Trapezoid W'X'Y'Z' is the image of trapezoid WXYZ
under a dilation through point C.

What scale factor was used in the dilation?

1.) -6/5
2.) -5/6
3.) 5/6
4.) 6/5

Answer:

(read explanation)

Step-by-step explanation:

AJ Manufacturing Company incurred a total of $97,200 in fixed costs and $57,000 in variable costs during its first year of operation.

To calculate the total fixed costs incurred by AJ Manufacturing Company, we need to add the fixed production costs of $54,000 and the fixed selling and administrative costs of $17,200. This gives us a total of $54,000 + $17,200 = $71,200 in fixed costs.

To calculate the total variable costs incurred by AJ Manufacturing Company, we need to add the variable product costs of $43,200 and the variable selling and administrative costs of $13,800. This gives us a total of $43,200 + $13,800 = $57,000 in variable costs.

Thus, the total fixed costs and the total variable costs incurred by AJ Manufacturing Company during its first year of operation are $71,200 and $57,000, respectively. The company generated $176,000 in revenue by selling all of the units it produced, which means that it earned a profit of $176,000 - $71,200 - $57,000 = $47,800 during its first year of operation.

Answer:

12 girls

Step-by-step explanation:

30*(2/5)=12

Answer:

Below in bold.

Step-by-step explanation:

A).  9.9^2 is close to 10^2 = 100

Round 1.79 to 1.8

So an estimate is 1.8 * 100

= 180.

B).  √97.5 / 1.96

( I am assuming that the square root is of 97.5 only).

is approximately equal to √100 / 2

= 10/2

= 5.

The tax charged on Omari's monthly earning of Ksh 24,200 is Ksh 3,340.

To calculate the tax charged on Omari's monthly earning, we need to consider the tax brackets and rates applicable in the specific tax system or country. Since you haven't specified a particular tax system, I will provide a general explanation.

Assuming we have a simplified progressive tax system with three tax brackets:

For the first tax bracket, let's say income up to Ksh 10,000 is taxed at a rate of 10%.

For the second tax bracket, income between Ksh 10,001 and Ksh 20,000 is taxed at a rate of 15%.

For the third tax bracket, income above Ksh 20,000 is taxed at a rate of 20%.

To calculate the tax charged on Omari's monthly earning of Ksh 24,200, we can divide it into the respective tax brackets:

Ksh 10,000 falls in the first tax bracket. So, the tax for this portion is 10% of Ksh 10,000, which is Ksh 1,000.

Ksh 20,000 - Ksh 10,000 = Ksh 10,000 falls in the second tax bracket. The tax for this portion is 15% of Ksh 10,000, which is Ksh 1,500.

The remaining amount, Ksh 24,200 - Ksh 20,000 = Ksh 4,200, falls in the third tax bracket. The tax for this portion is 20% of Ksh 4,200, which is Ksh 840.

Now, we can sum up the taxes for each bracket:

Total Tax = Tax in the first bracket + Tax in the second bracket + Tax in the third bracket

Total Tax = Ksh 1,000 + Ksh 1,500 + Ksh 840

Total Tax = Ksh 3,340

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It should be noted:

Let's reread the sentence carefully.

A motorboat travels 196 meters in 20 seconds.

                                        ↥            ↥          ↥

                                 196 meters  =  20 seconds.

Equation formed: \(196 \space\ meters = 20 \space\ seconds\)

To find the unit rate (meters/second), divide both sides by 20.

Divide both sides by 20.

Thus, the unit rate is 9.8 meters per second.

Let x represents the unknown speed

So

Proportion is

Answer:
\(3x-2+\frac{5}{x}\)

Step-by-step explanation:

To divide the polynomial (9x^3 - 6x^2 + 15x) by the monomial 3x^2, we can write it as:

(9x^3 - 6x^2 + 15x) ÷ (3x^2)

To simplify the division, we divide each term of the polynomial by 3x^2:

(9x^3 ÷ 3x^2) - (6x^2 ÷ 3x^2) + (15x ÷ 3x^2)

To divide monomials with the same base, we subtract the exponents. So:

9x^3 ÷ 3x^2 = 9/3 * (x^3/x^2) = 3x^(3-2) = 3x

(-6x^2) ÷ (3x^2) = -6/3 * (x^2/x^2) = -2

15x ÷ 3x^2 = 15/3 * (x/x^2) = 5/x

Putting it all together, we have:

(9x^3 - 6x^2 + 15x) ÷ (3x^2) = 3x - 2 + 5/x

Therefore, the division of (9x^3 - 6x^2 + 15x) by 3x^2 is 3x - 2 + 5/x.

