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The polynomial to represent the volume of the rectangular prism is:

V = (0.5x - 3) × (x - 4) × (x + 5)

Simplifying this expression gives V = 0.5x³ - 6.5x² - 23x + 60

How to calculate the volume (V) of a rectangular prism?
The volume (V) of a rectangular prism can be calculated using the formula V = l × w × h, where l, w, and h are the length, width, and height of the prism respectively.

Here, the length (l) can be represented by (0.5x - 3), the width (w) can be represented by (x - 4), and the height (h) can be represented by (x + 5).

Therefore, the polynomial to represent the volume of the rectangular prism is:

V = (0.5x - 3) × (x - 4) × (x + 5)

Simplifying this expression gives V = 0.5x³ - 6.5x² - 23x + 60

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The probability that both the first and second student studied = p²

To find the probability that both the first and second students studied when two different students are randomly selected, we can use the multiplication rule of probability.

The multiplication rule of probability states that if the probability of event A is p(A), and the probability of event B, given that event A has occurred, is p(B|A), then the probability of the joint occurrence of A and B is given by p(A and B) = p(A) × p(B|A).

So, if we let A be the event that the first student studied, and B be the event that the second student studied, then we need to find the probability of the joint occurrence of A and B.

We can assume that the probability that any student studied is equal to some value p, and the probability that any student didn't study is equal to q = 1 - p. Since there are only two possibilities for each student (studied or not studied), then p + q = 1. So, we can use the complement rule of probability to write:

p(A) = probability that the first student studied = p, and

p(not A) = probability that the first student didn't study = q = 1 - p,

p(B|A) = probability that the second student studied, given that the first student studied = p, and

p(B|not A) = probability that the second student studied, given that the first student didn't study = p.To find the probability that both the first and second student studied, we need to find the probability of the joint occurrence of A and B. Using the multiplication rule, we get:

p(A and B) = p(A) × p(B|A) = p × p = p².

Which is the probability that both the first and second students studied.

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To estimate x, we can use the fact that 5% is approximately equal to 1/20. Therefore, if 5% of x is about 10 hours, then we can estimate that 1/20 of x is also about 10 hours.

Multiplying both sides of the equation 1/20 x = 10 by 20, we get x = 200.

To check our answer, we can verify that 5% of 200 hours is indeed about 10 hours.

We used the multiplication property of equality to solve for x, which states that we can multiply both sides of an equation by the same non-zero number without changing the solution. In this case, we multiplied both sides by 20.

Among the answer choices, the line that represents a row perpendicular to y = 1 is x = 4.

Coordinate geometry, also known as analytic geometry, is a branch of mathematics that deals with the study of geometric figures using coordinates.

The line y = 1 is a horizontal line that goes through all points on the y-axis with a y-coordinate of 1.

To find a line perpendicular to it, we need to find a line that has a slope that is the negative reciprocal of the slope of y = 1. The slope of y = 1 is 0, so the slope of the perpendicular line is undefined (since any number divided by 0 is undefined).

Therefore, the perpendicular line must be a vertical line, and its equation would be of the form x = c, where c is a constant.

Hence, among the answer choices, the line that represents a row perpendicular to y = 1 is x = 4.

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The points A', B', and C' are  (3, 1), (0, 3) and (-2, 4) respectively. The solution has been obtained by using the concept of transformation.

What is transformation?

Transformations allow for the translation, rotation, and reflection of shapes on a coordinate plane. Any line, point, or vector can be rotated, translated, or reflected.

We are given coordinates of triangle ABC as A (1, -3), B (3, 0) and C (4, -2).

Now, we need to rotate the triangle ABC 90 degrees about the origin.

We know that the rotation rule for rotating 90 degrees about the origin is that (x, y) becomes (y, -x).

So, from this we get the coordinates as

A' (3, -1)

B' (0, -3)

C' (-2, -4)

Now, on reflecting it over the x - axis, we get

A' (3, 1)

B' (0, 3)

C' (-2, 4)

Hence, the points A', B', and C' are  (3, 1), (0, 3) and (-2, 4) respectively.

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Rοunding up tο the nearest whοle cupcake, yοu shοuld buy 8 cupcakes tο ensure that yοur rοbοt has enοugh cupcakes tο last fοr the next 14 days.

