Part B: Logan made a profit of $235 as a mobile groomer. He charged $75 per appointment and received $40 in tips, but also had to pay a rental fee for the truck of $10 per appointment. Write an equation to represent this situation and solve the equation to determine how many appointments Logan had. (5 points)

well, let's get the info first.

so going forth the Cheetah goes 70mph and going back it modestly does 40mph.

can we say that on average it did 55mph?

well, what's that?  on average means, that in total if we sum all units up and divide them evenly by relevant intervals, that's our average value.

well, let's see both intervals, on is forth and another is back 2 intervals, and the speed values are 70 and 40, so the average will really be (70 + 40) ÷ 2 = 55, that is an average of 55mph, so yes, we can say that.

A)

since an hour is 60 minutes, the Cheetah is really doing 70 miles per 60 minutes, or we can say

[tex]70\cdot \cfrac{miles}{~~\begin{matrix} hour \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{~~\begin{matrix} hour \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{60~minutes}\implies \cfrac{70}{60}\cdot \cfrac{miles}{minutes} \implies 1.1\overline{66}\frac{miles}{minutes}[/tex]

[tex]{\Large \begin{array}{llll} \stackrel{\textit{miles covered}}{m(t)}~~ = ~~1.1\overline{66}t \end{array}}[/tex]

B)

[tex]\stackrel{\textit{miles covered}}{m(t)}~~ = ~~1.1\overline{66}t\implies \stackrel{t=10}{m(10)=1.1\overline{66}(10)}\implies \stackrel{\textit{miles in 10 minutes}}{m(10)=11.\overline{66}}[/tex]

The system of two equations can be represented as y = 10x + 40 and

y = 12x + 28.

The system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution if a system of equations only has two linear equations with two variables.

Because there are only three possible methods to graph two straight lines in the plane, there are only three matching forms of solution for a given system of equations.

Let, 'x' represent the number of days and 'y' represent the total cost.

Plan A can be represented as y = 10x + 40.

And, PlanB be can be represented as y = 12x + 28.

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Answer: 25

Step-by-step explanation: 5x5 =25

Answer: 25

20% is one-fifth of a whole. This means we must multiply our known number times five.

5 x 5 is 25.

To make sure that our answer is correct, we can figure out the 20% of 25, which is 5.

This means that  25 is our correct answer.

I hope this helps & good luck <3 !!!

Charlie could have used quota sampling instead of non-random sampling.

Given is that Charlie is studying the time it takes members of his company to travel to the office. He stands by the door to the office from 08 : 40 A.M. to 08 : 50 A.M. one morning and asks workers, as they arrive, how long their journey was.

Charlie could have used quota sampling instead of non-random sampling. He could have selected a sample that reflects the characteristics of the whole population.

Therefore, Charlie could have used quota sampling instead of non-random sampling.

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{COMPLETE QUESTION IS -

Charlie is studying the time it takes members of his company to travel to the office.

He stands by the door to the office from 0840 to 0850 one morning and asks workers, as they arrive, how long their journey was.

State and briefly describe an alternative method of non-random sampling Charlie could have used to obtain a sample of 40 workers.}

Answer:

Straight line Depreciation

The board should be 28 inches long.

What is an expression?

An expression or mathematical expression in mathematics is a finite combination of symbols that is well-formed in accordance with context-dependent principles.

Let's call the length of the first part "x". Then, the length of the second part would be x + 6 inches. The total length of both parts is 50 inches, so we can set up an equation to solve for x:

x + (x + 6) = 50

Expanding and solving for x:

2x + 6 = 50

2x = 44

x = 22

So, the first part should be 22 inches long, and the second part should be 22 + 6 = 28 inches long.

The board should be 28 inches long

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The perimeter of the rectangle is 36 cm.

A rectangle is a two-dimensional figure with length and width.

The area of a rectangle is Length x width.

We have,

Length = 10 cm

Width = 8 cm

Now,

The perimeter of the rectangle.

= 2 (length + width)

= 2 (10 + 8)

= 2 x 18

= 36 cm

Thus,

The perimeter of the rectangle is 36 cm.

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The complete question.

The length ad width of a  rectangle is 10 cm and 8 cm.

