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Answer:

2/9yd²

Step-by-step explanation:

We know that area is calculated by length × width, so we will do the same here. To get the area, we must multiply 1/3 by 2/3.

1/3 × 2/3 is 2/9. So, the area of the rectangle is 2/9yd². :D

Answer:

Step-by-step explanation:

every second we are increasing the sides by 4.4 in all 3 dimensions. This must mean that we need to do 4.4x4.4x4.4 to get

85.184in^3 per second

The Surface area of the given cuboid is found to be 872 sq, in.

Three-dimensional shapes with length, breadth, and height are called cuboids. Six of the cuboid's sides are referred to as faces.

Surface area of a cuboid is = 2(lw + 2lh + hw0

S.A = 2[(17)*(8) + (8)*(12) +(12)*(17)]

S.A = 2*436

S.A = 872

Thus, the Surface area of the given cuboid is found to be 872 sq, in.

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The cοοrdinates οf the fοurth vertex K must be the reflectiοn οf the pοint L(-4,3) acrοss the οrigin, which is (4,-3).

Thus, οptiοn D is cοrrect.

Cοοrdinate geοmetry is a branch οf mathematics that deals with the study οf geοmetry using the principles οf algebra.

The rectangle IJKL is fοrmed by cοnnecting the pοints I, J, K, and L in a clοckwise οr cοunterclοckwise manner. Since I and J have the same x-cοοrdinate and are οn οppοsite sides οf the x-axis, and L and K have the same y-cοοrdinate and are οn οppοsite sides οf the y-axis, it fοllοws that the diagοnals οf the rectangle IJKL intersect at the οrigin (0,0).

Therefοre, the cοοrdinates οf the fοurth vertex K must be the reflectiοn οf the pοint L(-4,3) acrοss the οrigin, which is (4,-3).

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Answer:

x > 3

Step-by-step explanation:

This is an open circle, meaning there will be no equal sign.

The line is going to the right of 3, meaning x > 3

So, our inequality is x > 3

The perimeter of the rectangle is approximately 208.9 meters.

To find the perimeter of the rectangle, we need to know the length of the other side.

Let's use the formula for the area of a rectangle:

area = length x width

We know that the area is 717.8 m^2 and one of the sides (width) is 7.4 m. So we can rearrange the formula to solve for the length:

length = area / width

length = 717.8 / 7.4

length ≈ 97.05 m

Now we have both the length and width of the rectangle, so we can find the perimeter:

perimeter = 2 x (length + width)

perimeter = 2 x (97.05 + 7.4)

perimeter = 2 x 104.45

perimeter = 208.9 m

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In the following question, Yes, the confidence interval suggests that the difference observed in this sample will also generalize to the larger population.

What is a confidence interval? A confidence interval is a probability statement that provides an interval of plausible values that are likely to contain the value of a population parameter. It is a way to infer the population parameter value from sample data.

A confidence interval is calculated as a range of values that are predicted to include the unknown population parameter, based on the sample statistic. The confidence interval suggests that the difference, if any, observed in this sample will also generalize to the larger population.

A confidence interval with a high level of confidence (e.g. 95%) would have a wider range of values and a higher probability of including the population parameter. The interpretation of the confidence interval is that we are 95% confident that the actual population parameter falls within the calculated interval. Therefore, it implies that the sample data is likely to be representative of the population data.

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Answer:c 4.2 cups

Step-by-step explanation:

just do 63 divided 15

Total volume of the composite figure using volume of cuboid formula is = 120ft³.

A cuboid's volume is a measurement of how much room it occupies. A three-dimensional shape with dimensions of length, breadth, and height is the cuboid. We can keep stacking them, starting with a rectangular sheet, until we achieve a shape with a particular length, breadth, and height.

The shape of this stack of sheets is a cuboid, which has 6 faces, 12 edges, and 8 vertices. The (unit)³ is used to represent a cuboid's volume.

In the given figure,

Length of cuboid = 6ft.

Breadth of cuboid = 3ft.

Height of cuboid = 5ft.

Length of second cuboid = 4ft.

Height of second cuboid = 5ft.

Breadth of second cuboid = 3ft.

Volume of first cuboid = length × breadth × height.

= 6 × 3 × 5

= 90ft³

Volume of second cuboid = 4 × 3 × 5

= 60ft³

Now the second cuboid is half.

So, volume becomes = 60/2

= 30ft³.

