1)
4 ft
5.4 ft
What is the area

The required  ST² = TW × RT has been proven for the triangle RST where SW is perpendicular from vertex S to RT.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
For the triangle RST where SW is perpendicular from vertex S to RT

Rewrite the equation,
ST² = TW × RT
ST/TW = RT/ST

It implies triangle SWT is similar to triangle RST,

Where,

∠S = ∠W and ∠T = ∠T

So triangle SWT is similar to triangle RST, by AA postulate of similarity.

If triangles are similar,
ST/TW = RT/ST   [became valid statement]

ST² = TW × RT

Thus, ST² = TW × RT hence proved.

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we can estimate that 762 adults in Eric's sample use their computer every day.

Each sample has an equal chance of being chosen as part of the sampling procedure known as random sampling. A randomly selected sample is intended to be a fair reflection of the entire population.

We can use the proportion from the article to estimate the number of adults who use their computer every day in Eric's sample.

The proportion of adults who use their computer every day from the article is:

15/25 = 0.6

This means that 60% of adults use their computer every day.

To estimate the number of adults who use their computer every day in Eric's sample, we can multiply the proportion by the sample size:

0.6 x 1,270 = 762

So we can estimate that 762 adults in Eric's sample use their computer every day.

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Answer:

Step-by-step explanation:

5 x 10^3 x 9 x 10^7 can be written as follows in standard form:

5 x 10^3 = 5 x 10^3 x 1 = 5 x 10^3

9 x 10^7 = 9 x 10^7 x 1 = 9 x 10^7

So,

5 x 10^3 x 9 x 10^7 = (5 x 10^3) x (9 x 10^7) = 45 x 10^(3 + 7) = 45 x 10^10 = 4.5 x 10^11

In standard form, the coefficient (45) is written as a number between 1 and 10, and the exponent (10) gives the number of places the decimal point must be moved. So, 4.5 x 10^11 is written in standard form as 4.5 x 10^11.

Answer:

Step-by-step explanation:

45*10^10=4.5*10^11

The rate of decrease is 89%.

The function shows exponential decay.

An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time.

The exponential decay function:

Aₙ = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.

Given:

An exponential function,

y = 8600(0.11)ˣ.

When we put x = 0,

we get,

y = 8600

And when we put x = 1

we get,

y = 946

So, 1 - r = 0.11

Rate of decrease, r = 0.89

Therefore, the function shows exponential decay.

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The length of edging material needed to enclose the garden is approximately 37.68 feet to the nearest hundredth.

The circumference of a circle is the distance around its outer boundary, also known as its perimeter. It is one of the fundamental properties of a circle, along with its radius and diameter.

Since the garden is circular, its widest point is its diameter, which is twice the radius. Therefore, the widest point of the garden is 12 feet across.

To find the length of the edging material needed to enclose the garden, we need to find the circumference of the circle. The formula for the circumference of a circle is C = 2πr, where r is the radius and π (pi) is approximately 3.14. Substituting,  r = 6 into the formula, we get:

C = 2π(6)

C = 12π

To approximate this value using 3.14, we can substitute π = 3.14 and get:

C ≈ 12(3.14)

C ≈ 37.68

Therefore, the length of edging material needed to enclose the garden is approximately 37.68 feet to the nearest hundredth.

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Answer:

x = -91 8/35

Step-by-step explanation:

Challenging, but lets take it step by step.  We have two sets each  of complex fractions being multiplied, and then added.  As per PEDMAS, do the multiplication first and then add. [I changed the -71/7 as per your note in the comment section.]

[-7 1/7 * (3 2/5)]    +       [6 3/5*(-7 1/7)]     =  x

Convert the two numbers into fractions.  Eg., 7 1/7 becomes 50/7 and 3 2/5 becomes 17/5.  6 3/5 becomes 33/5 and 7 1/7 becomes 50/7.

[-50/7 * (17/5)]    +       [33/5*(-50/7)]     =  x

Now multiply the numerators and denominators.

[-850/35]    +       [-2343/35]     =  x

Now we can add the two fractions since they have the same denominator.

-(3193/35)  = x

x = -91 8/35

The value x is used often in algebra to specify an unknown variable.

Variables are often alphabets or letters used to represent an unknown number or value.

It is called a variable because it may change it's value according to the value of the others.

x is a variable which is commonly used to solve problems in algebra.

It represents the unknown variable.

We have to do certain operations to find the value of y.

Consider the equation, x + 5 = 13.

Here x is a unknown variable.

We can find the value of x as x = 13 - 5 = 8

Hence x is commonly used to represent an unknown variable.

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The boat will coast a total distance of approximately 40/ln(0.5)/(-10) ft.

