A designer wants to
place a fountain at the intersection of the
shortest paths from each side to the opposite
vertex. What mistake is made on her model?
At what point of concurrency should the
fountain be located?

The percent of container A that is empty after the pumping is complete is 46.29%

Container A:  radius = 14 feet and height = 19 feet

Container B: radius = 10 feet and height = 20 feet

The formula for the volume of a cylinder is given by:

volume of cylinder = πr²h

where r is the radius and h is the height

volume of container A =  π × 14²× 19 = 11699.29 cubic feet

volume of container B =  π × 10²× 20 = 6283.19 cubic feet

water from container B is pumped into container A

empty space in container  A = 11699.29 - 6283.19 = 5416.1 cubic feet

The percent of container A that is empty after the pumping is complete will be:

percent of container A that is empty = (5416.1 /11699.29)× 100

percent of container A that is empty = 46.3%

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Complete Question

Two containers are designed to hold water two containers design to hold water side by side both in the shape of a cylinder. Container A has a radius of 14 feet and a height of 19 feet. Container B has a radius of 10 feet and a height of 20 feet container is full of water and the water is pumped into the container B until container B is completely full. To the nearest 10th, what is the percent of container A is empty after the pumping is complete?

The measures of the angles of the triangles are

m∠1 = 55°

m∠2 = 125°

m∠3 = 35°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the first triangle be represented as ΔABC

Let the second triangle be represented as ΔCDE

And ∠BAC = m∠1

And , ∠CDE = m∠3

Now , from the triangle ΔABC

∠ABC = 180° - 110° ( Angle of a straight line is 180° )

So , the measure of angle ∠ABC = 70°

The sides of the triangle AC and BC are similar

So , The angles of the triangle are = 70° + x + x = 180°

On simplifying the equation , we get

70° + m∠1 + m∠1 = 180°

Subtracting 70° on both sides of the equation , we get

2m∠1 = 110°

Divide by 2 on both sides of the equation , we get

m∠1 = 55° = ∠ACB

And , ∠ACB and m∠2 are on a straight line

So , m∠2 = 180° - 55°

On simplifying the equation , we get

m∠2 = 125°

The triangle ΔCDE is a right triangle with ∠DCE = m∠1 ( vertically opposite angles )

So , the angles of the triangle are = 90° + 55° + m∠3 = 180°

On simplifying the equation , we get

145° + m∠3 = 180°

Subtracting 145° on both sides of the equation , we get

m∠3 = 35°

Hence , the measures of the angles of the triangles are are m∠1 = 55° , m∠2 = 125° , m∠3 = 35°

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The total number of fasnacht doughnuts is given by the equation A = 384

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total number of fasnacht doughnuts be represented as A

Now , the equation will be

The amount of butter Tran has = 8 pounds

1 pound of butter = 2 cups

So , 8 pounds of butter = 8 x 2 cups

8 pounds of butter = 16 cups

And , recipe calls for 1 cup of butter per 2 dozen fasnachts

So , 16 cups of butter = 16 x 2 dozen fasnachts

On simplifying the equation , we get

16 cups of butter = 32 dozens of fasnachts

And , the total number of fasnacht doughnuts A = 32 dozens

The total number of fasnacht doughnuts A = 32 x 12

The total number of fasnacht doughnuts A = 384 fasnachts doughnuts

Therefore , the value of A is 384 doughnuts

Hence , the total number of doughnuts is 384

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The standard form of the expression is -5-81i.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

A complex number is a number system element that extends the real numbers with a specific element denoted by 'i' known as the imaginary unit.

The given expression is -5 - √81. The number in a standard form will be written as,

Number = -5 - √81

Number = -5 - 81i      i = √-1

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Answer:

9 because 1, 2,6,are factors of 18 and since 8 is not a factor of 10 9 is a factor because9×2 =18

The interval notation for all real numbers greater than or equal to 5, is [ ∞, 5 ].

Continuous sets of real numbers can be represented using interval notation by the numbers that bound them. When written, intervals resemble ordered pairs in several ways.

When writing in interval notation, using " [ " means that the number next to this is to be included in the interval.