Answer:(x-3)² + (y-2)² = 25

Step-by-step explanation:

A circle's equation is (x-h)² + (y-k)² = r². When centered at the origin, h and k equal 0. If you shift the circle, say, one unit up, then k equals 1, and the equation is x² + (y-1)² = r².

So for your circle, the equation would be (x-3)² + (y-2)² = 5² or (x-3)² + (y-2)² = 25.

Answer:

(x - 3)² + (y - 2)² = 25

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

Here (h, k ) = (3, 2 ) and r = 5 , then

(x - 3)² + (y - 2)² = 5² , that is

(x - 3)² + (y - 2)² = 25 ← equation of circle

Answer:

3/8 or 3:8

Step-by-step explanation:

pink : not pink

6 : 16

Think of it as a fraction. Simplify it in the same way.

6/16 simplifies to 3/8

So the pink:notpink ratio is 3/8 or 3:8

Answer: B

Step-by-step explanation:

\((-3)^2 = 9\)

It does not equal –9.

Answer:

X is greater than negative 4

Step-by-step explanation:

1.-2 from both sides

2. divide 4 from both sides

3. solution set X is greater than negative 4

Answer:

What is a linear function? A linear function is a function whose graph is a straight line. The rate of change of a linear function is constant. The function shown in the graph below, y = x + 2, is an example of a linear function.

Graph of linear function

Graph of linear function

A linear function has a constant rate of change. The rate of change is the slope of the linear function. In the linear function shown above, the rate of change is 1. For every increase of one in the independent variable, x, there is a corresponding increase of one in the dependent variable, y. This gives a slope of 1/1 = 1.

A linear function is typically given in the form y = mx + b, where m is equal to the slope, or constant rate of change.

Examples of linear functions include:

If a person drives at a constant speed, the relationship between the time spent driving (independent variable) and the distance traveled (dependent variable) will remain constant.

Assuming no change in price, the relationship between the number of pounds of bananas a person buys (independent variable) and the total cost of the bananas (dependent variable) will remain constant.

If a person earns an hourly wage at their job, the relationship between the time spent working (independent variable) and the amount earned (dependent variable) will remain constant.

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Exponential Functions

What is an exponential function? An exponential function is a function that involves exponents and whose graph is a smooth curve. The rate of change in an exponential function is not constant. The functions shown in the graph below, y = 0.5x and y = 2x, are examples of exponential functions.

Graphs of exponential functions

Graphs of exponential functions

An exponential function does not have a constant rate of change. The rate of change in an exponential function is the value of the independent variable, x. As the value of x increases or decreases, the rate of change increases or decreases as well. Rather than a constant change, as in the linear function, there is a percent change.

An exponential function is typically given in the form y = (1 + r)x, where r represents the percent change.

Examples of exponential functions include:

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

The state equation for the given system is: x' = Ax + Bu where A = [3 2; 0 2] and B = [1; 0].

To find the state equation of the given system, we first need to rewrite it in the matrix form. Let x1 = x and x2 = z, then we have:

x' = [3 2; 0 2]x + [1; 0]f(t)

z' = [2 3; 1 0]z + [0; 1]f(t)

where x' and z' denote the derivatives of x and z with respect to time, respectively. The matrix A in the state equation * = Ax + Bu is given by:

A = [3 2; 0 2]

This is because the state variables x1 and x2 are multiplied by A in the first equation of the state equation. The input matrix B is given by:

B = [1; 0]

This is because only x1 is affected by the input f(t) in the first equation of the state equation.

Therefore, the state equation for the given system is:

x' = Ax + Bu

where A = [3 2; 0 2] and B = [1; 0].

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The speed of the plane is equal to 120 mph.

In Mathematics and Geometry, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using miles per hour (mph).

Mathematically, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Time = distance/speed

Let the variable s represent the speed of the plane in miles per hour. Therefore, an equation that models the situation can be written as follows;

240/s = 80/s - 80

80s = 240s - 19200

19200 = 160s

s = 19200/160

s = 120 mph.

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The value of the expression is 22.

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

8 (6 + 5) / 2²

= 8 x 11 / 4

= 88/4

= 22

Thus,

The value is 22.

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Answer:

10

Step-by-step explanation:

it is 10 cause 634+10=644

Answer:

10

Step-by-step explanation:

What is the missing addend?

We can fill in the blank with x

634+x=644

Now we need to get x to the other side

The rule to do this is what we do on one side we have to do the same thing to the other side

so if we subtract 634 on one side we also have to do that on the other side as well:

634-634+x=644-634

634-634 is 0

So it is

x=644-634

644-634 is 10

x=10

So the missing addend is 10

Hope this helps!

Answer:

the answer is 1760

Step-by-step explanation:

Answer: Cytokinesis

Step-by-step explanation:

Hope this helped :)

Answer:

Try Cytokinesis

Step-by-step explanation:

This might help!

