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worty [1.4K]
3 years ago
9

A state transportation worker records the number of miles traveled on a thruway and the corresponding tolls. The worker creates

a scatter plot of the data and determines that the line of best fit is T(m) = 0.04m + 1.26, where T is the amount of the toll, in dollars, and m is the number of miles traveled on the thruway.
Based on this linear model, how many miles can be traveled on the thruway for each additional $1 increase on the toll?
Mathematics
1 answer:
ad-work [718]3 years ago
7 0
<span>Suppose the toll is $10. Then, .04m + 1.26 = 10. We can simplify that to .04m = 8.74 and again to m =218.5. Now, suppose the toll is $11. Then, .04m + 1.26 = 11. Going through the same steps as before we find that m = 243.5. So a $10 fair will allow a passenger to travel 218.5 miles while an $11 fare will allow 243.5 miles of travel. The difference between these two is 25 miles. Since the fares are $1 apart, that means each additional $1 increase results in 25 additional miles. More simply, 0.04m gives the slope of the line telling us how many miles are traveled per dollar of fare, which is to say 0.04. So we could divide 1 by .04 to get the same result.</span>
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Sara buys a book for $17.50 and a pen for $6.50. If the sales tax rate is 8.25%, what will be the total amount of sales tax on h
Nuetrik [128]

Answer:

$25.98

Step-by-step explanation:

Add the items Sara buys to find the total:

17.50 + 6.50 = 24

Convert 8.25% into a decimal:

8.25/100 = 0.0825

Multiply 0.0825 by 24:

0.0825 x 24 = 1.98

1.98 is the amount of tax, then add the tax to the total amount you got before tax.

24 + 1.98 = 25.98

Your answer would be 25 dollars and 98 cents!

8 0
2 years ago
Divide.<br><br> (6x^2+36x+35)/(x+5)<br><br> Your answer should give the quotient and the remainder.
zheka24 [161]

Answer:

6x+6+\frac{5}{x+5}

Step-by-step explanation:

When we divide polynomials by polynomials with more than one term, we use long division or factorization to simplify.

This polynomial isn't easily divided after factorization so we will use long division. And we will use the remainder theorem to write any remainder.

\frac{(6x^2+36x+35)}{(x+5)}

We start long division by finding what multiplies with x+5 to get  6x^2+36x. This is 6x.

So 6x(x+5)=6x^2+30x. We have 6x left as a remainder from 36x.

We now divide x+5 into 6x+35. What multiplies with x+5 to get 6x+35? 6.

So we have 6x+6 as our answer so far and after we multiply 6(x+5)=6x+30 we will have a final remainder of 5.

We write our answer as 6x+6+\frac{5}{x+5}.


3 0
3 years ago
Rewrite the polynomial in the form ax^2 + bx + C and then identify the values of a, b, and c.
sergejj [24]

Answer:

a = 5\\\\b = -1\\\\c=1

Step-by-step explanation:

Given

-x+5x^2+1

Required

Rewrite and identify a, b and c

The required form is:

ax^2 + bx + c

Equate both expressions

ax^2 + bx + c = -x+5x^2+1

Rewrite as:

ax^2 + bx + c = 5x^2-x+1

Compare the expressions on either sides

a = 5\\\\b = -1\\\\c=1

8 0
3 years ago
A bakery sold 32 bagels in the first hour of business and 37 bagels in the second hour. If the bakery had 228 bagels to start wi
bearhunter [10]

Answer:

159 bagels left

Step-by-step explanation:

add the 32 and 37 then subtract the answer from 32 and 37 from 228 and your answer is 159

4 0
2 years ago
A box contains 100 colored chips; some are pink and some are blue. Milton chooses a chip at random, records the color, and place
Lena [83]

The approximate number of pink chips is 40. Here's why: what you need to do is set up the problem as shown below. 12 goes above 30 because you have to know what the total number of chips chosen is in order to relate it to 100 chips. From there, all you have to do is cross-multiply and divide (or my middle school teacher used to call it fish.... I'll explain why). First you are going to draw a line from the 100 to the 12 and multiply them. then you are going to curve the line that you will draw from the 12 to the 30 and divide the product of 12 and 100 by 30. Then you will draw a line from the 30 to the X meaning that the quotient that you find from the product of 120 and 100 divided by 30 equals X.  Hope that helps.

12      x    

30   100  

4 0
3 years ago
Read 2 more answers
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