Part B


In the equation you wrote in part A, which is the independent value and which is the dependent value?

Each section of the garden will be 3.4 feet long.

To find the length of each section, we can divide the total length of the garden by the number of sections.

Length of the garden: 40.8 feet

Number of sections: 12

Length of each section = Total length of the garden / Number of sections

Length of each section = 40.8 feet / 12

Length of each section = 3.4 feet

Therefore, each section of the garden will be 3.4 feet long.

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A sample of n = 5 scores has a mean of M = 12. If one person with a score of X = 18 is added to the sample, the new mean, can be calculated as 14.

The initial sample of n = 5 scores has a mean of M = 12. To find the new mean after adding a score of X = 18 to the sample, we can use the formula for the mean: M = (sum of scores) / (number of scores).

The sum of the original scores is 5 * 12 = 60. When we add the score of 18, the new sum becomes 60 + 18 = 78. Since the total number of scores is now 6, the new mean is calculated as 78 / 6 = 13.

Therefore, the new mean after adding a score of 18 to the sample is 14.

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Let x be the number of large frames and y be the number of small frames that a woman bought from the closeout sale.Therefore, the two equations that we can use to solve the problem are:

x + y = 27 ...(1)and19x + 9y = 343 ...(2)Multiplying equation (1) by 9 and subtracting it from equation (2), we get:19x + 9y = 343  ...(2)- (9x + 9y = 243) ...(3)10x = 100x = 10Thus, the woman bought 10 large frames

.Substituting x = 10 in equation (1), we get:10 + y = 27y = 27 - 10y = 17Thus, the woman bought 17 small frames. Therefore, the woman bought 10 large frames and 17 small frames.

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We can use a proportion to determine how long it would take a worker to make 45 days.

Let's set up the proportion:

(5 hours) / (300 deyas) = (x hours) / (45 deyas)

To solve for x, we can cross-multiply and then divide:

5 hours * 45 deyas = 300 deyas * x hours

225 hours = 300 deyas * x hours

Now, divide both sides by 300 days to isolate x:

x hours = 225 hours / 300 deyas

Simplifying the right side:

x hours = 0.75 hours

Therefore, a worker would take approximately 0.75 hours (or 45 minutes) to make 45 days.

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For a triangle with base= 2 cm and perimeter= 10 cm, total area of the plastic triangles on the spinner is=18 square centimeters or 18 cm²

Let us assume that the two sides that are not the base of the triangle are x each.

Therefore, the perimeter of the triangle is: x + x + 2

Now,

     2x + 2 = 10 cm

=> x = 4 cm

Thus, we have a right triangle with sides 2 cm, 4 cm, and a hypotenuse of =√(2^2 + 4^2)

                                                                                                                             = √20

                                                                                                                             = 2√5.

The area of a triangle is= 1/2×(base)×(height).

For the plastic triangles, the base is 2 cm and the height is 2√5. Therefore, the area is given by:

=1/2(2)(2√5)

= 2√5 square centimeters.

The spinner has four plastic triangles, so the total area is:

=4(2√5)

= 8√5 square centimeters.

Now, we need to get an approximate value for the area using a calculator or by estimating √5 as 2.24:

8(2.24) ≈ 17.92 square centimeters, which is closest to 18.

Therefore, the answer is: 18 square centimeters or 18 cm².

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The expression that shows five less than the sum of 12 and a number is `12 + x - 5`, where `x` is the number. The expression can be simplified as `7 + x`.

An expression is a mathematical phrase containing variables, numbers, and mathematical operations. It is a combination of variables, constants, and mathematical operators that express a mathematical relationship. An expression can be evaluated to obtain a number.

An equation is a mathematical statement that equates two expressions. It consists of an equal sign between two expressions. The equal sign represents that the expressions on either side of it have the same value. An equation has an unknown value that can be calculated by solving it.

A sum is the result of adding two or more numbers together. The numbers that are added are called addends. The sum of two numbers is the result of adding them together. For example, the sum of 2 and 3 is 5. The sum of 5 and 7 is 12.A number is a mathematical object used to measure or count something. It represents a quantity or value. Numbers can be whole numbers, fractions, decimals, or negative numbers. Whole numbers are positive integers and zero.