An equatiοn is a mathematical statement that indicates that twο expressiοns are equal. It cοntains an equals sign (=) between twο expressiοns, with οne expressiοn οn each side οf the equals sign. Equatiοns can cοntain variables, cοnstants, cοefficients, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Here,

If yοur rοbοt eats 4 cupcakes every 7 days, it means it eats 4/7 = 0.57 cupcakes per day (rοunded tο twο decimal places).

Tο buy enοugh cupcakes fοr the last 14 days, yοu need tο multiply the number οf days by the daily cοnsumptiοn rate:

0.57 cupcakes per day x 14 days = 7.98 cupcakes

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Complete question:

If your robot eats 4 cupcakes every 7 days. So to buy enough cupcakes for the last 14 days, how much cupcake is consumed daily?

Answer:

Answer is 28

Step-by-step explanation:

Length = 5

Width = 9

Perimeter = length*2 + width*2

Perimeter = 5*2 + 9*2

Perimeter = 10 + 18 = 28

To conclude that quadrilateral LMNO is a parallelogram, we need either ML ∥ NO, LO ≅ MN, or ML ⊥ LO.

Since LO ∥ MN, we know that ∠LON = ∠OMN and ∠NOM = ∠LMO. To conclude that LMNO is a parallelogram, we need to show that opposite sides are parallel and equal in length.

The following statements would be sufficient to conclude that LMNO is a parallelogram:

ML ∥ NO: If ML is parallel to NO, then ∠LMO = ∠NOM, and since ∠NOM = ∠LMO, we have ∠LMO = ∠NOM = ∠NLO = ∠OML. Therefore, opposite angles are equal, and LMNO is a parallelogram.

LO ≅ MN: If LO is equal in length to MN, then we have LO = MN and ∠LON = ∠OMN. Therefore, triangle LON is congruent to triangle MON by the side-angle-side (SAS) congruence criterion. This implies that ∠LNO = ∠MNO and ∠LON = ∠MON. Since ∠LNO + ∠LON = 180° and ∠MNO + ∠MON = 180°, we have ∠LNO = ∠MON and ∠LON = ∠MNO. Therefore, opposite angles are equal, and LMNO is a parallelogram.

ML ⊥ LO: If ML is perpendicular to LO, then ∠LMO = 90° and ∠NOM = 90°. Therefore, opposite angles are equal, and LMNO is a parallelogram.

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The given question is incomplete, the complete question is:

In quadrilateral LMNO, LO ∥ MN. What additional information would be sufficient, along with the given, to conclude that LMNO is a parallelogram? Check all that apply. ML ∥ NO ML ⊥ LO LO ≅ MN ML ≅ LO MN ⊥ NO.

Answer:

The circle x^2+y^2-2x-8y+17=0 has translated 5 units to the leftand 2units down.

Step-by-step explanation:

If we translate this circle to the left 5 units, and 2 units down,

we will subtract 5 from the center x coordinate and 2 for the center y coordinate

The center is (1,-4)

So the new center prime is (-4,-6)

Since a translation keep angles and measures,

Our radius will remain untouched so our new equation is

[tex](x + 4) {}^{2} + (y + 6) {}^{2} = 16[/tex]

the area of the porch is 228 square centimeters. To calculate the area of a porch, we need to use the formula for the area of a rectangle, which is:

Area = length x width

In this case, the length of the porch is 19 cm and the width is 12 cm. So, we can plug these values into the formula:

Area = 19 cm x 12 cm

Area = 228 cm^2

Therefore, the area of the porch is 228 square centimeters.

It's important to note that when we use the term "area," we are referring to the amount of space that is enclosed within the boundaries of the porch. In other words, we are calculating the size of the surface area of the porch, which is measured in square units.

Knowing the area of a porch can be useful in a variety of contexts. For example, if you were planning to install new flooring on the porch, you would need to know the area in order to calculate how much material you would need to purchase. Similarly, if you were planning to paint the porch, you would need to know the area in order to estimate how much paint you would need to cover the surface.

In summary, the area of a porch can be calculated by multiplying its length and width, and is measured in square units.