So, total volume of the figure = 90 + 30 = 120ft³.

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The probability of observing exactly 4 errors in the carpet is 0.0165 or 1.65%.

The number of weaving errors in a twenty-foot by ten-foot roll of carpet follows a Poisson distribution with a mean of 0.5. We can use the Poisson probability distribution formula to find the probability of observing exactly 4 errors in the carpet:

[tex]P(X = 4) = (e^{-0.5} * 0.5^4) / 4![/tex]

where X is the random variable representing the number of weaving errors. Plugging in the values, we get:

[tex]P(X = 4) = (e^{-0.5} * 0.5^4) / 4! = 0.0165[/tex] (rounded to four decimal places)

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The correct interpretations of the given quantity are C and E.

C. Your daily viewing time is greater than 90% of all Netflix users.

E. 90% of all Netflix users viewing times per day are less than your daily viewing time.

To understand the correct interpretation, we need to first understand what the 90th percentile means. It refers to the value below which 90% of the data falls.

If your daily viewing time is in the 90th percentile of all Netflix users, it means that your viewing time is greater than 90% of all users. In other words, only 10% of users watch more Netflix than you, and your viewing time is greater than the viewing time of 90% of users.

Therefore, options C and E are the correct interpretations.

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Complete Question:

Suppose the amount of time (in minutes) per day that you spend watching Netflix is in the 90th percentile of all account users. Which interpretation(s) of this quantity are correct? Select ALL that apply.

A. You spend approximately 90 minutes per day watching Netflix.

B. 90% of all viewers spend more time on Netflix per day than you.

C. Your daily viewing time is greater than 90% of all Netflix users.

D. There is a 90% probability that a randomly selected viewer spends less time than you watching Netflix per day.

E. 90% of all Netflix user viewing times per day are less than your daily viewing time.

F. 90% of all Netflix user viewing times per day are less than or equal to your daily viewing time.

Answer:

For the original triangle:

A is at (-3, 6), B is at (1, 2), C is at (-5, 1).

For the new triangle:

A' will be at (-3 - 3, -(6 + 2)) = (-6, -8)

B' will be at (1 - 3, -(2 + 2)) = (-2, -4)

C' will be at (-5 - 3, -(1 + 2)) = (-8, -3)

The error made by the student is in simplifying the expression inside the square root.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The student made an error in simplifying the expression inside the square root.

The expression should be simplified as follows:

25 + 4(2)(-12) = 25 - 96 = -71

So the correct expression inside the square root is -71, not 121.

Therefore, the correct solution using the Quadratic Formula is:

x = (-(-5) ± √((-5)² - 4(2)(-12)))/(2(2))

x = (5 ± √(25 + 96))/4

x = (5 ± √121)/4

x = (5 ± 11)/4

Hence, the solutions are x = -3 and x = 4/2, which simplifies to x = 2.

Therefore, the error made by the student is in simplifying the expression inside the square root.

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Answer:

The area that represents elements contained in the complement of the intersection of swimmers and weightlifters is the region outside the circles labeled as D. Therefore, the answer is D.

Step-by-step explanation:

chatgpt

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Lori will receive a semiannual interest of $950 from the bond with a face value of $20,000 and a coupon rate of 9.5%, which will mature in 20 years.

To calculate the semiannual interest that Lori will receive from the bond, we need to use the following formula:

Semiannual interest = (Coupon rate x Face value) / 2

Substituting the given values, we get:

Semiannual interest = (9.5% x $20,000) / 2

Semiannual interest = ($1,900) / 2

Semiannual interest = $950

Therefore, Lori will receive a semiannual interest of $950 from the bond. This means that she will receive a total of $1,900 in interest every year until the bond matures in 20 years.

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Using the scale factor of 4:1, the side lengths of the real objects are:

B. Side a is 5 inches long and side b is 4.5 inches long.

A scale factor is a number that represents the ratio of the size or dimensions of an object in relation to another object. It is a proportional relationship between two similar objects, where the scale factor is the ratio of any corresponding lengths or dimensions.

Thus, given that the scale factor is 4:1, it means 4 inches of the scale drawing represents 1 inch of the real object.

Therefore, the sides would be:

Side a = 20/4 = 5 in.

Side b = 18/4 = 4.5 in

The answer is B.

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The new box would need approximately 8 ounces of paint and would hold 120 cups of sugar.

