The sun is shining on a house and fence. The roof of the house is 16 feet from the ground and makes a shadow 24 feet long. The fence is 4 feet tall. How long is the fence's shadow?

Answers

Answer 1

The length of the shadow of fence will be equal to 6 feet.

Proportionality may be defined as the term which can be used to describe or denote a relationship between two entities which are always in the same ratio. For example, the number of bananas is proportional to the number of trees with the proportionality being average number of bananas per number of trees. Here, we are given the height of house = 16 feet and length of its shadow = 24 feet and also the height of fence = 4 feet. Since, both house and fence lie in the same area they both are proportional. Let the length of shadow be x. Since, they are proportional

16/24 = 4/x

2/3 = 4/x

=> x = 12/2

=> x = 6 feet.

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Related Questions

Please help me with this question

Answers

Notice from the graph that data are mostly to the right.

Answer: Option C The distribution is tailed.

In a standard normal distribution, the range of values of z is from _____.

Answers

In a standard normal distribution, the range of values of z is from: D. d. -∞ to ∞.

What is a z-score?

A z-score is also known as a standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

What is a normal distribution?

A normal distribution is also referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which shows that all data near the mean have a higher frequency than the data that are far from the mean.

In conclusion, the range of values of z in a standard normal distribution are all real numbers which typically ranges from negative infinity (-∞) to positive infinity (∞).

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Complete Question:

In a standard normal distribution, the range of values of z is from ______.

a. -3.09 to 3.09

b. -1 to 1

c. 0 to 1

d. -∞ to ∞

The ratio of the area between a small square of land and a large squareof land is 3: 7. Given that the total area of the two squares of land is4,000 m2, find the area of each square of land.

Answers

Given:

The ratio of the area between a small square of land and a large square

of land is 3: 7.

Total area of the two squares of land (in sq. meter) is 4000.

Required:

The area of each square of land.

Answer:

We have the ratio of the area between a small square of land and a large square of land is 3: 7.

Let

[tex]x^[/tex]

be the area of the square of land.

Then their ratio is given by,

[tex]3x^:7x^[/tex]

Also given that the total area of the two squares of land (in sq.meter) is

4,000.

The area of

Therefore,

[tex]\begin{gathered} 3x^+7x^=4000 \\ \Rightarrow10x^=4000 \\ \Rightarrow x^=400 \\ \end{gathered}[/tex]

Therefore,the area of small square (in sq. meter) is,

[tex]3x=3(400)=1200[/tex]

and the area of large square (in sq. meter) is,

[tex]7x=7(400)=2800[/tex]

Final Answer:

The area of small and large square respectively (in sq. meter) is,1200 and 2800.

please show all work

Answers

The point that lies on the graph y = tanx is ([tex]\frac{4\pi }{3},\sqrt{3}[/tex]),([tex]\frac{\pi }{3},\sqrt{3}[/tex])

What is coordinate plane ?

Two number lines combine to form a two-dimensional surface known as a coordinate plane. It is created when the origin, a point where the X- and Y-axes coincide, is crossed by a horizontal line. Points are located using the numbers on a coordinate grid. You can graph points, lines, and many other things using a coordinate plane. It serves as a map and provides clear directions between two points.The following is a definition of a coordinate plane: The intersection of the Y-axis, a vertical line, and the X-axis, a horizontal line, creates a coordinate plane, also referred to as a rectangular coordinate plane grid.

The point that lies on the graph y = tanx is ([tex]\frac{4\pi }{3},\sqrt{3}[/tex]),([tex]\frac{\pi }{3},\sqrt{3}[/tex])

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18 is 50% of what????????

Answers

Let the unknown value be x.

18 is 50% of ________n can also be written as;

18 = 50% of x

of means multiplication;

18 = 50% * x

18 = 50/100 * x

18 = 50x/100

cross multiply

18 * 100 = 50x

1800 = 50x

Divide both sides by 50

1800/50 = 50x/50

180/5 = x

x = 180/5

x = 36

Hence 18 is 50% of 36

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=
O DECIMALS, PROPORTIONS, PERCENTS
Simplifying a ratio of whole numbers: Problem type 1
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
40 L: 72 L

Answers

Answer:

5/9

Step-by-step explanation:

You want the reduced fraction equivalent to the ratio 40L : 72L.

