A plumber charges a flat fee of $73 to visit a home and examine a clogged drain. The plumber charges an additional $25 per hour spent fixing the drain. The total cost, C (in dollars), for fixing a drain that takes h hours is given by the following. C=25h+73 (a) What is the total cost for fixing a drain that takes 5 hours? (b) If the plumber charged a total of $398, how many hours did he spend fixing the drain?​

let's convert the mixed fraction to improper fraction first.

[tex]\stackrel{mixed}{5\frac{1}{4}}\implies \cfrac{5\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{21}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{21}{4}\div \cfrac{1}{4}\implies \cfrac{21}{4}\cdot \cfrac{4}{1}\implies \cfrac{21}{1}\cdot \cfrac{4}{4}\implies \text{\LARGE 21}[/tex]

Answer: 5 1/4 ÷ 1/4 = 21

Step-by-step explanation: Because the denominator is four, you would combine and create a mixed fraction. 5 × 4 = 20 and 20 + 1 = 21. So 5 1/4 equals 21 fourths which is why 5 1/4 ÷ 1/4 = 21

================================================

Explanation:

The x and y are placeholders for numbers.

Think of them as boxes so to speak, and we fill each box with a number.

In this case we will plug in x = 6 and y = 2.

The steps are shown below.

[tex]\frac{3\text{x}+4}{\text{y}}\\\\\frac{3*6+4}{2}\\\\\frac{18+4}{2}\\\\\frac{22}{2}\\\\11\\\\[/tex]

The final answer is choice B

-----------

This means,

[tex]\frac{3\text{x}+4}{\text{y}} = 11 \ \text{when} \ \text{x} = 6 \ \text{and y} = 2 \\\\[/tex]

Put another way

[tex](\text{x},\text{y}) = (6,2) \ \text{ is a solution to } \frac{3\text{x}+4}{\text{y}} = 11[/tex]

In a visual sense, the point (6,2) is on the equation of [tex]\frac{3\text{x}+4}{\text{y}} = 11[/tex]

Logs are a type of mathematical operation used to solve exponential equations.

Logs are written as log boxes, where b is the base. The base is the number that the logarithm is being calculated concerning. The x is the number that the logarithm is calculated. Logarithms allow us to convert multiplication and division problems into addition and subtraction.

For example, log2 (8) can be calculated by taking the logarithm of 2, which is 0.301029996, and then multiplying it by 8, which is 2.408239965. This means that log2 (8) is equal to 2.408239965.

Another example is log10 (100). This can be calculated by taking the logarithm of 10, which is 1 and then multiplying it by 100, which is 100.

This means that log10 (100) is equal to 100. Logs are an important tool in mathematics and are used in a variety of fields, such as chemistry, engineering, and economics.

To know more about Log or Logarithm:

brainly.com/question/1626212

#SPJ4

Answer: x= 8+ x over 2 = x over 2 + 8

Step-by-step explanation:

(A) There is only one solution to the given system.

(B) There is no solution to the given system

(C) There are infinite solutions to the system.

What is solution of the system?

A set of values for a variable that simultaneously satisfy each equation is the solution to a system of equations. A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.

Given:

3(- n + 4) + 5n = 2n ← distribute and simplify left side

- 3n + 12 + 5n = 2n

2n + 12 = 2n ( subtract 12 from both sides )

2n = 2n - 12 ( subtract 2n from both sides )

0 = - 12 ← not possible

This indicates the equation has no solution

Comparing the types of solutions

A n = 3

Indicates that there is only one unique solution to the equation.

B no solutions

This is indicated when you solve and obtain a ridiculous statement, similar to the one obtained in part A, that is

0 = 12

C infinite solutions

This is indicated when you solve the equation and obtain

4 = 4 or - 3 = - 3

Hence,

(A) There is only one solution to the given system.

(B) There is no solution to the given system

(C) There are infinite solutions to the system.

To know more about solution of the system, click on the link

https://brainly.com/question/13729904

#SPJ4

Answer:

Step-by-step explanation:

slope is the coefficient of x when the coeficient of y is 1.

we need change the form.

2y=x+8

y=[tex]\frac{1}{2}[/tex]x+4

so, the slope of a line parallel to the line is 1/2

18x - 9 = 72 and x = 4.5 represents the same value as 3/5(30x - 15) =72.

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.

Here,

2x – 5 and 13 are expressions

The sign that connects these two expressions is “=”.

Given

x = 4.5

And equation

3/5(30x - 15) =72

Simplifying

90x/5 - 45/5 = 72

18x - 9 = 72     -----------(a)

18x = 81

x = 81/18

x = 4.5             ------------(b)

Equation (a) and (b) are among the equations given in the options.

