How was pre-image ABC transformed to create image A′B′C′ ?
Responses

reflection over BC⎯
90° clockwise rotation around point C
translation up
translation down

By finding the ratio of total volume to lemmon juice, we can see that In 600ml of juice we have 150ml of lemmon juice.

We know that 1000 ml of lemonade contains 250 ml of lemon juice. Then the ratio to total volume to lemon juice is:

R = 250/1000 = 0.25

Then in 600ml of juice, we will have 0.25 times that of lemmon juice, it gives:

0.25*600ml = 150 ml

In 600ml of juice we have 150ml of lemmon juice.

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Answer:

Step-by-step explanation:

Infra-red waves commonly known as heat waves and light rays are travel in a speed [tex]3*10^{8} ms^{-1}[/tex] in a vacuum.

The mode, mean, and median are relatively close together (mode=33, mean=32.125, median=32), we can conclude that this data set is symmetric and does not have any significant outliers.

The area of mathematics known as statistics is concerned with the gathering, examination, interpretation, presentation, and arrangement of data.

The mean, median, and mode are all measures of central tendency that describe the center of a data set in different ways.

The mean is calculated by dividing the total number of values in a data collection by their sum.

The median is the median of the data set when the values ​​are ordered.  It is not affected by outliers.

The value that appears most frequently in a data collection is the mode.

It may not be unique or exist in a data set.

For the given data set, the mode is likely to be the best measure of center as it is the value that occurs most frequently. In this case, the mode is 33, which occurs three times, whereas all other values occur only once or twice. Therefore, the mode is the most representative value for this data set.

Alternatively, we can also calculate the mean and median to see how they compare with the mode:

The mean is (33+33+33+31+31+34+32+31)/8 = 32.125

The median is the middle value when the values are arranged in order, which is 32.

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The true statements are:

p(factor of 24) = 6/8: The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Among these, the numbers 1, 2, 3, 4, 6, and 8 are on the 8-sided die. So, there are 6 favorable outcomes out of 8 possible outcomes. This statement is true.

p(odd number) = 1/2: There are 4 odd numbers (1, 3, 5, 7) on the 8-sided die, so the probability of rolling an odd number is 4/8 = 1/2. This statement is true.

p(number less than 8) = 1: All numbers on the 8-sided die are less than or equal to 8, but not all are less than 8. There are 7 numbers less than 8 (1, 2, 3, 4, 5, 6, 7), so the probability is 7/8, not 1. This statement is false.

p(multiple of 3) = 1/4: There are 2 multiples of 3 on the 8-sided die (3 and 6), so the probability of rolling a multiple of 3 is 2/8 = 1/4. This statement is true.

p(even number) = 1/8: There are 4 even numbers (2, 4, 6, 8) on the 8-sided die, so the probability of rolling an even number is 4/8 = 1/2, not 1/8. This statement is false.

P(the number 9) = 0: The 8-sided die only has numbers 1 through 8, so it is impossible to roll a 9. The probability of rolling a 9 is indeed 0. This statement is true.

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Answer:

A

Step-by-step explanation:

the answer would be a because it is shown more than the others

Answer: the missing angle has a measure of 90 degrees, which is option (d).

Step-by-step explanation:

20 + 70 + x = 180

We are able include the two known angles and after that subtract the result from 180 to induce the degree of the lost point:

20 + 70 = 90

180 - 90 = 90

Answer:

Step-by-step explanation:

A

the central angle of the arc is π/3 radians.

What is circumference of a circle?

Circumference or perimeter of a circle refers to the measuring of its limits. Contrarily, a circle's radius influences the amount of space it takes up. If a circle is opened up and represented by a straight line, its circumference is equal to its length. It is usually measured in units like centimetres or metres. While utilising the formula, the radius of the circle is taken into account when calculating the circle's circumference. Therefore, we need to know the radius or diameter value to determine the circle's perimeter.

Central angle (in radians) = arc length / radius

In this case, we are not given the radius of the circle directly, but we know that the circumference of the circle is 6. We can use the formula for circumference to find the radius:

Circumference = 2 * pi * radius

6 = 2 * pi * radius

radius = 3 / pi

Now we can use the formula for the central angle:

Central angle (in radians) = arc length / radius

Central angle = 1 / (3/pi) = pi/3

Therefore, the central angle of the arc is π/3 radians.

