The rectangular floor of a classroom is 36 feet in length and 27 feet in width.A scale drawing of the floor has a length of 12 inches.What is the area, in square inches, of the floor in the scale drawing?

A dilation or combination of stiff movements and dilations constitutes a similarity transformation.

Similar figures don't always have to have the same size but share the same form.

A transition called a dilation keeps shape but not size. So a dilatation is a motion that is not rigid. A dilation or combination of stiff movements and dilations constitutes a similarity transformation. If and only if a similarity transformation translates one of the geometric figures onto the other, then two figures are said to be similar. Similar figures don't always have to have the same size but share the same form.

Similarity transformations include translation, reflection, rotation, and dilation. Rotation, reflection, and translation retain both size and form since they are rigid movements, whereas dilation just makes sure that the shape is preserved.

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No matter how far it is moved away, the midline of a function stays the same. because a sinusoidal function is involved.

A function's amplitude is the distance that the graph of the function moves above and below its midline. The value of the amplitude when graphing a sine function is comparable to the value of the sine coefficient. the greatest displacement or distance that a point on a wave or vibrating body can travel in relation to its equilibrium position A wave or vibration's amplitude or peak amplitude is a gauge of how far from the central value it deviates. All amplitudes are positive numbers.

given

( A)if pendulum were pulled away from its resting position, then Amplitude is the distance from its resting position to the end where it was released.

Amplitude is the same distance it was pulled away if more distance was pulled away then Amplitude is more.

(B). The midline of function s will not change, it will same irrespective of the distance pulled away. Because it's a sinusoidal function.

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Answer:

488 adults and 276 children

Step-by-step explanation:

So, we need two linear equations here to start, and we do have them.

Our first linear equation tells us how we get the number of forks:

2c + 5a = 2992

And the second tells us the number of people there:

c + a = 764

I will solve this using substitution. We start by minusing a from both sides in the second equation, giving us:

c = 764 - a

Then, we will substitute this into our first equation, giving us:

2(764 - a) + 5a = 2992

Then, we will open the parentheses, giving us:

1528 - 2a + 5a = 2992

Combining like terms and subtracting 1528 from both sides gives us:

3a = 1464

Dividing by 3:

a = 488

So there were 488 adults. Then, we take our original second equation and substitute 488 for a, giving us:

488 + c = 764

Minus 488 from both sides gives us:

c = 276

So, there were 276 children. In total, we had 488 adults and 276 children.

Hope this helped!

Answer:

Step-by-step explanation:

Answer: Y = 1/3x^2 - 4x + 12

Step-by-step explanation:

Hope this helps, sorry I don't have an explanation...

Answer:

The surface area of this cuboid is 420 square inches.

Step-by-step explanation:

All we have to do is calculate each rectangle. For the width, we have 10 x 5 which is 50. Then we multiply it by 2 because we have two of those sides. Then we get 100. Then we have 11 x 5 which is 55. We multiply that by 2 and we get 110. Then we do that to the final two sides and we get 220. So the final answer if we add them all up is 420 square inches.

The family's monthly payment for their new minivan is $6,664.52

To calculate the monthly payment, we first need to find the total amount that the family is financing by subtracting the down payment from the total cost of the minivan: $45,000 - $12,000 = $33,000.

Then, we can use the monthly payment factor to calculate the monthly payment. The formula to do this is:

Monthly Payment = Financed Amount * Monthly Payment Factor

So in this case:

Monthly Payment = $33,000 * 0.202764 = $6,664.52

Therefore, the family's monthly payment for their new minivan is $6,664.52

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Step-by-step explanation:

a line passing through 2 points get a slope just by these 2 points.

all we can do is to verify that the given slope is the same as the slope defined by the 2 points.

the slope is the ratio

y coordinate change / x coordinate change

when going from one point on the line to another.

for our 2 points that gives us

x changes by + 2 (from 2 to 4).

y changes by -2 (from -7 to -9).

the slope is therefore

-2/+2 = -1

the question asks for a slope of -5.

that is a contradiction. there is no line possible to pass through both points and have a slope of -5.

Answer:

Set1 = 1/12

Set2 = 1/12

Set3 = -12

Step-by-step explanation:

Substitute, use Keep-Change-Flip to handle division when there's fractions involved. See image.

Also to multiply fractions, multiply

top×top and bottom×bottom straight across. Also negative times a negative is a positive and negative is like opposite so -(-6) is 6 and -(-1/2) is 1/2.

see image.

The amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

If a random variable has a limited number of outcomes or a countable number, it is discrete (i.e. the integers are infinite, but are able to be counted).

The discrete distribution presented reveals that the expected value of Kelsie's time spent completing daily sales reports is 9.5 minutes.

The discrete distribution given is:

P(X = 0) = 0.3

P(X = 10) = 0.5

P(X = 20) = 0.15

P(X = 30) = 0.05

The average of a discrete distribution is equal to the sum of each result times the probability associated with that outcome, so:

E(X) = 0(0.3) + 10(0.5) + 20(0.15) + 30(0.05) = 9.5

Therefore, the amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

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a. E(B) = 9.5

b. The amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

c. Standard variable shows how much deviation from mean variable.

In statistics, a discrete distribution is a probability distribution that estimates the probability of a certain discrete, finite outcome. Simply put, as opposed to a continuous distribution, the discrete probability distribution aids in determining the probabilities of the occurrence of a specific event expressed in terms of positive, non-decimal, or whole integers.

The discrete distribution given is:

P(X = 0) = 0.3

P(X = 10) = 0.5

P(X = 20) = 0.15

P(X = 30) = 0.05

The average of a discrete distribution is equal to the sum of each result times the probability associated with that outcome, so:

E(B) = 0(0.3) + 10(0.5) + 20(0.15) + 30(0.05) = 9.5

Therefore, the amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

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a) 7 examples are:

[tex]2x + 3y\\(4a - 5b) / 2c\\(5 + 8) * 3\\8^2 - 6\\√(64)\\(1/3) * π * r^2\\2(3x + 4y) - 5z[/tex]

b) Fabric Larry will have left after using [tex]2\frac{2}{3}[/tex] yard out of [tex]5\frac{5}{6}[/tex] yard to make a bag for his computer is: [tex]3\frac{3}{6} yard[/tex]

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

7 examples of mathematical expression are:

[tex]2x + 3y\\(4a - 5b) / 2c\\(5 + 8) * 3\\8^2 - 6\\√(64)\\(1/3) * π * r^2\\2(3x + 4y) - 5z[/tex]

For the second part of the question:

Larry had 5 3/6 yards of fabric. He used 2 2/3 yards to make a bag for his computer. Write an expression that will show how much of the fabric Larry will have left.

The mathematical expression that represents the amount of fabric Larry has left is:

5 3/6 - 2 2/3 = 2 7/18

You can simplify this further:

2 7/18 = 2 1/6

The amount of fabric Larry will have left is 2 1/6 yards.

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The area of the surface obtained by rotating the circle [tex]x^2 + y^2 = r^2[/tex] about the line y = r is π²r² square units.

To find the area of the surface obtained by rotating the circle

[tex]x^2 + y^2 = r^2[/tex] about the line y = r, we can use the method of cylindrical shells.

The circle [tex]x^2 + y^2 = r^2[/tex] is centered at the origin (0, 0) with a radius r. The line y = r is the line y-axis but shifted up by r units.

When we rotate the circle about the line y = r, it forms a 3D shape called a torus or a donut shape.

Consider a small strip on the circle at a distance y from the line y = r.

This small strip is at a distance r - y from the y-axis.

The length of this strip is the circumference of the circle at y, which is 2πy (since the circumference of a circle is 2π times its radius).

The width of this strip is the change in x, which we can denote as dx.

The area of this small strip is then given by the product of its length and width, which is 2πy dx.

Now, to find the total surface area, we integrate this area over the range of y values from -r to r (since the circle is symmetric about the y-axis):

Total Surface Area = ∫[from -r to r] 2πy dx

Now, we need to express y in terms of x using the equation of the circle [tex]x^2 + y^2 = r^2:\\y^2 = r^2 - x^2[/tex]

y = ±√(r² - x²)

Since we are considering the upper half of the circle, we take the positive square root:

y = √(r² - x²)

Now, we can rewrite the integral with respect to x:

Total Surface Area = ∫[from -r to r] 2π√(r² - x²) dx

To solve this integral, we can make a trigonometric substitution:

Let x = r sin(θ), then dx = r cos(θ) dθ.

When x = -r, θ = -π/2, and when x = r, θ = π/2.

