Assume that when you take a bath, you fill a tub to the halfway point. The tub measures 6 feet by 2 feet by 2.5 feet.
When you take a shower, you use a shower head with a flow rate of 1.71 gallons per minute, and you typically spend
10 minutes in the shower. There are 7.5 gallons in one cubic foot. Complete parts (a) through (c) below.

The data set: 21, 22, 22, 24, 25, 26, 28, 28 have two values of mode, which are, 22 and 28.

What is meant by the mode of a data set?

The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. Yet, occasionally there is either no mode or more than one mode. When every observed value occurs exactly once in a data collection, there is no mode. When the highest frequency was noted for more than one value in a data collection, there are many modes. The mode cannot be utilised in either of these examples to identify the distribution centre. Categorical variables can be summarised using the mode.

a)2, 2, 2, 5, 6, 7, 9, 10

Here most repeated value is only 2.

So the mode is 2.

b) 5, 6, 8,10, 11, 11, 15, 18

Here most repeated value is only 11.

So the mode is 11.

c)12, 12, 13, 13, 14, 14, 15, 15

Here the values 12,13,14 and 15 are repeated twice.

So this has 4 values as mode.

d) 21, 22, 22, 24, 25, 26, 28, 28

Here 22 and 28 are repeated twice.

So this data set has 2 values for the mode.

Therefore the data set: 21, 22, 22, 24, 25, 26, 28, 28 have two value of mode, which are, 22 and 28.

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Answer:

D

Step-by-step explanation:

here is a pic for proof

Answer:

E. none​

Step-by-step explanation:

Let's use algebra to solve the problem:

Let's start by defining some variables. We'll use T for Tim's current age, and M for Mary's current age.

According to the first sentence of the problem, "Tim's age was three-quarters of Mary's age 5 years ago." In other words, we can write:

T - 5 = (3/4)(M - 5)

We can simplify and rearrange this equation to get:

4T - 20 = 3M - 15

4T = 3M + 5

According to the second sentence of the problem, "Tim will be five-sixth of Mary's age in 3 years." In other words, we can write:

T + 3 = (5/6)(M + 3)

Again, we can simplify and rearrange this equation to get:

6T + 18 = 5M + 15

6T = 5M - 3

Now we have two equations with two variables (4T = 3M + 5 and 6T = 5M - 3). We can use these equations to solve for T and M.

Multiplying the first equation by 2, we get:

8T = 6M + 10

Multiplying the second equation by 3, we get:

18T = 15M - 9

We can now solve for M by subtracting the first equation from the second:

10T = 21

T = 2.1

Substituting this value of T into one of the equations (e.g. 4T = 3M + 5), we can solve for M:

4(2.1) = 3M + 5

M = 8.3

Therefore, Tim's current age is 2.1 years and Mary's current age is 8.3 years.

The sum of their ages right now is T + M = 2.1 + 8.3 = 10.4 years.

So the sum of Tim and Mary's ages right now is 10.4 years.

Answer:

Step-by-step explanation:

4x-22.2=1.90

22.20-4x=1.90

4x + 1.90 = 22.20

The True Statement are:

20/21 of students in Manuel Class either walk or take bus to school.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

We have 2/7 of the students walk to school

and, 2/3 take the bus to school.

So, if both choices are considered

= 2/7 + 2/3

= 6/21 + 14/ 21

= 20/ 21

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If u and v be linearly independent unit vectors then  the set of all possible values of u⋅v is zero.

Vectors are used in science to describe anything that has both a direction and a magnitude.

Since u and v are unit vectors, their magnitudes are both 1.

|u + v|² = (u + v)⋅(u + v) = u⋅u + 2u⋅v + v⋅v

= 1 + 2u⋅v + 1

= 2 + 2u⋅v.

On the other hand, we also have:

|u + v|² = (u + v)⋅(u + v) = u⋅u + 2u⋅v + v⋅v = 2,

since u and v are linearly independent and hence orthogonal.

Equating the two expressions for |u + v|² we get:

2 + 2u⋅v = 2,

u⋅v = 0.

Therefore, the only possible value for u⋅v is 0.

Hence,  u and v be linearly independent unit vectors then  the set of all possible values of u⋅v is zero.

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Answer:

{x = -1, 3}

Step-by-step explanation:

See picture below :)

The probability that both adults think most celebrities are good role models is  0.046

Probability is a branch of mathematics that deals with the study of random events or processes. It is the measure of the likelihood or chance of an event or outcome occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

Given that the probability that the celebrities are good role models is 192/900

Then if we pick two adults without replacement; 192/900 * 192/899

= 0.046

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Missing parts;

In a sample of 900 U.S. adults, 192 think that most celebrities are good role models. Two U.S. adults are selected from this sample without replacement.Find the probability that both adults think most celebrities are good role models.