Reduced ratio

A ratio is reduced by removing the greatest common factor from all parts of the ratio. Here, that factor is 8L.

40L : 72L = (8L)(5) : (8L)(9) = 5 : 9 = 5/9

The ratio is 5/9.

Additional comment

The greatest common factor can be found several ways. The easiest is for you to make use of your knowledge of multiplication tables:

40 = 5·8

72 = 9·8

8 is a common factor. Since 5 and 9 have no common factors, 8 is the greatest common factor of 40 and 72.

Volume is 10x3 + 67x2 + 30x − 72, length is 5x − 4, width is 2x + 3

Answers

Answer:

height = x + 6

Step-by-step explanation:

Volume = length x width x height

V = 10x³ + 67x² + 30x − 72

length = 5x - 4 and width = 2x + 3

So length x width = (5x - 4 ) x (2x + 3)

Using the FOIL method:

= (5x)(2x) + (5x)(3) + (-4)(2x) + (-4)(3)

= 10x² + 15x - 8x - 12

= 10x² + 7x -12

So to find height, divide Volume by (length x width)

10x³ + 67x² + 30x − 72 ÷ 10x² + 7x -12

Use polynomial long division. See image ( I did the best I could to capture the process)

The answer is x + 6

To verify
Multiply (5x-4) (2x + 3) (x + 6) = 10x³ + 67x² + 30x − 72

7. Jill was 80th in a class of 200, whereas Nathan, who is in the same class, has a percentile rank of 80. Which student has the higher standing in the class?

Answers

The student that has the higher standing in the class is Jill

How to determine the student that has the higher standing in the class?

The given parameters are:

Number of students = 200

Jill's position =80th

Nathan's position = Percentile rank of 80

The above means that

Nathan's position = 80 percentage of the number of students in the class

Substitute the known values in the above equation

So, we have the following equation

Nathan's position = 80 percentage of 200

Rewrite as

Nathan's position = 80 percentage * 200

Express as percentage

Nathan's position = 80% * 200

Express 80% as decimal

Nathan's position = 0.80 * 200

Evaluate the product

Nathan's position = 160

So, we have

Jill's position =80th

Nathan's position = 160th

By comparing the positions, 80th is greater than 160th

Hence, Jill has the higher standing in the class

Answers

In order to rationalize the denominator of the fraction, we need to multiply the fraction by the conjugate of the expression in the denominator.

The conjugate is the same expression but with the signal between the numbers changed.

So we have:

[tex]\frac{4}{3+\sqrt[]{7}}=\frac{4}{3+\sqrt[]{7}}\cdot\frac{3-\sqrt[]{7}}{3-\sqrt[]{7}}=\frac{4(3-\sqrt[]{7})}{3^2-(\sqrt[]{7})^2}=\frac{12-4\sqrt[]{7}}{9-7}=\frac{12-4\sqrt[]{7}}{2}[/tex]

So the new denominator of the fraction is 2, therefore the correct option is D.

List the first 6 common multiples of 8
List the first 6 common multiples of 12

Answers

The first six common multiples of 6 and 8 are :

24,48,72, 96, 120 and 144.

The first six common multiples of 12 and 18 are :

24, 36, 72, 108, 144, 216.

In order to resolve this, we shall use the multiples idea.

(A) The two numbers given are 6 and 8.

Six is the first multiple of which there are the following: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, and 144.

multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, and 144.

Therefore, common multiples are: 24, 48, 72, 96, 120 and 144.

(B) The two numbers given are 18 and 12.

The first few multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, and 240.

Similarly, the multiples of 18 are: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, and 270.

Therefore, common multiples are: 24, 36, 72, 108, 144, 216.

Hence we get the required common multiples.

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The length of a ruler is 12 inches. There are approximately 25.4 millimeters in 1 inch.

Answers

The length of the ruler is approximately 304.8 millimeters .

Length is used to measure distance.

