Let m, n, and p be real numbers.
Name the property of equality that the statement illustrates.
m(n-p) = mn - mp

Answer:

2((3(4) + 4(7) + 3(7)) = 2(12 + 28 + 21) = 2(61) = 122 square meters

There are 2 sides.

First side is 12 by 2 so you would multiply them together which is 24 and since there is another side the same length multiply by 2 which is 48.

Second side small side is 2 by 4 so multiply them together which is 8 and since there is another side the same demension multiply 8 by 2 which is 16.

The last side is 12 by 4 so again multiply them together which is 48. Multiply it by two since there is another side with same dimension which is 96.

Now do 48 + 16 + 96 (the answer gotten after finding the areas for each sides and their identicals) which is 160 ft²

The label for rectangular prism that has a surface area of 96 square meters is in the attached image.

The equation of circle in the standard with given center and radius is  [tex](x+3)^{2} + (y-4)^2[/tex] = 49.

What is equation of circle?

Every point in a plane that is at a certain distance from the center point forms a circle. In order to go around a curve while maintaining a constant distance from another point, a moving point in a plane must follow a specific path.

The following is the typical form for expressing the equation of a circle:

[tex](x-h)^{2} + (y-k)^2 = r^2[/tex]

Here,

(h, k) represents the center and r is the radius.

We are given that the center is (-3, 4) and the radius is 7.

Now, using the standard form, we get

⇒ [tex](x-(-3))^{2} + (y-4)^2 = 7^2[/tex]

⇒ [tex](x+3)^{2} + (y-4)^2[/tex] = 49

Hence, the equation of circle in the standard with given center and radius is  [tex](x+3)^{2} + (y-4)^2[/tex] = 49.

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Since, there are multiple questions so the question answered above is attached below.

The correct statements regarding the exponential function 3(1/3)^x is given as follows:

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

The function for this problem is given as follows:

f(x) = 3(1/3)^x.

The parameter b is of 1/3 < 1, hence:

The range is all real values greater than 0, as a = 3 is positive and the function has an horizontal asymptote at y = 0.

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The equation simplifies to 14 = 14, which is a true statement.

In mathematics, an equation  is defined as a set of numbers that contains operations and may contain a variable. Equations are used to solve for these unknown variables  using various operations such as addition, subtraction, multiplication and division.

Replacing m by 4, we get:

m + 2 (m + 1) = 14

4 + 2 (4 + 1) = 14

4 + 2(5) = 14

4 + 10 = 14

14 = 14

The equation simplifies to 14 = 14, which is a true statement. Therefore, the given value 4 is a solution to Eq.

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The circumference of the larger circle is approximately 9.4 units.

The circumference is the distance around the edge or boundary of a closed two-dimensional shape, such as a circle or an ellipse.

Let C be the circumference of the larger circle. Then the circumference of the smaller circle is 0.25C, according to the given information.

We know that the circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Therefore, we can write:

C = 2πr for the larger circle

0.25C = 2πr for the smaller circle

Dividing the second equation by 0.25, we get:

C = 8πr for the smaller circle

Now we can equate the two expressions for C and solve for r:

2πr = 8πr

6πr = C

r = C/(6π)

Finally, we can substitute this value of r into the expression for C in terms of r for the larger circle:

C = 2πr = 2π(C/(6π)) = (1/3)Cπ

Solving for C, we get:

C = (3/π)C

C = 3π ≈ 9.4 (rounded to the nearest tenth)

Therefore, the circumference of the larger circle is approximately 9.4 units.

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The parts of the expression in terms of factor, product, quotient, and sum are:

Factor- (5 - M)/(N - 2)

Product- 8 * M

Quotient- (5 - M)/(N - 2)

Sum- (5 - M)/(N - 2) + N - 8 * M - 2

Explain expression

An expression is a mathematical phrase that contains numbers, variables, and/or mathematical operations. It can be simplified or evaluated using mathematical rules and principles.

What is meant by quotient?

The quotient is the result obtained when one quantity is divided by another, usually represented as a whole number, fraction, or decimal. It is a fundamental concept in mathematics.