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Answethe two digit is a multiple of 5

Step-by-step explanation:

the two-digit number is 65 so, options that must be true are a and b.

Addition is a basic arithmetic operation that combines two or more numbers to produce a sum or total

Let x stand for the tens digit and y for the units digit.

x + y = 11 (the digits of the two-digit number sum to 11)

x - y = 1 (the positive difference of the digits is 1)

Adding these two equations gives:

2x = 12

So x = 6.

Substituting x = 6 into either of the equations gives y = 5.

Therefore, the two-digit number is 65.

Now we can check which of the options is true:

a. The two-digit number has a product of 30 digits.

6 x 5 = 30, so this is true.

b. The number has two digits and is a multiple of 5.65 is a multiple of 5, so this is true.

c. The two-digit number is even.

65 is not even, so this is false.

d. The two-digit number is 83.

The two-digit number is 65, not 83, so this is false.

Therefore, the options that must be true are a and b.

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This problem can be solved by the unitary method. If Lee Ann bought 2 cartons of yoghurt, she would take 16 days to finish two cartoons as there were 8 yoghurt in each cartoon.

The unitary method involves first determining the value of a single unit, followed by the value of the necessary number of units.

Always write the things that need to be calculated on the right side and the things that are known on the left side to simplify things. In the aforementioned issue, the number of apples is known, but it is unclear what they are worth. It should be noted that issues with this method are solved using the concepts of ratio and proportion.

Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when applying the unitary method to a problem.

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These steps in the design process are often iterative, meaning that architects may revisit earlier steps as they refine and develop the design. The overall goal of the design process in architecture is to create a functional, safe, and aesthetically pleasing building that meets the needs and goals of the client.

The following are the steps in the design process, organized in architecture:

Programming: In this first step, architects work with their clients to understand the project requirements, goals, and objectives. They may gather information about the site, zoning and building codes, budget, and other constraints.

Schematic Design: In this step, architects use the information from the programming phase to create rough sketches and drawings that show the basic layout and massing of the building. This phase is an opportunity to explore various design options and to get feedback from the client.

Design Development: In this step, the architects refine the design, incorporating structural and mechanical systems, and developing detailed drawings and specifications. This phase also includes working with consultants such as engineers and contractors.

Construction Documents: In this step, the architects prepare the final construction documents, which include detailed drawings and specifications that will be used by contractors to build the project.

Bidding and Negotiation: In this step, the architects help the client solicit bids from contractors and negotiate the terms of the construction contract.

Construction Administration: In this final step, the architects oversee the construction process, ensuring that the project is built according to the design documents and that any changes or issues are addressed.

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Answer:

because triangle ABD is congruent to triangle CBD

by CPCT

AB = CD

The sale price of the computer after a single reduction of 30% is $455.

The double reduction (25% off and then 5% off) and the single reduction of 30% are different.

The sale price after the double reduction is $463.13, while the sale price after a single reduction of 30% is $455.

What is a percentage?

The percentage is a way of expressing a fraction or proportion out of 100. It is commonly used in many different areas such as finance, math, science, and everyday life.

First, we need to find the sale price of the computer after the double reduction.

When the price of all computers in the store is reduced by 25%, the sale price of the computer that originally cost $650 becomes:

Sale price after first reduction ,

=> 650 - 25% 0f 650

=> 650 - [tex]\frac{25}{100}\times[/tex]650 = $ 487.5

Then, when the sale price is reduced by an additional 5%, the sale price of the computer becomes:

Sale price after double reduction

=> 487.5 - 5% of 487.5

=>  487.5 - [tex]\frac{5}{100}\times[/tex]487.5 = $463.13

Therefore, the sale price of the computer after the double reduction is $463.13.

Next, we need to find the sale price of the computer after a single reduction of 30%.

When the original cost of the computer is reduced by 30%, the sale price becomes:

Sale price after single reduction ,

=> 650- 30% of 650

=>  650 - [tex]\frac{30}{100}\times[/tex] = $455

Therefore, the sale price of the computer after a single reduction of 30% is $455.

The double reduction (25% off and then 5% off) and the single reduction of 30% are different.

The sale price after the double reduction is $463.13, while the sale price after a single reduction of 30% is $455.