All real numbers greater than 5 would therefore mean real numbers till infinity so the symbol is ∞. The interval notation would therefore be :

[ ∞, 5 ]

This includes both all the real numbers and 5.

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Full question is:

Write in interval notation, all real numbers greater than or equal to  5

Answer: x=2, y=4

Step-by-step explanation:

Use the elimination method to find x and y.

3x-y=2

2x+y=8

5x=10

x=2

Using the value of x, plug it in the equation to get the value of y.

4+y=8

y=4

Answer:

The width

Step-by-step explanation:

you would first need a width to subtract into first

Answer: y=-x+10

Step-by-step explanation:

In this graph, we can see 2 distinct points on the line. They are (2,8) and (4,6). To find the equation, we want to use the slope formula to find the slope.

[tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{8-6}{2-4} =\frac{2}{-2} =-1[/tex]

Now with the slope, let’s find the y-intercept. The y-intercept can be found on the y-axis. Looking back to the graph, the y-axis is 10. The final equation is y=-x+10.

Yes, a hole in a function is considered a type of discontinuity. A hole occurs when a point is missing from the graph of a function, which causes the graph to have a break in it.

A discontinuity is a break or jump in the graph of a function. A hole in a function is a type of discontinuity where a point is missing from the graph, causing the graph to have a break in it. This type of discontinuity is usually caused by a function having a denominator that is equal to zero, as this creates an undefined point on the graph. This can also occur when two parts of the function are not connected, causing an open gap in the graph. In both cases, the graph is not continuous and has a discontinuity at the point where the hole is present.

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Yes, the function has a hole in discontinuity.

The term function in math is called as a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables.

Here we to identify is a hole in a function a discontinuity.

the term discontinuity is defined as is discontinuous at a point if it becomes undefined or the limit at that point does not exist. And whether this point is known as the point of discontinuity.

While we looking the hole on a graph looks like a hollow circle. And which  represents the fact that the function approaches the point, here it is not actually defined on that precise value. Where the major reason why this function is not defined at is because is not in the domain of the function.

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y(x) = tan(x + C) where C is an arbitrary constant of integration. Thus, the equilibrium solutions are y = 1 and y = -1. The non-equilibrium solutions are the values of y that make y' not equal to 0.

y(x) = tan(x + C)

Where C is an arbitrary constant of integration.

The solution y(x) = tan(x + C) is a family of functions indexed by the arbitrary constant C. The constant C cannot be determined from the information given in the problem, and so the general solution contains all possible specific solutions.

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Answer: 5 + a = t

Step-by-step explanation:

She fed her five in the morning,  the a is a variable representing the amount she fed in the afternoon, and the t is a variable representing the total amount of apple chunks fed. Because we do not know how many chunks she fed him these two values have to be variables.

The function for x = -2 is 56, x = 0 is 0 and x=2 is 24 for function g(x)= 10x² - 8x

A relation is a function if it has only One y-value for each x-value.

The given function is g(x)= 10x² - 8x

we need to find the value when x is -2

Replace x with -2

g(-2)=10(-2)²-8(-2)

=10×4+16

=40+16=56

Now when x =0

g(0)= 10(0)² - 8(0)=0

Now when x =2

Replace x with 2

g(2)=10(2)²-8(2)

=40-16

=24

Hence, the function for x = -2 is 56, x = 0 is 0 and x=2 is 24 for function g(x)= 10x² - 8x

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Answer:

1 is the answer.After you minus and plus it,you will definitely get 1 as the answer.Trust me guys.

The solution does not exist, as the equation does not satisfy any value of x and y

What is the equation?

An equation is a mathematical statement that asserts the equality of two expressions. It is a statement that asserts the equality of two expressions, and it is represented by an "equals" sign (=) between them. The expressions on either side of the equals sign are called the left-hand side and the right-hand side of the equation. Equations can be written in different forms, such as the standard form, factored form or in the form of roots.

The equation x - 2y = -4 represents a straight line in the x-y plane. To find the solution to this equation, we can find the x and y coordinates that satisfy the equation.