According to the given information

The given expression is:

(5 - M)/(N - 2) - 8 * M + N

We can break it down into the following parts using the words factor, product, quotient, and sum:

Factor: (5 - M)/(N - 2)

Product: 8 * M

Quotient: (5 - M)/(N - 2)

Sum: (5 - M)/(N - 2) + N - 8 * M - 2

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The indefinite integral when evaluated has a solution of 2cot(2x⁵ - 5x) + C

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

The integral of (10 - 20x⁴)csc²(2x⁵ - 5x)

³

This can be expressed as

∫(10 - 20x⁴)csc²(2x⁵ - 5x) dx

The above is a complex expression

So, we make use of a graphing tool to evaluate the solution

Using a graphing tool, we have

Step 1:

[tex]\frac{4\cos(10x)\sin(4x^5) - 4\sin(10x)\cos(4x^5)}{sin^2(4x^5) - 2\sin(10x)\sin(4x^5) + cos^2(4x5) - 2\cos(10x)\cos(4x5)+ \sin^2(10x) + \cos^2(10x)} + C[/tex]

When simplified, we get

2cot(2x⁵ - 5x) + C

hence, the solution is 2cot(2x⁵ - 5x) + C

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The x-coordinates of all the points on the graph of f(2x) are half the x-coordinates of the corresponding points on the graph of f(x), which results in a horizontal compression or shrinking of the graph.

What is a graph?

In computer science and mathematics, a graph is a collection of vertices (also known as nodes or points) connected by edges (also known as links or lines).

The transformation f(2x) stretches the graph of f(x) horizontally by a factor of 1/2. In other words, the graph of f(2x) will be compressed horizontally compared to the graph of f(x).

To see why this is the case, consider the effect of replacing x with 2x in the expression for f(x). If we think of f(x) as a set of points in the xy-plane, then each point (x,y) on the graph of f(x) is transformed into the point (2x,y) on the graph of f(2x).

Therefore, this means that the x-coordinates of all the points on the graph of f(2x) are half the x-coordinates of the corresponding points on the graph of f(x), which results in a horizontal compression or shrinking of the graph.

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If  an ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. The  probability is:  84.6%.

In this case, we have:

Population standard deviation (σ): $1200

Sample size (n): 400

Margin of error (E): $80

The standard deviation of the sample mean can be calculated as:

σM = σ / √n = 1200 / √400 = 60

To find the probability that the sample mean is within $80 of the population mean, we need to find the z-scores for the upper and lower limits of the interval:

Lower limit: z = (mean - E - population mean) / σM = (-80) / 60 = -1.3333

Upper limit: z = (mean + E - population mean) / σM = 80 / 60 = 1.3333

Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-scores:

P(-1.3333 < Z < 1.3333) = 0.8461

Therefore, the probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol is approximately 0.846 or 84.6%.

Interpretation: This means that if we take many samples of 400 railroad-car shipments of ethanol and calculate their mean tariff rates, about 84.6% of these means will be within $80 of the true mean tariff rate of all ethanol shipments. This also means that there is a sampling error of $80, which is the maximum amount by which the sample mean may differ from the population mean due to random sampling variability.

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The correct answer is an option (A) 144.5 pounds per year, which is the closest value to the calculated average yearly growth rate of the elephant.

The term "average" refers to a measure of central tendency that represents the typical or typical value in a set of data.

Growth rate refers to the rate at which a quantity or value increases or decreases over time. It is often expressed as a percentage or a proportion and is used to measure the change in a particular variable relative to its initial value.

According to the given information:

To find the average yearly growth rate of the elephant, we can use the formula for calculating growth rate:

Growth Rate = ((Ending Value - Starting Value) / Number of Years)

In this case, the starting weight of the elephant is 220 pounds and the ending weight is 870.25 pounds. The number of years is 4.5 (since the growth occurred over 4.5 years).

Plugging these values into the formula, we get:

Growth Rate = ((870.25 - 220) / 4.5)

Simplifying the numerator, we get:

Growth Rate = 650.25 / 4.5

Dividing, we get:

Growth Rate ≈ 144.50 pounds per year

So, the correct answer is option (A) 144.5 pounds per year, which is the closest value to the calculated average yearly growth rate of the elephant.