Hence, from the above calculation equations 18x - 9 = 72 and x = 4.5 express the same value of x as 3/5(30x - 15) =72 .

Learn more about equation here:

https://brainly.com/question/29538993

#SPJ1

Since Mary and Max are playing a game with complex numbers, Max's score must be equal to 1/(3 + 2i), so that the product of their score is one.

A reciprocal function simply refers to a type of function which comprises a constant on its numerator and an algebraic expression or complex number in its denominator such as: f(x) = 2/3 + 7i.

In Mathematics, a reciprocal function is typically used when describing relationships that are inversely proportional to one other.

Let the variable n represent Max's score. Therefore, a mathematical expression which models the product of both Mary and Max's score is given by the following:

Product = 3 + 2i × n = 1

Making n the subject of formula, we have the following as Max's score;

n = 1/(3 + 2i)

Check:

3 + 2i × 1/(3 + 2i) = 1

(3 + 2i)/(3 + 2i) = 1

Read more on reciprocal function here: brainly.com/question/11268242

#SPJ1

Answer: The first and third options are correct.

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

I timesed 11 by 12 which is 132 and then timesed 10 with 11 which then gave me 110. I then subtracted 132 with 110 which gave me the answer 22. if we remove 11 from the 22 books we then end up with 11. then times it by 12 = 132. then if you subtract 10 of the 22 books then we end up with 12. then times it by 11 which is 132 as well.

The solution of the equation 2x+y=4 and 3x-2y=-1 is the value of x = 1, while the value of y = 2

We have, the sets of equations as:

2x+y=4 and 3x-2y=-1?

As here, let 2x+y = 4 ----(i) and 3x-2y = -1 ----(ii)

As here to solve the value of x and y we will first equalise the co-efficient of x.

Here, the co-efficient of x in the first equation is 2, while in the second equation it is 3

So, for equalising, we will first multiply the first equation by 3 and the second by 2,

Thus, we will get it as:

6x+3y=12 ----(iii)

6x-4y=-2----(iv)

Now subtracting (iv) from (iii)

We will get,

7y = 14

=>y=2

Putting the value of y in (i),

2x=4-y = 4-2 =2

=>x = (2/2)=1

For more questions on Linear equations:

https://brainly.com/question/28732353

#SPJ4

The complete question may be like:

What is the solution of the equations 2x+y=4 and 3x-2y=-1?​

The cuboidal tank has a volume of [tex]6m^3[/tex] with dimensions of 4 m in length, 2 m in width, and 0.75 m in height.

The total amount of room or volume that a cuboidal tank can hold is known as its capacity. By multiplying the tank's length, width, and height collectively, it is determined.

The tank in this instance measures 4 metres long, 2 metres wide, and 0.75 metres high. We must multiply these three parameters collectively to determine the tank's capacity:

[tex]4m * 2m * 0.75m = 6m^3[/tex]

The tank can therefore hold [tex]6m^3[/tex] of liquid.

To know more about capacity visit:-

brainly.com/question/13967806

#SPJ4

The likelihood event:

Player 1 is more likely to hit the ball than Player 2 because P (Player 1) > P (Player 2).

The correct option is A.

Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.

Given:

Three softball players discussed their batting averages after a game.

Probability:

Player 1 = six tenths = 6/10

Player 2 = five ninths = 5/9

Player 3 = four sevenths = 4/7

To find better batting averages:

LCM of 10, 9 and 7.

10 = 2 x 5. 9 = 3 x 3, 7 = 7

So, the LCM (10, 9, 7) = 630

Now we have the number of chances are equal for each of the three players.

So, the P(Player 1) = 6/10 = 378/630

P(Player 2)= 5/9 = 350/630

P(Player 3)= 4/7 = 360/630

The Player 1 has better batting average than Player 2 and Player 3.

Therefore, Player 1 is more likely to hit the ball than Player 2 because P (Player 1) > P (Player 2).

To learn more about the LCM;

https://brainly.com/question/20739723

#SPJ1

Answer:

737

Step-by-step explanation:

Answer:

Step-by-step explanation:

a.we set the first integers is A, because they are consecutive Integer, so the three Integers are A, A+1, A+2

b.we konw (A+2-A)×4-1=A+1, so A=6

therefore, the three Integer are 6, 7, 8.

