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The probability of rolling a 3 on a single six-sided die is 1/6, or 16.7%.

Probability is a mathematical study of outcomes in uncertain situations it is used to describe the like would an event occurring and it can be expressed as a number between 0 to 1 probability is used to quantify the uncertainty associated with any given event it helps us understand how likely it is that something will happen and it can be used to make a prediction about futures even probability theory is it of modern statistic and is widely used in fields such as financial economics and science.

Therefore, the probability of rolling at least one 3 when rolling two six-sided dice is 2 × 1/6, or 33.3%. This is because the probability of rolling a 3 on one die is independent of the probability of rolling a 3 on the other die. This means that the probability of rolling at least one 3 is equal to the sum of the probabilities of rolling a 3 on each of the two dice (1/6 + 1/6 = 2/6). As a result, the probability of rolling at least one 3 when rolling two six-sided dice is 33.3%.

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The domain are the possible input while the range are the possible output of a function.

(a) The domain = [-√2, √2], the range = [0, 2]

(b) The domain = [-1, 1], the range = [0, 1]

(c) The domain = [-1, 1], the range = [0, -1]

(d) The domain = [0, 2], the range = [0, 1]

(e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]

Reasons:

The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1

Therefore, we have;

(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2

The x-intercept of the above function are, x = √2, and x = -√2

Which gives;

The domain = [-√2, √2]

The range = [0, 2]

(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3

At the x–intercepts, we have;

-3·x² + 3 = 0

x = ±1

The domain = [-1, 1]

The maximum value of y is given at x = 0, therefore;

= -3 × 0² + 3 = 3

The range = [0, 1]

(c) y = -f(x) = -(-x² + 1) = x² - 1

At the x–intercepts, x² - 1 = 0

x = ± 1

The domain = [-1, 1]

The minimum value of y is given at x = 0, which is y = -1

The range = [0, -1]

(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x

At the x–intercepts, we have;  -x² + 2·x = 0, which gives;

(-x + 2)·x = 0

Which gives, x = 0, or x = 2

The domain = [0, 2]

The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1

y = f(1) =  -1² + 2×1 = 1

Therefore;

The range = [0, 1]

(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2

At the x–intercepts, we have;  -x² - 4·x - 2 = 0, which gives;

x = -(2 + √2) or x = x = √2 - 2

The domain = [-(2 + √2), (√2 - 2)]

The maximum value of y is given when x = -4/(2)) = -2

Which gives;

-(-2)² - 4·(-2) - 2 = 2

The range = [0, 2]

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Answer:

x = 12

m∠UTS = 87

m∠TSR = 143

Step-by-step explanation:

We know that the angles 56, (3 + 7x), and UST, add up to 180, and that UST and (12x - 1) also add up to 180

Therefore we can say UST = 180 - (12x - 1)

and that:

56 + 3 + 7x + (180 - (12x - 1)) = 180

59 + 7x + 180 - 12x + 1 = 180 (combine like terms and distribute negative)

240 - 5x = 180 (subtract 240 from both sides)

-5x = -60 (divide both sides by -5)

x = 12

Therefore,

m∠UTS = 3 + 7(12) = 87

and

m∠TSR = 12(12) - 1 = 143

There are total 15 students who take all three subjects.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We know that;

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C)- n(A ∩ C)+ n(A∩B ∩C)

Here, Total number of students in the school = 62

Hence, By using theorem;

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C)- n(A ∩ C)+ n(A∩B ∩C)

Here, Let n(A) = Mathematics, n(B) =Physics and n(C) = Chemistry

so putting values,

62 =  40 + 42 + 38 - 20 - 28 - 25 + n(A∩B ∩C)

62 + 73 - 120 = n(A∩B ∩C)

n(A∩B ∩C) = 15

Therefore, There are total 15 students who take all three subjects.

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Yes, to see if there is a non-linear relationship between X and Y.

The intensity and direction of a relationship between two variables is indicated by a correlation coefficient, which is a number between -1 and 1. In other words, it illustrates the degree to which measurements of two or more variables are comparable throughout a dataset.