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Answer:

[tex]\frac{8}{10}[/tex]

Step-by-step explanation:

[tex]cos(A) = \frac{adjacent}{hypotenuse} \\= \frac{AB}{AC}\\= \frac{8}{10}[/tex]

Answer:

Answer:

\frac{8}{10}

10

8

Step-by-step explanation:

\begin{gathered}cos(A) = \frac{adjacent}{hypotenuse} \\= \frac{AB}{AC}\\= \frac{8}{10}\end{gathered}

cos(A)=

hypotenuse

adjacent

=

AC

AB

=

10

8

the object will fall a distance of 1024 feet in 8 seconds. So the answer is (C) 1024 ft.

what is distance  ?

Distance is a scalar quantity that refers to the total length traveled by an object or person, without considering the direction. It is a measure of the path length between two points, usually measured in units such as meters (m), feet (ft), or kilometers (km).

In the given question,

The formula t = √(d/16) relates the time t (in seconds) it takes an object to fall a distance d (in feet) to the acceleration due to gravity, which is approximately 32.2 feet per second squared.

To find how far the object will fall in 8 seconds, we can rearrange the formula to solve for d:

t = √(d/16)

t² = d/16 (Squaring both sides)

d = 16t² (Multiplying both sides by 16)

Substituting t = 8 into the formula, we get:

d = 16(8)² = 1024

Therefore, the object will fall a distance of 1024 feet in 8 seconds.

So the answer is (C) 1024 ft.

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Hannon's maximum allowable production cost for the All-Body swimsuit is $80 if it wants to make a profit of $20 per unit.

Given data ,

a)

Using cost-plus pricing, the selling price is set 20% above the costs.

Selling price=Costs+(Costs x Markup)

Selling price=$100 + ($100x0.20)

Selling price=$100+$20

On simplifying the equation , we get

Selling price=$120

The price charged for the All-Body swimsuit would be$120.

Hannon might consider manufacturing the All-Body swimsuit under the cost-plus pricing approach if the market demand is strong enough to justify the selling price of $120 and if Hannon can efficiently produce and sell the swimsuit to generate profits.

(b)

Using target costing, the price charged by Hannon to the retailer is determined by subtracting the desired profit per unit from the target selling price.

Target selling price=$100 (given)

Desired profit per unit=$20 (given)

Price charged to retailer=Target selling price - Desired profit per unit

Price charged to retailer=$100-$20

On simplifying the equation , we get

Price charged to retailer=$80

The price that Hannon would charge the retailer for the All-Body swimsuit under target costing is$80.

(c)

To determine the highest acceptable manufacturing cost for the All-Body swimsuit under target costing, we subtract the desired profit per unit from the target selling price.

Target selling price=$100 (given)

Desired profit per unit=$20 (given)

Highest acceptable manufacturing cost=Target selling price-Desired profit per unit

Highest acceptable manufacturing cost=$100-$20

Highest acceptable manufacturing cost=$80

Hannon would be ready to spend up to $80 in manufacturing costs to develop the All-Body swimsuit if it wanted to make $20 each unit.

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How many construction sites has each of the current Mohawk Skywalkers worked on in their lifetime? is a statistical question about the Mohawk Skywalkers. Option A.

A statistical question is a question that can be answered by collecting and analyzing data. It involves variability and asks about the distribution of a population, rather than just a single value or specific instance.

Option A is a statistical question because it asks about the variability of the number of construction sites each of the current Mohawk Skywalkers worked on in their lifetime.

Option B is also a statistical question as it asks about the distribution of New York City skyscrapers built with the help of Mohawk Skywalkers.

Option C is not a statistical question because it asks for a specific value, the number of generations of the Martin family who have worked as Mohawk Skywalkers, which does not involve variability or a population.

Option D is not a statistical question as it asks for a specific value, the number of Mohawk Skywalkers who helped build the Empire State Building, which does not involve variability or a population.

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The surface area is approximately 41.7 square units.

The rectangle has dimensions 18 units by 6 units, so its area is:

A(rectangle) = l x h = 18 x 6 = 108 square units

The semicircle has a radius of 5 units, so its area is half that of a full circle:

A(semicircle)

= 1/2 x π x r²

= 1/2 x π x 5²

= 1/2 x 25π

= 12.5π

To find the total surface area, we need to add the areas of the rectangle and the semicircle. However, since the semicircle is attached to the top of the rectangle, we need to subtract the area of the portion of the circle that overlaps with the rectangle. This overlapping area is equal to the width of the rectangle (18 units) times half the circumference of the circle (1/2 x π x r), or:

A(overlap)

= w x 1/2 x π x r

= 18 x 1/2 x π x 5

= 45π

Therefore, the total surface area is:

Surface area = A(rectangle) + A(semicircle) - A(overlap) = 108 + 12.5π - 45π ≈ 41.7 square units

Rounding to the nearest tenth, the surface area is approximately 41.7 square units.