The area of the figure can be expressed using the formula A = (x + 1)2.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

This formula is derived from the fact that the figure is a square with sides of length x + 1. Since a square is a special type of rectangle, the area of a square is simply equal to the product of its two sides, or (x + 1)2.

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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:

≈ 315

Step-by-step explanation:

To find the number that 105 is 33 1/3 of, we can use algebra.

Let x be the number we are looking for. Then we can write the equation:

105 = (33 1/3)% of x

To solve for x, we can first convert the percentage to a decimal by dividing by 100:

33 1/3% = 33 1/3 ÷ 100 = 0.3333

Substituting this in the equation, we get:

105 = 0.3333x

To solve for x, we can divide both sides by 0.3333:

x = 105 ÷ 0.3333

Using a calculator, we get:

x ≈ 315

Therefore, 105 is 33 1/3 of 315.

Are you more likely to see a twelve-pack from the local brewery or a twelve-pack from the large chain with an average fill of 327.9 ml?

Local brewery.

a. At the local brewery the middle 95% of six-packs will have an average fill between ml 326.828 and 329.572 ml

b. At the large chain brewery, the middle 95% of six-packs will have an average fill between 326.824 ml and 329.176 ml.

X ζ N (328.2, 0.7^2)

YζN (328, 0.6^2)

P (X> 327.9) = 0.6659

P (Y> 327.9) = 0.5662

Since, P (X> 327.9) > P (Y> 327.9)

We are more likely to see 12-pack from the local brewery.

a. To find a, b such that P(a<x<b) = 0.95

a= 326.828

b= 329.572

b. To find c, d such that P(c<Y<d) = 0.95

c= 326.824

d= 329.176

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1) A(1,2),A'(-1,2) : a reflection across the y-axis

2) A(1,2), A'(-2,1): a rotation 270⁰ clockwise around the origin

3) A(1,2),  A'(-1,4):  a translation of 2 units left and 2 unit up

4) A(1,2),A'(-1,-2): a rotation 180⁰ around the origin

5) A(1,2),A'(-3,-7): a translation of 4 units left and 9 units down

What is the transformation of a point?

The transformation, or f: X →X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the image X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one direction or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.

The given point is A(1,2).

The rule of a rotation 180⁰ around the origin is (x,y)→(−x,−y).

Therefore, A(1,2)→A'(-1,-2).

A rule of translation of 2 units left and 2 unit up is (x,y)→(x-2,y+2)

Therefore, A(1,2)→A'(1-2,2+2) = A'(-1,4).

The rule of a reflection across the y-axis is (x,y)→(−x,y).

Therefore, A(1,2)→A'(-1,2)

A rule of translation of 4 units left and 9 units down is (x,y)→(x-4,y-9)

Therefore, A(1,2)→A'(1-4,2-9) = A'(-3,-7).

The rule of a rotation 270⁰ clockwise around the origin is (x,y)→(-y,x)

Therefore, A(1,2)→A'(-2,1)

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

10.468 rounded to the nearest hundredth would be 10.47

4 = tenths place

6 = hundredths place

8 = thousandths place

8 >= 0.5 so 10.468 --> 10.47

Answer: 10.47

Step-by-step explanation: After the decimal, it goes tenths, hundredths, thousandths. So we're looking at the second place after the decimal, which is a 6, and the next number is 8. Think of it like 68, rounding up to the next ten, or 70. So that turns it into 10.470, and you get to drop the zero to make it 10.47.

Answer:

3.00000000000

Step-by-step explanation:

2.77247497343 is closer to 3.00000000000 than 2.00000000000

Answer:

y = x + 3 --- 1

y = 4x + 9 --- 2

By combining 1 and 2, we have

x + 3 = 4x + 9

3-9 = 4x-x

-6 = 3x

x = -2

Sub x = -2 into 1

y = (-2) + 3 = 1

Intersection = (-2,1)

Yes, in ggplot2, mapping refers to the process of connecting variables in a data set to visual elements of a plot, such as points, lines, or other shapes.

Yes, in ggplot2, mapping refers to the process of connecting variables in a data set to visual elements of a plot, such as points, lines, or other shapes. This is done by mapping variables to aesthetic properties of the plot, such as the x and y coordinates, the size, color, or shape of the points, or other visual properties that can be customized.

For example, if we have a data set with two variables, x and y, we can create a scatterplot of the data by mapping the x variable to the x-axis and the y variable to the y-axis, using the aes() function in ggplot2. We can also customize the appearance of the points by mapping other variables to the size, color, or shape of the points, as well as adding other elements to the plot, such as a title or legend.

The mapping process is an important part of data visualization in ggplot2, as it allows us to explore the relationship between different variables and to communicate our findings in a clear and effective way. By mapping variables to visual elements of a plot, we can create informative and visually appealing graphics that can help us understand and communicate complex data sets.