Now the integral becomes:

Total Surface Area = ∫[from -π/2 to π/2] 2π√(r² - (r sin(θ))²) (r cos(θ)) dθ

Total Surface Area = 2πr² ∫[from -π/2 to π/2] √(1 - sin²(θ)) cos(θ) dθ

Now, we can use the trigonometric identity:

sin²(θ) + cos²(θ) = 1

√(1 - sin²(θ)) = cos(θ)

Total Surface Area = 2πr² ∫[from -π/2 to π/2] cos²(θ) dθ

Now, use the trigonometric identity: cos²(θ) = (1 + cos(2θ))/2

Total Surface Area = 2πr² ∫[from -π/2 to π/2] (1 + cos(2θ))/2 dθ

Total Surface Area = 2πr² [θ/2 + (sin(2θ))/4] [from -π/2 to π/2]

Total Surface Area = 2πr² [(π/2 + sin(π) - (-π/2 + sin(-π)))/4]

Since sin(π) = 0 and sin(-π) = 0:

Total Surface Area = 2πr² [(π/2 - (-π/2))/4]

Total Surface Area = 2πr² (π/2)

Total Surface Area = π²r²

So, the area of the surface obtained by rotating the circle [tex]x^2 + y^2 = r^2[/tex] about the line y = r is π²r² square units.

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The graph of the linear function f(x) = 2/(x + 5) is attached.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the linear function as -

f(x) = 5/(2x + 5)

Refer to the graph of the linear function attached. This graph represents the function f(x).

Therefore, the graph of the linear function f(x) = 2/(x + 5) is attached.

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Answer:

Step-by-step explanation:

hello follow me on zepeto if this helps

16 is 33.3333% of 48. 33 is the whole number hope you get a

Answer:

Refer to the image attached. If you have ANY questions about what I did/how I did it, please ask in the comments. I will be happy to help you understand! :)

Step-by-step explanation:

Given that the sum of two numbers is 71 and one number is 27 more than the other, we can set up the following system of equations:

What is the straightforward definition of a system of equations solution?

A collection of values for a variable that simultaneously fulfill each equation is the solution to a system of equations. A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.

x + y = 71 (equation 1 represents the fact that the sum of the numbers is 71)

y = x + 27 (equation 2 represents the fact that one number is 27 more than the other)

To solve the system of equations, we can use the substitution method. We'll substitute equation 2 into equation 1:

x + (x + 27) = 71

Combining like terms:

2x + 27 = 71

Subtracting 27 from both sides:

2x = 44

Dividing both sides by 2:

x = 22

Now we can substitute x = 22 back into equation 2 to find the value of y:

y = x + 27

y = 22 + 27

y = 49

So the two numbers are x = 22 and y = 49, and they satisfy the given conditions that the sum of the two numbers is 71 and one number is 27 more than the other.

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Answer:

Step-by-step explanation:

18. m∠1 = 104°

19. m∠2 = 79°

20. m∠3 = 65°

21. m∠5 = 73°

The value of GI, given that GH = 2x - 9 , HI = 14 , and GT = 3x - 8 will be 31.

An algebraic equation is formed by comparing two algebraic expressions to one another.

In G-H-I, GH = 2x - 9, HI = 14 , and GT = 3x - 8

If G-H-I is a line and GH, HI and GT lies between G to I

To find G to I ⇒ GI = GH + HI = GT

GI = 2x - 9 + 14 = 3x - 8

2x + 5 = 3x - 8

2x - 3x = -8 - 5

-x = -13

x = 13

Substituting x in GT = 3x - 8; GI = GT

GI = 3(13) - 8

GI = 39 - 8

GI = 31

Using algebraic expressions, if x is 13 then, 3x - 8 or 2x - 9 will be GI = 31

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Answer: Sara's mean quiz score is 12

Step-by-step explanation:

Mean is the Sum of the Terms divided by the number of terms.

If we add up every score we get 60, we then will divide this by how many scores there were (5).

60/5 = 12

100

Step-by-step explanation:

because after 105 it's 100

Answer:

d

Step-by-step explanation:

Therefore , the solution of the given triangle comes out to be  AC = 10 units and PD = 6 units.

Triangles, which have three sides and three angles, can be made by joining any three points in a plane. They are among the earliest geometric shapes to be studied. Triangles are especially important since they may be divided into each polygon, whether it has four, five, six, or n sides.

Here,

Let AD and DC are 2x and x respectively.

