A computer technician charges $190 for a 3-hour appointment and $370 for a 7-hour appointment. Which of these represents a linear function that models the charge for hiring the technician for x hours? A y=55x+190 B y=55x+45 C y=45x+190 D y=45x+55

Answers

Answer 1

Answer:

The linear function that models the charge for hiring the technician for x hours is y=45*x + 55

Step-by-step explanation:

The linear function is defined by the equation

f(x) = mx + b or y = mx + b

where m is the slope of the line and b is the y-intercept.

In this case you want to represent a linear function that models the charge for hiring the technician for x hours, that is, y represents the charge for hiring the technician and x the number of hours.

Given the coordinates of two points (x1, y1) and (x2, y2), you can determine the equation of the line first knowing the slope m by:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

In this case, the points are:

(x1,y1)= (3,190)(x2,y2)= (7,370)

So:

[tex]m=\frac{370-190}{7-3}[/tex]

Solving:

m=45

To obtain the value of b, once you have replaced the value of m in the equation, you must substitute the values ​​of x and y for the values ​​of the coordinates of one of the points, and solve for b to obtain its value. In this case you replace the value of point 1:

[tex]y=45*x+b[/tex]

[tex]190=45*3+b[/tex]

And you get:

190= 135 + b

190 - 135= b

55= b

So, the linear function that models the charge for hiring the technician for x hours is y=45*x + 55

Answer 2

We want to find a linear equation that models the charge for hiring the technician for x hours.

The correct option is D, the equation is:

y = ($45/h)*x + $55

We know that a general linear equation is written as:

y = a*x + b

where a is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope can be written as:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we have two points, one given by:

(3 hours, $190)

The other given by:

(7 hours, $370)

Then the slope is given by:

[tex]a = \frac{\$ 370 - \$ 190}{7h - 3h} = \$ 45/h[/tex]

This means that he charges $45 per hour.

Replacing that in the general equation we get:

y = ($45/h)*x + b

To find the value of b, we use the fact that he charges $190 for 3 hours, then we can solve:

$190 = ($45/h)*3h + b

$190 = $135 + b

$190 - $135 = b = $55

Then the equation is:

y = ($45/h)*x + $55

So the correct option is D.

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Related Questions

Mrs. Robert’s vegetable garden is 6 feet wide and 8 feet long. A drawing of the garden has a scale of 1 inch 2 feet. What is the area of the garden on the scale drawing? a. 192 in b. 12 in c. 7 in d. 28 in

Answers

Answer:

Step-by-step explanation:

It’s 24

Answer:

b.12 inch squared

Step-by-step explanation:

6 feet become 3 inches and 8 feet becomes 4 inches 3×4 = 12

If cosθ=3/5, find tanθ

Answers

Answer and step-by-step explanation:

cos = adj/hyp (in a right triangle)

cos0 = 3/5

adj = 3

hyp = 5

opp = sqrt( 5^2 - 3^2) = sqrt( 25-9) = sqrt(16) = 4 (Pythogorean theorem)

tan0 = opp/adj = 4/3

Answer:

[tex]\boxed {\boxed {\sf tan( \theta)=4/3}}[/tex]

Step-by-step explanation:

Cosine is equal to adjacent over hypotenuse.

cos(x)=adjacent/hypotenuse

We are given: cosθ=3/5

Therefore, the adjacent is 3 and the hypotenuse is 5.

We want to find tanθ. Tangent is equal to opposite over adjacent.

We need to find the other leg of the triangle, which is the "opposite". Use Pythagorean Theorem.

[tex]a^2+b^2=c^2[/tex]

The hypotenuse (c) is 5.

[tex]a^2+b^2=5^2[/tex]

One leg (a) is 3, the other (b) is unknown.

[tex]3^2+b^2=5^2[/tex]

Evaluate all the exponents.

[tex]9+b^2=25[/tex]

Subtract 9 from both sides of the equation.

[tex]9-9+b^2=25-9[/tex]

[tex]b^2=16[/tex]

Take the square root of both sides.

[tex]\sqrt{b^2} =\sqrt{16}[/tex]

[tex]b=4[/tex]

Now we know the "opposite" is 4. We can find the tangent now.

[tex]tan(x)=opposite/adjacent[/tex] (opposite=4, adjacent=3)

[tex]tan( \theta)=4/3[/tex]

The tangent of theta is 4/3

I am having trouble finding this out will anyone help?

Answers

Answer: g = 4

Step-by-step explanation:

30 = 26+g

4 = g

Please help with this as soon as you can. Really need help and no idea how to do it.

