Based on data from the environmental protection agency, 18 gallons of water is used on average to take a shower, which translates to one trillion gallons of water used for showers across the united states. Which activities can help conserve water when taking showers? check all that apply.

In the given cube-shaped cake, the value of c + s = 32/5.

In the given figure of the cube-shaped cake, let [RNQ] be the area of the triangle RNQ. The volume of the corresponding piece c = 2[RNQ]. The cake piece has icing on the top and on the vertical side that contains the edge QR. Hence the total area with icing is [RNQ] + 2^2 = [RNQ] + 4. Hence, c+s = 3[RNQ] + 4.

In order to determine [RNQ], introduce a coordinate system. Let Q be the origin. As the length of each edge is 2. Hence,

Q = (0,0)

P = (2, 0)

R = (0, 2)

In the coordinate system, as M is the midpoint of PS, M = (2, 1). The equation of the line QM is:

m = (1- 0)/(2 – 0) = ½

y – 0 = ½(x – 0)

2y – x = 0

As the line RN is orthogonal to QM, it has an equation is y + 2x + q = 0. As the point R lies on the line RN,

2 + 2(0) + q = 0

q = -2

Hence, RN is y + 2x -2 = 0

Substituting x = 2y into the line RN,

y + 2(2y) -2 = 0

5y = 2

y = 2/5

x = 2(2/5) = 4/5

In the triangle RNQ, x is the height from N onto RQ, the area [RNQ] = (x*RQ)/2 = 2x/2 = x = 4/5.

Hence, 3[RNQ] + 4 = 3(4/5) + 4 = 32/5.

Note: The question is incomplete. The complete question probably is: A cubical cake with edge length 2 inches is iced on the sides and the top. It is cut vertically into three pieces as shown in this top view, where M is the midpoint of a top edge. The piece whose top is triangle B contains c cubic inches of cake and s square inches of icing. What is c+s?

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Answer:

32=3x-7

Step-by-step explanation:

The answer to the question is 17/140 fraction.

A fraction is a numerical expression that represents a part of a whole or a ratio of two numbers. It consists of two parts: a numerator (the number on top) and a denominator (the number on the bottom). For example, 3/4 is a fraction that represents 3 parts out of 4. It can also represent the ratio of 3 to 4.

To move the fraction to each box, you would need to multiply the denominator of the first fraction (10) by the numerator of the second fraction (14). The result is 140. Then, you would add the numerator of the first fraction (3) to the numerator of the second fraction (14), giving you 17. The answer to the question is 17/140.

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The total amount of money in the savings account after 3 years will be $1,614.00. This is calculated by multiplying $1500 by 1.04 three times, which equals $1,614.00.

1. 1500 x 1.04 = 1560

2. 1560 x 1.04 = 1624.40

3. 1624.40 x 1.04 = 1683.76

4. 1683.76 rounded to two decimal places = $1,614.00

Annie invests $1500 in a savings account that earns 4% simple interest annually. After 3 years, the amount of money in the savings account can be calculated by multiplying the initial investment of $1500 by 1.04 three times. This results in a total of $1,614.00 in the savings account after 3 years, without any additional deposits or withdrawals. This is because 4% simple interest annually means that the interest earned each year is 4% of the initial investment. This is calculated by multiplying the initial investment by 1.04. The 1.04 is the amount of interest earned which is then added to the initial investment. This process is repeated for 3 years, resulting in the total of $1,614.00.

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A two-variable equation having a graph in the form of a line is referred to as linear.

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

A two-variable equation with a line-shaped graph is said to be linear. The set of points in the coordinate plane that make up the graph of the linear equation are all the solutions to the problem.

Given, 2x - 3y = 7

(k + 1)x + (1 - 2k)y = 5k - 4

Here [tex]$a_1=2, b_1=-3, c_1=7$[/tex]

[tex]$$\mathrm{a}_2=\mathrm{k}+1, \mathrm{~b}_2=1-2 \mathrm{k}, \mathrm{c}_3=5 \mathrm{k}-4$$[/tex]

Since equations (1) and (2) have infinite solutions

[tex]$& \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_3} \\[/tex]

substitute the values in the above equation, we get

[tex]$& \Rightarrow \frac{2}{\mathrm{k}+1}=\frac{-3}{1-2 \mathrm{k}}=\frac{7}{5 \mathrm{k}-4} \\[/tex]

simplifying the equation, we get

[tex]$& \therefore \frac{2}{\mathrm{k}+1}=\frac{3}{1-2 \mathrm{k}} \\[/tex]

[tex]& \Rightarrow 2(1-2 \mathrm{k})=-3(\mathrm{k}+1) \\[/tex]

[tex]& \Rightarrow 2-4 \mathrm{k}=-3 \mathrm{k}-3 \\[/tex]

[tex]& \Rightarrow 2+3=-3 \mathrm{k}+4 \mathrm{k} \\[/tex]

Therefore, the value of K = 5.