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A ) ⅔ x + 6 = 16

→ ⅔ × 15 + 6 = 16

→ 10 + 6 = 16

→ 16 = 16

Proved

B ) ⅓ x + 4 = 22

→ ⅓ × 15 + 4 = 22

→ 20 = 2

Not Proved

C) 3x + 15 = 30

→ 3×15+15 = 30

→ 3× 30 =30

→ 90= 30

Not Proved

D) x + 25 = 50

→ 15 + 25 = 50

→ 40 = 50

Not Proved

10r -24 = 7r + 12

→ 10r - 7r = 12+24

→ 3r = 36

→ r = 12

3r -2r-8 = -8r + 10

→ 3r - 2r + 8r = 10+8

→ r + 8r = 18

→ 9r = 18

→ r = 2

m/3-18 = m + 6

→ 54- m/ 3 = m + 6

→ 54- m = m + 6×3

→ 54- m = m + 18

→ 18 - 54

→ -36

Answer:

10

Step-by-step explanation:

I do not know how to make a possibility tree, but I can explain it in words. the possibilities could be at lost, 10  

The area of the triangle with the given vertices is 11.5 square units.

The area of a triangle can be calculated using the coordinates of its vertices using the following formula.

To find the area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), we can use the following formula:

A = (x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂))/2

Using this formula with the given vertices (0, 6), (2, −3), and (3, 4), we get:

A = (0(-3 − 4) + 2(4 − 6) + 3(6 − (-3)))/2

A = (0 - 4 + 27)/2

A = 23/2

A = 11.5

Therefore, the area of the triangle with the given vertices is 11.5 square units.

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Answer:

t = 6.8 years

Step-by-step explanation:

The formula for compound interest is

[tex]A(t)=P(1+r/n)^n^t[/tex], where P is the principal/amount invested, r is the interest rate, n is the number of compound periods per year (4 for quarterly), and t in the time in years.

We know that A = $5900, P = $4000, and r = 0.0575 (we must convert the percentage to a decimal).  We must solve for t and round to the nearest tenth:

[tex]5900=4000(1+0.0575/4)^(^4^t^)\\\\59/40=(1623/1600)^4^t\\\\log(59/40)=log(1623/1600^4^t)\\\\log(59/40)=4t*log(1623/1600)\\\\log(59/40)/log(1623/1600)=4t\\\\1/4(log(59/40)/log(1623/1600))=t\\\\6.80773607=t\\\\6.8=t[/tex]

Answer:

The answer is d.

Step-by-step explanation:

Let m = a number

Let n = a different number

[tex]log(m^n)=nlog(m)[/tex]

[tex]log(10^3)=3*log(10)[/tex]

[tex]log(10)=1[/tex]

[tex]log(10^3)=3[/tex]

The required rate of return for the stock with a beta of 0.5 is 7.5% and for the stock with a beta of 2 is 15%.

Rate of return is the amount of profit or loss earned on an investment over a certain period of time, expressed as a percentage of the initial investment or total asset value.

A stock is a type of security that represents ownership in a company. Investors buy stocks to become shareholders and share in the company's profits and losses.

According to the given information:

The Capital Asset Pricing Model (CAPM) is expressed as:

R = Rf + beta*(Rm - Rf)

Where:

R = Required rate of return

Rf = Risk-free rate of return

beta = Beta coefficient (systematic risk)

Rm = Expected market return

Using the given values, we can compute the required rate of return for each stock:

Stock with beta of 0.5:

R = 5% + 0.5*(10% - 5%)

R = 7.5%

Stock with beta of 2:

R = 5% + 2*(10% - 5%)

R = 15%

Therefore, the required rate of return for the stock with beta of 0.5 is 7.5%, and the required rate of return for the stock with beta of 2 is 15%.

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Answer:

16801.2cm²

Step-by-step explanation:

Cone :

SA = πrl

SA = π · 28 ·  45                     90-45 = 45

SA = 3958.406744

Cylinder :

SA = 2 · π · r · ( r+h)

SA = 2 · π · 28 ( 28 +45 )

SA = 2 · π · 28 (73)

SA = 12842.83077

12842.83077 + 3958.406744 =

16801.2cm²

Answer:

The answer to this question is D

Step-by-step explanation:

i solved it

Answer:

a) (2x+9) + (3x-4) + 36 = 180

b) x = 27.8

c) 79.4°

Step-by-step explanation:

a) (2x+9) + (3x-4) + 36 = 180

This is because all 3 angles of a triangle equal to 180 degrees.

b) Firstly add like terms

5x + 41 = 180

Subtract 41 from both sides.

5x = 139

Divide 5 on both sides.

x = 27.8

c) <GTN = 3x-4

Plug in x = 27.8

3(27.8)-4 = 79.4

<GTN is 79.4 degrees

The correct answers are A) 7cm, C) 9cm and D) 12cm

The process of changing a given quantity that is expressed in one unit of measurement to another unit of measurement that is equivalent in value is referred to as conversion of units.

If every 2 cm on a scale drawing is equal to 7 feet in real life, then we can use proportions to find out which lines on the drawing would be greater than 21 feet in real life.