We can solve for one of the variables by adding or subtracting the constant from both sides of the equation.

x = 2y + 4

We can then substitute this expression for x into the other equation to find the value of the other variable.

x-2y=-4

2y+4-2y=-4

4 = -4

Hence, The solution does not exist, as the equation does not satisfy any value of x and y

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The percent of games lost by the baseball team is 20%

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

Games won = 24

Games lost = 6

The percent of games lost by the baseball team is then calculated as

Percentage lost = Games lost/(Games lost + Games won) * 100%

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

Percentage lost = 6/(6 + 24) * 100%

Evaluate

Percentage lost = 20%

Hence, the percentage lost is 20%

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Let x and Y represent the unknowable costs of a single hot dog and soft drink, respectively. We require two equations in order to solve for the two unknowns.

Equation 1 states that ten hot dogs and five soft drinks cost $35, or 10x + 5y = 35.

Equation 2: The total cost of 7 hot dogs and 4 soft drinks is $25.25, or 7x + 4y = 25.25.

Let's start by reformulating equation 1 to account for y:

10x + 5y = 35

5y = 35 - 10x  

y = 7 - 2x    

Let's change y in equation 2 to be 7 - 2x:

7x + 4y = 25.25

7x + 4(7 - 2x) = 25.25

Simplifying the above equation,

7x + 28 - 8x = 25.25

-x + 28 = 25.25

Then we get,

x - 28 = -25.25

Calculate x, which is the price of a single hot dog. Use y = 7 - 2x to calculate the price of a single soft drink after you have that information.

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It will take 3 weeks for both of us to have collected  the same amount. Each of us will have collected 23 items at that  time.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Let x = weeks

Me: y = 14+3x

Friend: y = 8+5x

Equating the two equations

14+3x=8+5x

14=8+2x

6=2x

dividing both sides by 2

3=x

y=14+3(3)=23

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The numeric value of the function C(68) at f = 68 is given as follows:

C(68) = 20.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

C(f) = 5/9 x (f - 32).

The input at which we want to find the numeric value for the function is then given as follows:

f = 68.

Which means that the lone instance of f in the definition of the function is replaced by 68, and then the numeric value is calculated as follows:

C(68) = 5/9 x (68 - 32) = 5/9 x 36 = 5 x 4 = 20.

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A mathematical state of the presumed relationship between two or more variables is called a model.

A model is a simplified representation of a real-world system that allows us to better understand and predict the behavior of the system. A model is a simplified representation of a real-world system that allows us to better understand and predict the behavior of the system.

In order to create a model, we need to understand the relationships between the variables in the system. These relationships can be represented mathematically.

Once we have a mathematical representation of the relationships between the variables, we can use this model to make predictions about the behavior of the system.

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The area of the yellow region to the nearest tenth is 48.4 cm².

The diagram is a square. Part of the square is cut to form quarter of a circle. Therefore, let's find the area of the yellow region.

Area of the yellow region = area of the square - area of the quarter circle

area of the square = l²

where

area of the square = 15²

area of the square = 225 cm²

area of the quarter circle = 1 / 4 πr²

area of the quarter circle = 1 / 4 × 3.14 × 15²

area of the quarter circle = 1 / 4 × 3.14 × 225

area of the quarter circle = 706.5 / 4

area of the quarter circle = 176.625

Therefore,

Area of the yellow region = 225 - 176.625

Area of the yellow region = 48.4 cm²

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The domain and range are: domain: [0, 12.76], range: [0, 590.9]

We have the following equation:

h(t)=-4.92t^2+17.69t+575

For the domain we have:

We match zero:

-4.92t ^ 2 + 17.69t + 575 = 0

We look for the roots:

t1 = -9.16, t2 = 12.76

We are left with the positive root, so the domain= [0, 12.76]

For the range we have:

We derive the function:

h '(t) = - 9.84t + 17.69

We equal zero and clear t:

-9.84t + 17.69 = 0

t = 17.69 / 9.84

t = 1.80

We evaluate the time in which it reaches the maximum height in the function:

h (1.80) = - 4.92 * (1.80) ^ 2 + 17.69 * (1.80) +575

h (1.80) = 590.90

Therefore, the range:[0, 590.9]

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The general solution to the differential equation is y(x) = (5/2)x^3 - (4/3)x^2 + (1/2)x + C1e^(-x) + C2e^(-2x).