The complete question is:

What value of K will be following pair of linear equations have infinite solutions

[tex]$$\begin{aligned}& 2 \mathrm{x}-3 \mathrm{y}=7 \\& (\mathrm{~K}+1) \mathrm{x}+(1-2 \mathrm{~K}) \mathrm{y}=(5 \mathrm{~K}-4)\end{aligned}$$[/tex]

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The expanded form of the expression is  1/2 x - 1/2 y which is determined by the distributive property.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression is given in the question, as follows:

-1/2 (y - x)

We have to determine the expanded form of the expression.

As per the question, we have

⇒ -1/2 (y - x)

Apply the distributive property of the multiplication,

⇒ -1/2 × y - (-1/2) × x)

⇒ -1/2 y + 1/2 x

⇒ 1/2 x - 1/2 y

Hence, the expanded form of the expression is 1/2 x - 1/2 y.

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There are basically 6 ratios used for finding the elements in Trigonometry. They are called trigonometric functions. The six trigonometric functions are sine, cosine, secant, cosecant, tangent and cotangent.

By using a right-angled triangle as a reference, the trigonometric functions and identities are derived:

sin Î= Opposite Side/Hypotenuse

cos Î= Adjacent Side/Hypotenuse

tan Î= Opposite Side/Adjacent Side

sec Î= Hypotenuse/Adjacent Side

cosec Î= Hypotenuse/Opposite Side

cot Î= Adjacent Side/Opposite Side

All these are taken from a right-angled triangle.

When the height and base side of the right triangle are known, we can find out the sine, cosine, tangent, secant, cosecant, and cotangent values using trigonometric formulas.

The reciprocal trigonometric identities are also derived by using the trigonometric functions.

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Option B is Correct. An specific place in space is called a point. A dot indicates a point.

A point in space is a location. No length, width, or thickness exist in a point. In geometry, a dot stands in for a point. We typically use a (capital) letter to name a point. The simplest basic geometric object is a point. It is named with a capital letter and symbolised by a dot.

A point has no size and solely represents position (that is, zero length, zero width, and zero height). In a line, a line segment has two distinct endpoints. The line segment's length, which is the separation of two fixed points, is constant.

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Correct Question:

An exact location in space is called a _______

A. Line

B. Point

C. Circle

D. Line segment

The derivative of a logarithmic function is the inverse of the exponential function. That is, if y = logb(x) then the derivative of y is given by dy/dx = 1/xb.

Step 1: Recall that the derivative of a function is defined as the rate of change of the output of the function with respect to the input.

Step 2: Logarithmic functions are inverse of exponential functions, which means that the output of a logarithmic function is the input to an exponential function.

Step 3: Therefore, the derivative of a logarithmic function is the inverse of the derivative of an exponential function.

Step 4: The derivative of an exponential function is given by dy/dx = bx, where b is the base of the exponential function.

Step 5: Therefore, the derivative of a logarithmic function is given by dy/dx = 1/xb, where b is the base of the logarithmic function.

The derivative of a logarithmic function is the inverse of the exponential function. That is, if y = logb(x) then the derivative of y is given by dy/dx = 1/xb.

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Therefore , the solution of the given problem of fraction comes out to

be  = 43/9.

To represent a whole, any number of equal parts or fractions may be employed. The quantity of a particular size is expressed as a fraction in standard English. 8, 3/4. Fractions are included in wholes. In mathematics, the exponent to denominator ratio is used to represent numbers. These are all simple fractions of integers.

Here,

Given :

Let's transform the mixed fraction to an improper fraction with an equivalent value.

1 [tex]\frac{4}{9}[/tex] = 3[tex]\frac{1}{3}[/tex]

Consequently, the second fraction is now 13/9 = 10/3.

The LCD is now located. The LCD is nine.

We now set each denominator to LCD, which equals 9. Therefore, we multiply the second fraction's numerator and denominator by 3.

=> 13/9 + 10*3 /3*3

=> 13/9 + 30/9

Given that the denominator is equal, now.