According to the International System of Quantities, length has the dimension of distance. In most measurement systems, length is represented by a base unit from which all other units are derived. The International System of Units (SI) system's fundamental unit of length is the metre.The longest dimension of an object is typically understood to be what is meant by length.However, this isn't always the case depending on the object's position.The length of a fixed object is referred to by a number of names, including height, also referred to as vertical length or vertical extension, and width, breadth, or depth.

Given that there are approximately 25.4 millimeters in 1 inch.

Therefore the length of the ruler = 25.4 × 12 = 304.8 mm

Hence the length of the ruler is approximately 304.8 millimeters .

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Answer:

304.8

Step-by-step explanation:

12*25.4 = 304.8

A contractor bought 8.2 ft2 of sheet metal. He has used 3.7 ft² so far and has $90 worth of sheet metal remaining. The equation 8.2x-3.7x = 90 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?

Answers

By solving the equation, we get the cost of sheet metal =$20 per sq. feet

What is an equation?

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. Solving an equation with variables entails finding which variables' values make the equality true. The variables for which the equation must be solved are also known as unknowns, and the values of the unknowns that fulfill the equality are known as equation solutions. Identity equations and conditional equations are the two types of equations.

Given equation 8.2x-3.7x = 90

or, 4.5x = 90

or, x = 90/4.5 = 20

Hence, the cost of sheet metal is $20 per sq. feet

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Perform the given operations on the functions
21) f(x)=x² + 3x, g(x) = 2x + 2,
A. (f+g)(x)
B. (f- g)(x)

Answers

Answer:

see explanation

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= x² + 3x + 2x + 2 ← collect like terms

= x² + 5x + 2

(f - g)(x)

= x² + 3x - (2x + 2)

= x² + 3x - 2x - 2 ← collect like terms

= x² + x - 2

convert 0.43 to a percent

Answers

0.43 convert to a percent is 0.00432

Answer:

43%

Step-by-step explanation:

To convert a decimal to a percent, you have to move the decimal over 2 times to the right.

how could you use a graph of a proportional relationship to find any ratio in the the proportional relationship why does this work?

Answers

It should be noted that when the graph of a relationship is a line that passes through the origin, then it is proportional.

How to illustrate the information?

A connection is proportional if its graph is a line that goes through the origin. The ratio is not proportionate if it is not a line or ray that doesn't accomplish this. K = y/x is the equation for the proportionality constant. The equation for the slope of a straight line with respect to the origin is the same as this.

A relationship is proportionate if its graph is a line or ray that passes through the origin. It is not proportionate if the line or ray does not go through the origin. Additionally, something is not proportionate if it is not linear.

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Where do you find a vertical shift in the exponential parent function?
What happens when (x-4) is in the exponent?
What happens when (x+9) is in the exponent?
Where do you find a horizontal shift in the exponential parent function?
What happens when there is a +7 at the end of the exponential parent function?
What happens when there is a -6 at the end of the exponential parent function?

Answers

For the given expressions we will have:

y = exp(x - 4) →we have a shift of 4 units to the right.

y = exp (x +9) → we have a shift of 9 units to the left.

y = exp(x) + 7 → we have a shift of 7 units up.

y = exp(x) - 6 → we have a shift of 6 units down.

How to work with vertical and horizontal shifts?

Remember that the shifts work as follows.

For a function f(x), we define a vertical shift of N units as:

g(x) = f(x) + N

If N > 0, the shift is upwards.If N < 0, the shift is downwards.

For a function f(x), we define a horizontal shift of N units as:

g(x) = f(x + N)

If N > 0, the shift is to the left.If N < 0, the shift is to the right.

Then, if we have:

exp(x - 4) we have a shift of 4 units to the right.

exp (x +9) we have a shift of 9 units to the left.

exp(x) + 7 we have a shift of 7 units up.

exp(x) - 6 we have a shift of 6 units down.

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Write an equation in standard form for the line that passes through the given points.
(5,0) and (0,3)
The equation of the line in standard form is
(Type your answer in standard form.)

Answers

3x + 5y = 15 is the equation of the line in standard form that passes through the point (5,0) and (0,3).

What is the equation of line that passes through the given points?