In programming, a variable is a named storage location that can hold a value or a reference to a value. Variables are used to store and manipulate data in a program, and they can take on different values at different times during the execution of the program.

In most programming languages, variables are defined by specifying a name and a data type. The data type determines the kind of data that can be stored in the variable, such as numbers, strings, or Boolean values, and also affects the size and behavior of the variable.

Variables can be assigned a value using the assignment operator, which stores the value in the variable's memory location. Once a value has been assigned to a variable, it can be accessed and manipulated using its name.

In addition to simple data types, programming languages also support more complex types of variables, such as arrays, objects, and pointers, which can store collections of values or references to other variables.

Variables are a fundamental concept in programming, and they are used extensively in all kinds of software applications, from simple scripts to complex systems. Understanding how to use variables effectively is an essential skill for any programmer.

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By integration of monthly revenue we will get total revenue of the shop for a year is $51,600.

What is integration ?

Integration is a fundamental operation in calculus that involves finding the area under a curve, or the antiderivative of a function. It is the reverse operation of differentiation, which is used to find the rate of change of a function.

Integration is represented by the symbol ∫ (the integral sign), and the result of the operation is called the indefinite integral or antiderivative of the function. The antiderivative is a family of functions that differ only by a constant, known as the constant of integration.

Given by the question:

The monthly revenue can be calculated by multiplying the unit price and the quantity of goods sold in a given month. Therefore, the monthly revenue function is:

[tex]R(t) = P(t) * Q(t) = (t^2 + 9t + 36) * (t + 12)[/tex]

To find the total revenue over a year, we need to integrate the monthly revenue function over the interval [0,12] (since we are considering a year):

[tex]Total revenue = \int\limits^a_0 {R(t)} \, dt[/tex]

= [tex]\int\limits^a_b (t^2 + 9t + 36) * (t + 12) } \, dt[/tex]

= [tex]\int\limits^a_b {(t^3 + 21t^2 + 132t + 432) } \, dt[/tex]

=[tex][t^4/4 + 7t^3/3 + 66t^2 + 432t][/tex]evaluated from 0 to 12

=[tex](20736/4 + 12096 + 9504 + 5184) - (0 + 0 + 0 + 0)[/tex]

= [tex]51600[/tex]

Therefore, the total revenue of the shop for a year is $51,600.

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The height of the tower is 17.32 meters

Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.

Given that, Ical is 10 meters away from a tower [since angle is not given let the angle of the top of the tower be 60°], we need to find the height of the tower, [see the figure attached]

The whole scene is making a right triangle, so using the concept of trigonometric ratios,

We get,

Tan 60° = height of the tower / distance of Ical from the tower

Tan 60° = height of the tower / 10

Height of the tower = 10 × Tan 60°

Height of the tower = 10 × √3

Height of the tower = 10√3

Height of the tower = 10 × 1.73

Height of the tower = 17.32

Hence, the height of the tower is 17.32 meters

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The number of solutions of the system y = 3x + 5 is one because it is a linear equation.

An equation in which is  the highest power of to the  variables 1 is knowns as the  linear equation. Mathematically: it is an  algebraic equations that can be also  written in the form of  ax + b = 0 or ax + by + c = 0, where a, b and c are definitely real numbers and x and y are variables with the highest power one.

Linear equations are equations in which the variables are raised to the power of 1, and the graph of the equation is a straight line. As a result, there is only one solution to the equation, which is when the line intersects the x-axis. This means that the equation has only one set of x- and y-coordinates, where x is the independent variable and y is the dependent variable, that satisfy the equation. The x-coordinate of the solution is the same as the value of x that makes the equation true and the y-coordinate is the value of y for this same x-value.

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Answer:

112cm³

Step-by-step explanation:

Let us ignore the bottom part of the figure and first find only the volume of the cuboid at the top

from the figure we know that

length of the cuboid is 10 cm

Width is 2 cm

height is 5 cm

now the formula for Volume of cuboid is Length×Width×Height

so,

Volume of the Upper Cuboid = 10×2×5= 100cm³ ---(1)

Now we will ignore the cuboid on top and find the volume of the one at the bottom

From the figure, we know that its dimensions are

length = 2cm

height = 3cm

width = 2cm

Volume of the lower cuboid = 2×2×3 = 12cm³ ---(2)

Adding (1) and (2)

100cm³ + 12 cm³ = 112cm³

Therefore the volume of the given figure is 112cm³

The volume of the box is 112 cm³.

We have,

The figure can be considered as two boxes.

Now,

One box:

Volume.

= Length x Width x height
= 10 x 2 x 5

= 100 cm³

Another box:

Volume.

= Length x Width x height
= 2 x 2 x 3

= 12 cm³

Now,

The volume of the box.

