The function f(x)= -45x + 270 represents the total distance, in miles, a traveler is from home x hours after beginning the trip home. What is the average rate of change over the interval from x = 1 to x = 3, in miles per hour?

Answers

Answer 1

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

Given :-

We have given one function f(x) = -45x + 270 The given function represents the total distance in miles. The initial interval was x = 1 and final interval was x = 3

To Find :-

We have to find the rate of change over the given interval

Let's Begin :-

Here, We have

Function = f(x) = -45x + 270

The given function represents the total distance in miles covered by the traveller.

Therefore,

For initial interval that is x = 1 , Distance covered by the traveller

[tex]\sf{ f(x) = -45x + 270 }[/tex]

[tex]\sf{ f(1) = - 45(1) + 270 }[/tex]

[tex]\sf{ f(1) = - 45 + 270 }[/tex]

[tex]\sf{ f(1) = 225 }[/tex]

For final interval that is x = 3, Distance covered by the traveller

[tex]\sf{ f(x) = - 45x + 270 }[/tex]

[tex]\sf{ f(1) = - 45(3) + 270 }[/tex]

[tex]\sf{ f(1) = - 135 + 270 }[/tex]

Now,

We have to find the average rate of change over the given time interval

Therefore,

Average rate of change in the given time interval

[tex]\sf{ = }{\sf{\dfrac{ f(1) + f(3) }{3 - 1}}}[/tex]

[tex]\sf{ = }{\sf{\dfrac{ 225 + ( -135) }{ 2}}}[/tex]

[tex]\sf{ = }{\sf{\dfrac{ 225 - 135 }{ 2}}}[/tex]

[tex]\sf{ = }{\sf{\dfrac{ 90 }{ 2}}}[/tex]

[tex]\sf{ = 45 }[/tex]

Hence, The average rate of change over the given interval is 45 miles per hour.


Related Questions

is y – 2 = –5(x – 2) a linear function

Answers

Answer:

Yes

Step-by-step explanation:

y-2=-5(x-2)

y=-3(x-2)

Use synthetic or long division to divide x^3+ 5x^2+ x- 10 by x+ 2. What is the new
expression?

Answers

Answer:

x2+3x−5

Step-by-step explanation:

Set up the synthetic division using the coefficients of the numerator and the root in the denominator. Divide using the rules for synthetic division.

Answer:

1x^2 + 7x + 4/x+2

Step-by-step explanation: x^3+ 5x^2+ x- 10 by x+ 2.

    |  1        5      -10

2   | ----      2        14

     ________________

         1       7        4

X+2 = not a factorable --

1x^2 + 7x + 4/x+2

Use the properties of equality to find the value of x in this equation.

4(6x – 7) = 44

Answers

answer: x=3
explanation: calculator

Answer:

x = 3

Step-by-step explanation:

4(6x - 7) = 44

divide both sides by 4

6x - 7 = 11

add 7 to both sides

6x = 18

divide both sides by 6

x = 3

Carol and Peter to schoolCarol walks 3/5 a mile to walk to school Peter walks 0. 65 Which student has a father walk

Answers

Answer:

Peter.

Step-by-step explanation:

I’m assuming from context (your question was written poorly) you’re asking which student walked farther. This would be Peter. Why? Carol walked only 3/5 miles of the way to school, which would be .6 or .60

Peter walked .65 miles to school which is more than .60

A tablecloth of round Table is full and the radius 9 yd what is the diameterg

Answers

Answer:

18

Step-by-step explanation:

The radius is half of the diameter, so we would multiply 9 x 2 and get 18.

Hope this helps!

ABCD is a rectangle.Diagonal AD=10 and AB=8. What is the perimeter of the rectangle? *
A. 36
B. 16
C. 30
D. 40

Answers

Perimeter is going to be all sides added up. Because it’s a rectangle we know that side AD is the same as the opposite parallel side, which would be BC. And AB is the same as CD. Therefore 10+10+8+8
Answer : A. 36

on Saturday five girls held a car wash to earn money for each car they charged $6 the girls washed a total of 22 cars and collected an extra $10 in tips if they divide the money equally how much will each girl receive
This is due at 4:20 Can you please help

Answers

Answer:

$28.40

Step-by-step explanation:

First let's find how much they earned from washing the cars. They charged $6 for each car and washed 22 so 6x22=$132 from washing cars. After that they earned 10 more dollars so we have to add that. 132+10=$142 earned in total. Then we have to divide this total income between all of the girls. 142/5=$28.40 for each girl.

