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nadezda [96]
3 years ago
9

Lesson 6.11

Mathematics
1 answer:
garik1379 [7]3 years ago
5 0

Answer:Bill should not play he Is bound to lose more money (-20)(0.3)+(-40)(0.2)+(50)(0.1)+(5)(0.4) = -7

Step-by-step explanation: 30% you of time you will lose 20 dollars

20% of time you will lose 40 dollars

10% of time you will win 50 dollars

40% of the time you will win 5 dollars

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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}

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