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Answer:

[tex] \sqrt{36 + x {}^{2} } - (2) {}^{2} \\ 6 + x + - 2 \\ 6 - 2 + x \\ 4 + x \\ \: \:answer = 4 + x \\[/tex]

Step-by-step explanation & Answer

No, the answer is not correct

In the second step, the student did not use the quotient of powers property correctly. Instead, they should have subtracted inside the parentheses instead of dividing. This would have left them with [tex]x^{(\frac{4}{5} )}[/tex]. They should have then multiplied this power by [tex]^{\frac{1}{2} }[/tex] resulting in [tex]x^{(\frac{4}{10})}[/tex] which simplified is [tex]x^{(\frac{2}{5}) }[/tex] which is the correct answer.

That is just an example on how the answer is done.

Answer:

1) X0=1

2) 19m2

3) there is something missing i think

4) 6x3y

Work out the probability that all three pens are green p = 10/40 * 4/44 * 8/48 = 3/352.

a) p = 10/40 * 4/44 * 8/48 = 3/352

b) p = 3/352 + 30/40 * 24/44* 28/48

=3/352+ 203/704

= 209/704

= 19/64

c) p= 1 - 19/64

= 64/64 - 19/64

= 45/64

Probability is just the way that possible something is to occur.

Whenever we're uncertain about the result of an occasion, we can discuss the probabilities of specific results — how likely they are. The investigation of events administered by probability is called insights.

The probability of an occasion must be somewhere in the range of 0 and 1 and can likewise be composed as a rate.

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7p + q /3

p = 6 and q = 12

7(6) + (12) / 3

42 + 12/ 3

54/3

18

18 is the correct answer, but isn't present as an option in the list.

Answer:D.46

Step-by-step explanation: because 7(6)+12/3

First 7(6)=42

Then 12/3=4

Finally 42+4=46

Answer: y=mx+c

Step-by-step explanation:

Answer:

-9 and -2

Step-by-step explanation:

-9 and -2

two negatives multiply to make a positive (18)

and -9 add -2 is -11

Answer: 475 is ur answer

Step-by-step explanation:

After answering the presented question, we can conclude that Account B: $5463.84 ($5000 multiplied by 1.0223) $5474.60 in Account C ($5000 x e(0.022 x 3))

In mathematics, interest is the amount of money earned or payable on an original investment or loan. You can use either simple or compound interest. Simple interest is calculated as a percentage of the initial amount, whereas compound interest is calculated on the principal amount plus any previously earned interest. If you invest $100 at a 5% annual simple interest rate, you will get $5 in interest every year for three years, for a total of $15.

Mika's account balance after 6 months would be $1413.33 ($1400 + $14.67 interest generated). His account balance after two years would be $1456 ($1400 + $56 interest earned).

Marquis would repay $907.02 after two months ($900 x e(0.038/12 x 2)). He would owe $1,033.72 after 18 months ($900 x e(0.038 x 1.5)).

a. 6 months later:

Account A: $5050 ($5000 + $55 earned in interest)

Account B: $5061 ($5000 multiplied by 1.0220.5).

$5061.68 in Account C ($5000 x e(0.022 x 0.5))

c. One year later:

Account A: $5100 ($5000 + $110 earned in interest)

Account B: $5112.20 ($5000 multiplied by 1.022).

$5113.85 in Account C ($5000 x e(0.022 x 1))

c. After three years:

Account A: $5330 ($5000 + $330 generated interest)

Account B: $5463.84 ($5000 multiplied by 1.0223)

$5474.60 in Account C ($5000 x e(0.022 x 3))

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To cover the entire yard, Mya needs to plant 150 square feet of grass.

Mya's rectangular yard is 10 feet wide and 15 feet long. To find the area of the yard, we need to multiply the width by the length:

Area of yard

= width x length

= 10 ft x 15 ft

= 150 square feet    

Therefore, Mya needs to plant 150 square feet of grass to cover the entire yard

A rectangular yard is a type of outdoor space that is often used for gardening, outdoor activities, or as a place for relaxation. To calculate the area of a rectangular yard, you need to know its dimensions, which are typically expressed in feet or meters. The area of a rectangular yard can be found by multiplying its length by its width. The formula for the area of a rectangle is A = L x W, where A represents the area, L represents the length, and W represents the width. Once you have calculated the area of the yard, you can use this information to determine how much grass or other landscaping materials you need to cover the area.