By algebra properties and trigonometric formulas, the roots x₁ = 30° + n · 360° and x₂ = 210° + n · 360° are solutions of trigonometric function tan x - √(1 - 2 · tan² x) = 0. (Correct choice: B)

In this problem we find a given trigonometric function, whose solution must be found by combining algebra properties and trigonometric formulas. First, write the entire expression:

tan x - √(1 - 2 · tan² x) = 0

Second, use algebra and root properties:

tan x = √(1 - 2 · tan² x)

tan² x = 1 - 2 · tan² x

3 · tan² x = 1

Third, clear x by algebra properties and inverse trigonometric properties:

tan² x = 1 / 3

tan x = √(1 / 3)

tan x = 1 / √3

tan x = √3 / 3

x = tan⁻¹ (√3 / 3)

x  = 30° or x = 210°

Since tangent function has a period of 2π (360°), then the solutions of the trigonometric function is:

x₁ = 30° + n · 360°, x₂ = 210° + n · 360°.

To learn more on trigonometric equations: https://brainly.com/question/22624805

#SPJ1

Therefore , the solution of the given problem of triangle comes out to be  ΔA"B"C "≅ ΔABC is congruent.

The fact that a triangle has sides or vertices qualifies it as a polygon. It is an elementary geometric form. The name given to a triangle with vertices A, B, & C is Triangle ABC. A singular planes and triangle are obtained in Euclidean geometry when the vertices are not collinear. Any triangle that has three sides and three corners is a polygon.

Here,

Triangle A'B'C' is created by reflecting triangle ABC across the y-axis.

Afterward, it was dilated by a ratio of 1/3 to create triangle A "B"C".

Find the right answer for the triangles ABC and A"B"C."

So,

We are aware that reflection undergoes a rigorous transformation, meaning the shape and size of the original object do not change.

As a result, after reflection, figures always match their pictures.

"ABC," "A'B'C," etc (i)

The process of dilation is flexible. Although the size is changed, the shape is still the same.

Figures after dilatation therefore always resemble their photographs.

ΔA'B'C' ≅ ΔA "B"C" ... (ii)

With I and (ii), we obtain

ΔA"B"C "≅ ΔABC

Similar triangles include ABC and ABC.

As a result, choice A is the right one.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ4

The midpoint for zero is (0,0).

The midpoint can be zero. This is dependent on the value of the two points. For two points on a number line on points with values -4, and 4, the midpoint is 0. And for two points such as (-2, 5), and (2, -5), the midpoint is equal to (0, 0).

The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

A compass and straightedge setup can be used to locate the midpoint of the line segment they determine given two points of interest. By initially building a lens out of circular arcs with equal radii centered at the two endpoints and joining the cusps of the lens, one can determine the midpoint of a line segment immersed in a plane. The midpoint of the segment is then the place where the line joining the cusps intersects the segment.

To learn more about Midpoint :

https://brainly.com/question/5566419

#SPJ4

Statement A,B is true rest all statement are false about the given function.

Given the function: [tex]2x^3+8[/tex]

Statement A:

The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value).

For the function 2x^3 + 8, the domain is all real numbers, which is represented as (-infinity, +infinity).

It is because the expression inside the function, 2x^3, is defined for all real numbers.

so above statement is true.

Statement B:

statement A and B are same so it's also true.

Statement C:

The range of a function is the set of all possible output values (y-values) that the function can produce.

For the function 2x^3 + 8, the range is also all real numbers (-infinity, +infinity)

It is because the function is a polynomial of odd degree (3) and it does not have any restriction on the output value. Since the function does not have any restriction, it can take any real number as an output value and thus the range is all real numbers.

so this statement is false.

Statement D:

The y-intercept of the function 2x^3 + 8 is 8. It is the point at which the graph of the function crosses the y-axis, which occurs when x = 0. So when x = 0, y = 2(0)^3 + 8 = 8.

so this statement if false.

Statement E:

A function has a center of symmetry if it is unchanged (i.e. is symmetric) when reflected across a line or point. The line or point across which the function is symmetric is called the axis of symmetry or center of symmetry.

The function 2x^3 + 8 does not have a center of symmetry. It is because the function is a polynomial of odd degree and it does not have any symmetry. The polynomials of odd degree are not symmetric about any point or line.

So this statement is also false.

To know more about domain of a function click below:

https://brainly.com/question/13113489#

#SPJ4

Answer:

Step-by-step explanation:

WX≅VY

VY = 7

CD≅BE

BE = 13

Answer:

48cm^2

Step-by-step explanation:

Rectangle=LxW

Triangle=bh/2

Rectangle: 10x4=40cm^2

Triangle: 4x4=16/2=8cm^2

40+8=48cm^2

Hope this helps :)

Answer: The reciprocal of a number is defined as 1 divided by that number. The opposite of a number is the number with the opposite sign. Therefore, the opposite reciprocal of a number is equal to the reciprocal of the opposite of that number.

