20π cm², we determine the radius of the circle.

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

[tex]20\pi \ \text{cm}^2 = \pi \times \text{r}^2[/tex]

[tex]\text{r}^2= \dfrac{ 20\pi \ \text{cm}^2}{\pi }[/tex]

[tex]\text{r}^2 = 20 \ \text{cm}^2[/tex]

[tex]\text{r} = \sqrt{20 \ \text{cm}^2}[/tex]

[tex]\text{r} = 4.47 \ \text{cm}[/tex]

Now, we determine the circumference of the circle.

[tex]\text{C} = 2\pi \text{r}[/tex]

[tex]\text{C} = 2 \times \pi \times 4.47 \ \text{cm}[/tex]

[tex]\text{C} = 8.94 \ \text{cm}\times\pi[/tex]

[tex]\text{C} = 8.94\pi[/tex]

Therefore, the circumference of the circle is 8.94π centimeters.

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Answer:

  A.  X

Step-by-step explanation:

You want to know which graph is decreasing for x > 3.

A graph is decreasing when it slopes down to the right. The only graph in the group that has any decreasing portion is graph X. The decreasing part of that graph is to the right of x = 3, where x > 3.

Graph X is the one you want.

__

Additional comment

All the other graphs are increasing everywhere, so aren't even worth any consideration.

The equation is given as y = -x + 8

The purpose of an equation is to find the value of the variable that makes the equation true. Equations are used in various fields of mathematics and science to represent relationships between different quantities and to solve problems.

To create an equation that represents the relationship between x and y in the table, we need to first determine the pattern or trend in the data.

From the given data, we can see that as x increases by 2, y decreases by 2. This suggests that there is a linear relationship between x and y.

Using the two points (-2,10) and (0,8), we can find the slope:

m = (y2 - y1) / (x2 - x1) = (8 - 10) / (0 - (-2)) = -1

Now that we have the slope, we can use any point on the line to find the y-intercept. Let's use the point (0,8):

8 = (-1)(0) + b

b = 8

Therefore, the equation that represents the relationship between x and y in the table is:

y = -x + 8

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Step-by-step explanation:

The number of non square numbers between 12square and 13square are

Answer:

Scientific notation = 8.434 × 10^5

Scientific e notation = 8.434e5

Engineering notation = 843.4 × 10^3 ---> (thousand; prefix kilo- (k) )

Standard form = 8.434 × 10^5

The proof of the three distributions as required as shown in the explanation part.

For x² distribution:

Let's start with the sample variance, which is defined as:

s^2 = ∑(y_i - y_bar)² / (n-1)

where;

We can rewrite this formula as:

s^2 = (∑y_i² - n*y_bar²) / (n-1)

Multiplying both sides by (n-1)/σ², we get:

s^2 / σ² = (∑y_i² - ny_bar²) / (σ²(n-1))

Now, let's define a new variable:

x² = ∑y_i² / σ²

Substituting x² into the above equation, we get:

s^2 / σ² = (x² - n*y_bar²/σ²) / (n-1)

Notice that n*y_bar²/σ² is just the sample mean squared in units of variance. We can rewrite it as:

n*y_bar²/σ² = (y_bar - μ)² / (σ²/n)

where;

Substituting this into the above equation, we get:

s^2 / σ² = (x² - (y_bar - μ)² / (σ²/n)) / (n-1)

Now, let's define a new variable:

ss = ∑(y_i - y_bar)² / σ²

Substituting ss into the above equation, we get:

s^2 / σ² = (x² - ss/(n-1)) / n

This is the desired result. We have shown that s²/σ² follows a x² distribution with n-1 degrees of freedom.

For t distribution:

Let's start with the sample mean, which is defined as:

y_bar = ∑y_i / n

We can rewrite this formula as:

y_bar - μ = (∑y_i - n*μ) / n

Now, let's define a new variable:

t = (y_bar - μ) / (s/√n)

where;

Substituting y_bar - μ and s into the above equation, we get:

t = (∑y_i - nμ) / (s√n)

This is the desired result. We have shown that t follows a t distribution with n-1 degrees of freedom.