As a result, we may simply add numerators.

=> 43/9

Therefore , the solution of the given problem of fraction comes out to be  

= 43/9.

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The required symbol of logarithmic function is [tex]\log_{e}x[/tex].

A logarithmic equation is one that uses the logarithm of an expression involving a variable. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 is equal to 103, its logarithm in base 10 is 3, or log10 (1000) = 3. When there is no possibility of mistake or when the base is irrelevant, The logarithm of x to base b is expressed as logb (x), logb x, or even without the specified base, log x, just like in big O notation.

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Text messages costing $0.05/text will have an expression C = 0.05t for cost of t amount of text messages.

What is an expression?

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

The cost of 1 text message is = $0.05

Let the number of text messages be t.

The cost (C) for t number of text message will be -

C = t × 0.05

C = 0.05t

Therefore, the expression is C = 0.05t.

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Carlos has 28 pennies, 28 dimes, and 20 quarters.

Value is a concept that is used to describe the worth or importance of something or someone. It is often related to an individual's beliefs and opinions and is used to measure the quality of an item or service. Value is a subjective concept, as what is considered valuable to one person may not be valuable to another. Value can also be measured in terms of money, with items or services valued at a certain price.

The total value of the coins is $6.59. Each penny is worth 1 cent, each dime is worth 10 cents, and each quarter is worth 25 cents. Therefore, 28 pennies plus 280 dimes (28 x 10) plus 500 quarters (20 x 25) equals 858 cents, which is equal to $6.59.

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Answer:-2, 4

Step-by-step explanation:

An algebraic expression that contains one or more monomials.

A polynomial factor P(x) is any polynomial that divides evenly into P. (x). x + 2 is, for example, a factor of the polynomial x2 – 4. A polynomial’s factorization is its representation as a product of its components. For example, (x – 2)(x + 2) is the factorization of x2 – 4.

Step 1: Group the first two terms together, followed by the last two terms. Step 2: Extract a GCF from each binomial separately. Step 3: Remove the common binomial. It is worth noting that if we multiply our answer by itself, we get the original polynomial. Polynomial. An algebraic expression containing one or more monomials. Monomial. A number, a variable, or a number-variable product

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Depending on how many variables there are in the equations, there are several ways to solve algebraic problems.

There is only one way to solve a one-variable equation, which involves bringing all the terms that include the variable to one side before determining the value of the variable.

There are several ways to solve a problem when there are two variables, starting with the

1.  Elimination technique.

2. The substitution approach.

and several additional techniques

An algebraic equation is a mathematical sentence when two algebraic expressions are related with an equality sign (=).

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The IQR (interquartile range) of the data set expressed by this box plot is 22 units.

Each number of the data set pictured as a box plot is something the numbers have individually. The lowest number there (the first number), 38, is known as the minimum. The highest number there (the last number), 75, is known as the maximum. The second number there, 45, is known as the lower quartile. The third number there, 50, is known as the median or middle quartile. The fourth number, 67, is known as the higher quartile. In order to find the interquartile range, we need to find the difference between the lower quartile and higher quartile, which means subtracting.

67 (highest quartile)- 45 (lower quartile) = 22 (interquartile range)

Therefore, the IQR (interquartile range) of the data set expressed by this box plot is 22 units.

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Answer:

y = 163°

Step-by-step explanation:

Vertically opposite angles are equal. So, y = 163°

Also, the points u give for the question is halved for the person who writes the answer. So, I will get 10 points, not 20. Anyways, Cheers!

Pablo and Johanna have too many D. variables that they didn't control and not enough replicates.

Variables are generally referred to as such due of their diversity. The term "control variable" refers to a variable that is purposefully kept constant in scientific research (or sometimes simply just a control). Information is stored in variables so it may be accessed and changed.

They also give us a means to give data a name that is descriptive, which helps the reader and us understand our programmes better. Variables can be thought of as storage spaces for data, which is a useful metaphor. A term can either be a variable, a constant with an associated mathematical operation, a product of variables, or a combination of a number and a variable.

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The proof of the area of the circle equation is shown below

From the question, we have the following parameters that can be used in our computation:

Area of radius 1 = π

The area of a circle is proportional to the square of its radius.

When the radius is multiplied by a scale factor of "r," the area is multiplied by the square of that factor: r^2.

So, the area of a circle of radius "r" is given by π * r^2 square units.

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The scale factor is 1/2.

What is a scale factor?