Fractions are numbers that represent a part of a whole. Decimals are numbers that represent fractions in decimal form. Negative numbers are numbers less than zero.

The expression that shows five less than the sum of 12 and a number is `12 + x - 5`, where `x` is the number.

The expression can be simplified as `7 + x`.

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The expression that represents this week's price, in dollars, of a gallon of gasoline is 1.05g.

Given that last week, the price, in dollars, of a gallon of gasoline was g. This week, the price of gasoline per gallon increased by 5%.We are to find which expressions represent this week's price, in dollars, of a gallon of gasoline.

If the price of gasoline per gallon last week was g, and it has increased by 5% this week, then this week's price of gasoline per gallon will be 5% greater than last week's price, which is equal to 1.05 times the price of last week's gasoline per gallon.Therefore, this week's price, in dollars, of a gallon of gasoline is given by the expression 1.05g.

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The only like terms are StartFraction 2 x over 5 EndFraction and StartFraction x over 3 EndFraction.Like terms are those terms that have the same variables and the same exponent in them, and they can be combined or added.

Like terms are those terms that have the same variables and the same exponent in them, and they can be combined or added. From the given algebraic expressions, the like terms are:StartFraction 2 x over 5 EndFraction and StartFraction 2 x over 5 EndFraction2.2 and 5.2yStartFraction x over 3 EndFraction and StartFraction 2 x over 5 EndFraction

Given algebraic expression isStart Fraction 2 x over 5 EndFraction - 5.2y2. 2StartFraction x over 3 End FractionStart Fraction 2 x over 5 End Fraction and -5.2y are not like terms because the variable x is in different forms and y is also in different forms.So, the only like terms are StartFraction 2 x over 5 EndFraction and StartFraction x over 3 EndFraction.

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The correct answer is option (b) 15.125 ft², representing the amount of material required for the patch.

The amount of material required for the patch, which is in the shape of the region defined by the equation y = (1/2)x^3, can be determined by calculating the area under the curve.

The patch's shape is defined by the equation y = (1/2)x^3. To find the area under the curve, we need to integrate the equation with respect to x over the appropriate interval. In this case, we are not given specific limits of integration, so we assume the interval is from x = 0 to x = 3 (based on the curve's shape shown in the equation).

The integral for finding the area under the curve is: A = ∫[0 to 3] (1/2)x^3 dx.

Evaluating the integral, we get: A = [(1/2) * (1/4)x^4] evaluated from 0 to 3.

Plugging in the limits, we have: A = (1/2) * (1/4) * (3^4 - 0^4) = (1/2) * (1/4) * (81 - 0) = (1/2) * (1/4) * 81 = 15.125 ft².

Therefore, the correct answer is option (b) 15.125 ft², representing the amount of material required for the patch.

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The numbers 340, 253, 5352740, 253, and 535 can be written as "three hundred forty," "two hundred fifty-three," "five million three hundred fifty-two thousand seven hundred forty," "two hundred fifty-three," and "five hundred thirty-five" respectively.

The number 340 can be written as "three hundred forty." It consists of three hundreds, four tens, and zero ones.

The number 253 can be written as "two hundred fifty-three." It consists of two hundreds, five tens, and three ones.

The number 5352740 can be written as "five million three hundred fifty-two thousand seven hundred forty." It consists of five million, three hundreds of thousands, five tens of thousands, two thousand, seven hundred, and forty ones.

The number 253 can be written as "two hundred fifty-three." It consists of two hundreds, five tens, and three ones.

The number 535 can be written as "five hundred thirty-five." It consists of five hundreds, three tens, and five ones.

These are the written forms of the given numbers.

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the clown would need to buy 138 packs of balloons to have a total of 275 balloons for the party.

IfIf the balloons only come in packs of 2, we need to determine how many packs the clown would need to buy in order to have a total of 275 balloons.

To find the number of packs needed, we divide the total number of balloons (275) by the number of balloons in each pack (2).

275 balloons ÷ 2 balloons per pack = 137.5 packs

Since we cannot have a fraction of a pack, we round up to the nearest whole number.

Therefore, the clown would need to buy 138 packs of balloons to have a total of 275 balloons for the party.

Note: Rounding up to the nearest whole number ensures that the clown has enough balloons and avoids having a fractional number of packs.