The formula for equation of line is expressed as;

y = mx + b

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

Given the data in the question;

Point 1 ( 5,0 )

x₁ = 5y₁ = 0

Point 2 ( 0,3 )

x₂ = 0y₂ = 3

First, we determine the slope of the line.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 3 - 0 )/( 0 - 5 )

Slope m = ( 3 )/( -5 )

Slope m = -3/5

Now, we plug the slope and coordinates of one the point into the equation of line to determine the y-intercept b.

y = mx + b

0 = (-3/5)5 + b

Solve for b

0 = -15/5 + b

0 = -3 + b

b = 3

Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.

y = mx + b

y = (-3/5)x + 3

Convert to standard form; Ax + Bx = C

Multiply each term by 5

y = (-3/5)x + 3

5y = 5(-3/5)x + 5(3)

5y = -3x + 15

Reorder the equation

3x + 5y = 15

Therefore, the equation of the line is in standard form is 3x + 5y = 15.

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Simplify the fraction 112 144 as much as possible.

Answers

Answer:

7/9

Step-by-step explanation:

Answer:

7/9

Step-by-step explanation:

I took the quiz

A zookeeper is 6 14 feet tall. A young giraffe in his care is 93/8 feet tall. How many times as tall as the zookeeper is the giraffe?

Answers

[tex]\begin{gathered} \Rightarrow6\frac{1}{4}=\frac{25}{4}\text{ is the height of the zook}eeper \\ \Rightarrow9\frac{3}{8}=\frac{75}{8}\text{ is the height of the giraffe} \\ \Rightarrow\frac{\frac{75}{8}}{\frac{25}{4}}=\frac{75}{8}\times\frac{4}{25}=\frac{3}{2}=1.5 \\ \text{zookeper is 1.5 higher than the giraffe. } \end{gathered}[/tex]

someone help please, dk what to do

Answers

Step-by-step explanation:

equation format: y = mx + b where m is slope and b is the y intercept.

From the points given we find that it is a horizontal line, which means slope or m = 0. So we know so far:

y = 0x + b or y = b

The y-intercept occurs where x = 0. This occurs at y = -7. So the equation for these two points:

EQUATION: y = -7

(Plotted graph attached)

Which of the following ordered pairs is either the
x- or y-intercept of the function 3x + 2y = -6?

A. (-3,0)
B.(-2,0)
C.(0,2)
D.(0,3)

Answers

B is the Y-intrercect

3.5 divided by 85
answers:
at least 500/ at least 50/ at least 20/ at least 200
Ive looked up answers to this question in iready but everyone says the answer is 24?

Answers

The value of 3.5 divided by 85 will be 0.4118.

What is division?

Division is one of the four basic arithmetic operations, or the process by which two numbers are added together to produce a new number. Multiplication, addition, and subtraction make up the remaining operations.

Division's opposite is multiplication. Dividend Divisor = Quotient + Remainder is a formula for calculating the division of two numbers.

The dividend in this situation refers to the number that is being divided. The divisor is the number that divides the number (dividend) into equal parts.

In this case, 3.5 ÷ 85 = 0.4118. This can be computed through the use of a calculator.

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Determine whether the mean, median, or mode would be the best choice to describe the center of the following set of data.

An elementary school has 92 first graders. Because the first graders are all about the same age, they have heights that are pretty similar to one another.

Would it be best to use the mean, median, or mode to describe the height of the first-graders?

Group of answer choices

Mean

Median

Mo

Answers

First graders in an elementary school number 92. We use mode.

Given that,

Determine which statistic would be most appropriate to characterize the middle of the next set of data: the mean, median, or mode.

First graders in an elementary school number 92. The first graders' heights are fairly similar to one another because they are all roughly the same age.

We have to find which statistic—the mean, median, or mode—does the first-graders' height best represent.

First graders in an elementary school number 92.

Depending on which their birthday walls, the first graders might be six, seven and eight on the last day of the second year.

Therefore, We use mode.