When both the original dimensions and the new dimensions are known, the scale factor may be determined. The following is a basic formula to determine a figure's scale factor: Scale factor is equal to the difference between the dimensions of the old and new shapes.

Here, we have

Given: ΔDEF is a dilation image of ΔABC.

Let

z is the scale factor

z = DE/AB

We have

DE = 4units

AB = 8units

z = 4/8

z = 1/2

Hence, the scale factor is 1/2.

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The exponential function that grows the least quickly is given as follows:

f(x).

The general format of an exponential function is defined as follows:

y = ab^x.

In which:

To grow the least quickly, we want a function with the lowest rate of change, hence it is function f(x), which has a rate of change of b = 3, while the other functions have a rate of change of 3.5 and of 4.

This means that the correct option is given by the first option.

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Explanation:

We have

(2x+3)(4x^2-5x+6)

Distribute it

(2x) (4x^2)=8x^3

(2x)(-5x)=-10x^2

(2x)(6)=12x

(3)(4x^2)=12x^2

(3)(-5x)=-15x
(3)(6)=18

Now we add all of them up:

8x^3-10x^2+12x^2+12x-15x+18

Now we simply it:

8x^3+2x^2-3x+18

Step-by-step explanation:

a. The profit function, P(x), can be found by subtracting the cost function from the revenue function.

P(x) = R(x) - C(x)

P(x) = (-0.04x² + 320x) - (85x + 120,000)

P(x) = -0.04x² + 235x - 120,000

b. To find the profit if 1000 bicycles are produced and sold, substitute x=1000 into the profit function:

P(1000) = -0.04(1000)² + 235(1000) - 120,000

P(1000) = -40,000 + 235,000 - 120,000

P(1000) = 75,000

So, the profit would be $75,000 if 1000 bicycles are produced and sold.

c. To find the break-even point, we set the profit function equal to zero and solve for x:

P(x) = 0

-0.04x² + 235x - 120,000 = 0

Using the quadratic formula or factoring, we can find that the break-even point occurs when:

x = (235 +/- sqrt(235^2 - 4(-0.04)(-120,000)))/(2(-0.04))

x = (235 +/- sqrt(55,089,000))/(-0.08)

x = (235 +/- 7,500)/(-0.08)

x = (235 - 7,500)/(-0.08) or (235 + 7,500)/(-0.08)

x = -31,250/ -0.08 or 5,375/-0.08

x = 3906.25 or -64,375

Since negative values of x do not make sense in this context, the break-even point occurs when 3906.25 bicycles are produced and sold.

Answer: We can start by using the identity sin^2(A) + cos^2(A) = 1.

We can square the equation 3 sin A + 4 cos A = 5, to get:

9sin^2(A) + 12sin(A)cos(A) + 16cos^2(A) = 25

Substituting the identity sin^2(A) + cos^2(A) = 1, we get:

9sin^2(A) + 12sin(A)cos(A) + 16(1-sin^2(A)) = 25

12sin(A)cos(A) = 6

Now,we can use identity tan(A) = sin(A) / cos(A) and sec(A) = 1 / cos(A)

tan(A) = sin(A) / cos(A) = (2sin(A)cos(A)) / (cos^2(A)) = 2 * (sin(A)cos(A)) / (1-sin^2(A)) = 2 * (6 / 12) = 1

sec(A) = 1 / cos(A) = 1 / sqrt(1 - sin^2(A)) = 1 / sqrt(1 - (3/5)^2) = 1 / sqrt(1 - 9/25) = 5/sqrt(16) = 5/4

Now we can add them:

tan(A) + sec(A) = 1 + 5/4 = (4+5) / 4 = 9/4 = 2.25

Hence proved that tan A + sec A = 2.25

Step-by-step explanation:

If the composite figure consists of of a cube of side length 6cm and a hemisphere of radius 3cm , then the surface area of composite figure is  [tex]236.52 \; cm^{2}[/tex] .

The Composite Figure consists of a Cube and Hemisphere ;

the radius of the hemisphere is given as = 3 cm ;

So, formula for curved surface area of hemisphere is = [tex]2\pi r ^{2}[/tex] ;

= [tex]2\pi 3 ^{2}[/tex] = [tex]56.52cm^{2}[/tex] ;

the side length of the cube is = 6cm ;

only the area of the 5 sides will be calculated because on one side there is a hemisphere ;

Surface Area of Cube = [tex]5a^{2}[/tex]

= [tex]5\times 6^{2}[/tex] ;

= [tex]5 \times 36[/tex] = [tex]180 \; cm^{2}[/tex] .