In this case, the opposite reciprocal of 0/6 is the reciprocal of the opposite of 0/6. The opposite of 0/6 is 0/-6, which is equal to -0/6. The reciprocal of -0/6 is 1/(-0/6) = -6/0.

However, division by 0 is not defined, so it is not possible to find the reciprocal of -0/6. Therefore, the opposite reciprocal of 0/6 is undefined.

Step-by-step explanation:

Answer:

there is no reciprocal for 0/6

Step-by-step explanation:

Retail price of the product will be double its mean will have a prbability of 0.0401.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.

A probability distribution that is symmetric around the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

The value of the product considering = $37*2 = $74(x)

Mean = $37

Standard Deviation (SD)= $20

here z= [tex]\frac{x - mean}{SD}[/tex] = [tex]\frac{74 - 37}{20} = \frac{37}{20} = 1.75[/tex]

P(z>1.75) = 1 - [tex]\phi(1.75)[/tex] = 1 - .9599 = 0.0401

Retail price of the product will be double its mean will have a prbability of 0.0401.

To learn more about Normal Distribution refer to :

https://brainly.com/question/21408338

#SPJ4

Answer: the answer is the option

Employee B: gross pay $32,900, total job benefits $34,000

hope this helped you

Answer:

Step-by-step explanation:

The equation  y = x + 0.4x is the retail price y in dollars for an item with the original cost and a markup of 40% .

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

So, we choose the first equation.

To learn more about equation from the given link  

https://brainly.com/question/2972832

#SPJ1

Answer: I think it's 6816606.576

Step-by-step explanation: Hope this helps?

The length of the line is 5 units.

The distance between two points is the length of the line joining the two points.

Formula: distance= √(x_2-x_1)²+(y_2-y_1)²

Given that, endpoints are (-1,4) and (2,0) of the line segment.

The length= √(2+1)²+(0-4)²

                 =5units

Hence, The length of the line is 5 units.

To learn more on Distance click:

brainly.com/question/15172156

#SPJ1

Answer:

Step-by-step explanation:

Given that Angie can mow her lawn 4 times using 1/3 gallon of gas, you want to know how much gas is required for each mowing, and how many times Angie can mow on one gallon of gas.

To find the number of gallons required for each mowing of the lawn, divide the number of gallons by the number of mowings:

  (1/3 gal)/(4 mowings) = 1/(3·4) gal/mowing = 1/12 gal/mowing

It takes 1/12 gallon to mow the lawn once.

The reciprocal of this value has the reciprocal units.

  1/(1/12 gal/mowing) = 12 mowings/gal

Angie can mow the lawn 12 times with one gallon of gas.

__

Additional comment

It often proves useful to keep the units with the numbers when working rate problems. This can eliminate a lot of mistakes. The units are treated as you would treat a variable.

-4°F is equal to -20°C, or 253°K, which is the temperature above absolute zero. Thus, the temperature at midnight was 759°K, or almost 1400°F.

The physical concept of temperature indicates in numerical form how hot or cold something is.

A thermometer is used to determine temperature.

Thermometers are calibrated using a variety of temperature scales, which historically defined distinct reference points and thermometric substances.

The most popular scales are the Celsius scale, sometimes known as centigrade, with the unit symbol °C, the Fahrenheit scale (°F), and the Kelvin scale (K), with the latter being mostly used for scientific purposes. One of the seven base units in the International System of Units is the kelvin (SI).

The lowest point on the thermodynamic temperature scale is absolute zero, or zero kelvin, or 273.15 °C. It can be very closely approximated experimentally but never actually reached, as stated in the third rule of thermodynamics.

Hence, -4°F is equal to -20°C, or 253°K, which is the temperature above absolute zero. Thus, the temperature at midnight was 759°K, or almost 1400°F.

learn more about temperature click here:

https://brainly.com/question/25677592

#SPJ4

The function f(x - 5/3) is translated 5/3 units right and the function f(x) - 5/3 is translated 5/3 units down.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over the y-axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

Given, A function f(x) is transformed to f(x - 5/3) this results in f(x) is translated 5/3 units to the right along the x-axis.

And, The transformation f(x) - 5/3 is translated 5/3 units down along the y-axis.

learn more about the transformation of functions here :

https://brainly.com/question/13810353

#SPJ1