To find out how much paint the new box would need and how much sugar it would hold, follow these steps:
1. The original box holds 15 cups of sugar, and it takes 2 ounces of paint to cover it completely. When you double the dimensions of the box, areas are scaled by [tex]k^2[/tex] (k is the scale factor), and volumes are scaled by[tex]k^3.[/tex]
2. Since you double the dimensions, the scale factor k is 2.
3. The surface area of the box will be scaled by [tex]k^2, which is 2^2 = 4.[/tex]So, the new box will need 4 times the amount of paint that the original box needed. Since the original box needed 2 ounces of paint, the new box will need 2 × 4 = 8 ounces of paint.
4. The volume of the box will be scaled by [tex]k^3, which is 2^3 = 8[/tex]. So, the new box will hold 8 times the amount of sugar that the original box held. Since the original box held 15 cups of sugar, the new box will hold 15 × 8 = 120 cups of sugar.
In conclusion, the new box would need approximately 8 ounces of paint and would hold 120 cups of sugar.

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Translation: The blue figure can be moved to the red figure by a translation of three units to the right and one unit down.

Reflection: The blue figure can be moved to the red figure by a reflection over the x-axis.

Rotation: The blue figure can also be moved to the red figure by a rotation of 90 degrees counterclockwise.

Transformation in mathematics is the process of changing an object or figure in some way. This includes changing the size, position, rotation or reflection of an object. Transformations can also be used to move a figure from one coordinate system to another. Common transformations include translation, rotation, reflection and scaling.

To demonstrate this transformation, imagine the blue figure being shifted three units to the right and one unit down, such that it is now completely overlapping the red figure.

This transformation can be visualized by imagining the figure being flipped along the x-axis, so that the right side of the figure is now on the left side and vice versa.

To demonstrate this transformation, imagine the blue figure being spun 90 degrees counterclockwise, so that the top of the figure is now on the left side and the bottom is on the right side. This rotation will align the figure with the red figure.

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Population will be 43,160 in 76 years if a town doubles its size every 38 years if the current population is 6,790.

Since the town doubles in size every 38 years, we can use the formula:

P = P0 * 2^(t/T)

where P0 is the initial population, P is the population after time t, and T is the doubling time (38 years in this case).

We know that the current population is P0 = 6,790, and we want to find the population in 76 years, which is t = 76. Plugging these values into the formula, we get:

P = 6,790 * 2^(76/38)

P = 6,790 * 2^2

P = 6,790 * 4

P = 27,160

Therefore, the population of the town will be 27,160 in 76 years.

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Answer:

Step-by-step explanation:

Since △PQR ~ △STU, their corresponding angles are congruent, and their corresponding sides are proportional.

First, we can find the measure of angle Q as follows:

m∠Q = 180 - m∠P - m∠R = 180 - 70 - 46 = 64 degrees

Next, we can use the fact that the sides of the similar triangles are proportional to set up the following proportions:

frac{ST}{21} = frac{SU}{14} and frac{ST}{28} = frac{TU}{21}

Solving for ST gives us:

ST = frac{21}{14} SU = frac{3}{2} SU

and

ST = frac{28}{21} TU = frac{4}{3} TU

Substituting these values into the second proportion, we get:

frac{3}{2} SU = frac{4}{3} TU

Multiplying both sides by 2/3, we get:

SU = frac{8}{9} TU

Now we can use the fact that the angles in a triangle add up to 180 degrees to find the measure of angle T.

m∠T = 180 - m∠S - m∠U = 180 - m∠S - (180 - m∠P - m∠R)

m∠T = m∠P + m∠R - m∠S = 70 + 46 - m∠S = 116 - m∠S

Finally, we can use the fact that the angles in △STU add up to 180 degrees to find the measure of angle S.

m∠S + m∠T + m∠U = 180

Substituting the previously found values for m∠T and SU into the equation, and solving for m∠S gives us:

m∠S = 52 degrees

Therefore, the missing measures are:

SU = 6 x 8/9 = 16/3

ST = 3/2 x 6 = 9

TU = 4/3 x 9 = 12

m∠S = 52 degrees

m∠T = 116 - 52 = 64 degrees

m∠U = 180 - 52 - 64 = 64 degrees

During bracket off, when 6x⁴ * 6x⁴= 36x⁸ instead of 36x¹⁶ using Perfect square method.

