Area of composite shapes, There is a pair of parallel sides in the following shape.
What is the area of the shape?

The perimeter and area of the original square are 4s and s², respectively, and the perimeter and area of the dilated square are 192 and 2304, respectively.

What is area of square ?

Area of square can be defined as the square of given side.

Given ,

Let's assume that the side length of the original square is 's'. The perimeter of the original square is then 4s and its area is s².

The perimeter of the dilated square will be 4 times longer than the original square, so it will be 4 * 4s = 16s.

The area of the dilated square will be 4 times greater than the original square, so it will be 4^2 * s² = 16s².

Here s is 12

so ,

16s = 16 * 12 = 192

16s*s = 16 * 12 * 12 = 2304

Therefore, The perimeter and area of the original square are 4s and s², respectively, and the perimeter and area of the dilated square are 192 and 2304, respectively.

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Answer: 97%

Step-by-step explanation:

If for the 3 exams, the mean was 83% and the first two were 76%, that means..

76 + 76 = 152 (divided by two = 76%/current mean)

In order to get an average of 83%, Colin has to have a score that is higher than 76% and somewhat closer to above 90%.

By doing trial and error (testing different percents between 76% and 80%),  you can come to the conclusion that, 76% + 76% + 97% = 249 / 3 = 83

The coordinates of the image of triangle ABC are A''(x, y) = (- 4, 2), B''(x, y) = (0, 0) and C''(x, y) = (2, 4).

Triangles are generated by the location of three distinct points on Cartesian plane. In this problem we find the representation of a triangle, whose vertices are listed below:

A(x, y) = (1, 0), B(x, y) = (3, - 1), C(x, y) = (4, 1)

We need to apply the following rigid transformations:

Translation

(x, y) → (x - 3, y + 1)

Dilation centered at the origin with scale factor 2

(x, y) → (2 · x, 2 · y)

Now we proceed to determine the coordinates of the image:

Translation

A'(x, y) = (- 2, 1), B'(x, y) = (0, 0), C'(x, y) = (1, 2)

Dilation

A''(x, y) = (- 4, 2), B''(x, y) = (0, 0), C''(x, y) = (2, 4)

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The error in the expression 4 + 2x - 1/2(10 - 4x) is the missing parentheses.

Parentheses are a sort of punctuation mark that is used to separate or distinguish content inside a phrase. They frequently assist to clarify the meaning of a statement by adding information. Parentheses can also be used to denote a break or to divide items in a list.

Error in the given question: Missing parentheses

Corrected expression: 4 + 2x - 1/2(10 - 4x)

The problem may be fixed by ensuring that the proper syntax is used when declaring variables. If the variable is a string, for example, it should be stated as "var myVariable ='string value';". If it is an integer, define it like "var myVariable = 42;".

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Answer:

Step-by-step explanation:

The effective tax rate is the amount of tax paid as a percentage of the total purchase price. To calculate the effective tax rate, you can divide the amount of tax by the total purchase price and multiply the result by 100 to get the answer as a percentage.

In this case, the effective tax rate would be:

(1200 / 24000) * 100 = 5%

So Chris's effective tax rate on the purchase of his car is 5%.

Answer:

degree 2 and 10

Step-by-step explanation:

the degree of a polynomial is the value of the largest exponent of the variable.

r(x) = 10x² + 4x - 7

has largest exponent 2

this is a polynomial of degree 2

the leading coefficient is the coefficient of 10x²

that is leading coefficient is 10

73 degrees is the equivalent meausure of m<A

From the given line geometry below, the sum of the adjacent angles is 180 degrees as shown:

m∠A + m∠B = 180

Given the following

∠A = 6x - 35

∠B = 3x + 53

Substitute the given parameters

6x - 35 + 3x + 53 = 180

9x + 18 = 180

9x = 180 - 18

9x = 162
x = 162/9

x = 18

Determine the measure of <A

<A = 6x - 35

<A = 6(18) - 35

<A = 108 - 35

<A = 73 degrees

Hence the measure of angle A from the given diagram is 73 degrees

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On solving the provided question, we can say that Area of Rhombus is 24 cm²

A rhombus is an equal-sided quadrilateral in Euclidean plane geοmetry. The term "equilateral triangle" alsο refers to a quadrilateral whose sides are of the same length. A parallelοgram has a unique variation knοwn as a rhombus. In a rhombus, the οpposite sides and angles are parallel and equal.