To solve this problem, we can use the concept of exponential decay. If we let v(t) be the velocity of the boat as a function of time t, then we can write the differential equation that describes its motion as:

dv/dt = -kv(t)

where k is the proportionality constant between resistance and velocity. We can separate variables and integrate both sides to get the velocity as a function of time:

∫(dv/dt) = -k∫(v(t))dt

v(t) = Ce^(-kt)

where C is an arbitrary constant of integration. We can use the initial condition v(0) = 40 ft/s to find C:

C = 40

So the velocity of the boat as a function of time is:

v(t) = 40e^(-kt)

We can use the condition v(10) = 20 ft/s to solve for k:

20 = 40e^(-10k)

Taking the natural logarithm of both sides:

ln(0.5) = -10k

k = ln(0.5)/(-10)

Next, we can use the velocity as a function of time to find the distance traveled by the boat:

∫(v(t))dt = ∫(40e^(-kt))dt = 40/k * (1 - e^(-kt))

Let's call the total distance traveled by the boat "D". Then we can write:

D = 40/k * (1 - e^(-kt))

We can plug in the value of k we found earlier and evaluate the expression at t = ∞:

D = 40/ln(0.5)/(-10) * (1 - e^(-∞)) = 40/ln(0.5)/(-10)

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The value of 'x' in similar triangles is 6.9 units.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know, A line segment parallel to one side of the triangle divides the other two sides in the ratio of their respective lengths.

Therefore, The ratio can be formed as,

13/5 = 18/x.

13x = 90.

x = 6.9 units.

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Answer:

Step-by-step explanation:

Change in demand refers to a shift in the entire demand curve, either to the right or to the left, resulting in a higher or lower demand for a good or service, respectively. It can be caused by a variety of factors, such as changes in consumer preferences, changes in the price of related goods, changes in income, changes in the population, or changes in consumer expectations.

Change in quantity demanded, on the other hand, refers to a movement along the demand curve, resulting from a change in the price of a good or service, without any change in the underlying demand for the good or service. For example, if the price of a good decreases, the quantity demanded of that good will increase, and vice versa. This relationship between price and quantity demanded is known as the law of demand.

In summary, change in demand represents a shift in the demand curve, while change in quantity demanded represents a movement along the demand curve.

Answer:

the area of the circle is approximately

201.06 ft^2

The solution of the equations 3y - 2x = 7 and y = 3x + 7 will be (-2, 1). Then the correct option is B.

The possible value of the variables that satisfy the equation which is known as the solution of the equation.

The equations are given below.

-2x + 3y = 7            ...1

y = 3x + 7               ...2

From equations 1 and 2, then we have

- 2x + 3(3x + 7) = 7

- 2x + 9x + 21 = 7

7x = - 14

x = - 2

Then the value of 'y' is given as,

y = 3(-2) + 7

y = - 6 + 7

y = 1

The solution of the equations 3y - 2x = 7 and y = 3x + 7 will be (-2, 1). Then the correct option is B.

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To find multiple of 3 and 5 we need to add 15 to the previous multiple of 15.

To find multiples of 3 and 5, you can use the following steps:

1. Start with the number 3 and 5, respectively.
2. Add 3 or 5 to the previous number to get the next multiple. For example, 3 + 3 = 6, 6 + 3 = 9, and so on. Similarly, 5 +    5 = 10, 10 + 5 = 15, and so on.
3. Repeat step 2 until you have found the desired number of multiples.

Here are the first 10 multiples of 3 and 5:

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Note that some numbers, such as 15 and 30, are multiples of both 3 and 5. These are called common multiples.

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Answer:

We know that half of the choir members are women, which means:

Number of women = 80/2 = 40

We also know that the number of men is one-quarter of the number of women, which means:

Number of men = 40/4 = 10

Now, we're given that the ratio of children to men in the choir is n:1. Let's call the number of children in the choir "c".

So, we have:

c : 10 = n : 1

We can cross-multiply to get:

c = 10n

Since we know that the total number of people in the choir is 80, we can set up another equation:

40 (women) + 10 (men) + c (children) = 80

Substituting c = 10n, we get:

40 + 10 + 10n = 80

Simplifying the left side, we get:

50 + 10n = 80

Subtracting 50 from both sides, we get:

10n = 30

Dividing both sides by 10, we get:

n = 3

Therefore, the value of n is 3

As the x-values go to positive infinity, the function's values go to positive infinity. Then the correct option is D.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The graph of the function is given below.

From the graph, we can conclude that the value of the graph is always positive. So, the function will be an exponential function.

From the graph, as the x-values go to positive infinity, the function's values go to positive infinity. Then the correct option is D.

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The fraction of nine times two thirds is 18/3 (option D)

What is fraction ?