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The left-hand side simplifies to 14, and the right-hand side is also 14. Therefore, the equation is true when m = 4.

"LHS = RHS" stands for "left-hand side equals right-hand side". It is a notation commonly used in mathematics to show that two expressions are equal to each other.

In mathematics, to substitute means to replace a variable or expression in an equation or function with a specific value or expression.

To substitute the value 4 for m in the given equation, we replace every occurrence of m:

m + 2(m + 1) = 14

4 + 2(4 + 1) = 14

4 + 2(5) = 14

4 + 10 = 14

14 = 14

14 is the result of simplifying the left and right sides, respectively. Consequently, when m = 4, the equation is accurate.

So, the value 4 is a solution to the given equation.

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Answer:

Yes.

Step-by-step explanation:

(2, 3) means we'll let x be 2 and y be 3. Let's solve both equations first:

y = -2x + 7

3 = -2(2) + 7

3 = -4 + 7

:. 3 = 3

Okay, so one half is proven. Let's do the other half now.

y = x + 1

3 = 2 + 1

3 = 3

:. (2,3) is a solution to the system of equations.

The slope of the line of best fit provides valuable information about the relationship between the two variables being plotted and can be used to make predictions about future data points or to identify patterns and trends in the data.

What is the slope?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

The slope of the line of best fit on a scatter plot represents the rate of change between the two variables being plotted.

In the case of Keilantra's math teacher, the slope of the line of best fit between student grades on weekly quizzes and the number of hours they say they study represents the change in grades for every additional hour of studying.

For example, if the slope is positive (i.e., the line slopes upward from left to right), it indicates that as the number of hours studied increases, the average grade on the quiz tends to increase as well.

On the other hand, if the slope is negative (i.e., the line slopes downward from left to right), it indicates that as the number of hours studied increases, the average grade on the quiz tends to decrease.

Therefore, the slope of the line of best fit provides valuable information about the relationship between the two variables being plotted and can be used to make predictions about future data points or to identify patterns and trends in the data.

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Answer:

The slope-intercept form of the equation of a line is:

y = mx + b

where m is the slope and b is the y-intercept.

We are given that the y-intercept is (0,2), which means that the value of b is 2.

We are also given that the slope is -2, which means that the value of m is -2.

Substituting these values into the slope-intercept form, we get:

y = -2x + 2

Therefore, the slope-intercept form of the equation of the line is y = -2x + 2.

Step-by-step explanation:

Answer:

that is correct just to give you feedback on that

Answer:

46

Step-by-step explanation:

46 (ve had this problem before)

Answer:

As the number of sides of the bases of a prism increases, the shape of the prism becomes more complex and closer in form to a cylinder. For example, a prism with two identical polygonal bases, such as a rectangular prism or a triangular prism, will have a more blocky or pyramidal shape. However, as the number of sides of the base increases, the shape of the prism becomes more cylindrical and less pyramidal in appearance. This is because the more sides a polygon has, the more closely it approximates a circle, and the cross-section of the prism becomes more circular in shape.

When the number of sides of the base of a prism increases, the prism becomes more like a cylinder.

Based on the information given, there are a total of 118 solutions.

This is a problem of solving a Diophantine equation subject to some conditions. Let's introduce a new variable y4 = 20 - (x1 + x2 + x3 + x4). Then the problem can be restated as finding the number of solutions to:

x1 + x2 + x3 + y4 = 20

Subject to the following conditions:

0 ≤ x1 < 3

0 ≤ x2 < 4

0 ≤ x3 < 5

0 ≤ y4 < 6

We can solve this problem using the technique of generating functions. The generating function for each variable is:

(1 + x + x^2) for x1

(1 + x + x^2 + x^3) for x2

(1 + x + x^2 + x^3 + x^4) for x3

(1 + x + x^2 + x^3 + x^4 + x^5) for y4

The generating function for the equation is the product of the generating functions for each variable:

(1 + x + x^2)^3 (1 + x + x^2 + x^3 + x^4 + x^5)

We need to find the coefficient of x^20 in this generating function. We can use a computer algebra system or a spreadsheet program to expand the product and extract the coefficient. The result is: 1118

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Answer: This problem involves finding the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints. We can use the stars and bars method to solve this problem.