Given:

The correlation coefficient r between x and y is 0.97.

As, On a scatterplot, the correlation coefficient, or r, quantifies the magnitude and axis of a linear relationship between two variables.

and, The relationship between two variables is generally considered strong when their r value is larger than 0.7.

So, here the correlation of 0.97 indicates a strong positive linear relationship between variable x and y.

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The probability of obtaining a specific outcome on a coin toss is 1/2. Using this information, we can calculate the probabilities for the following outcomes:
1. Excalty one head  = 1/2
2. No tail                  = 1/4
3. A least two tails    = 1/2
4. A head and two tails = 3/8

Probability can be defined as the ratio of favorable outcomes to the total number of events.

To obtain exactly one head, we can either get a head on the first toss and tails on the second, or tails on the first toss and heads on the second. The probability of each of these outcomes is (1/2) × (1/2) = 1/4. Therefore, the probability of obtaining exactly one head is the sum of these two probabilities, which is 1/4 + 1/4 = 1/2.

To obtain no tails, we must get heads on both tosses. The probability of this is (1/2) × (1/2) = 1/4.

To obtain at least two tails, we must get tails on both tosses or tails on the first toss and heads on the second. The probability of getting tails on both tosses is (1/2) × (1/2) = 1/4, and the probability of getting tails on the first toss and heads on the second is also 1/4. Therefore, the probability of obtaining at least two tails is the sum of these two probabilities, which is 1/4 + 1/4 = 1/2.

To obtain one head and two tails, we must get heads on one of the tosses and tails on the other two tosses. There are three ways to do this: heads on the first toss and tails on the second and third, heads on the second toss and tails on the first and third, or heads on the third toss and tails on the first and second.
The probability of each of these outcomes is (1/2) × (1/2) × (1/2) = 1/8.

Therefore, the probability of obtaining one head and two tails is the sum of these three probabilities, which is 1/8 + 1/8 + 1/8 = 3/8.

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By solving the logarithmic equation for x when y = 5, we determined that the graph would meet the line y = 5 when x = 10^5

From the question, we are to determine when the graph will meet the line y = 5

From the given information,

The given function is

y = log10 (x)

To determine when the graph would meet the line y = 5, we will determine the value of x when y = 5 in the function

y = log10 (x)

5 = log10 (x)

Applying the exponent law of logarithm, we get

10^5 = (x)

Therefore, x = 10^5

Hence, the graph would meet the line y = 5 when x = 10^5

The point (100, 2) is on the graph because, x = 100, y = 2 is true for the function

That is,

y = log10 (x)

2= log10 (100)

Applying the exponent law

10^2 = 100

100 = 100

This shows why the point (100, 2) is on the graph

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Answer:

7 + (8 × t) = p, 15 + (6 × t) = p

Step-by-step explanation:

The equation you can use for charging a $7 entrance fee and then $8 for each ride ticket can look like this:

(let t = ride ticket & p = price)

The equation you can use for charging a $15 entrance fee and then $6 for each ride ticket can look like this:

Therefore, the equations you can use are listed above.

Point-slope form: y - (-2) = -4(x - 2)

Slope-intercept form: y = -4x - 6

Own integers:

Point-slope form: y - 2 = -2(x - 4)

Slope-intercept form: y = -2x - 6

Point slope form is a type of linear equation that describes the relationship between two points on a line. It is written in the form: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. Point slope form is used to find the equation of a line when given its slope and one point on the line. It can also be used to find the slope of the line when given two points on the line.

For example, if the point (2, 3) is given and the slope is 4, the point-slope form of the equation would be y - 3 = 4(x - 2).

The point-slope form of an equation of a line is an equation of the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this equation, (x1, y1) = (2, -2) and m = -4, so the point-slope form of the equation is y - (-2) = -4(x - 2).

The slope-intercept form of an equation of a line is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept of the line. In this equation, m = -4 and b = -6, so the slope-intercept form of the equation is y = -4x - 6.

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Answer: greater than 6 cm. less than 20 cm

Step-by-step explanation:

The length of DE is 12 centimeters.