A fraction is a way of representing a part of a whole or a ratio between two numbers. It consists of two numbers written one above the other and separated by a horizontal line called a fraction bar.

The number above the fraction bar is called the numerator, and it represents the part of the whole or the quantity being considered. The number below the fraction bar is called the denominator, and it represents the total number of equal parts into which the whole has been divided.

Given by the question:

Nine times two thirds can be written as:

9 × 2/3 = 18/3=6

Simplifying this fraction, we can divide both the numerator and denominator by their greatest common factor of 3, which gives:

18/3
so the correct option is D.

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Yes multiplying the matrices shows that it is inverse matrix

The inverse of a matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix.

Using multiplication of matrices product is sort as follows

Row 1 column 1

= 5 * - 5 + 2 * 13 = -25 + 26 = 1

Row 1 column 2

= 5 * -2 + 2 * 5 = -10 + 10 = 0

Row 2 column 1

= 13 * -5 + 5 * 13 = -65 + 65 = 0

Row 2 column 2

= 13 * 2 + 5 * -5 = 26 + -25 = 1

The identity matrix is

Row 1 column 1    Row 1 column 2           1      0

Row 2 column 1   Row 2 column 2           0      1

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Equations and inequalities based on numbers and algebra are effective tools for tackling both mathematical and real-world issues. The general steps you can take to use equations and inequalities to tackle such issues are listed below:

What is Linear Inequality?

In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

Solution:

Equations and inequalities based on numbers and algebra are effective tools for tackling both mathematical and real-world issues. The general steps you can take to use equations and inequalities to tackle such issues are listed below:

1. Consider the issue carefully and note what you are looking for. You can use this to decide which variables to include in your equations.

2. The equations that describe the issue should be written down. This could entail writing expressions that relate the variables or utilizing formulas.

3. Use algebraic strategies to solve the equations, such as grouping like terms, multiplying or dividing both sides of the equation by a constant, or focusing only on one side of the problem's variables.

4. Verify your answers to make sure they make sense in light of the issue at hand.

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Equations and inequalities based on numbers and algebra are effective tools for tackling both mathematical and real-world issues. The general steps you can take to use equations and inequalities to tackle such issues are listed below:

In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

According to question:

Equations and inequalities based on numbers and algebra are effective tools for tackling both mathematical and real-world issues. The general steps you can take to use equations and inequalities to tackle such issues are listed below:

1. Consider the issue carefully and note what you are looking for. You can use this to decide which variables to include in your equations.

2. The equations that describe the issue should be written down. This could entail writing expressions that relate the variables or utilizing formulas.

3. Use algebraic strategies to solve the equations, such as grouping like terms, multiplying or dividing both sides of the equation by a constant, or focusing only on one side of the problem's variables.

4. Verify your answers to make sure they make sense in light of the issue at hand.

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The surface area of the given figure is 200 yd².

The area of a three dimensional object on it's outer surface is called the surface area of the object.

Representing the figure as three dimensional, this consists of two triangular bases and three rectangular faces.

Area of triangle = [tex]\frac{1}{2}[/tex] × base × height

                          = [tex]\frac{1}{2}[/tex] × 6 × 4

                          = 12 yards²

Area of two triangular faces = 12 × 2 = 24 yd²

Of the three rectangular faces, two of them have a length of 11 yd and width of 5 yd.

Area of a rectangle = Length × Width

Area of two rectangular faces = 2 × Length × Width

                                                  = 2 × 11 × 5

                                                  = 110 yd²

Area of the third rectangular face = 11 × 6 = 66 yd²

Total surface area = 24 yd² + 110 yd² + 66 yd²

                              = 200 yd²

Hence the total surface area is 200 yd².

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Answer:

70

The top line should add up to 180 and both sides other than x are 55 so since 55+55=110  180-110=70

Answer: 108 degrees.

Step-by-step explanation:

I think this is how you solve it:

A circle has a total of 360 degrees.

Having 5 equally placed sensors with a certain detection angle means that the sensors form a regular pentagon.

Finding the measure of the interior angles of a regular pentagon can be found using the formula

(180(n-2))/n, with n being the number of vertices of the polygon.

180(5-2)/5 ; 180(3)/5 ; 540/5 = 108

I think this means the detection angle is 108 degrees. Hope this helps!

If you get it wrong I'm terribly sorry T-T

No, not all fixed costs are considered sunk costs. Sunk costs are costs that have already been incurred and cannot be recovered, regardless of any future actions.

Fixed costs, on the other hand, are costs that do not vary with changes in output or sales, such as rent or salaries. While some fixed costs may be sunk costs (such as a non-refundable deposit for a lease), other fixed costs may still be recoverable or avoidable with different decisions, and therefore are not considered sunk costs. Sunk costs are only relevant in decision making to the extent that they cannot be recovered and should not be factored into future decisions.