When 4y² * 4y² = 16y^4 instead of 25y⁴⁴ gotten in the question. To correct the error, using the perfect square method, it can be corrected.

The answer will be (6x⁸ - 5y²)(6x⁸ + 5y²)The last error found is sign rule-4y^2  x -4y^2 = +16y⁴ instead of -4y² * +4y² = -16y⁴

Perfect square is  is a number that is generated by multiplying two equal integers by each other.

Given 36x¹⁶ - 25y⁴

The rule = A difference of two perfect squares, A² - B²²  can be factored into (A+B) x (A-B)36x¹⁶ is a perfect square = 6₂ * x⁸2)= (6x⁸)^225y⁴ is also a perfect square= 5² * x²(2)= (5x²)²

Using the rule for Perfect square,

When A² - B² = (A + B) x (A - B)

So,(6x⁸)₂ - (5x²)²

=(6x⁸ + 5x²) * (6x⁸ - 5x²)

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1) The price of one senior citizen ticket is $16 and the price of one student ticket is $8.

2) The price of one adult ticket is $12 and the price of one student ticket is $6.

3) The cost of one hasta is $180 and the cost of one shrub is $302.

4) The cost of one daylily is $10.40 and the cost of one bunch of ornamental grass is $10.

5) The cost of one daylily is $6.88 and the cost of one bunch of ornamental grass is $3.67.

Algebra uses symbols to represent unknown values, and equations to describe the relationships between those values. It is used to solve for those unknown values in order to perform calculations and solve real-world problems.

These answers can be determined by using basic algebraic equations to solve for the unknown variables. In the first example, the equation can be written as: 7S + 7C = 112, where S is the cost of one student ticket and C is the cost of one senior citizen ticket. Solving for S, we can get: S = (112-7C)/7. The same technique can be used for the other examples. This process of solving equations is useful in determining the prices of items when given certain information. It is also important for businesses to use this technique when pricing items, in order to maximize their profits.

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By using system of equations, following are the solutions:

1) The price of one senior citizen ticket is $3 and the price of one student ticket is $13.

2) The price of one adult ticket is $4 and the price of one student ticket is $6.

3) The cost of one hosta is $10 and the cost of one shrub is $12.

4) The cost of one daylily is $12 and the cost of one bunch of ornamental grass is $8.

5) The cost of one daylily is $10 and the cost of one bunch of ornamental grass is $3.

Algebra uses symbols to represent unknown values and variables, and equations to describe the relationships between those values. It is used to solve for those unknown values in order to perform calculations and solve real-world problems.

1) Assume that the cost for the senior citizen tickets is x and for the students is y.

On the first day: 7x + 7y = 112                                             [eq. 1]

On second day: 4x + 7y = 103                                            [eq. 2]

By solving, 7x + 7y = 112

x = (112 - 7y)/7

We have,

x = (112/7) - y

Now substitute the value of x in [eq. 2]

4[(112/7) - y] + 7y = 103  

4[(112/7) - y] = 103 - 7y

y = 13

Place the value of y in one of the above equations:

4x + 7(13) = 103

4x = 103 - 91

4x = 12

x = 3

2) Assume that the cost for the adult tickets is x and for the students is y.

On the first day: 3x + 6y = 48                                              [eq. 1]

On second day: 3x + 3y = 30                                              [eq. 2]

By solving, 3x + 6y = 48

3x = 48 - 6y

We have,

x = (48/3) - 2y

Now substitute the value of x in [eq. 2]

3[(48/3) - 2y] + 3y = 30

3[(48/3) - 2y] = 30 - 3y

3[(48/3) - 2y] = 3(10 - y)

(48/3) - 2y = 10 - y

y = 6

Place the value of y in one of the above equations:

3x + 3y = 30

3x + 3(6) = 30

3x = 30 -18

x = 4

3) Assume the price of hostas to be x and shrubs to be y.

For Ashley: 3x + y = 42                                                  [eq. 1]

For Asanji: 7x + y = 82                                                   [eq. 2]

By solving, 3x + y = 42

y = 42 - 3x

Now substitute the value of y in [eq. 2]

7x + (42 - 3x) = 82

4x = 40

x = 10

Place the value of x in one of the above equations:

7x + y = 82

7(10) + y = 82

y = 82 - 70

y = 12

4) Assume the price of dailylily to be x and ornamental grass to be y.