Since triangles ABC and DEF are similar, we know that their corresponding sides are in proportion. That is:

AB/DE = BC/EF = AC/DF

We can use any of these proportions to find the length of DE, since they are all equal.

To use the proportion that involves DE, we can rearrange it as follows:

AB/DE = BC/EF

DE = AB * EF / BC

Now we can substitute the given lengths:

DE = 4 cm * 9 cm / 3 cm = 12 cm

Therefore, the length of DE is 12 centimeters.

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Step-by-step explanation:

let the number be 'x'

x*-10+7=3x

-10x*7=3x

-3x=3x

Answer:

I ammm really sorry for the question

i don't know sorry

Answer:

Step-by-step explanation:

The domain and range of the given function :

Domain: {x | x ∈ ℝ, x ≠ -2}

Range: {y | y ∈ ℝ, y ≠ -12/5}

The given function is:

f(x) = (x^2 - 4x - 12)/(x + 2)

To find the domain of the function, we need to consider the values of x that make the denominator (x + 2) zero. If x + 2 = 0, then x = -2. Therefore, the function is undefined at x = -2, since division by zero is not allowed. Hence, the domain of the function is all real numbers except -2. We can express this mathematically as:

Domain: {x | x ∈ ℝ, x ≠ -2}

To find the range of the function, we need to consider the values that f(x) can take for all valid values of x. As x approaches infinity or negative infinity, the value of the function also approaches infinity (or negative infinity) since the degree of the numerator is greater than the degree of the denominator. Therefore, the range of the function is all real numbers except for a single point which is the vertical asymptote at x = -2.

Range: {y | y ∈ ℝ, y ≠ -12/5}

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Answer:

Step-by-step explanation:

Let's call the distance from Planet A to one of the possible positions of Planet B "x". We can use trigonometry to relate the angle between the star and Planet B (19°), the distance from the star to Planet A (65 million miles), and the distances from Planet A to Planet B (x).

In a right triangle with angle 19°, the opposite side is x and the adjacent side is 65 - 45 = 20 million miles. Therefore, we can use the tangent function to relate these sides:

tan(19°) = x / 20

Solving for x, we get:

x = 20 tan(19°) ≈ 6.7 million miles

So one possible distance from Planet A to Planet B is approximately 6.7 million miles.

However, there is another possible position for Planet B, which is on the other side of Planet A as shown in the figure. In this case, the distance from Planet A to Planet B is:

y = 65 + 45 + 20 = 130 million miles

Therefore, the two possible distances from Planet A to Planet B are approximately 6.7 million miles and 130 million miles (rounded to the nearest tenth).

If Ashley has a deck that measures 12 feet by 10 feet. Ashely should  increase each dimension by 8feet.

The original area of the deck is:

12 feet x 10 feet = 120 square feet

To triple this area, Ashley needs to increase the area by a factor of 3. That means the new area should be:

3 x 120 square feet = 360 square feet

Let's say Ashley increases the length and width of the deck by x feet. The new dimensions of the deck will be:

(12 + x) feet by (10 + x) feet

The new area of the deck will be:

(12 + x) feet x (10 + x) feet = 120 + 22x + x^2 square feet

We want this area to be 360 square feet, so we can set up the equation:

120 + 22x + x^2 = 360

Simplifying this equation, we get:

x^2 + 22x - 240 = 0

We can solve this quadratic equation by factoring:

(x + 30)(x - 8) = 0

The solutions are x = -30 and x = 8, but we can discard the negative solution since we are looking for a positive increase in dimension.

Therefore, Ashley should increase each dimension by 8 feet in order to triple the area of her deck.

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Answer:

12 tractors

Step-by-step explanation:

30/100 multiplied by 40 is 0.3 multiplied by 40

This gives you 12.

[tex]\frac{30}{100} \\ = 0.3\\0.3*40 = 12\\[/tex]

9,600 kilobytes have been downloaded so far.

Kilobytes (KB) are a unit of digital information storage that is commonly used to measure the size of computer files and data. One kilobyte is equivalent to 1,000 bytes, or 2^10 (1024) bytes. Kilobytes are often used to describe small files and data sets, such as text documents, images, and audio files.

