on average a customer waits 10 minutes in a queue and customers arrive at the rate of two per minute. how many customers are waiting in the queue on average

Answer: To write a linear equation to model the relationship between the height h of the candle and time t, we need to find the slope and y-intercept of the line that represents this relationship.

The slope of the line is given by the rise over the run, or the change in the y-value (the height of the candle) over the change in the x-value (the time). We can calculate the slope by taking the difference in the height of the candle after 5 hours and 3 hours, and dividing it by the difference in the time:

slope = (16.5 - 18) / (5 - 3) = (-1.5) / (2) = -0.75

The y-intercept of the line is the point at which the line crosses the y-axis. This is the height of the candle when the time is 0. We can use the height of the candle after 3 hours as the y-intercept, since this is the height when the time is 3:

y-intercept = 18

We can use these values to write a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept.

Plugging in the values we found, we get:

h(t) = -0.75t + 18

This is the linear equation that models the relationship between the height h of the candle and time t.

To predict how tall the candle will be after burning for 8 hours, we can plug in t = 8 into the equation:

h(8) = -0.75(8) + 18 = -6 + 18 = 12 inches

This means that the candle will be 12 inches tall after burning for 8 hours.

Therefore, the correct answer is (d) h(t) = 0.75t + 20.25; 14.25 inches.

To write a linear equation to model the relationship between the height of the candle and time, we can use the information given. We know that after 3 hours, the candle is 18 inches tall, and after 5 hours, it is 16.5 inches tall.

We can set up a system of linear equations to represent this information. Let's call the height of the candle h and the time t. Then we can set up the following system:

h = 18 - 3t

h = 16.5 - 5t

To solve this system, we can set the two equations equal to each other and solve for t:

18 - 3t = 16.5 - 5t

1.5 = 2t

t = 0.75

This tells us that the height of the candle decreases by 0.75 inches per hour.

Now we can use this information to predict how tall the candle will be after 8 hours. We can plug in 8 for t in the equation h = 18 - 3t to find the height of the candle:

h = 18 - 3(8)

h = 18 - 24

h = -6 inches

So the candle will be about 6 inches shorter after burning for 8 hours. This means it will be about 10.5 inches tall.

The correct option is c, h(t) = -0.75t + 15.75; 9.75 inches.

This is because we found that the height of the candle decreases by 0.75 inches per hour, which is represented by the coefficient of t in the equation. The y-intercept, 15.75, represents the initial height of the candle, which we found to be 16.5 inches.

Happy to help!

Answer:

-------------------

Step-by-step explanation:

Answer:

5 minutes

Step-by-step explanation:

Given:
It takes five machines five minutes to make five widgets

Let's first determine how much time it takes one machine to make one widget

1 machine will take 5 times as long to make 5 widgets

Therefore for 1 machine to make 1 widget it will take 1/5th of the time

To make 100 widgets, 1 machine will take 5 x 100 minutes or 500 minutes

If we use 100 machines this time will be reduced by 100

Answer:

x=13/3

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

the equation of a line passing through the origin is

y = mx ( m is the slope )

calculate m using the slope formula

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

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (4, - 1) ← 2 points on the line

m = [tex]\frac{-1-0}{4-0}[/tex] = [tex]\frac{-1}{4}[/tex] = - [tex]\frac{1}{4}[/tex]

y = - [tex]\frac{1}{4}[/tex] x ← equation of line

An equilateral triangle is a triangle that has three equal-length sides, commonly referred to as a "regular" triangle.

Find the attachment answer

Learn more about equilateral triangle refer to :

https://brainly.com/question/17264112

#SPJ1

Answer: Alex Paid $175 for 40 months

Step-by-step explanation:

$4000 = y-int or b

$11000 = y

40 months = x

Slope - intercept form : Y=mx+b

We are solving for m which is the slope (How much Alex Paid per month)

11000=m(40)+4000

11000=40m+4000

7000=40m

7000/40

m=175

The co-ordinates will be(x,y) by the given equation the co-ordinates (9,1).

How to co-ordinate using subtraction method?

So, the given equations are

-2x+9y=-9  ⇒ (i)

-3x+5y=12  ⇒ (ii)

(i) * 5 ⇒ -10x + 45y = -45

(ii) * 9 ⇒ -27x + 45y = 108

⇒ 17x =  153

x = 9

Now, substitute x=9 in equation (i)

-2(9) + 9y = -9

-18 + 9y = -9

9y = -9 + 18

y = 9/9

y = 1

Hence, the co-ordinates will be(x,y) by the given equation the co-ordinates (9,1).

To know more about co-ordinates check the below link:

https://brainly.com/question/17206319

#SPJ1

Yes the given C and D lines are parallel

How to know two lines are parallel lines?

Any two parallel lines that are crossed by a transversal can be recognized by the following characteristics.

The fundamental characteristics listed below make it simple to recognize parallel lines.

as the sum of the given angle c and d i.e. 48+132 is 180 it clearly shows that it is the Pairs of interior angles on the same side of the transversal which proves that the given lines C and D are parallel  

Learn more about parallel lines from the link below

https://brainly.com/question/16701300

#SPJ1

Answer: -4/9

Step-by-step explanation:

12 - 8 / -18 - (-9)

4 / -18 + 9

4 / -9

- 4/9

Answer: The answer is 97

Step-by-step explanation:

Since Adam is above sea level, the number 73 is positive. The number 24 would be negative since it's below sea level.

73 - ( -24) = 97

To check to make sure it's right we can do this:

-24 + 97 = 73

73 - 97 = -24

Answer: (x+5)(2x+10)

Step-by-step explanation: I see your comment, so try to help you fast, I am in a rush, so can't type all the work on paper yet, sorry!

The Total number of registered doctors will be 246753.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Let the total number of doctors be x.

Since 23.1% of all registered doctors were female. If there were 55,700 female registered doctors that year. This will be:

23.1% × x = 55700

0.231x = 55700

Divide

x = 57000 / 0.231

x =246753

The doctors are =246753.

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

Answer:

Plot each graph on the same coordinate system.

TSP

TP=12cm

T

Step-by-step explanation:

The sequence of transformations that can generate the transformed image are the reflection of the quadrilateral across the y - axis, followed by the graph transformation (x - 2, y - 0). At the end, image is reduced by a scale factor of [k].

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

Given is a quadrilateral ABCD and its transformed form.

The following transformations are done to obtain the transformed image -

Therefore, the sequence of transformations that can generate the transformed image are the reflection of the quadrilateral across the y - axis, followed by the graph transformation (x - 2, y - 0). At the end, image is reduced by a scale factor of [k].

To solve more questions on graph transformation, visit the link below -

https://brainly.com/question/10059147

#SPJ1

Answer: read below and learn how to do it so you won’t struggle the rest of highschool college and the real world!

Step-by-step explanation:

you just plug in 2 for p and -1 for q and solve.

(4x2+3x-1)^2

4x2 =8 3x-1 =-3

(8+-3)^2

(5)^2

5x5=25

••therefore your answer is 25

it’s basic algebra. it’s not calculus:)

The score of the netball team in 5th game is 26.

A number that is calculated by adding quantities together and then dividing the total by the number of quantities is called average.

Given that, a team scored average 31 points in first four game, and then 30 points average in first five game.

Score in 4 games = 4x31 = 124

Score in 5 games = 5x30 = 150

Score in 5th game = 150-124 = 26

Hence, The score of the netball team in the 5th game is 26.

For more references on averages, click;

https://brainly.com/question/24057012

#SPJ1

Answer:

The lie is #3

Step-by-step explanation:

The only way to solve this is by testing each equation to see if it's true. Remember that dividing powers with the same base, in this case b, means you're just subtracting the exponents.

Substituting 5 for y in #1 gives us the equation [tex]\frac{b^9}{b^5}=b^4[/tex]. This is the same as saying [tex]b^9^-^5=b^4[/tex], which is true.

Substituting 7 for z and 2 for x in #2 gives us [tex]\frac{b^7}{b^2}=b^5[/tex]. Like we did for the first one, this is the same as [tex]b^7^-^2=b^5[/tex], which is also true.

That means that #3 is a lie, but substituting 2 for x anyway gives us [tex]\frac{b^8}{b^2}=b^8[/tex], or [tex]b^8^-^2=b^8[/tex]. This is not a true statement, and x would have to equal 0 for this to be true.

Answer:

The equation that represents the line of Paul's grade downfall is:

y = (-20)x + 130

This equation states that for every decrease of 1 in the value of x (representing the number of weeks), the value of y (representing Paul's math average) decreases by 20.