A rhombus's diagοnal is split in half by a right angle, and each of its sides is the same length. Rhombic diamοnds and diamonds are other names for rhοmbuses. The length οf every side is the same. Diagοnals are equal in a rhοmbus. At a 90° angle, parallel lines split in half, 180 degrees is the sum of adjacent angles.

By distance formula

BD = [tex]\sqrt{(-2-4)^2 + (-1-5)^2}[/tex]

BD = [tex]\sqrt{36 + 36}[/tex]

BD = 6√2

similarly,

AC = 4√2

and, Area = 1/2 × (product of diagonals)

Area of Rhombus = 1/2 × 6√2 × 4√2 = 24 cm²

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Answer:

162π - 324 (exact) or 184.938

Step-by-step explanation:

You probably don't even need help on this one anymore, its just the same as the previous one I helped you with.

Diameter = a^2 + b^2 = c^2 = 18^2 + 18^2 = c^2

√648 = c (this is exact) so radius is √648/2

Area of square = lw = 324

Area of circle = (√648/2)^2π = (648/4)π = 162π

Area of shaded region = 162π - 324 (exact) or 184.938

The equation of the polynomial function graphed is given as follows:

y = -0.125(x³ + x² - 14x - 24).

From the graph, the roots of the polynomial are given as follows:

Considering the roots, the linear factors of the polynomial are given as follows:

Applying the Factor Theorem, the function, as a product of it's linear factors, is given as follows:

y = a(x + 3)(x + 2)(x - 4).

y = a(x² + 5x + 6)(x - 4)

y = a(x³ + x² - 14x - 24).

When x = 0, y = 3, hence the leading coefficient a is obtained as follows:

-24a = 3

a = -0.125.

Hence the function is:

y = -0.125(x³ + x² - 14x - 24).

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Answer:

simple interest is $6.8

Miguel pay the amount to Julio at the end of 6​ months was $206.8

Step-by-step explanation:

Given : Miguel Rodriguez borrowed ​$200 from his brother Julio to pay for books and tuition. He agreed to pay Julio in 6 months with simple annual interest at 6.8​%.

To Find : ​a) How much will the interest amount​ to?

​b) What amount must Miguel pay Julio at the end of 6​ months?

Solution :

Formula for simple interest :

Where rate is in decimal

Time is in years

So, rate of interest = 6.8 % = 0.068

Time = 6 months = 6/12=0.5

Principal = $200

Thus= 200x0.068x0.5=6.8

Using the equation provided, you can estimate the number of hours worked each week for a student with a GPA of 2.21. The equation can be rearranged to solve for h, the number of hours worked each week.

h = (g - 3.04) / (0.012 + 0.0007)

Plugging in the GPA of 2.21, we get:

h = (2.21 - 3.04) / (0.012 + 0.0007)

h = -4.83 hours

Therefore, a student with a GPA of 2.21 would need to work an average of -4.83 hours per week in order to achieve that GPA.

Using the proportions of the side lengths of the pair of similar triangles, we have:

1. x = 35

2. x = 20; y = 23.3

3. x = 11

4. x = 9

5. x = 10

Triangles that are similar to each other, will have side lengths that are proportional to each other.

Therefore, using proportions, we would have:

1. x/14 = 40/16

Cross multiply:

16x = 40 * 14

16x = 560

x = 560/16

x = 35

2. x/12 = 15/9

9x = 12 * 15

9x = 180

x = 20

y/14 = 15/9

9y = 210

y = 23.3

3. (x + 5)/24 = 36/54

Cross multiply:

54(x + 5) = 36 * 24

54x + 270 = 864

54x = 864 - 270

54x = 594

x = 11

4. 20/28 = 15/(2x + 3)

Cross multiply:

20(2x + 3) = 28 * 15

40x + 60 = 420

40x = 420 - 60

40x = 360

x = 9

5. 24/28 = x + 8 / 3x - 9

Cross multiply:

24(3x - 9) = 28(x + 8)

72x - 216 = 28x + 224

72x - 28x = 216 + 224

44x = 440

x = 10

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Answer:yes

Step-by-step explanation:

Answer:

Step-by-step explanation: Yes, that is correct. The solution to the system of equations is (x, y) = (-7, 0), which is not in the given options, so none of the options are the correct answer.