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What are the coordinates of a point 4/5 of the way B to A

A(3,-4)
B(13,11)

Answers

[tex]\textit{internal division of a segment using a fraction}\\\\ B(\stackrel{x_1}{13}~,~\stackrel{y_1}{11})\qquad A(\stackrel{x_2}{3}~,~\stackrel{y_2}{-4})~\hspace{8em} \frac{4}{5}\textit{ of the way from B to A} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_2}{3}-\stackrel{x_1}{13}~~,~~ \stackrel{y_2}{-4}-\stackrel{y_1}{11})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment BA}}}{\left( -10 ~~,~~ -15 \right)} \\\\[-0.35em] ~\dotfill\\\\ \left( \stackrel{x_1}{13}~~+~~\frac{4}{5}(-10)~~,~~\stackrel{y_1}{11}~~+~~\frac{4}{5}(-15) \right) \\\\\\ (13~~ - ~~8~~,~~11~~ - ~~12)\implies {\Large \begin{array}{llll} (5~~,~~-1) \end{array}}[/tex]

Shauna calculated the net sales for her company using the following figures: Gross sales = $72,900 Sales discounts = $2,450 Purchase returns and allowances = $3,750 Sales returns and allowances = $2,550 The net sales of Shauna's company are __________.

Answers

The net sales of Shauna's company when she calculated the sales for her company using the figures is $66700.

What are net sales?

The total of a company's net sales is its gross sales less any returns, allowances, and discounts. Externally, net sales calculations are not always obvious. They can frequently be taken into account when calculating top-line revenues that are shown on the income statement.

The total number of units sold is multiplied by the price per unit for the purpose of calculating gross sales. The term "returns" or "sales returns" refers to products that customers have sent back in exchange for reimbursement.

The nets sales based on the information given will be:

Gross sales = $72900

Less: Retuned sales = $3750

Less Discount = $2450

Net sales = $66700

Therefore, the net sale is $66700.

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Estimate 5.209 + 2.667 by rounding to the nearest whole number.

Answers

Answer:

I'm pretty sure it would be 8 though forgive me if I'm wrong

solve for x. 7/13=x/48

Answers

Answer:

25.7

Step-by-step explanation:

7/13=x/48. By cross multiplication 13 x=326 = 25.7

using the path method for multivariable limits, demonstrate that the limit doesn't exist:
[tex]lim_{(x,y) \to (1,1)} \frac{x y - x - y + 1}{x^2 + y^2 - 2 x - 2 y + 2}[/tex]

Answers

Demonstrating that the limit doesn't exist

What is Limits?

The value that a function approaches when the input approaches a certain value is known as a limit. Calculus and mathematical analysis are not possible without limits, which are used to define continuity, derivatives, and integrals.

The limit exists only if the value of the limit along every direction that leads to (1,1) is same.

So by calculating,

lim xy -x-y + 1 / x^2 + y^2 - 2x - 2y + 2

x->1

calculating the limit along the line x = 1

Similarly,

lim xy -x-y + 1 / x^2 + y^2 - 2x - 2y + 2

x->1

calculating the limit along the line y = 1

And the last limit you calculated is along line y=x.

To answer your question, the calculation of the limit along y=1 would not have been necessary. It is sufficient to demonstrate the absence of a limit by giving just two cases in which it appears to vary along several directions.

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Use the square root property to solve the equation.(x + 8)² = 2Select one:O A. (-8+√√2)OB. √2-√√8O C. (√2+8,-√2+8}O D. (-8± √2)

Answers

[tex]\begin{gathered} (x+8)^2=2 \\ \sqrt{(x+8)^2}=\pm\sqrt{2} \\ x+8=\pm\sqrt{2} \\ x=-8\pm\sqrt{2} \end{gathered}[/tex]

Answer: D

Please answer question 5 and 6.

5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).

6.Graph the function

Answers

The definition of the functions implies that the value of x if f(x) = g(x) is 3

The solution for the value of x

The equations of the functions are given as

f(x) = -2x + 4

g(x) = 2x - 8

This means that, we have the following equation

f(x) = g(x)

Substitute the known values in the above equation

So, we have the following equation

-2x + 4 = 2x - 8

Collect the like terms in the above equation

So, we have

2x + 2x = 8 + 4

Evaluate the like terms in the above equation

So, we have

4x = 12

Divide both sides by 4

x = 3

Hence, the value of x such that the equations are equal is 3

The graph of the functions

The graph of the functions can be plotted using a graphing tool

See attachment for the graph of the functions