Let x be the length of a line on the scale drawing in centimeters. Then, we can set up the following proportion:

⇒  [tex]\frac{2cm}{7 feet} = \frac{x cm }{yfeet}[/tex]

where y is the length of the line in real life. Solving for y, we get:

⇒  [tex]y = \frac{7 feet} {2cm} *x[/tex]  

⇒  [tex]y = 3.5 x feet[/tex]

If we put x = 2cm (given) then, y = 7 feet

For y = 21 feet, the value of x = 6cm.

Therefore, any line on the scale drawing that is greater than 6cm in length corresponds to a length greater than 21 feet in real life.

So, the lines on the drawing that are greater than 21 feet in real life are:

A) 7cm, C) 9cm, D) 12cm

Therefore, the correct answers are A) 7cm, C) 9cm and D) 12cm

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Answer: 64

Step-by-step explanation:

First you do, 237+192+179 which is 608.

Then you do, 800-608 which is 192.

Lastly, you do 192 divided by 3 which gives you 64 as your final answer. So you have to do 192/3 for the 3 7th grade classes to get an equal amount of the prize money.

                                            [tex]192/3=64 \dollars[/tex]

                                             Hope this helps!

The shape that is a concave hexagon with two pairs of congruent sides is an irregular hexagon.

A hexagon is defined as the type of polygon that is made up of six sides and six angles that sums up to 720° and also have 6 vertices.

A hexagon can be of various irregular shapes such as concave, convex and complex irregular shapes.

The properties of irregular hexagon include the following:

The concave irregular hexagon has two pairs of congruent sides that are equal in measurement.

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Answer:

CAB is 37 degrees

Step-by-step explanation:

90 + 53 = 143

180 - 143 = 37

We can use factorization method to solve quadratic equation.

And, The value of solution of the quadratic equation is,

⇒ x = 2, 6

We have to given that;

Quadratic equation is,

⇒ x² - 8x = - 12

Now, We can simplify as;

⇒ x² - 8x = - 12

⇒ x² - 8x + 12 = 0

Factorized it as;

⇒ x² - (6 + 2)x + 12 = 0

⇒ x² - 6x - 2x + 12 = 0

⇒ x (x - 6) - 2 (x - 6) = 0

⇒ (x - 2) (x - 6) = 0

⇒ x = 2, 6

Thus, We can use factorization method to solve quadratic equation.

And, The solution is,

⇒ x = 2, 6

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So the volume of the cylindrical pool is approximately 1884.96 cubic feet.

So the volume of the soccer ball is approximately 329.59 cubic inches.

So the volume of the small container is approximately 56.55 cubic inches.

So the volume of the tank is 63 cubic feet.

In mathematics, volume is a measure of the amount of space that a three-dimensional object occupies. It is typically expressed in cubic units, such as cubic meters, cubic centimeters, cubic feet, or cubic inches. The volume of a simple shape, such as a cube, rectangular prism, cylinder, or sphere, can be calculated using a specific formula based on its dimensions.

Here,

13. The diameter of the cylindrical pool is 20 feet, which means the radius is 10 feet (half of the diameter). The depth of the pool is 6 feet. The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height or depth. Substituting the given values, we get:

V = π(10 ft)²(6 ft)

≈ 1884.96 cubic feet

14. The soccer ball has a radius of 4.3 inches. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius. Substituting the given value, we get:

V = (4/3)π(4.3 in)³

≈ 329.59 cubic inches

15. The conical container has a radius of 3 inches and a height of 6 inches. The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius and h is the height. Substituting the given values, we get:

V = (1/3)π(3 in)²(6 in)

≈ 56.55 cubic inches

16. The tank is in the shape of a pyramid, which means it has a rectangular base with length 3 feet and width 7 feet, and a height of 9 feet. The volume of a pyramid is given by the formula V = (1/3)Bh, where B is the area of the base and h is the height. The base of the tank is a rectangle, so its area is given by the formula A = lw, where l is the length and w is the width. Substituting the given values, we get:

A = (3 ft)(7 ft)

= 21 square feet

V = (1/3)(21 sq ft)(9 ft)

= 63 cubic feet

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At the end, Antonio has 4 cups of milk leftover.

We know that Antonio has 1 gallon of mil, and he needs to use 3 quarts of milk for the recipe.

Then we need to perform a change of units, we know that:

1 gallon = 4 quarts.

Then after he uses 3 quarts, he will have 1 quart remaining, and now we want to know how many cups is that, we know that:

1 quart = 4 cups.

So Antonio has 4 cups leftover.

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Answer:

To find the maximum height of the ball, we need to determine the vertex of the parabolic function f(t) = -16t^2 + 5t + 11. The vertex of a parabola is the point where the function reaches its maximum or minimum value.