For F distribution:

Let's start with the sample variances, which are defined as:

s₁² = ∑(y_i - y₁)² / (n₁-1)

s₂² = ∑(y_i - y₂)² / (n₂-1)

where;

We can rewrite these formulas as:

s₁² = (ss₁ - n₁*(y₁-μ)²) / (n₁-1)

s₂² = (ss₂ - n₂*(y₂-μ)²) / (n₂-1)

where;

ss₁ = ∑(y_i - y₁)²

ss₂ = ∑(y_i - y₂)²

Dividing these equations, we get:

s₁² / s₂² = (ss₁ / (n₁-1)) / (ss₂ / (n₂-1))

Now, let's define a new variable:

F = s₁² / s₂

Substituting s₁² / s₂² into the above equation, we get:

F = (ss₁ / (n₁-1)) / (ss₂ / (n₂-1))

This is the desired result. We have shown that F follows an F distribution with (n₁-1) and (n₂-1) degrees of freedom.

It's worth noting that the F distribution is only defined for positive values. Therefore, if s₁² / s₂² is less than 1, we need to take the reciprocal of the above equation to ensure that F is positive:

F = (ss₂ / (n₂-1)) / (ss₁ / (n₁-1))

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There are [tex]144 + 336 = 480[/tex] square units of surface area overall. The shape has a surface area of 480.0 square units, rounded to the closest tenth.

The dimensions and shape of the object are taken into account while calculating surface area. The volume of water of a cube, for instance, can be computed by adding the areas of the all six of its equal-sized faces. The surface temperature of something like a sphere, while on the other hand, must be calculated using mathematical methods that take into consideration its radius. The concept of surface area is crucial to many branches of mathematics, science, & engineering.

given

The area of each of the two triangles is [tex](1/2) * 3 * 8 = 12[/tex] square units since each triangle has a base of 3 and a height of 8, respectively.

The trapezium features an 8-inch height, a 6-inch top base, a 12-inch bottom base, and a 10-inch slant height.

two rectangles, each measuring 72 square units: 144 square units (2 x 72)

Four trapezoidal sides, each with a surface area of 12 + 72 = 84 square units 336 square units (4 x 84)

There are [tex]144 + 336 = 480[/tex] square units of surface area overall. The shape has a surface area of 480.0 square units, rounded to the closest tenth.

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according to the question the sample mean used to obtain the confidence interval was 173.

The arithmetic means (in contrast to the geometrical mean) of a dataset is the average of all values split by the total amount of values. The most popular way to measure central tendency is with the "mean," which is widely utilised. This is obtained by dividing the number of values in the dataset by the total number of all the values. Either raw information or information that has been included in frequency tables can be used for calculations. The average of a number is known as the average. Simple math can be used to determine: After summing up all the digits, divide by the number of digits. the sum divided by the number.

given,

The confidence interval's midpoint is determined by the sample mean. Therefore, to find the sample mean, we add the lower and upper bounds of the confidence interval and divide by 2:

Sample mean = (Lower bound + Upper bound)/2

Sample mean = (168.685 + 177.315)/2

Sample mean = 173

Therefore, the sample mean used to obtain the confidence interval was 173.

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The pair of the functions that are inverse is

The inverse of the function is solved by the operations as follows

f(x) = x - 4 let y = f(x)

y = x - 4

solving for x

x = y + 4

interchanging the variables

y = x + 4  (this is the inverse)

the inverse x + 4 is equal to g(x) hence they are inverse functions

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The total surface area to paint is 22000 sq. ft.

Surface area is the measurement of the outer surface of an object. It is often used to calculate the area of a three-dimensional object, such as a cube, cylinder, or sphere, and is also used to calculate the area of the faces of a solid object. Surface area is measured in square units such as square centimeters (cm2), square meters (m2), or square inches (in2).

Surface Area = 2(lw + lh + wh)

Surface Area = 2((100' x 50') + (100' x 40') + (50' x 40'))

Surface Area = 2(5000' + 4000' + 2000')

Surface Area = 2(11000')

Surface Area = 22000 sq. ft.

Answer: The total surface area to paint is 22000 sq. ft.

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