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In "Highest Duty: My Search for What Really Matters," Captain Sully's childhood is described as characterized by curiosity, discipline, and a sense of responsibility.

Evidence from the text reveals that he displayed a keen interest in aviation from a young age, built model airplanes, and read aviation books. Moreover, his father's military background instilled discipline and taught him the importance of responsibility. These traits shaped his character and laid the foundation for his future career as a pilot.

The book "Highest Duty: My Search for What Really Matters" provides insights into Captain Sully's childhood and highlights certain aspects of his character. One key inference is his curiosity and passion for aviation. The text mentions that as a child, Sully built model airplanes, spent time at the library studying aviation books, and even constructed a small airfield in his backyard. These activities indicate his early fascination with flying and his drive to learn more about the subject.

Additionally, the influence of Sully's father is evident in his upbringing. His father, a military officer, instilled discipline in his son, emphasizing the importance of adhering to rules and regulations. This upbringing likely contributed to Sully's disciplined approach to his work as a pilot and his commitment to following procedures meticulously.

Furthermore, Sully's sense of responsibility is evident throughout the book. As a child, he took on responsibilities such as taking care of his younger siblings and helping his mother. This early sense of responsibility laid the groundwork for his future career, where he would be entrusted with the lives of passengers and crew members.

In conclusion, Captain Sully's childhood can be described as marked by curiosity, discipline, and a strong sense of responsibility. His passion for aviation, disciplined upbringing, and early sense of responsibility shaped his character and played a significant role in his successful career as a pilot.

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A parallelogram is a quadrilateral where both pairs of opposite sides are parallel. Therefore, we will consider if the opposite sides are parallel or not.In order to determine if A(-2,3) B(2,2), C(10,5), D(6,7) is a parallelogram or not, we can follow the given steps:

Step 1: First, we will calculate the slope of AB and CD to check if they are equal or not.Slope of AB = (y2-y1)/(x2-x1)= (2-3)/(2-(-2))= -1/4Slope of CD= (y2-y1)/(x2-x1)= (7-5)/(6-10)= 2/-4= -1/2

Therefore, AB and CD have different slopes. They are not parallel.Step 2: Now, we will calculate the slope of BC and AD to check if they are equal or not.Slope of BC= (y2-y1)/(x2-x1)= (5-2)/(10-2)= 3/4Slope of AD= (y2-y1)/(x2-x1)= (7-3)/(6-(-2))= 4/2= 2As AD and BC have different slopes.

They are not parallel.Therefore, the given coordinates of A(-2,3) B(2,2), C(10,5), D(6,7) do not form a parallelogram. We can conclude that A(-2,3) B(2,2), C(10,5), D(6,7) is not a parallelogram.Hopefully, this answer helps you.

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The sum of (x - 8x^2 - 15) and (2 + 12x - 3x^2) is represented by the expression -11x^2 + 13x - 13.

To find the sum of the two given expressions, we add the corresponding terms together.

The given expressions are:

(x - 8x^2 - 15) and (2 + 12x - 3x^2)

When we combine like terms, we get:

x + 2 - 8x^2 + 12x - 3x^2 - 15

Simplifying further, we combine the terms with the same power of x:

(-8x^2 - 3x^2) + (x + 12x) + (2 - 15)

This simplifies to:

-11x^2 + 13x - 13

Therefore, the sum of the two expressions is represented by the expression -11x^2 + 13x - 13.

Understanding how to combine like terms and simplify expressions allows us to find the sum of given expressions. By adding the corresponding terms and simplifying, we arrive at the final expression that represents the sum.

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additional information to prove that the two triangles have all three corresponding sides and angles congruent. Hence option d is correct.

When we sa that two triangles are congruent, it means that they have all three pairs of corresponding sides and angles that are congruent

t. So, in order to know that the triangles are congruent using the SAS (Side-Angle-Side) method, we need to have additional information to prove that the two triangles have all three corresponding sides and angles congruent.

Option a): OP = OV. This is not sufficient to show congruence between the triangles using the SAS method. The given reason does not provide any angle information.

Option b): RO = TO or OP = OV. This is also not sufficient to show congruence using the SAS method. The given reason provides only two corresponding sides and no angle information.

Option c): RO = TO. This is not sufficient to show congruence using the SAS method. The given reason provides only one pair of corresponding sides and no angle information.

Option d): Angle R = Angle T. This is sufficient to show congruence using the SAS method. This given reason provides one pair of corresponding sides and an included angle that is congruent in both triangles. Thus, the two triangles have two pairs of congruent sides and a congruent angle between them, which satisfies the SAS condition.

From the above analysis, we can conclude that option (d) is the correct answer. To know whether two triangles are congruent using the SAS method, we need to have additional information to prove that the two triangles have all three corresponding sides and angles congruent

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The acceleration due to gravity is typically denoted as -32.2 ft/sec^2, as it acts in the opposite direction of the rocket's upward motion.

The given function "14001" seems to be incomplete or incorrect, as it does not properly represent the height of the rocket in feet, 2 seconds after the rocket is launched. However, I can provide you with a general explanation of how the rocket's height can be modeled using the given information.

To model the height of the rocket in feet, 2 seconds after launch, we need to consider its initial velocity and starting height.

The rocket's initial velocity is given as 275 ft/sec, which represents the rate at which it is ascending. This velocity will affect the rocket's upward motion.

Additionally, the rocket starts at a height of 3 feet above the ground.

To determine the rocket's height after 2 seconds, we need to take into account the initial velocity, the effect of gravity, and the time elapsed.

Without a specific function or equation, we cannot provide an exact answer. However, in general, we can use the formula for vertical displacement under constant acceleration:

Height = Initial height + (Initial velocity * time) + (0.5 * acceleration * time^2)

Given that the rocket starts at a height of 3 feet and the time is 2 seconds, we can calculate the height of the rocket using the appropriate values of acceleration and initial velocity.

It's important to note that the acceleration due to gravity is typically denoted as -32.2 ft/sec^2, as it acts in the opposite direction of the rocket's upward motion.

Using the formula mentioned above and the provided values, we can determine the height of the rocket 2 seconds after launch. However, without a valid function or additional information, we cannot provide a specific value for the rocket's height.

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The answer is option A: $8.To find the cost of one 5-inch-by-7-inch picture, we need to solve the system of equations:

Equation 1: 3x + 2y = 52

Equation 2: 2x + 2y = 40

We can solve this system of equations using various methods, such as substitution or elimination. Let's use the elimination method:

Multiply Equation 2 by -1 to create opposite coefficients for y:

-1(2x + 2y) = -1(40)

-2x - 2y = -40

Now, we can add Equation 1 and Equation 2 together:

(3x + 2y) + (-2x - 2y) = 52 + (-40)

x + 0y = 12

x = 12

Substitute the value of x into Equation 1:

3(12) + 2y = 52

36 + 2y = 52

2y = 52 - 36

2y = 16

y = 8

Therefore, the cost of one 5-inch-by-7-inch picture is $8.

So, the answer is option A: $8.

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To calculate the volume of a rectangular prism such as a swimming pool, you need to multiply the length, width, and depth of the pool.

Therefore, we can calculate the volume of the swimming pool as follows:

Volume of the swimming pool= Length × Width × Depth

Given that, The length of the swimming pool is 50 meters, the width of the swimming pool is 30 meters, the depth of the swimming pool is 1.75 meters.

Therefore, Volume of the swimming pool= Length × Width × Depth

= 50 × 30 × 1.75

= 2625 cubic meters.

The volume of the swimming pool is 2625 cubic meters. To find out the volume of a swimming pool with a length of 50 meters, a width of 30 meters and a depth of 1.75 meters, we will use the formula for the volume of a rectangular prism which is V = l × w × h.

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The new pressure of the nitrogen gas after it is transferred to a 15.0 L container is 833.3 mmHg.

We are given that;

Capacity of nitrogen gas= 25L

Pressure= 500mmHg

Now,

To find the new pressure of the nitrogen gas, we need to use Boyle’s law, which states that the product of pressure and volume of a gas is constant at constant temperature 12. The formula for Boyle’s law is:

P1V1 = P2V2

where P1 and V1 are the initial pressure and volume of the gas, and P2 and V2 are the final pressure and volume of the gas.

We are also given the final volume of the gas as 15.0 L. We need to find the final pressure of the gas.

Plugging in these values into the formula, we get:

(500.0 mmHg)(25.0 L) = P2(15.0 L)

Solving for P2, we get:

P2 = (500.0 mmHg)(25.0 L) / (15.0 L) P2 = 833.3 mmHg

Therefore, by algebra the answer will be 833.3 mmHg.

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The area of the polygon JKLMNP, representing the bus route, is 6400 square miles based on the given scale of 16 square miles per grid square.

In the given information, the polygon JKLMNP represents a bus route with specific vertices, and each grid square represents 16 square miles.

The vertices of the polygon are given as:

J (2, 4)

K (2, 7)

L (7, 7)

M (7, 2)

N (5, 2)

P (5, 4)

To determine the area of the polygon in terms of square miles, we need to calculate the area of the shape enclosed by the given vertices.

The distance between the vertices on the x-axis represents the width of the polygon, and the distance between the vertices on the y-axis represents the height.

Calculating the width:

KJ = 7 - 2 = 5 units

Calculating the height:

ML = 7 - 2 = 5 units

To convert these units to miles, we multiply by the given scale of 16 square miles per grid square:

Width = 5 * 16 = 80 square miles

Height = 5 * 16 = 80 square miles

Finally, to find the area of the polygon, we multiply the width by the height:

Area = Width * Height = 80 * 80 = 6400 square miles

Therefore, the area of the polygon JKLMNP, representing the bus route, is 6400 square miles based on the given scale of 16 square miles per grid square.

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To dilate the points H(-1, -1), A(1, 0), and T(-1, 2) by a scale factor of 2 from the point (-1, 2), So the answer is: the dilated points are H(-3, 3), A(-1, 4), and T(-3, 6) when dilated by a scale factor of 2 from the point (-1, 2).

The following steps are:

1. Calculate the translation vector from (-1, 2) to the origin (0, 0). Subtract the coordinates of the origin from the coordinates of the point (-1, 2):

Translation vector = (-1 - 0, 2 - 0) = (-1, 2).

2. Apply the dilation to each point using the scale factor of 2. Multiply the translation vector by the scale factor:

Dilation vector = Scale factor * Translation vector

= 2 * (-1, 2)

= (-2, 4).

3. Translate the points back to their original position by adding the dilation vector to each point:

Dilated point H: (-1, -1) + (-2, 4) = (-3, 3)

Dilated point A: (1, 0) + (-2, 4) = (-1, 4)

Dilated point T: (-1, 2) + (-2, 4) = (-3, 6)

So, the dilated points are H(-3, 3), A(-1, 4), and T(-3, 6) when dilated by a scale factor of 2 from the point (-1, 2).

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The cost of the apples is 4 euros per kilo and the cost of the bananas is 6 euros per kilo.

We know that Juan has apples that cost 4 euros per kilo, and Fran has banans that cost 2 more euros than tha apples.

Then if the cost of the apples is A, and the cost of the bananas is B, we can write the linear equation:

B = A + 2

We know that A = 4, replacing that we will get:

B = 4 + 2

B = 6

The bananas cost 6 euros per kilo.

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To calculate the trimmed mean for each sample by deleting the smallest and largest observation, we remove the extreme values and find the mean of the remaining data. The corresponding trimming percentage is the percentage of observations excluded from the calculation.

The trimmed mean is a way to reduce the influence of outliers or extreme values in a data set by excluding them from the calculation. By deleting the smallest and largest observations, we remove the outliers and focus on the central tendency of the data.

To find the trimming percentage, we need to determine the number of observations excluded relative to the total number of observations in the sample. Suppose the sample has "n" observations.

When we remove the smallest and largest values, we eliminate 2 observations. Therefore, the trimming percentage can be calculated as (2 / n) * 100.

For example, if the sample has 10 observations, the trimming percentage would be (2 / 10) * 100 = 20%. This means that the smallest and largest values are excluded, representing a trimming of 20% of the data.

In summary, the trimmed mean is calculated by removing the smallest and largest observations and finding the mean of the remaining values. The corresponding trimming percentage is determined by dividing the number of observations excluded by the total number of observations in the sample and multiplying by 100.

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The algebraic expression that represents the amount of money in Helena's account after the transactions is "x + 1,788.20 + k - t". Hence, the correct option is O x + 1,788.20 +kt.

Helena had x dollars in her account.

On July 8, she deposited $1,870, k dollars, and $469.30.

Therefore, the amount deposited by Helena is "1,870 + k + 469.30".

She also cashed a check for t dollars and one for $91.40.

Therefore, the amount she cashed is "t + 91.40".

To find the algebraic expression that represents the amount of money in her account after the transactions, we have to add the deposited amount and subtract the cashed amount from her initial balance.

x + 1,870 + k + 469.30 - t - 91.40x + 1,788.20 + k - t

Therefore, the algebraic expression that represents the amount of money in Helena's account after the transactions is "x + 1,788.20 + k - t".Hence, the correct option is O x + 1,788.20 +kt.

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the lengths of the three sides of the triangle are approximately:

Side one: 4.875 units

Side two: 19.5 units

Side three: 14.625 units

Let's denote the lengths of the sides of the triangle as follows:

Side one: x

Side two: 4x (since it is four times the length of side one)

Side three: 3x (since it is three times the length of side one)

The perimeter of a triangle is the sum of the lengths of all three sides. In this case, the perimeter is given as 39 units. We can set up an equation to solve for x:

x + 4x + 3x = 39

Combining like terms:

8x = 39

Dividing both sides by 8:

x = 39/8

Simplifying the fraction:

x = 4.875

Now, we can find the lengths of all three sides by substituting this value of x back into our expressions for each side:

Side one: x = 4.875 units

Side two: 4x = 4.875 * 4 = 19.5 units

Side three: 3x = 4.875 * 3 = 14.625 units

Therefore, the lengths of the three sides of the triangle are approximately:

Side one: 4.875 units

Side two: 19.5 units

Side three: 14.625 units

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To find the probability of selecting Monopoly as the first gift and Scrabble as the second gift without replacement, we need to consider the total number of board games and the number of favorable outcomes. Hence, the probability that the first gift chosen is Monopoly and the second gift is Scrabble is 1/90.

Let's assume there are 10 different board games in the pile. The first person chooses a gift, and since they want to select Monopoly, there is 1 favorable outcome out of the 10 board games. After the first gift is chosen, there are now 9 board games remaining, with 1 of them being Scrabble, which is the desired outcome for the second gift.

The probability of the first gift being Monopoly and the second gift being Scrabble without replacement can be calculated as the product of the probabilities of each event. The probability of choosing Monopoly as the first gift is 1/10, and the probability of choosing Scrabble as the second gift is 1/9.

Therefore, the overall probability can be calculated as (1/10) * (1/9) = 1/90.

Hence, the probability that the first gift chosen is Monopoly and the second gift is Scrabble is 1/90.

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The domain and the range of the function in this problem are given as follows:

The function is defined for all real values except x = 3, which is the vertical asymptote, and assumes negative values, hence:

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Darryl should add 8 gallons of water to the 8-gallon 10% bleach solution to make a 5% bleach solution.

Darryl should add 8 gallons of water to the 8-gallon 10% bleach solution to make a 5% bleach solution .The correct equation that Darryl can use to find x, the number of gallons of water he should add, is:

0.8 / (8 + x) = 5/100

Let's break down the equation and explain each part:

The numerator 0.8 represents the amount of bleach in the original 8-gallon solution.

The denominator (8 + x) represents the total volume of the new solution after adding x gallons of water.

5/100 represents the desired concentration of the new solution, which is 5% bleach.

By setting up this equation, we equate the amount of bleach in the original solution (0.8 gallons) to the amount of bleach in the new solution (5% of the total volume, which is (8 + x) gallons).

Simplifying the equation:

0.8 / (8 + x) = 5/100

To solve for x, we can cross-multiply:

0.8 * 100 = 5 * (8 + x)

80 = 40 + 5x

Subtracting 40 from both sides:

80 - 40 = 5x

40 = 5x

Dividing both sides by 5:

40 / 5 = x

8 = x

Therefore, Darryl should add 8 gallons of water to the 8-gallon 10% bleach solution to make a 5% bleach solution.

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Answer:

[tex]8( {2}^{3} ) = 8(8) = 64[/tex]

The total combined volume of the 8 cubical dice is 64 cm³.