Answers

Answer:

DE, BC, BA, CA

Step-by-step explanation:

basically just find the ones that do not cross and those are parellel.

I NEED HELP WITH THIS PICTURE IS PROVIDED

Answers

Is this an exam? Nehshdgdsusu

After writing a check mike had -$34.50 in his account, he deposited $20.00 how much did he have now?

Answers

Answer:

-$14.50

Step-by-step explanation:

This is easily solved on a calculator.

-34.50 + 20.00 = -14.50

EAST MATH PLS HELP ASAP PLEASE PLEASE
If one side of a square is represented by x + 7, and the perimeter of the square is
represented by 8x - 20, what is the value of X?

Answers

4(x+7)=8x-20

4x+28=8x-20

28=4x-20

48=4x

x=12

Cara's new car holds 13.5 gallons of gas. If gas costs $2.98 per gallon, how much would it
cost her to fill the gas tank from empty?
Submit
O
Lenovo

Answers

Answer:

$40.23

Step-by-step explanation:

Answer:

40.23

Step-by-step explanation:

easy just do 13.5*2.98

Use the method of lagrange multipliers to find

a. The minimum value of x+y, subject to the constraints xy=196, x>0, y>0
b. The maximum value of xy, subject to the constaint of x+y=196

Answers

Answer:

a) The function is: f(x, y) = x + y.

The constraint is: x*y = 196.

Remember that we must write the constraint as:

g(x, y) = x*y - 196 = 0

Then we have:

L(x, y, λ) = f(x, y) +  λ*g(x, y)

L(x, y,  λ) = x + y +  λ*(x*y - 196)

Now, let's compute the partial derivations, those must be zero.

dL/dx =  λ*y + 1

dL/dy =  λ*x + 1

dL/dλ = (x*y - 196)

Those must be equal to zero, then we have a system of equations:

λ*y + 1 = 0

λ*x + 1 = 0

(x*y - 196) = 0

Let's solve this, in the first equation we can isolate  λ to get:

λ = -1/y

Now we can replace this in the second equation and get;

-x/y + 1 = 0

Now let's isolate x.

x = y

Now we can replace this in the last equation, and we will get:

(x*x - 196) = 0

x^2 = 196

x = √196 = 14

then the minimum will be:

x + y = x + x = 14 + 14 = 28.

b) Now we have:

f(x) = x*y

g(x) = x + y - 196

Let's do the same as before:

L(x, y, λ) = f(x, y) +  λ*g(x, y)

L(x, y, λ) = x*y +  λ*(x + y - 196)

Now let's do the derivations:

dL/dx = y + λ

dL/dy = x + λ

dL/dλ = x + y - 196

Now we have the system of equations:

y + λ = 0

x + λ = 0

x + y - 196 = 0

To solve it, we can isolate lambda in the first equation to get:

λ = -y

Now we can replace this in the second equation:

x - y = 0

Now we can isolate x:

x = y

now we can replace that in the last equation

y + y - 196 = 0

2*y - 196 = 0

2*y = 196

y = 196/2 = 98

The maximum will be:

x*y = y*y = 98*98 = 9,604

help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help

Answers

Answer:

41/200

This is solved and put in standard form

0.205
My explanation: 2*1/10=0.2
5*1/1000=0.005
0.2+0.005= 0.205, I think I’m right, hope this helps! :)

Find n and r 10 pointsssss

Answers

Answer:

r = 11.623cm (aprox)

n = 6.153cm (aprox)

Step-by-step explanation:

Proportions:

9.8 ⇔ 4.3

n ⇔ 2.7

r ⇔ 5.1

n = 9.8*2.7/4.3 = 6.153 (aprox)

r = 9.8*5.1/4.3

r = 11.623 (aprox)

what is the slope of the following line?

Answers

Answer:

-2

Hope this helps,

PumpkinSpice1

The slope of the line will be ( -1 / 2 ). The correct option is C.


What is the slope?

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The two points are (0,3) and ( 6,0). The slope of the line will be calculated by using the formula below;-

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 0 - 3 ) / ( 6 - 0 )

Slope = -3 / 6 = -1 / 2

Therefore, the slope of the line will be ( -1 / 2 ). The correct option is C.

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Can anyone answer this simplify question

Answers

Answer:

y^3/4x

Step-by-step explanation:

An industrial factory makes / yards of chain every minute. The cost of each yard of chain is $2.00. What is the total cost for all chain produced in 10 minutes?

Answers

Answer:

Cost = $86.67

Step-by-step explanation:

Given

Yards = 4⅓ (missing part of the question)

Cost per yard = $2.00

Required

Determine cost of chains produced in 10 minutes

If 4⅓ yards is made in a minute, then

4⅓ * 10 yards are made in 10 minutes

Total = 4⅓ * 10

Total = 13/3 * 10

Total = 130/3 yards

Cost of a yard of chain is $2.00.