For Ashley: x + 5y = 52                                                  [eq. 1]

For Kali: 5x + 5y = 100                                                    [eq. 2]

By solving, x + 5y = 52

x = 52 - 5y

Now substitute the value of x in [eq. 2]

5(52 - 5y) + 5y = 100

5(52 - 5y) = 5(20 - y)

52 - 5y = 20 - y

y = 8

Place the value of y in one of the above equations:

x + 5y = 52

x + 5(8) = 52

x = 12

5) Assume the price of dailylily to be x and ornamental grass to be y.

For Dan: 8x + 6y = 50                                                  [eq. 1]

For Kali: x + 6y = 22                                                     [eq. 2]

By solving, x + 6y = 22

x = 22 - 6y

Now substitute the value of x in [eq. 1]

8(22 - 6y) + 6y = 50

126 = 42y

y = 3

Place the value of x in one of the above equations:

x + 6y = 22

x + 6(3) = 22

x = 10

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Answer:

A

Just Because They Produce more Automobiles, does not mean they sell them all, which it also does not tell us the quantity.

The solution to the system of equations is: x = 1/2 and y = 4. The steps and justification are given below.

Given the equations, -4x + y = 2 and 4x + y = 6, the following shows the justification for each step taken to solve the system.

Step                                   Justification                                            

1. 2y = 8                            1. Add the equations

2. y = 4                             2. Divide each side by 2

3. 4x + y = 6                     3. Write equation 2

4. 4x + (4) = 6                   4. Substitute 4 for y

5. 4x = 2                           5. Subtract 4 from each side

6. x = 1/2                           6. Divide each side by 4

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The total number of units produced in an 8-hour day is approximately 22.86 units.

There are different ways to approach this problem, but one possible method is to use the concept of cycle time and the total available production time to determine the number of units produced in a day.

An operation is performed on a batch of 100 units.

Setup time is 20 minutes and run time is 1 minute.

The total number of units produced in an 8-hour day is:

Step 1: Find the cycle time per unitThe cycle time per unit is the sum of the setup time and the run time:

Cycle time = setup time + run time = 20 minutes + 1 minute = 21 minutes.

Step 2: Find the total available production time in a day

One day has 24 hours, but 8 hours are not available for production due to breaks, maintenance, and other factors. Therefore, the total available production time is:

Total available production time = 8 hours × (60 minutes per hour) = 480 minutes.

Step 3: Calculate the number of units produced in a day

The number of units produced in a day is the total available production time divided by the cycle time per unit:

Units produced = total available production time ÷ cycle time= 480 minutes ÷ 21 minutes≈ 22.86 units (rounded to two decimal places)

Therefore, the total number of units produced in an 8-hour day is approximately 22.86 units.

This assumes that there is no variability in the process, and that all units are of good quality.

If there are any defects, rework, or other disruptions, the actual production may be lower.

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There are 6 possible arrangements of four children on a 4-animal merry-go-round if Andy is seated on the giraffe.

If Andy is seated on the giraffe in a 4-animal merry-go-round, the arrangement of four children on the merry-go-round can be determined as follows:

Since Andy is already seated on the giraffe, only three children are left to be seated on three other animals. The first child can be seated on any of the three remaining animals. The second child can be seated on either of the two remaining animals since one has already been occupied.

Finally, the third child can be seated on the only remaining animal. Therefore, there are three options for the first child, two options for the second child, and one option for the third child, resulting in 3*2*1 = 6 possible arrangements of four children on a 4-animal merry-go-round if Andy is seated on the giraffe.Answer:6.

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Answer: rectangleular pyramid

Step-by-step explanation:

2 and 2/3 divided by 6 equals 4/9.

So, 2 and 2/3 divided by 6,

we can simplify it step by step as follows:

First, we need to convert the mixed numbers 2 and 2/3 to an improper fraction:

2 and 2/3 = (2 × 3 + 2) / 3 = 8/3

Therefore, the expression becomes:

8/3 ÷ 6

To divide fractions, we need to invert the second fraction and multiply:

8/3 ÷ 6 = 8/3 × 1/6

Simplifying the multiplication of fractions:

8/3 × 1/6 = (8 × 1) / (3 × 6) = 8/18

Now, we can simplify the fraction 8/18 by dividing both the numerator and denominator by their greatest common factor, which is 2:

8/18 = (8 ÷ 2) / (18 ÷ 2) = 4/9

Therefore, 2 and 2/3 divided by 6 equals 4/9.

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