The value of the segment in the geometry of the triangle is 17.5.

A triangle is a sort of polygon with three sides, as was said in the introduction. The vertex of a triangle is where two of its sides meet at an angle. There is an angle created between two sides. One of the crucial elements of geometry is this.

Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.

If a line is parallel to one side of the triangle and intersects the other two sides, then it divides the side into segments of proportional length.

Thus,

12 / (12 + 14) = 15 / (15 + x)

12(15 + x) = 15(26)

180 + 12x = 390

12x = 210

x = 17.5

Hence, the value of the segment in the geometry of the triangle is 17.5.

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if the ratio of two sample variances exceeds the critical value of f at a defined confidence level, then the level of confidence also exceeds the critical level.

All tests that make use of the F-distribution are collectively referred to as "F Tests." The F-Test to Compare Two Variances is often what is meant when the term "F-Test" is used. However, a number of tests, including regression analysis, the Chow test, and the Scheffe test, use the f-statistic. If we are conducting an F-Test, we might employ a variety of technological tools. since doing an F-test manually while accounting for variations is a difficult and time-consuming operation.

if the ratio of two sample variances exceeds the critical value of f at a defined confidence level, then the level of confidence also exceeds the critical level.

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The context that represents linear growth is "A music service has a fixed monthly cost and charges $0.35 for each downloaded song".

A linear growth function has a constant slope, increases by a consistent amount over time, and is represented graphically as a line.

In other words, when a quantity rises in proportion to another factor or variable in a connection it is said to be a linear growth.

Let's check the given option to check whether it is linear growth or not.

1. A music service has a fixed monthly cost and charges $0.35 for each downloaded song.

Here there is a fixed cost and the cost will increase when the number of songs is increased

Let's say the constant charge is 'y' and the number of songs is 'x' then the equation that can represent the situation is

=> f(x) = y + x(0.35)

Here there is a constant increase in cost

∴ The given situation can represent Linear growth.

2. An elevator descends at a rate of 32 feet per second.

Here descends indicated the elevator decreases in speed of the elevator at a point the elevator speed will be zero

∴ It doesn't show the linear growth

3. OA town's population shrinks at a rate of 9.4% every year.  

Here the town's population is shrinking means It doesn't show any growth

∴ It doesn't show the linear growth  

4. The amount of certain medication in a person's bloodstream decreases by 1/4 every day.  

Here, the person's bloodstream decreases by 1/4 every day.  

∴ It doesn't show the linear growth    

Therefore,

The context that represents linear growth is "A music service has a fixed monthly cost and charges $0.35 for each downloaded song".

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The margin of error for the confidence interval for a population is 0.71 ± 0.1.

The degree of error in survey findings from random sampling is known as the margin of error in statistics. A wider margin of error in statistics denotes a reduced likelihood of relying on a survey's or poll's findings, meaning that there will be less confidence in the results' ability to accurately reflect a community. It is a very important tool for market research since it shows the degree of assurance that should be placed in survey data by the researchers.

The margin of error is given as:

MOE = U - L / 2

MOE = 0.81 - 0.61 / 2

MOE = 0.2 / 2

MOE = 0.1

The interval is:

Interval = P ± 0.1

Interval = (0.61 + 0.1) ± 0.1

Interval = 0.71 ± 0.1

Hence, the margin of error for the confidence interval for a population is 0.71 ± 0.1.

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Answer: $272.60

Step-by-step explanation:

9.75x5.4= 52.65

52.65+15.50=68.15

68.15x4=272.6

The solution to the equation "negative x = 9" is "x = -9". There is no invisible number in front of "x" in this equation.

To solve the equation "negative x = 9" algebraically, we want to isolate the variable "x" on one side of the equation.

First, we notice that "negative x" means "-x", so we can rewrite the equation as:

-x = 9

To isolate "x", we need to perform an inverse operation on both sides of the equation. Since "-x" means the opposite of "x", we need to perform the opposite operation, which is to add "x" to both sides:

-x + x = 9 + x

Simplifying the left-hand side by canceling out the "-x" and "+x", we get:

0 = 9 + x

We can further simplify this equation by subtracting 9 from both sides:

0 - 9 = 9 + x - 9

-9 = x

So the solution to the equation "negative x = 9" is "x = -9".