Cost of 130/3 yards would be:

Cost = $2.00 * 130/3

Cost = $260.00/3

Cost = $86.67 (approximated)

Hence, the required cost is approximately $86.67

If the radius r of a circle is decreasing at the rate of 5 cm per minute, find the rate of change of area when radius is 6 cm.

Answers

Answer:

-94.2 [tex]cm^2/min[/tex]

Step-by-step explanation:

Rate of change of radius = -5 cm per minute (as it is decreasing)

Radius of circle = 6 cm

Formula for area of Area:

[tex]A = \pi r^2[/tex]

Formula for differentiation of [tex]y = x^n[/tex]:

[tex]\dfrac{dy}{dt} = nx^{n-1}\dfrac{dx}{dt}[/tex]

Differentiating area w.r.to [tex]t[/tex]:

[tex]\dfrac{dA}{dt} = 2\pi r\dfrac{dr}{dt}[/tex]

Putting the values, [tex]r = 6, \frac{dr}{dt} = -5[/tex] cm per minute.

[tex]\dfrac{dA}{dt} = 6\pi \times (-5)\\\Rightarrow \dfrac{dA}{dt} = -30 \times 3.14\\\Rightarrow \dfrac{dA}{dt} = -94.2\ cm^2/min[/tex]

Negative sign indicates that area is decreasing.

Rate of change of area is -94.2 [tex]cm^2/min[/tex].

The area decreases at a rate of -188.4 square centimeter per minute

The area (A) of a circle of radius (r) is represented as:

[tex]A = \pi r^2[/tex]

Differentiate the area, with respect to r

[tex]A' = 2\pi r r'[/tex]

From the question, we have:

Radius (r) = 6cmRate of change of radius (r') = -5cm per minute

So, the equation becomes

[tex]A' = 2\times 3.14 \times 6 \times (-5)[/tex]

[tex]A' =- 188.4[/tex]

Hence, the area decreases at a rate of -188.4 square centimeter per minute

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Help for mon pls I’ll make you famous

Answers

Answer:

1. x>-1

2. x<4

3. x<-1

4. x>-2

5. x<-3

6. x<7

Step-by-step explanation:

1. 2x>-2  Divide both sides by 2.

  /2   /2

x>-1

2. 4x<16  Divide both sides by 4.

   /4   /4

x<4

3. x+4<3 Subtract both sides by 4.

      -4  -4

x<-1

4. 5x>-10  Divide both sides by 5.

  /5     /5

x>-2

5. 3x<-9   Divide both sides by 3.

   /3   /3

x<-3

6. x-4<3  Add 4 to both sides.

    +4 +4

x<7

Hope this helps you out...next time, try to figure it out yourself without asking a lot of questions. By looking at one example, you can probably apply what to do for the other inequalities.

I need help with this question

Answers

Answer:

dfjkdhfhdsjfkldsjkljsdk;lv

Step-by-step explanation:

fjwdnjksnvl;snv;s

The length of Line AB would be 40

Find the value of θ from the following equation.(θ≤90°)​

Answers

Answer:   10°

__________________________________________________________

We are given:

Sin(6θ)  = Cos(3θ)

Solving for θ:

Simplifying Cos(3θ):

We know that:  

Cos(θ) = Sin(90-θ)

So, we can say that:

Cos(3θ) = Sin(90 - 3θ)

Finding the value of θ:

Sin(6θ) = Cos(3θ)

Sin(6θ) = Sin(90 - 3θ)                             [Since Cos(3θ) = Sin(90 - 3θ)]

6θ = 90 - 3θ                                            [If Sin(θ) = Sin(A) ; θ = A]

9θ = 90                                                   [adding 3θ on both sides]

θ = 10°                                                     [dividing both sides by 9]

Which equation represents a line that is parallel to the line whose equation is y=-3x?


A) 4x+2y=5
B) 2x+4y=1
C) y=3-4x
D) y=4x-2

Answers

It’s c skdjbssjsksjdbdb

Evaluate the expression.
1.2 exponent 2
answer choices =
1.44
14.4
1.728
1.5

Answers

Answer:

1.44

Step-by-step explanation:

Answer:

the answer is 1.44

Step-by-step explanation:

Because the exponent of a number says how many times to use the number in a multiplication. In 1.2 exponent 2 the "2" says to use 1.2 twice in a multiplication, so 1.2'2 = 1.2 × 1.2 = 1.44 In words: 1.2'2 could be called "1.2 to the power 2" or "1.2 to the second power.

                      Your welcome

At the start of the month, the value of an investment was $53.92. By the end of the month, the value of the investment changed by a loss of $17.40. What was the value, in dollars, of the investment at the end of the month​

Answers

Answer:

$36.52

you're welcome :)

in need help wihe lateral asn and total surface area

Answers

Just look it up on safari for help

There are a total number of 38 possible equally likely outcomes on a roulette wheel. Out of the 38 outcomes, there are 18
odd-numbered outcomes. What's the probability of spinning an odd number?
• Express your answer as a fraction.

Answers

Answer:

9/19

Step-by-step explanation:

just put the total odd numbers, 18,  over the total outcomes, 38, and divide them and simplify

Answer:

9/19

Step-by-step explanation:

By visual inspection, determine the best-fitting regression model for the data plot below.

Answers

Answer:

Quadratic

Step-by-step explanation:

It looks like it’s forming a very wide arch so quadratic formulas are arches

The equation of the regression line model for the data plot determines a quadratic equation

What is linear regression line?

The connection between the independent (x) and dependent (y) variables in the graph can be graphically represented using regression lines.

In a linear model, the terms are added rather than multiplied, divided, or provided as a non-algebraic function, as has been the case thus far in this section. Analysis of experimental, monetary, and biological data as well as complex system prediction are both possible using linear modelling.

A statistical technique used to build a linear model is called linear regression. The model explains how one or more independent variables Xi relate to a dependent variable y (also known as the response) (called the predictors). The distance between each data point and the regression line is called a residual.

Given data ,

Let the linear regression line be represented as A

Now , the value of A is

Let the first coordinate on the graph be P ( 1 , 5.5 )

Let the second coordinate on the graph be Q ( 2 , 6 )

And , the data plots on the graph represents a curve or parabolic equation

So , it is a quadratic equation

Hence , the data plot of the regression line is quadratic

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How do you know which standardized test statistics you will use? A Z or T?

Answers

Answer:

If you're taking the AP Statistics test, you'll need to know the general formula for a standardized test statistic. Standardized test statistics are used in hypothesis testing. The general formula formula is: Standardized test statistic: (statistic-parameter)/(standard deviation of the statistic).

Step-by-step explanation:

Answer:

Standardized test statistics are used in hypothesis testing. The general formula formula is: Standardized test statistic: (statistic-parameter)/(standard deviation of the statistic).

Use the distributive property to remove the parentheses (x+12)8

Answers

Answer:

Using distributive property to solve [tex](x+12)8[/tex] we get [tex]\mathbf{8x+96}[/tex]

Step-by-step explanation:

We need to used distributive property to solve (x+12)8

The distributive property of multiplication or addition states that: [tex]a(b+c)=ab+ac[/tex]

Using the property:

[tex](x+12)8\\=8x+8*12\\=8x+96[/tex]

So, using distributive property to solve [tex](x+12)8[/tex] we get [tex]\mathbf{8x+96}[/tex]

Brainliest to RIGHT answer

Answers

Answer:

It's C

Step-by-step explanation:

What is 56/15 as a decimal rounded to the nearest tenth

Answers

Answer:

3.73

Step-by-step explanation:

56/15

3 11/15

3.73

56/15 = 3.7333333...

3.733333... —————> 3.7

A professional language translator gets paid an average of $320 per hour with a standard deviation of $41.75 per hour. What proportion of professional language translators get paid less than $250 per hour? Assume the population is normally distributed. Round your answer to four decimal places

Answers

Answer:

0.0475 or 4% professional language translators get paid less than $250 per hour

Step-by-step explanation:

Mean = 320

Standard Deviation = 41.75

We need to find proportion of professional language translators get paid less than $250 per hour i.e P(x<250)

First we will find value of z

Using formula: [tex]z=\frac{x-\mu}{\sigma}[/tex]

We have x=250, finding z

[tex]z=\frac{x-\mu}{\sigma}\\z=\frac{250-320}{41.75}\\z=-1.67[/tex]

Now we will find P(z<-1.67) by looking into the normal distribution table

[tex]P(z<-1.67)=0.0475\\[/tex]

So,0.0475 or 4% professional language translators get paid less than $250 per hour

Please help me!!!!!​

Answers

Answer:

The answer is A.

Step-by-step explanation:

The ratio is 1 second/2 centimeters, but since they're asking for a unit ratio, you need to divide the top and bottom by 2 which gives you a unit ratio of ½ second/1 centimeter.

Answer:

Perhaps, B or A

Step-by-step explanation:

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