We have, BC = 10 units

=> 2x =10

=> x = 10/2

=> x= 5

Now ,

=> AP + PF = 8 + y

=> 8 + y = 12

=> y =4

Therefore , the solution of the given triangle comes out to be  AC = 10 units and PD = 6 units.

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Answer:

B

Step-by-step explanation:

180-152=28

t=180-(28+90)

t=62

To see the table:

Symbol Symbol Name  Meaning / definition

+            plus                              or

∨      reversed caret                      or

|        vertical line                      or

x'       single quote                    not - negation

Now, According to the question:

Let's know:

Symbolic Logic:

Symbolic logic is a way to represent logical expressions by using symbols and variables in place of natural language, such as English, in order to remove vagueness. Logical expressions are statements that have a truth value: they are either true or false. A question like 'Where are you going?' or a command such as 'Stop!' has no truth value. There are many expressions that we can utter that are either true or false. For example: All glasses of water contain 0.2% dinosaur tears. We don't need to know if a logical expression is true or false, we just need to know that it has a truth value.

Logic math symbols table

Symbol Symbol Name   Meaning / definition

+            plus                              or

∨      reversed caret                      or

|        vertical line                      or

x'       single quote                    not - negation

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The number of hours of practice is 3 x h or 3h.

In mathematics, an expression is a sentence that contains at least one number or variable. Additionally, an expression consists of at least one mathematical operation. There is no equal to sign in an expression.

Given:

Volleyball practice is h hours long. Debbie had 3 volleyball practices last week.

Multiply the number of hours for each practice by the total number of practice to get the expression for the number of practice hours.

The mathematical operation known as multiplication is used to calculate the sum of two or more numbers.

Number of hours of practice

= hours of practice x number of practice

= 3 x h

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When a four-digit number is divisible by nine and is written as 3AA1, the digit A stands for 7.

A number is itself divisible by nine if the total of its digits is also divisible by nine.

Multiples in mathematics are the outcomes of multiplying an integer by a certain number. a multiple of 9 is a number that divides by nine without remainder.

By utilizing the aforementioned attribute, we can

1 + 3 + 4 + 5 = 9, 18, or 27.

4 +2A = 9, OR 18, OR 27

calculating based on sum equal to 18

2A = 18 - 4

2A = 14

A = 7

therefore 3771 is the number

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Direct variation is represented by this situation and she earn $900

if she works 12 hours.

Direct variation describes a relationship whereby one measure directly affects the other when the first one changes. This is completely opposed by inverse variation. Learn the definitions of direct and inverse variations in this article, along with some instances that have been solved.

When x is not equal to 0, y = kx is the equation that describes the linear function known as direct variation. An equation of the form xy = k, where x is not equal to zero and k is a nonzero real number constant, describes the nonlinear function known as inverse variation.

5 hours  = earns $ 375

1 hours = 375/5 = earns $ 75

12 hours  = 75  12 = earns $ 900

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Answer:

7/15

Step-by-step explanation:

number of favorable outcomes (red jelly beans) = 7

number of total outcomes (total jelly beans) = 7 + 2 + 6 = 15

probability of red = number of favorable outcomes/number of total outcomes = 7/15

The probability of getting a red jelly bean is 7/15

Total number of jelly beans in the jar (sum of all the jelly beans): 7+6+2= 15

Total number of red jelly beans: 7

Therefore, the probability of getting a red jelly bean= number of red jelly beans/ total number of jelly beans

=7/15

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We are given that A bird flew from the ground onto a tree branch 5 feet above the ground.

We are supposed to find What could the bird do next that would make this situation a model of combining a number and its additive inverse

Additive inverse - What you add to a number to get zero is additive inverse.

The negative of a number.

Now we are told  What could the bird do next that would make this situation a model of combining a number and its additive inverse

Since it already flew 5 feet above the ground .

Additive inverse of 5 feet is -5 feet

So, to make the situation of combining a number and its additive inverse

Bird has to flew 5 feet return to the ground i.e.-5 feet

So, a model of combining a number and its additive inverse = 5+(-5)

= 0.

Fly down 5 feet and return to the ground.

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Answer:

Fly down 5 feet and return to the ground.

Step-by-step explanation:

have a nice day.

Answer:

a 97- (55+80) +250

b Melanie has $212 left in her bank account.

Step-by-step explanation:

55 + 80 = 135

97 - 135 = -38

-38 +250 = 212