= 100 + 12

= 112 cm³

Thus,

The volume of the box is 112 cm³.

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The probability that a random sample of 150 bowlers will have an average score greater than 165 is 0

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is used to measure the likelihood or chance of an event occurring, ranging from impossible (0 probability) to certain (1 probability).

The basic concept of probability involves determining the ratio of the number of favorable outcomes to the total number of possible outcomes. This ratio is expressed as a fraction, decimal, or percentage.

For example, if you toss a fair coin, there are two possible outcomes: heads or tails. The probability of getting heads is 1/2 or 0.5 or 50%, and the probability of getting tails is also 1/2 or 0.5 or 50%.

To give the probability that a random sample of 150 bowlers will have an average score greater than 165

P( [tex]\bar X[/tex]> 165) = P(z > (165 - 157)/(12/√(150)))

= P(z > 8.16)

= 0 [since from z table]

= 0

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The system of equations can be represented as a vector equation A x = b, where A is the coefficient matrix, x is the variable vector, and b is the constant vector.

Using matrices and vectors, a system of linear equations can be expressed as a vector equation. Consider a set of n variables and m linear equations. It may be written as follows:

A x = b

where A is a m x n matrix of the coefficients of the variables, x is a n x 1 column vector of the variables, and b is a m x 1 column vector of the constants on the right-hand side of each equation.

To match the rows of the system of equations to the corresponding row of the matrix A and vector b in the vector equation, we can represent the system of equations as:

a 21 x 1 + a 22 x 2 +... + a 2n x n = b 2 a 11 x 1 + a 12 x 2 +... + a 1n x n = b 1

a mn x n = b m, where a m1 x 1 = a m2 x 2 +...

The vector form of this is as follows:

Beginning with "a 11" and "a 12," adding "cdots and a 1n," going on to "a 21" and "a 22," adding "cdots and a 2n," adding "vdots and vdots and ddots and vdots," ending with "a m1" and "a m2," adding "cdots and a mn,"

With A serving as the coefficient matrix, x serving as the variable vector, and b serving as the constant vector, the system of equations can thus be expressed as a vector equation, A x = b.

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Answer:

x=11.34

Step-by-step explanation:

Answer:

Slope = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Slope of a graph = [tex]\frac{rise}{run}[/tex]

Steps to follow:

1. Select two points along this linear graph by reading them:

For example (0, 3) and (8, 7)

2. Draw a vertical line from Point (8, 3) to Point (8, 7). This line is considered as the rise

3. Draw a horizontal line connecting (0, 3) with (8, 3). This line represents the run

4. Substitute the x and y coordinates of the two points mentioned in Step 1 in the formula below:

Slope = [tex]\frac{y_{2} - y_{1}}{x_{2} -x_{1}}[/tex]

          = [tex]\frac{7 - 3}{8 - 0}[/tex]

          = [tex]\frac{4}{8}[/tex]

Divide the numerator and denominator by the Highest Common Factor ‘4’ to simplify the fraction:

            = [tex]\frac{1}{2}[/tex]

The value for the [tex]\lim_{x \to 3^{+}}[/tex]f(x) = 3.

A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value.

A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit.

Given:

We have given the graph, from the graph we can se a red dot.

So, the [tex]\lim_{x \to 3^{+}}[/tex]f(x) = 3

Also, limit is defined as a value that a function approaches the output for the given input values.

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We can write tan(− 0.9) as -

tan(− 0.9) = -1.26.

Tangent function is defined as the ratio of perpendicular and base. Mathematically, we can write -

tan(Ф) = p/b

tan(Ф) = perpendicular/base

Given is to find the value of tan(− 0.9).

We know -

1 radian = 57.2958 degrees

0.9 radian = 57.3 x 0.9 = 51.57 degrees

0.9 radian = 51.57 degrees                           ... { 1 }

So, we can write -

tan(− 0.9) = tan( - 51.57°) = - 1.26

Therefore, we can write tan(− 0.9) as -1.26.

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Answer:

24 days.

Step-by-step explanation:

Since the clock loses 15 minutes per day, it will show the correct time after gaining back 24 hours, equivalent to 1 day.

Therefore, the clock will show the correct time for the first time after 24 days, which is calculated as follows:

One day to gain back the first 15 minutes

One day to gain back the second 15 minutes

...

One day to gain back the 24th 15 minutes

So the answer is 24 days.

Answer:20

Step-by-step explanation:2 times with 10 hours becase per hour the temperature 2 degree celsius

Answer: Using the formula F=9/5C+32, we can convert 59°C to degrees Fahrenheit:

F = 9/5 * 59°C + 32

F = 118.2°F + 32

F ≈ 150.8°F

Therefore, 59°C is approximately equal to 150.8°F.

Step-by-step explanation: