Which equations have the same value of x as

A certain car rental location charges a daily fee as well as a mileage charge. On one trip a businessman rented a car for the da

nikklg [1K]

Answer:

$x\approx 267\ miles$

Step-by-step explanation:

<u>Linear Modeling</u>

Some events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The linear function can be expressed in the slope-intercept format:

$f(x)=mx+b$

For the problem at hand, we must pick the adequate variables according to the data provided.

The question states the charge for renting a car is a function of the mileage. It also provides two points from which we can build our model. Let's set the following variables:

c = the charge for renting a car in dollars

x = the distance driven by the businessman in miles

Representing the ordered pair as (x,c), we have the points: (150,79) and (65,63.70). Our model will be expressed as:

$c = mx+b$

We must find the values of m and b with the data provided. Substituting the first point:

$79 = 150m+b$

Substituting the second point:

$63.70 = 65m+b$

Both equations form the following system:

$\left\{\begin{matrix}150m+b=79\\ 65m+b=63.70 \end{matrix}\right.$

Subtracting both equations:

$150m-65m=79-63.70$

Note the variable b was canceled out in the operation, leaving only the variable m to solve. Joining like terms:

$85m=15.3$

Solving:

$m=15.3/85=0.18$

From the first equation

$79 = 150m+b$

Solving for b:

$b=79-150m=79-150(0.18) = 52.$

The model for the problem is:

$c=0.18x+52$

Now we need to calculate how many miles (x) could be driven for c=$100. From the equation above, substitute c=100

$100=0.18x+52$

Solve for x:

$0.18x+52=100$

$0.18x=100-52=48$

$x=48/0.18=266.67$

Rounding to the closest integer:

$\boxed{x\approx 267\ miles}$

7 0

3 years ago

Identify the response variable and whether the setting involves a single sample, a matched pairs, or two independent samples.

Helga [31]

Answer:

1. single sample design

2. matched pairs

3. two independent samples.

Step-by-step explanation:

the response variable is known as the dependent variable, it is the variable that the researcher is interested i finding. the response variable is the x variable that responds to changes in the independent variable.

1.

In this question the researcher has only one sample that is the specimen. that is the reference specimen that she obtained. Therefore it is a single sample design.

the response variable here is the measurement of concentration.

2. In this question we have two pairs, men and women. The researcher is interested in comparing attitudes as she interviews them. so response variable is attitude or behavior

3. this is a 2 independent sample design. The researcher is using two different methods to test and their average is being compared.

6 0

2 years ago

Aha please help!!!!! im a bit confused lol

Stels [109]

Answer:

e : g = 2 : 7

Step-by-step explanation:

e/f = 3/7

e = 3f/7

f/g = 2/3

g = 3f/2

e/g = (3f/7)/(3f/2) = 2/7

3 0

2 years ago

Which term is the perfect square of 3x^4

iragen [17]

The answer is 9x^8
Hope it helped!!

7 0

3 years ago

Read 2 more answers

Consider these functions

vitfil [10]

9514 1404 393

Answer:

C. 3x² +24

Step-by-step explanation:

Use the given function definitions and simplify.

$g(f(x))=g\left(\dfrac{1}{3}x^2+4\right)\\\\=9\left(\dfrac{1}{3}x^2+4\right)-12\\\\=3x^2+36-12\\\\\boxed{g(f(x))=3x^2+24}\qquad\textbf{matches C}$

5 0

2 years ago