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The transformations from the parent cube root function to generate function g(x) are given as follows:

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

For this problem, the transformations are given as follows:

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Using the relationship between speed, distance and time, Jen's average walking speed was approximately 1.75 meters per second over the 20-second window.

To find Jen's average walking speed, we need to first find the total distance that she walked in 20 seconds. We can do this by multiplying the number of strides she took by the distance of each stride, which is given as 140 cm.

From the graph provided, we can see that Jen took 25 strides in the 20-second window. Therefore, the total distance she walked is:

distance = number of strides * distance per stride = 25 * 140 cm = 3500 cm

To convert this to meters, we divide by 100:

distance = 3500 cm / 100 = 35 meters

Finally, we can find Jen's average walking speed by dividing the total distance by the time it took her to walk it, which is 20 seconds:

average speed = distance / time = 35 meters / 20 seconds ≈ 1.75 meters per second

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Answer: 1.33 m/s

Step-by-step explanation:

We need meters per second, not centimeters per second, so convert the stride of 140 cm to meters:

140 cm times 1 m/100 cm = 1.4 meters.

The number of pulses going above the dashed line for the 3 g threshold to

count as strides are 19. Therefore, a total assumed distance of $19 times 1.4 meters  is covered in 20 seconds, making the average speed

19 times 1.4/20 = 19 times 0.07 = 1.33m/s.

Jimbo approximately 5.09 minutes to solve the problem by himself.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The amount of time it takes Jimbo to solve the problem by himself = x.

The amount of time Jimmy takes to solve the problem.

= 8 minutes

The amount of time it takes Jimmy to solve the problem by himself.

= 1/8

Jimbo and Jim Bob together can solve the problem in 6 minutes, so their combined rate of work is 1/6 of the problem per minute.

The amount of time it takes Jim Bon to solve the problem by himself.

= 1/14

Now,

We can make an equation:

1/8 + 1/x + 1/14 = 1/6

We can solve for x to find the amount of time it would take Jimbo to solve the problem by himself.

1/8 + 1/x + 1/14 = 1/6

Multiply both sides by 168x.

We get,

21x + 168 + 12x = 28x

33x = 168

x = 168/33

x = 5.09

Thus,

Jimbo approximately 5.09 minutes to solve the problem.

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Using the distributive property to write the expression, we have:

12+4 = 4(3 + 1)

The distributive property states that a(b + c) = ab + ac, where a, b, and c are any real numbers.

We can use this property to write an expression that is equivalent to 12 + 4 as follows:

12 + 4 = 4(3) + 4 (here, we have factored out 4 from 12 using the distributive property)

         = 4(3 + 1) (we have combined the terms inside the parentheses)

Therefore, 12 + 4 is equivalent to 4(3 + 1).

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Jimmy’s total income is the sum of all the incomes which is $91838.61 .

How to determine Jimmy's income?

You should understand that total income' refers to the sum of certain incomes (in cash and, in some circumstances, in kind) of the statistical unit during a specified reference period .

Now in the given question ,

The given parameters that will help us to determine the income are

wages from accounting job,             $75,937.84;

interest,                                                   $839.40

wages from museum job,                  $14,937.92;

dividends,                                                $123.45.

Therefore Jimmy's total income is the sum of all the incomes

$(75,937.84 + 839.40 + 14,937.92 + 123.45)

Total income = $91838.61

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The value of the wanted limit is:

[tex]\lim_{x \to 0} \frac{1}{4} (f(x))^4 = 64[/tex]

So the correct option is the third one.

Here we know that:

[tex]\lim_{x \to 0} f(x) = 4[/tex]

And we want to find the value of the limit:

[tex]\lim_{x \to 0} \frac{1}{4} (f(x))^4[/tex]

Notice that because neither the fraction nor the power depend on the value of x, we can put the limit inside the parenthesis to get:

[tex]\lim_{x \to 0} \frac{1}{4} (f(x))^4 = \frac{1}{4} (\lim_{x \to 0} f(x))^4[/tex]

And we know that the thing inside the parenthesis is 4, then:

[tex]\frac{1}{4} (\lim_{x \to 0} f(x))^4 = \frac{1}{4} (4)^4 = 4^3 = 64[/tex]

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Answer:

x=10,y= -2).

Step-by-step explanation:

The given system of equations is:

x = 10

3x + 5y = 20

We can use substitution to solve for y. Starting with the first equation:

x = 10

We can substitute the value of x into the second equation:

3x + 5y = 20

3 * 10 + 5y = 20

30 + 5y = 20

5y = 20 - 30

5y = -10

Finally, we can solve for y by dividing both sides of the equation by 5:

y = -10 / 5

y = -2

x=10,y= -2).