There is no invisible number in front of "x" in this equation, so we don't need to worry about any additional steps or calculations.

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Answer: Option 1

Step-by-step explanation:

I'd say the easiest way would be to find the prize per oz in both options

Option 1: $1.10/12oz = approx 0.092 (so around 9 pennies)

Option 2: $0.98/10oz = 0.098 (also 9 pennies but still slightly more than option 1)

You can check by choosing a random number of oz and multiplying them by the price to see which costs more

ex: 120 oz

option 1 : 10 x 1.10 = $11

option 2: 12 x 0.98 = $11.76

Answer:

Step-by-step explanation:

area of pole=75×8=600 square inch

area if sign=12×12+1/2×12×4

=144+24

=168 square inches

total area=600+168

=768 square inches

The single payment 2 years from now will be of $13,287.26

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Given that money earns 7.74% compounded quarterly, a payment of $2,070 due 2 years ago, but not paid, and $300 today.

To calculate investments or debts with compound interests.

Where:

V(n) is the value of the debt after n years,

R is the annual interest rate,

t is the number of times the debt is going to be compounded annually,

n is the number of years the debt is going to be compounded,

P is the principal amount being owed.

we know that the debt will be cancelled in 2 years from now. Therefore we have that n = 2 for both debts, because after the 2rd year the debts.

Then you have that t = 4, because the debt is compounded quarterly.

We can add up the two principals $2,070 + $300 = $2,370 to make it our value P, so P = 9000.

And finally we have that R = 7.74.

Then, solve the equation for P

P = A / (1 + r/n)^nt

P = 2,370 / (1 + 7.74/365)(365)^(2)

P = $13,287.26

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Answer:

Step-by-step explanation:

3/2*2/3(6y)=30*3/2

6y=45

6y/y=45/y

y=7.5

In the given figure angle CBF and angle CEF are supplementary angles. So Option C is correct.

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Given that,

A figure which contains one trapezium BCEF

And in this portion angle CBF and angle BCE are  opposite angles

and opposite angles are supplementary angles,

Hence, the pairs of angles are ∠CBF & ∠CEF

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The graph shows a positive association. There is a nonlinear association shown. There is no correlation shown on the scatter plot.

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The best way to figure out if there is a solution to the equation:

 --> solve this whole thing algebraically

Let's solve:

 [tex]-4x+7x=4(x+2)-(x+8)\\3x=4x+8-x-8\\3x=3x[/tex]

If we get this kind of circumstance:

 --> where the left/right part of the equation are equal and cannot be

      solved further

     ---> the solution is all real numbers

Answer: solution is all real numbers

Answer:

Step-by-step explanation:

The cross-price elasticity of demand measures the responsiveness of the quantity demanded of one good to a change in the price of another good. In other words, it shows how the demand for one good changes in response to changes in the price of another good. The cross-price elasticity of demand is a useful concept for understanding the relationship between two goods and can provide valuable information for firms in making pricing and marketing decisions.

The formula for cross-price elasticity of demand is as follows:

Cross-price elasticity of demand = (Percentage change in quantity demanded of good A) / (Percentage change in price of good B)

In this case, we are calculating the cross-price elasticity of demand between almond milk and oat milk. To do this, we first need to calculate the percentage change in quantity demanded of oat milk and the percentage change in price of almond milk.

Percentage change in quantity demanded of oat milk = (30,000 - 20,000) / 20,000 = 0.5

Percentage change in price of almond milk = ($5 - $3) / $3 = 0.67

Next, we use these values to calculate the cross-price elasticity of demand:

Cross-price elasticity of demand = 0.5 / 0.67 = 0.74

A positive cross-price elasticity of demand indicates that the two goods are substitutes. This means that as the price of one good increases, the demand for the other good increases. A cross-price elasticity of demand between 0 and 1 indicates that the two goods are weak substitutes. In this case, a cross-price elasticity of demand of 0.74 suggests that almond milk and oat milk are weak substitutes. This means that if the price of almond milk were to increase, the demand for oat milk would increase to some extent, but not by a significant amount.

In conclusion, the cross-price elasticity of demand provides valuable information for firms in making pricing and marketing decisions. A positive cross-price elasticity of demand indicates that two goods are substitutes, while a cross-price elasticity of demand between 0 and 1 suggests that they are weak substitutes.