Find the perimeter of the rectangle.

a) 28

b) 12

c) 6.4

d) 36

The exponential equation is given by the function y = 30.5(0.7)ˣ

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

The standard form of an exponential equation is:

y = abˣ

where b is the rate of change and a is the initial value.

Let y represent the number of games sold x years since 2015.

From the graph, at point (0, 30.5):

30.5 = ab⁰

a = 30.5

Also, at point (1, 21.35):

21.35 = ab¹;     but a = 30.5, hence:

21.35 = 30.5b

b = 0.7

The equation is y = 30.5(0.7)ˣ

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The cost to print 50 photos is $12.50

What is proportion?

The proportion formula is used to determine whether or not two ratios or fractions are equal.

We can use a proportion to find the cost to print 50 photos based on the cost to print 20 photos. Since Ms. Morris charges $5.00 to print 20 photos, we can set up the proportion:

[tex]\frac{cost \ of \ 20\ photos}{number \ of\ photos } =\frac{cost \ of \ 50 \ photos}{number\ of \ photos}[/tex]

Plugging in the given values, we get:

$5.00 / 20 photos = x / 50 photos

Simplifying, we can cross-multiply to get:

20 photos * x = $5.00 * 50 photos

Multiplying and simplifying further, we get:

20x = $250.00

Dividing both sides by 20, we get:

x = $12.50

Therefore, the cost to print 50 photos is $12.50.

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The linear equation that shows the relationship between y and x is y = x - 5

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

The slope intercept form of an equation is:

y = mx + b

where m is the rate of change and b is the y intercept.

From the values given, using (1, -4) and (2, -3):

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-(-4)=\frac{-3-(-4)}{2-1} (x-1)\\\\y=x - 1-4\\\\y=x-5[/tex]

The linear equation is y = x - 5

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By evaluating both equations in x = 8 we will see that the hawk will be closer to the ground.

We know that the height of the hawk is modeled by:

y=−20x+350

And the height of the eagle is modeled by:

y=−10x+400

Now we need to evaluate both equations in x = 8.

hawk:

y = -20*8 + 350 = 190

For the Eagle:

y = -10*8 + 400 = 320

We can see that the hawk is closer to the ground.

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Answer:

A parallelogram is a quadrilateral with 2 pairs of parallel sides

The least common denominator of the number 2, 3, 4, 7 is found to be 42.

Here, the least common denominator of the following numbers is asked,

2, 3, 4, 7

Now, first understand the meaning of least common denominator, it is basically meant that what is that least common value that will divide all of the four above mentioned numbers. So, it is actually ased about the least common multiple (LCM).

We can find the value which will be a multiple of all those numbers,

4 is multiple of 2 but 3 and 7 are not.

6 is a multiple of 2 and 3 but 7 is not.

42 is the number that is multiple of 6 as well as 7 and it also the smallest number doing so.

So, the least common denominator of 2, 3, 4, 7 is 42.

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Complete question - What is the least common denominator of 2, 3, 7, 4.

A measurement that shows the circumference of each of the buttons in centimeters is: D. 37.7 cm.

Mathematically, the area of a circle can be calculated by using this formula:

Area of a circle = πr²

Where:

r represents the radius of a circle.

By substituting the radius into the formula for the area of a circle, we have the following;

Area of a circle = πr²

36π = π × r²

Radius, r = √36

Radius, r = 6 centimeters.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

Circumference of a circle = 2πr

Circumference of a circle = 2 × 3.14 × 6

Circumference of a circle = 37.7 cm.

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Complete Question:

Rolando is making buttons that are shaped like circles. Each button has an area of 36π square centimeters. Which measurement shows the circumference of each of the buttons in centimeters?

Answer

A 113.1 cm

B 18.8 cm

C56.5 cm

D 37.7 cm

Answer: no exact answer

Step-by-step explanation:

Given one point and a slope:

To graph the line plot the given point first.

Then find the second point, consider the slope by adding 1 to the x-coordinate and -5 to the y-coordinate, this gives us:

Next, plot the second point (-2, - 9).

Now connect the two pints and extend either side. This is the line you need.

Among the continuous improvement tools listed in the query, the cause-and-effect (fishbone) diagram is often used to initiate a root cause analysis effort. This tool helps identify potential causes of a problem by breaking down a complex issue into smaller and more manageable components.

The diagram is shaped like a fishbone, with the problem at the head and the potential causes in the "bones" of the fish. By examining the various factors that could contribute to a problem, a team can begin to isolate the most likely root causes and develop targeted solutions to address them. Other tools like scatter plot, Pareto chart, and swim lane process map can also be useful in continuous improvement efforts, but they may not be the best choice for initiating a root cause analysis

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Answer:

Non biased (kind of)

Step-by-step explanation:

It depends on how they randomly chose but if it was truly random it would be non biased as many people will read newspapers for things such as sports or catalogs

Suri has 10.00, and Savi has 3 times as much, or 30.00.

What is algebraic expression?

When we use numbers and words to solve a mathematical problem, we are using algebraic expressions.

Let's use algebra to solve the problem.

Let's say Suri has x amount of money. Then we know that Savi has 3 times as much money, or 3x. We also know that together they have 40.00. So we can write an equation:

x + 3x = 40

Simplifying this equation, we get:

4x = 40

Dividing both sides by 4, we get:

x = 10

So Suri has 10.00, and Savi has 3 times as much, or 30.00.

To check, we can verify that their total is 40.00:

10 + 30 = 40

So, the solution checks out.

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The expression which represents the perimeter of the rectangle is 2x + 14

The following expressions represent the descriptions respectively;

6x

(x - 5)

(x + 2.99)

The total cost of membership of each gym is represented by;

Gym A total cost = 80 + 25m

Gym B total cost = 40m

Length= x + 3

Width = 4

Perimeter of a rectangle= 2(length + width)

= 2{(x + 3) + 4}

= 2(x + 3 + 4)

= 2(x + 7)

Perimeter of the rectangle = 2x + 14

Area of the rectangle= length × width

= (x + 3) × 4

Area of the rectangle = 4x + 12

If x = 7

Area of the rectangle = 4x + 12

= 4(7) + 12

= 28 + 12

= 40 square units

If x is the cost of each apple, the total cost of 6 apples = 6x

Adam is x years old. John is 5 years younger.

So, John's age = (x - 5) years

Ben spent x dollars on a book and $2.99 on a pack of pencil.

Ben spent a total of x + 2.99

Gym A total cost:

80 + 25m

Gym B total cost:

40m

Where,

number of months= m

If m = 6 months

Gym A total cost:

80 + 25m

= 80 + 25(6)

= 80 + 150

= $230

Gym B total cost:

40m

= 40(6)

= $240

Therefore, the gym which is the best deal for 6 months is gym A

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Answer:

Lisa would need to score 97 on her 5th test.

Step-by-step explanation:

If Lisa has an average score of 82 on 4 tests, then the total sum of her scores would be 82 multiplied by 4, which is equal to 328.

If she wants an average final score of 85 over 5 tests, then the total sum of her scores needs to be 425 (i.e. 85 multiplied by 5).

To determine what she needs to get on her 5th test we need to subtract 328 from 425.

425 - 328 = 97

So the temperature in City A was 8A C and the temperature in City B was y = x + 1 = 8 + 1 = 9A C.

The problem can be solved by setting up an equation using the information given. Let's call the temperature of City A "x" and the temperature of City B "y". We can then write two equations based on the information given:

4x = 3y + 8

x - 2y = -3

We can use substitution to solve for one of the variables and then use that information to solve for the other. For example, we can substitute 3y + 8 for 4x in the second equation:

x - 2y = -3

x - 2y = 3y + 8 - 3

x - 2y = 3y + 5

x - 5y = 5

We can then solve for y by multiplying both sides of the equation by -1/5:

-5x + 5y = -5

5y = 5x + 5

y = x + 1

We can then substitute this expression for y into one of the original equations and solve for x:

4x = 3(x + 1) + 8

4x = 3x + 3 + 8

x = 8

So the temperature in City A was 8A C and the temperature in City B was y = x + 1 = 8 + 1 = 9A C.

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The value of the expression is the same as the second option: !a || (b & !c).

Boolean variables are variables that can have only one of two possible values: true or false. They are named after the 19th-century mathematician George Boole, who developed a system of logic based on binary values. In computer programming, boolean variables are commonly used to represent conditions or states that can be either true or false, such as whether a certain condition is met or whether a certain task has been completed.