Step-by-step explanation:

To find the equation that represents the line of Paul's grade downfall, we can use the two given points to plot the line on a coordinate plane. The point (2, 90) represents the value that after 2 weeks, Paul's math average is 90, and the point (4, 50) represents the value that after 4 weeks, Paul's grade has dropped to 50. We can plot these two points on the coordinate plane as follows:

(2, 90)

(4, 50)

To find the equation of the line that passes through these two points, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the slope of the line, we can use the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates of the two points, we get:

m = (50 - 90) / (4 - 2)

= -40 / 2

= -20

To find the y-intercept of the line, we can substitute the coordinates of one of the points and the slope into the slope-intercept form of the equation:

y = mx + b

Substituting the coordinates of the point (2, 90) and the slope of -20, we get:

90 = (-20)(2) + b

= -40 + b

= b - 40

Solving for b, we get:

b = 90 + 40

= 130

The correct options are B and C, or 3x-21 and -3x21, since the inequality sign must be "flipped," or reversed, whenever you multiply or divide both sides of the inequality.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Here,

Anytime you multiply or divide both sides of the inequality, you must “flip” or change the direction of the inequality sign. This means that if you had a less than sign <, it would become a greater than sign >.

x≤-7

3x≥-21

-3x≤21

The correct options are B and C that is 3x≥-21 and -3x≤21 because anytime you multiply or divide both sides of the inequality, you must “flip” or change the direction of the inequality sign.

To know more about inequality,

https://brainly.com/question/12679763

#SPJ1

The correct option regarding who should the restaurant give samples to generate a representative sample is given as follows:

All diners diners who are willing to pay for the samples.

Sampling is a technique for when a group of elements from a population is taken to represent the entire population.

This group of elements has to be representative of the entire population, as to lead to correct conclusions.

In this problem, all the dinners who are willing to pay for the samples should be sampled, as if they are willing to pay, it means that they are interested in the new dish, hence their opinions should be considered as it would improve the restaurant's revenue with the new dish.

More can be learned about sampling at https://brainly.com/question/9910540

#SPJ1

Answer:

2/3

Step-by-step explanation:

1-1/3 is the same that   3/3 - 1/3

3/3 - 1/3 = 2/3

Answer: 168in^3

Step-by-step explanation:

6 x 7 x 4 = 168

Answer:

neither are functions

Step-by-step explanation:

For a relation to be a function each value of the input x must map to exactly one unique value in the output y

(1)

This relation is not a function since

7 → 2 and 5 → 2

Two different values of x have the same output , thus not a function

(2)

This relation is not a function since

3 → 10 and 3 → 8

Two different values of x have the same output, thus not a function

Answer:

Step-by-step explanation:

neither are functions

The line which is parallel to the given line y=-4/3x+1 is y = -4/3x + 2

What is the equation of the line?

The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. Key Point. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.

Given that the equation of the line is:

y = -4/3x + 1                                                           ..........(1)

To find the equation of the line is parallel to the given line equation.

We know that the given equation is in the slope-intercept form

y = mx+c, where m is the slope and c, is the intercept.

Compare with given equation(1) we get

m = -4/3  and c=1

Now change the y-intercept c=1 to an intercept of c= 2

Therefore (1) becomes

y = -4/3x + 2

Hence, The equation of line y = -4/3x + 2 is the parallel line to the given equation of the line.

To learn more about the equation of line visit,

https://brainly.com/question/13763238

#SPJ1

Answer:

I was going to answer but there is no attachment.

Step-by-step explanation:

The value of.x will be 20 and the angles will each have a value of 90 degrees.

When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.

When two lines meet at a point, an angle is created.

An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character. The circularity or rotation of an angle is often measured in degrees and radians.

Angles are a common occurrence in daily life.

Angles are used by engineers and architects to create highways, structures, and sports venues.

Hence, The value of.x will be 20 and the angles will each have a value of 90 degrees.

learn more about angles click here:

https://brainly.com/question/25716982

#SPJ1

The equation of the transformed function is (c) g(x) = 4(1/3x)²

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

f(x) = x²

g(x) = horizontally shrunk of f(x) by a factor 1/3 and vertical stretch by a factor of 4

The above equations implies that, we have the transformation to be:

Mathematically, this can be represented as

g(x) = 4f(1/3x)

Substitute the known values in the above equation, so, we have the following representation

g(x) = 4(1/3x)²

Hence, the transformed function si g(x) = 4(1/3x)²

Read more about transformation at

brainly.com/question/27224272

#SPJ1