Answer:

Dimensions of the box:

x =  1,26  ( the side of the square base )

h = 2,52   the heigh of the cube

Step-by-step explanation:

V(b)  = x² *h      x is the side of the square base, and h the heigh of the cube

The surface area of such cube is:

Area of the base   A(b)  = x²

Lateral area is  4*x*h

A(c) = x²  +  4*x*h

Now   x² * h  = v = 4 m³       ⇒  h = 4/x²   and

A(x)   =  x²   +  4/x

Tacking derivatives on both side of the equation:

A´(x)  =  2*x - 4/x²

A´(x) = 0       2*x  - 4/x²  =  0        ⇒   2*x³  -  4   = 0

x³  = 2

x  = 1,26 m

And  h = 4/(1,26)²        ⇒     h  =  2,52 m

How do we know the value of  x  =  1,26 is for a minimum value of A(x)

We find the second derivative of  A(x)

A´´(x)  =  2  -  (-4*2*x/x⁴)

A´´(x)  =  2  + 8/x³       is positive  A´´(x)  >  0

Then function A(x) has a minimum value at x = 1,26

Answer:

9x - 6

Hope this helps! <3

(If you need a step by step lmk)

Answer:

6x+3(x-2)

6x+3x-6

9x-6

Answer:  if with 3.14 v= 37512.5333

if with pi v= 37531.56

Step-by-step explanation:

the formula is 1/3hπr^2

r= 2d so radius is 32

plus numbers in (square it multiple times pi or 3.14 then multiply times height and divide by 3)

Answer:

The answer is 49

Step-by-step explanation:

We can use proportions to estimate the number of dogs in the entire population that have the disease, based on the sample of dogs with the disease.

We know that 42 dogs were selected for the study, and 14 of them had the disease. This means that the proportion of dogs in the sample with the disease is:

14/42 = 0.3333

We can use this proportion to estimate the number of dogs in the entire population that have the disease, by multiplying it by the total number of dogs:

0.3333 * 147 = 49

Therefore, the best estimate for the number of dogs that suffer from the disease is 49.

Using the arrangements formula, it is found that there are 40,320 ways for these swimmers to finish.

The number of possible arrangements of n elements is given by the factorial of n, that is:

\(A_n = n!\)

In this problem, there are n = 8 swimmers, hence they can finish arranged in 8! ways, that is:

\(A_8 = 8! = 40320\)

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Answer:

27.02% of boys aged 16 to 17 will not be able find shoes that fit in this​ store

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mean of 25.5 centimeters and a standard deviation of 1.4 centimeters.

This means that \(\mu = 25.5, \sigma = 1.4\)

These shoes will fit men with feet that are 24.6 to 28.8 centimeters long. What percentage of boys aged 16 to 17 will not be able find shoes that fit in this​ store?

Less than 24.6:

The proportion is the pvalue of Z when X = 24.6. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{24.6 - 25.5}{1.4}\)

\(Z = -0.64\)

\(Z = -0.64\) has a pvalue of 0.2611

More than 28.8:

The proportion is 1 subtracted by the pvalue of Z when X = 28.8. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{28.8 - 25.5}{1.4}\)

\(Z = 2.36\)

\(Z = 2.36\) has a pvalue of 0.9909

1 - 0.9909 = 0.0091

0.2611 + 0.0091 = 0.2702

0.2702*100% = 27.02%

27.02% of boys aged 16 to 17 will not be able find shoes that fit in this​ store

The probability of Miguel selecting a tile number less than 3 from each bag -1 is 1/5 and bag-2 is 2/5.

The given tiles in bag-1 = {2, 4, 5, 8, 9}

Total number of tiles in bag-1 = 5

The number of tiles less than number 3 in the bag - 1 = 1

The probability of Miguel selecting a tile number less than 3 =

number of tiles less than 3 / total number of tiles = 1/3

The given tiles in bag-2 = {0, 1, 3, 6, 7}

Total number of tiles in bag-2 = 5

The number of tiles less than number 3 in the bag-2 = 2

The probability of Miguel selecting a tile number less than 3 =

number of tiles less than 3 / total number of tiles = 2/3

From the above analysis, we solved the problem.

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The angles COA and POC are 22.5 and 67.5 degrees respectively as POA is a right angled triangle.

POA is a right angle so it is 90 degrees.

POC +COA = 90  .....(1)

Also, POC is 3 times as large as COA.

Let's take COA, "x"

POC = 3x

Substituting the values in equation (1) as follows:

x + 3x = 90

4x = 90

x= 22.5

Therefore,

COA = 22.5°

POC = 22.5*3 = 67.5°

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