So , the surface area of the composite figure = Area of hemisphere + area of 5 sides cube ;

Substituting the areas ,

we get ;

= [tex]56.52 + 180[/tex] ;

= [tex]236.52 \; cm^{2}[/tex] .

Therefore, Surface Area of given composite figure is [tex]236.52 \; cm^{2}[/tex] .

The given question is incomplete , the complete question is

Explain how to find the surface area of the composite figure that consists of a cube of side length 6cm and a hemisphere of radius 3cm .

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Since the variables or exponent raised to these variables are "unlike" or different, these terms are referred to as unlike terms.

A variable is, to put it simply, a quantity that may be altered and is not fixed. The two primary categories of variables are categorical and numeric. Then, for categorical and numerical variables, respectively, nominal or ordinal and discrete or continuous subcategories are created for each category. This section provides a quick overview of these types. a quantity that could take any of a range of values. a variable's sign; something that is variable; a component of a scientific experiment that is potentially subject to change.

given

Like terms are those terms that share the same factors.

Consequently, phrases that have identical variables raised to the same exponent are considered similar terms.

What are 25, -3x, and 3x called then , Since the variables or exponent raised to these variables are "unlike" or different, these terms are referred to as unlike terms.

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If x is not equal to -2 or -6, an expression that is comparable to the rational expression exists.

Math allows for addition, subtraction, multiplication, and division. Following is the structure of an expression: Calculator, number or variable, and expression The components of a mathematical expression include numbers, variables, and operations (such as addition, subtraction, multiplication or division etc.) You can contrast phrases and expressions.

given

Both the numerator and the denominator share the value x + 2, however there is a gap at x + 2 = 0, which also exists at x = -2.

Furthermore, if the denominator is zero, a function is undefined.

At x = -6, the denominator is zero as well.

Therefore, the function is undefined at x = -6, or there is a vertical asymptote at x = -6 and a hole at x = -2.

If x is not equal to -2 or -6, an expression that is comparable to the rational expression exists.

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Yes, f/x )= x² is a one to one function

One-to-one functions are those where each element in the domain has a unique and different element in the range. In other words, a one-to-one function has no repeating elements in its range.

To determine if f(x) = x² is a one-to-one function, we can look at the range of the equation. The range of f(x) = x² is all positive real numbers, and since all elements in the range are unique and different, we can conclude that f(x) = x² is a one-to-one function.

A one to one function is a function in which each element in the range is associated with exactly one element in the domain.

In the case of f/x )= x², each element in the range has exactly one associated element in the domain, which means it is a one to one function.

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The mean absolute deviation of Restaurant B's service ratings is equal to 1.0567111111111.

Mathematically, the mean for this set of service ratings can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of service ratings, we have;

F(x) = 4 + 4 + 2 + 1 + 4 + 4 + 2 + 3 + 5 + 1 + 5 + 3 + 2 + 2 + 2 + 3 + 1 + 2 + 2 + 4 + 2 + 2 + 3 + 2 + 2 + 3 + 2 + 4 + 5 + 3 + 3 + 2 + 5 + 3 + 5 + 1 + 3 + 1 + 3 + 1 + 2 + 4 + 3 + 3 + 2 + 4 + 4 + 1 + 3 + 5 + 1 + 3 + 3 + 4 + 5 + 4 + 2 + 3 + 5 + 2 + 4 + 3 + 2 + 4 + 4 + 4 + 1 + 2 + 5 + 5 + 5 + 3 + 5 + 4 + 1

F(x) = 226.

Note: The total number of data (n) is equal to 75.

Next, we would determine the mean ratings as follows;

Mean = [F(x)]/n

Mean ratings = 226/75

Mean ratings = 3.0133333333333.

In Mathematics, MAD is an abbreviation for mean absolute deviation and the mean absolute deviation (MAD) of a data set can be calculated by using this formula;

MAD = 1/n ∑|x - μ|

Where:

Substituting the given parameters into the MAD formula, we have the following;

MAD = 1/75 [(4 - 3.0133333333333) + (4 - 3.0133333333333) + (2 - 3.0133333333333) + (1 - 3.0133333333333) + ........ + (1 - 3.0133333333333)]

MAD = 1/75 × 79.25333333325.

MAD = 1.0567111111111.

In conclusion, the mean absolute deviation (MAD) for Restaurant B's service ratings is 1.0567111111111.

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