Kilobytes are part of a larger hierarchy of units used to measure digital information storage, which includes larger units such as megabytes (MB), gigabytes (GB), and terabytes (TB). In this hierarchy, each unit is 1,000 times larger than the previous one. For example, 1 MB is equivalent to 1,000 KB, 1 GB is equivalent to 1,000 MB, and so on.

Kilobytes are used in a variety of contexts, including computer storage, data transfer rates, and internet bandwidth. For example, the size of a typical email message might be measured in kilobytes, and the download speed of a file from the internet might be measured in kilobits per second (kbps).

Despite their relatively small size compared to larger units like gigabytes and terabytes, kilobytes remain an important unit of measurement in the digital world, as many files and data sets are still relatively small and easily manageable within this size range.

30% of 32,000 kilobytes can be found by multiplying 0.3 and 32,000:

0.3 × 32,000 = 9,600

So, 9,600 kilobytes have been downloaded so far.

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The probability that the teacher will choose two girls would be = 1/6

Probability is defined as the expression that shows the possibility of an outcome of an event which may or may not happen.

The total number of students in the class = 9

The total number of girls = 4

The total number of boys = 5

The formula for finding probability = No of favourable outcome/Total number of outcomes.

The probability that teacher choose first girl = 4/9

One girl is selected we must reduce the number of girls available for selection to 4 - 1 = 3.

We must also reduce the number of children available for selection 9 - 1 = 8.

The probability that teacher choose second girl = 3/8

Thus, the probability = 4/9 × 3/8 = 1/6

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The net income using FIFO, LIFO, and Weighted Average methods are $16200, $12700, $14100.3

To calculate the net income using different inventory valuation methods, we need to calculate the cost of goods sold (COGS) first, which is:

COGS = Beginning Inventory + Purchases - Ending Inventory

For each inventory valuation method, we will calculate the COGS and then subtract it from the total sales to find the net income.

1.

FIFO (First-in, First-out) method:

Under the FIFO method, we assume that the units sold are from the earliest inventory purchased. Therefore, the ending inventory consists of the most recently purchased units.

a. COGS:

Beginning inventory: 90 units at $40 = $3,600

Purchases: 310 units at $45 = $13,950

Total cost of goods available for sale = $3,600 + $13,950 = $17,550

Cost of goods sold = Total cost of goods available for sale - Ending inventory

= $17,550 - 30 units at $45 = $16,200

b. Net Income:

Sales = 370 units at $90 = $33,300

COGS = $16,200

Operating expenses = $4,100

Net income = Sales - COGS - Operating expenses

= $33,300 - $16,200 - $4,100

= $13,000

2.

LIFO (Last-in, First-out) method:

Under the LIFO method, we assume that the units sold are from the most recently purchased inventory. Therefore, the ending inventory consists of the earliest purchased units.

a. COGS:

Beginning inventory: 90 units at $40 = $3,600

Purchases: 310 units at $45 = $13,950

Total cost of goods available for sale = $3,600 + $13,950 = $17,550

Cost of goods sold = (Ending inventory at $40) + (Remaining units sold at $45)

= (30 units at $40) + (340 units at $45)

= $1,200 + $15,300

= $16,500

b. Net Income:

Sales = 370 units at $90 = $33,300

COGS = $16,500

Operating expenses = $4,100

Net income = Sales - COGS - Operating expenses

= $33,300 - $16,500 - $4,100

= $12,700

3.

Weighted Average method:

Under the weighted average method, we calculate the average cost per unit and use it to value both the cost of goods sold and ending inventory.

a. Average Cost per unit:

Total cost of goods available for sale = Beginning inventory + Purchases

= $3,600 + $13,950

= $17,550

Total units available for sale = Beginning inventory + Purchases + Ending inventory

= 90 + 310 + 30

= 430

Average cost per unit = Total cost of goods available for sale / Total units available for sale

= $17,550 / 430

= $40.81

b. COGS:

Cost of goods sold = Units sold x Average cost per unit

= 370 units x $40.81

= $15,099.7

c. Net Income:

Sales = 370 units at $90 = $33,300

COGS = $15,111.70

Operating expenses = $4,100

Net income = Sales - COGS - Operating expenses

= $33,300 - $15,099.7 - $4,100

= $14,100.3

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Answer: D

Step-by-step explanation:

Here, we let n be the number of sides of the regular polygon. Polygon area = n(12sh). As n increases, h approaches r so that rh approaches r² and hence, this statement is true. So, option 4 is the correct option.

When ns equals circumference or 2r, the polygon will turn into a circle.

A polygon must be converted into a circle.

Let s represent the polygon's side length, r represent the hypotenuse of the right triangle,

Let n be the regular polygon's number of sides and h be the height of the triangle.

The polygon's area is now specified as polygon area = n(1/2sh).

Now, we must suppose that the polygon's sides are infinite in order to obtain a circle. In order to do this, we must assume that the polygon's perimeter is the same as the circle's perimeter.

That's why when the number of sides of the polygon will increase its perimeter will become closer to 2πr and its area will become close to a circle.

The complete question that you might be looking for is-

A regular polygon inscribed in a circle can be used to derive the formula for the area of a circle. The polygon area can be expressed in terms of the area of a triangle. Let s be the side length of the polygon, let r be the hypotenuse of the right triangle, let h be the height of the triangle, and let n be the number of sides of the regular polygon. polygon area = n(12sh) Which statement is true?

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Answer:  My answer is long so I cannot write my answer here so i have attached my answer to your question (Notepad)

Step-by-step explanation:

Answer:

Step-by-step explanation:

y

The probability that now the card is indeed a diamond or a face card is [tex]\frac{11}{26}[/tex].

The probability that any random event will occur is referred to as probability. This expression is used to calculate the likelihood that a given event will occur. When we fling a coin into the air, as an illustration. Probability: P(A) = f / N calculates the probability that an event will take place. Ratios and probability are related, but the former determines the latter. When calculating the likelihood of an event, it is necessary to know the probability of that event.

When we find the probability, we obtain:

A typical deck of cards contains 52 cards. There are 12 face cards, known as the Kings, Queens, and Jacks, because there are four suits. There are a total of 13 diamonds, of which 3 are previously counted face cards. Hence, there are 10 diamonds that are faceless.

So, total Diamond & face card =22

Probability =[tex]\frac{22}{52}[/tex]=[tex]\frac{11}{26}[/tex].

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The probability that the arrival time between vehicles is 12 seconds or less found using exponential distribution is 0.6306.

What is meant by exponential distribution?

The exponential distribution is a continuous probability distribution used in probability theory and statistics that frequently addresses the amount of time until a given event occurs. Events occur continually, independently, and at a steady average pace during this process. The crucial characteristic of the exponential distribution is that it has no memory. Either more little values or fewer larger values can make up the exponential random variable. 

Given,

Mean = 12s

Mean = 1/λ = 12

λ = 1/12 = 0.083

Now we have to find CDF at 12s.

The probability that an observation from an exponential distribution, with the scale parameter, is smaller than or equal to x is returned by the CDF function for the exponential distribution.

CDF = F(x) = [tex]1- e^{-\lambda\*x}[/tex]

When x = 12

F(12) = [tex]1- e^{-0.083*12}[/tex] = 0.6306

Therefore the probability that the arrival time between vehicles is 12 seconds or less found using exponential distribution is 0.6306.

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The total number of students in the vans and buses is 484

Algebra is a branch of mathematics that deals with the study of mathematical symbols and the rules for manipulating these symbols to solve equations and understand the relationships between variables. In algebra, letters or symbols are used to represent unknown values or variables, and equations are used to describe the relationships between these variables.

Algebraic expressions and equations involve mathematical operations such as addition, subtraction, multiplication, and division, as well as more advanced operations such as exponentiation, logarithms, and trigonometric functions. These operations can be used to simplify expressions, solve equations, and analyze mathematical relationships.

Elementary algebra, which is concerned with the basic concepts and techniques of algebra, such as simplifying expressions, solving equations, and graphing functions.

Abstract algebra, which is concerned with the study of algebraic structures, such as groups, rings, and fields.

Linear algebra, which is concerned with the study of vector spaces and linear transformations.

Algebraic geometry, which is concerned with the study of geometric objects defined by algebraic equations.

Algebra has many practical applications in various fields, including science, engineering, economics, and computer science. It is used to model and analyze real-world problems, such as population growth, interest rates, and inventory management. It is also used in cryptography, where it is used to design secure encryption and decryption algorithms.

Let's start by using algebra to represent the information given in the problem.

Let x be the number of students in each van and each bus. Since every van had the same number of students as every bus, we can say that the total number of students in the vans and buses is:

10(x) + 12(x) = 256

Simplifying, we get:

22x = 256

Dividing both sides by 22, we get:

x = 11.6363636...

Since we can't have a fraction of a student, we need to round x to the nearest whole number. We have two options: rounding up to 12 or rounding down to 11.

If we round x up to 12, then each van and each bus had 12 students. The total number of students in the vans and buses is:

10(12) + 12(12) = 240

This is not equal to the given total of 256, so rounding up to 12 is not a valid solution.

If we round x down to 11, then each van and each bus had 11 students. The total number of students in the vans and buses is:

10(11) + 12(11) = 220 + 264 = 484

This is not equal to the given total of 256, so rounding down to 11 is not a valid solution either.

Therefore, there is no whole number solution for the number of students in each van and each bus. We can interpret this to mean that there was not an equal number of students in each van and bus. Alternatively, we can interpret this to mean that there was an error in the information given in the problem.

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Answer:

How many centimeters are there in 58 inches?

1 in. = 2.54 cm

Step-by-step explanation:

The set of truth values that make the three specifications true is FFT, TFT, TFF, and TTT.

Let's break it down step by step:

u: The software system is being upgraded.

a: Users can access the file system.

s: Users can save new files.

The given specifications are as follows:

Whenever the system software is upgraded, users cannot access the file system.
If users can access the file system, then they can save new files.
If users cannot save new files, then the system software is not being upgraded.

Given these specifications, we can set up the following truth table:

The set of truth values that make the three specifications true is therefore FFT, TFT, TFF, and TTT.

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The comparison of the volume of water used for bathing and showering are as follows;

A. The amount of water used bathing is 12.7 cubic feet more than the amount of water used for showering

B. The time it takes to use the amount of water for bathing while showering is about 65.8 minutes

The volume of a fluid is the product of the constant flowrate and the time of flow of the fluid.

The level to which the tub is filled when taking a bath = The halfway point

The dimensions of the tub = 6 feet by 2 feet by 2.5 feet

The flowrate of the shower head = 1.71 gallons per minute

The time usually spent in the shower = 10 minutes

The number of gallons per cubic foot = 7.5 gallons

The amount of water used in bathing = 6 × 2 × 2.5 × (1/2) = 15

The volume of water used for bathing is 15 cubic feet of water

A. The amount of water used for showering = 1.71 gallons/minute × 10 minutes = 17.1 gallons

17.1 gallons = (17.1 gallons/7.5 gallons/ft³) = 2.28 ft³

The volume of water used for showering = 2.28 cubic feet

The difference in the volume of water used for bathing and the volume used for showering = 15 - 2.3 = 12.7

Therefore; you are using 12.7 more cubic feet of water than you do taking a shower; you use 12.7 more cubic feet of water than taking a bath.

B. The duration of a shower, t, that is equivalent to a bath can be found as follows;

1.71 gal/min = (1.71 gal/7.5 gal/ft³) = 0.228 gal/min

t = 15 gal/0.228 gal/min ≈ 65.8 min

The time it takes to use as mush water showering as the amount of water used bathing is about 65.8 minutes

Part of the question, obtained from a similar question posted online includes;

A. The method that use more water, showering or bathing

B. The duration of showering such that the amount of water used for bathing is used

Learn more on flowrate of a fluid here: https://brainly.com/question/13959601

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