The expression !(a & !(b & !c)) can be simplified using De Morgan's laws and distributive property to obtain:

!(a & !(b & !c)) = !a || (b & !c)

Therefore, the value of the expression is the same as the second option: !a || (b & !c).

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One reason for using a t distribution instead of the standard normal curve to find critical values when calculating a level c confidence interval for a population mean is that (b) z requires that you know the population standard deviation s.

The t distribution is used when the population standard deviation is unknown and is estimated from the sample. The t distribution has fatter tails than the standard normal curve, which makes it more appropriate for smaller sample sizes. When the sample size is large, the t distribution approaches the standard normal curve, and the z distribution can be used instead.

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Answer:ab

Step-by-step explanation:

because..........

The standard deviation is used more frequently then the variance because  standard deviation is more stable and less sensitive to outliers.

The Standard Deviation and Variance are defined as two closely related measures of the spread or dispersion of a set of data.

The Variance is defined as average of squared differences from mean, while Standard Deviation is square root of variance.

The reason why the standard deviation is used more frequently than  variance is because the standard deviation is expressed in same units as the original data, whereas  the variance is expressed in squared units.

For Example, if we measure  heights of a group of people in inches, the standard deviation will be expressed in inches, whereas variance will be expressed in square inches.

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If the spherical snowball is melting , then the rate at which the radius changing after 6.5 hours is 0.208 ft/h  .

A spherical snowball has volume = 260 ft³ that is melting at a rate of 11 cubic feet per hour, while remaining spherical.

We have to find the rate at which the radius is changing after 6.5 hours.

So , let "V" = volume of snowball, "r" = radius of snowball, and "t" = time.

Volume Of Sphere is  V = (4/3)πr³ and dV/dt = -11 ft³/h ;

So,  dr/dt when t = 6.5 hours. is dV/dt = (dV/dr)×(dr/dt)  ;

derivative of volume formula with respect to "r", we get:

⇒ dV/dr = 4πr²   ;

Substituting the given values in chain rule equation, we get:

⇒ -11 = (4/3)πr² × dr/dt  ;

⇒ dr/dt = -11/((4/3)πr²)

For  rate of change of the radius when t = 6.5 hours, we find the radius at that time.

The initial volume of the snowball = 260 ft³.

After 6.5 hours of melting at a rate of 11 ft³/h, the remaining volume will be:  V = 260 - (11 × 6.5) = 188.5 ft³   ;

So , V = (4/3)πr³

⇒ 188.5 = (4/3)πr³

⇒ r³ = (188.5 × 3 / (4π))   ;

≈ 3.55ft

Now we substitute r = 3.55 feet

⇒ dr/dt = -11/[(4/3)π(3.55)²]  ;

⇒ dr/dt ≈ -0.208 ft/h  ;

Therefore , the rate at which radius is changing after 6.5 hours is approximately 0.208 feet per hour and negative sign represents that radius is decreasing  .

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Answer:

16.5 cm²

Step-by-step explanation:

the measure of an exterior angle (32°) is found by dividing the difference between the measures of the intercepted arcs (54° and arc abject BF) by two.

32 = (BF - 54)/2

64 = BF - 54

arc angle BF = 64 + 54 = 118°

the area of that sector is

pi×r² × 118/360 = pi×4² × 118/360 = pi×16 × 118/360 =

= pi×2 × 118/45 =

= 16.47590814... ≈ 16.5 cm²

The new perimeter of the quadrilateral is  157.2 ft

Consider the following diagram.

We name the quadrilateral ABCD such that side AB = 12.2 ft, side BC = 16 ft, side AD = 12 ft

Let us assume that the perpendicular or height be DE = 12 ft

From figure we can observe that side AB = side CD

So, side CD = 12.2 ft

The quadrilateral is enlarged by a scale factor of 3

so, the dimensions of the new quadrilateral would be,

A'B' = 3 × AB

     = 36.6 ft

So, C'D' = 36.6 ft                  ............(as AB = CD)

B'C' = 3 × BC

B'C' = 48 ft

And A'D' = 3 × AD

A'D' = 36 ft

We know that the perimeter of quadrilateral is the sum of all the four sides.

So, the perimeter of new quadrilateral A'B'C'D' would be,

A'B' + B'C' + C'D' + A'D'

= 36.6 + 48 + 36.6 + 36

= 157.2 ft

Therefore, the perimeter is 157.2 ft

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