The x-coordinate of the vertex is given by the formula x = -b/2a, where a and b are the coefficients of the quadratic function. In this case, a = -16 and b = 5, so the x-coordinate of the vertex is:

t = -b/2a = -5/(2*(-16)) = 0.15625

To find the y-coordinate of the vertex, we can substitute t = 0.15625 into the function f(t):

f(0.15625) = -16(0.15625)^2 + 5(0.15625) + 11 ≈ 11.36

Therefore, the maximum height of the ball is approximately 11.4 (rounded to 1/10th).

Answer:

0.25

Step-by-step explanation:

The cost per ounce of candy can be calculated by dividing the total cost of the box by the number of ounces in the box. Since 1 pound equals 16 ounces, the cost per ounce is $4.00 / 16 ounces = $0.25 per ounce.

So the cost per ounce of candy is $0.25.

Answer: 16/1 16x4 = 64/4

Answer:

180,000 (OR 90,000 if the figure is a triangle)

Step-by-step explanation:

3 x 3 x 5 x 5 x 4 x 8 x 5 x 5 = 180,000

Area = 180,000

IF THE FIGURE IS A TRIANGLE THEN DIVIDE 180,000 BY 2 AND YOU WILL GET 90,000 AS THE AREA

The answer of the given question based on the the sentence into an equation is , 2x - 3 = 4.

In mathematics, equation is statement that asserts equality of the two mathematical expressions. It typically contains variables, constants, and mathematical operations like  addition, subtraction, multiplication, division, exponentiation, and logarithm. An equation usually consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The values of the variables that satisfy the equation are called its solutions.

The sentence be translated into equation are as  follows:

2x - 3 = 4

where x is the unknown number.

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An exponential function can be used to calculate the number of trees in the warehouse at the end of any given number of months. This function uses the initial number of trees in the warehouse and the rate of 7.3% to determine the result.

A function is a block of organized, reusable code that is used to perform a single, related action. Functions provide better modularity for your application and a high degree of code reusing. As you already know, C programming is built around functions. All C programs have at least one function, which is main(). A function is a group of statements that together perform a task. Every C program has at least one function, main(), and all the other functions are called user-defined functions.

The function that can be used to find the number of trees in the warehouse at the end of m months is an exponential function given by:

N(m) = 45,000(1.073)^m

Where N(m) is the number of trees in the warehouse at the end of m months and 45,000 is the initial number of trees in the warehouse. The rate of 7.3% is represented by 1.073, which is the base of the exponential function.

For example, if we want to find the number of trees in the warehouse at the end of 5 months, we can substitute m = 5 into the exponential function and calculate the result. This gives us N(5) = 45,000(1.073)^5 = 60,731. Thus, the warehouse will contain 60,731 trees at the end of 5 months.

In conclusion, an exponential function can be used to calculate the number of trees in the warehouse at the end of any given number of months. This function uses the initial number of trees in the warehouse and the rate of 7.3% to determine the result.

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An exponential function can be used to calculate the number of trees in the warehouse at the end of any given number of months. This function uses the initial number of trees in the warehouse and the rate of 7.3% to determine the result.

What is function?

A function is a block of organized, reusable code that is used to perform a single, related action. Functions provide better modularity for your application and a high degree of code reusing. As you already know, C programming is built around functions. All C programs have at least one function, which is main(). A function is a group of statements that together perform a task. Every C program has at least one function, main(), and all the other functions are called user-defined functions.

The function that can be used to find the number of trees in the warehouse at the end of m months is an exponential function given by:

[tex]N(m) = 45,000(1.073)^m[/tex]

Where N(m) is the number of trees in the warehouse at the end of m months and 45,000 is the initial number of trees in the warehouse. The rate of 7.3% is represented by 1.073, which is the base of the exponential function.

For example, if we want to find the number of trees in the warehouse at the end of 5 months, we can substitute m = 5 into the exponential function and calculate the result. This gives us N(5) = 45,000(1.073)⁵ =60,731.

Thus, the warehouse will contain 60,731 trees at the end of 5 months.

In conclusion, an exponential function can be used to calculate the number of trees in the warehouse at the end of any given number of months. This function uses the initial number of trees in the warehouse and the rate of 7.3% to determine the result.

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The true statement regarding the line of best fit is that C. the equipment starts producing items after about 20 minutes of warming up

The line of best fit may be explained as a straight line which is drawn to pass through a set of plotted data point which gives the best and most approximate relationship between the data points.

The equipment starts producing items after about 25 minutes of warning up. This is false because machine takes 20 minutes to produce the items.

The equipment starts producing items after about 20 minutes of warming up. This is True.

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