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We then substitute -1 for x in the equation x + y = 4 to get -1 + y = 4, which we can then subtract -1 from both sides to get y = 5. The solution is x = -1 and y = 5.

3x + y = 7

-x + y = 1

Add the equations together:

2x + 2y = 8

Divide both sides by 2:

x + y = 4

Subtract the second equation from the first:

-x + y = 1

x - y = -3

Add the equations together:

2x = -2

Divide both sides by 2:

x = -1

Substitute -1 for x in the equation x + y = 4:

-1 + y = 4

Subtract -1 from both sides:

y = 5

The solution is x = -1 and y = 5.

We begin by solving the system of linear equations by elimination. We need to get the variables to one side of the equation and the constants to the other side. We start by adding the two equations together: 3x + y = 7 and -x + y = 1. This gives us 2x + 2y = 8, which we can then divide both sides by 2 to get x + y = 4. We then subtract the second equation from the first to get -x + y = 1 and x - y = -3. We then add these two equations together to get 2x = -2 and divide both sides by 2 to get x = -1. We then substitute -1 for x in the equation x + y = 4 to get -1 + y = 4, which we can then subtract -1 from both sides to get y = 5. The solution is x = -1 and y = 5.

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The vaIue οf n = 5 .

A mathematicaI statement knοwn as an equatiοn cοnsists οf twο aIgebraic expressiοns separated by equaI signs (=) οn either side.

It demοnstrates the equaIity οf the reIatiοnship between the printed statements οn the Ieft and right.

Left side equaIs right side in aII fοrmuIas.

Tο find the vaIues οf unknοwabIe variabIes, which stand in fοr unknοwabIe quantities, yοu can sοIve equatiοns.

A statement is nοt an equatiοn if it Iacks the equaIs sign.

When twο expressiοns have the same vaIue, a mathematicaI statement knοwn as an equatiοn wiII incIude the symbοI "equaI tο" between them.

Accοrding tο οur questiοn-

[tex]2 \times 10^{(n+5)} + 4.02 \times 10^5 = 2 x 10^{(n+5)} + 4.02 \times 10^n[/tex]

Subtracting [tex]2 \times 10^{(n+5)[/tex] frοm bοth sides:

[tex]4.02 \times 10^5 = 4.02 \times 10^n[/tex]

Dividing bοth sides by 4.02:

[tex]10^5 = 10^n[/tex]

Therefοre, n = 5.

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COMPLETE QUESTION-

if [tex](2\times10^n)+(4.02\times10^5)[/tex], what is n?

Answer:

54inch^2

Step-by-step explanation:

3×6=18

18÷2=9

6×6=36

36+9+9= 54

answer: 54inch^2

When driving in normal conditions on a rural roadway, your following distance should be four seconds or more because it gives you more time to respond to any unexpected occurrences that might occur. therefore option d) four seconds or more is correct.

Following distance is the amount of space between a car and the car in front of it when driving on the road. It's essential to keep a safe following distance because it gives you more time to react if the car in front of you makes a sudden stop or starts to slow down. It's critical to keep a safe following distance because it's not always possible to avoid sudden stops or slow-downs.

A rural roadway is a road that runs through the countryside. In comparison to city roads, rural roads are less congested, with less traffic and less likelihood of accidents. As a result, it's essential to maintain a safe following distance when driving on rural roads because they're often long and wide, with higher speed limits and less congestion than city roads.

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Each of the shapes below, The polygons are identified as:

A- Irregular polygon

B- Neither

C- Regular polygon

D- Regular polygon

E- Regular polygon

A polygon is a two-dimensional geometric shape that is defined as a closed figure with three or more straight sides and angles. Polygons can be convex or concave, depending on whether all of their interior angles are less than or greater than 180 degrees, respectively. Some common examples of polygons include triangles (3 sides), squares (4 sides), pentagons (5 sides), hexagons (6 sides), and octagons (8 sides). Polygons are frequently used in geometry, as they can be used to calculate areas, perimeters, and other properties of shapes.

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