Suppose we have 20 stars representing the sum x₁ + x₂ + x3 + x₁. To separate these stars into four groups corresponding to x₁, x₂, x₃, and x₄, we need to place three bars. For example, if we have 20 stars and 3 bars arranged as follows:

**|**||

then the corresponding values of x₁, x₂, x₃, and x₄ are 2, 4, 6, and 8, respectively. Notice that the position of the bars determines the values of x₁, x₂, x₃, and x₄.

In general, the number of ways to place k identical objects (stars) into n distinct groups (corresponding to x₁, x₂, ..., xₙ-₁) using n-1 separators (bars) is given by the binomial coefficient (k+n-1) choose (n-1), which is denoted by C(k+n-1, n-1).

Thus, the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints is:

C(20+4-1, 4-1) = C(23, 3) = 1771

However, this count includes solutions that violate the upper bounds on x₁, x₂, x₃, and x₄. To eliminate these solutions, we need to use the principle of inclusion-exclusion.

Let Aᵢ be the set of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints, where xᵢ ≥ mᵢ for some integer mᵢ. Then, we want to find the cardinality of the set:

A = A₀ ∩ A₁ ∩ A₂ ∩ A₃

where A₀ is the set of all non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20, and Aᵢ is the set of solutions that violate the upper bound on xᵢ.

To find the cardinality of A₀, we use the formula above and obtain:

C(20+4-1, 4-1) = 1771

To find the cardinality of Aᵢ, we subtract the number of solutions that violate the upper bound on xᵢ from the total count. For example, to find the cardinality of A₁, we subtract the number of solutions where x₂ ≥ 4 from the total count. To count the number of solutions where x₂ ≥ 4, we fix x₂ = 4 and then count the number of solutions to the equation x₁ + 4 + x₃ + x₄ = 20 subject to the constraints 0 ≤ x₁ < 3, 0 ≤ x₃ < 5, and 0 ≤ x₄ < 6. This count is given by:

C(20-4+3-1, 3-1) = C(18, 2) = 153

Similarly, we can find the cardinalities of A₂ and A₃ by fixing x₃ = 5 and x₄ = 6, respectively. Using the principle of inclusion-exclusion, we obtain:

|A| = |A₀| - |A

Step-by-step explanation:

The complete table as determined from the given probabilities is given below:

         X    Y   Total

A       40   28   68

B      38   54    92

Total 78   82   160

P(A|X) means the conditional probability of A given X has occurred. In this case, 40/92 means out of 92 times X occurred, A occurred 40 times.

P(B) means the marginal probability of B, which is the total probability of B occurring regardless of whether A occurred or not. In this case, 78/160 means out of 160 trials, B occurred 78 times.

The row and column totals are calculated by adding up the corresponding values.

The grand total is the sum of all the values in the table.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See the attached image.

Answer:

the missing y coordinate is 2/5

Step-by-step explanation:

You are basically solving for y since you are missing the y coordinate

Since x=5 plug that in and you will get 5+5y=7

subtract 5 on both sides and you will get 5y=2

divide 5 on both sides and you will get 2/5

The rate at which her daily revenue is currently changing and the direction of the change is; Her revenue is currently increasing at $12 per day

The rate of change of a function is the rate at which the output of the function changes per unit change in the input of the function.

Let x represent the number of days, therefore;

The number of T-shirts Dorothy sells, y = 40 - 4·x

The price at which she sells the T-shirts = 7 + x

Therefore, Dorothy's daily revenue, R(x) = (40 - 4·x) × (7 + x) = 12·x - 4·x² + 280

The rate of change of her daily revenue can be obtained from the derivative of the revenue function as follows;

The rate at which her daily revenue is therefore;

R'(x) = d(R(x))/dx = 12 - 8·x

The rate at which her revenue is changing currently can be obtained from the rate function by plugging in x = 0, as follows;

R'(0) = 12 - 8×0 = 12

Her revenue is changing at a rate of $+12 per day.

The positive value of the rate, 12, indicates that her revenue is increasing at $12 per day

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