To solve this initial value problem, we need to find the general solution to the differential equation and then use the initial conditions to find the particular solution.

The characteristic equation is r^2 + 3r - 2 = 0, which has two distinct real roots of r1 = -2 and r2 = -1.

The general solution to the differential equation is y(x) = (5/2)x^3 - (4/3)x^2 + (1/2)x + C1e^(-x) + C2e^(-2x)

Now we can use the initial conditions y(0) = 0 and y'(0) = 0 to find the values of C1 and C2.

y(0) = 0 = (5/2) * 0^3 - (4/3) * 0^2 + (1/2) * 0 + C1e^(0) + C2e^(0)

y'(0) = 0 = 5x^2 - (8/3)x + (1/2) + C1e^(-x) - C2e^(-2x)

Solving these equations, we find that C1 = 0 and C2 = 0, so the particular solution to the initial value problem is y(x) = (5/2)x^3 - (4/3)x^2 + (1/2)x.

This method is the standard way to solve Initial value problems for linear homogeneous differential equations with constant coefficients. It relies on finding the characteristic equation, and the general solution of the differential equation. Then we use the initial conditions to find the particular solution.

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The slope of the line that passes through the points (-4, 7) and (-6, -4) is 5.5

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

(-4, 7), (-6, -4

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (-4, 7) and (-6, -4)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (-4, 7) and (-6, -4)

Substitute the known values in the above equation

So, we have the following equation

Slope = (-4 - 7)/(-6 + 4)

Evaluate

Slope = 5.5

Hence, the slope of the line is 5.5

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What’s the answer for the slope of (-4, 7), (-6, -4)?

The percentage return you make on the stock is 12.9%

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

Initial value = $62

Final value = $70

The percentage return is then calculated as

Percentage return = (Final value - Initial value)/Initial value * 100%

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

Percentage return = (70 - 62)/62 * 100%

Evaluate

Percentage return = 12.9%

Hence, the percentage return is 12.9%

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After 8 years, the forest's area will be 2303.55 km2.

The "space enclosed within the perimeter or the boundary" of the specified shape is what is referred to as a shape's area. We use mathematical techniques to determine the area of various forms.

If the forest covers an area of  3400 km^2 and it decreased by 4.75%, the new area covered after a year will be equal to 3400 less the product of 3400 and 4.75%

= 3400 - 4.75% * 3400

= 3400 (1 - 0.0475)

After the second year, the area becomes

= 3400 (1 - 0.0475) - 4.75% * 3400 (1 - 0.0475)

= 3400 (1 - 0.0475)(1 - 0.0475)

= 3400 (1 - 0.0475)²

Following this pattern, the area after 8 years

= 3400 (1 - 0.0475)⁸

Area after the 8 years = 2303.55609

therefore, the area of the forest after the 8 years will be 2303.55 km².

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Answer:

n = 20

Step-by-step explanation:

there is a common difference between consecutive terms , tat is

0 - (- 3) = 3 - 0 = 3

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 3 and d = 3 with [tex]a_{n}[/tex] = 54 , then solving for n

- 3 + 3(n - 1) = 54 ( add 3 to both sides )

3(n - 1) = 57 ( divide both sides by 3 )

n - 1 = 19 ( add 1 to both sides )

n = 20

there are 20 terms in the sequence.

Answer: 5x-2

Step-by-step explanation:

2x+5 + 3x-7

2x-2 + 3x

5x-2

Answer:

3.) B

How to solve:

Just get the cubed root of all the numbers inside the fraction

The figures shows a graph of y = h(x) and h⁻¹(x), at h⁻¹(x) gives  -0.5

An inverse function in mathematics is a function that "undoes" another function.

In other words, if f(x) yields y, then y entered into the inverse of f yields the output x. x .

An invertible function is one that has an inverse, and the inverse is represented by the symbol f ⁻¹.

The second graph is for the inverse function, tracing point where x = -1 in the graph to the straight line and tracing back to the y direction gives 0.5

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