The number of absences for one week for all students at a high school were compiled, and the probability distribution below was created. What is the probability in any given week that a randomly selected student will be absent no more than one day? Probability Distribution Days Absent: X Probability: P(X) 0 0. 78 1 0. 14 2 0. 03 03 2000. 01 4 0 5 0. 04 0. 08 0. 14 0. 78 0. 92.

Answers

The probability of randomly selected students who will be absent no more than one day is 0.92. Option D is correct.

What is the probability?

The probability is defined as the number of favorable occurrences of an event.

Given the probability distribution of the number of absence for one week,

x:            0         1         2         3       4      5

P(X):    0.78    0.14    0.03    0.01    0    0.04

We know that the probability of any event is always less than equal to 1. We can write that,  [tex]P(x\leq 1)[/tex].

So the probability of randomly selected students who will be absent no more than one day is calculated as given below.

[tex]P = P (x=0) + P(x=1)\\P = 0.78 + 0.14[/tex]

[tex]P = 0.92[/tex]

Hence we can conclude that the probability of randomly selected students who will be absent no more than one day is 0.92. Option D is correct.

To know more about the probability, follow the link given below.

https://brainly.com/question/795909.

HELP FOR BRAINLEST!!!

Answers

Answer:

3/4

Step-by-step explanation:

add total NOT male (9) total NOT 0.3 to 0.7 seconds (11) and subtract the number that is both not male and not 0.3 to 0.7 seconds (5)

9+11-5 = 15

over total (20)

15/20 simplifies to 3/4

\frac{1}{2}=21​=\,\,-\frac{3}{4}+\frac{3}{5}x−43​+53​x

Answers

Answer:

what?

Step-by-step explanation:

Option 2: Increase by 10% each year
linear and exponential growth graph
Type 2:

d =
e =

Answers

Answer:

Type 2:  exponential growth

d =  121

e =  133

Answer:

Exponential growth

d: 121

e: 133.1

Step-by-step explanation:

edge 23

What is d?

-16 (d + 1) = -20


d=?

Answers

Answer:

Step-by-step explanation:

Simplify it. -16d-16=-20.

Add 16 to both sides. -16d=-4

Divide 16 by both sides.

d=1/4

-16(d+1)= -20
-20 divided by -16 = 1.25
1.25 - 1 = .25
D=.25

pls help me pic in the file .

Answers

Answer:

p = 33/100 = 33%

Step-by-step explanation:

p (probability) = 1.00 - [variables]

p = 1.00 - (0.12 + 0.07 + 0.05 + 0.28 + 0.15)

p = 1.00 - 0.67

p = 33/100

Estimation for 6.76 + 2.91

Answers

Step-by-step explanation:

156 6.76 + 2.91 equal to 9.67

Find g(x), where g(x) is the translation 3 units right of f(x)=x2.
Write your answer in the form a(x–h)2+k, where a, h, and k are integers.

Answers

Answer:

g(x)=x2 +8= (x-0)2+8

Step-by-step explanation:

draw the image of quadrilateral ABCD under the translation (x,y) (x+4,y-3)

Answers

Answer:

Without seeing or knowing the original coordinates for each point, all I can tell you is to take the original coordinates and add 4 to the x. Then subtract 3 from the y. Plot accordingly

I need help.Im not very smart.

Answers

[tex]\frac{2}{3} x = 4\\2x = 4 * 3\\2x = 12\\x = 6[/tex]

Hope that helps!

if the area of a triangle is 128 sqcm and height is 12cm, find its base?​

Answers

Area of triangle = 1/2 x base x height


128 = 1/2 x base x 12

Multiply both sides by 2:

256 = base x 12

Divide both sides by 12

Base = 21 1/3 cm

mr.spencer drives 200 miles in 5 hours what is the unit rate

Answers

200miles/5 hours is 40 miles per hour

good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.

Answers

Answer:

3rd option

Step-by-step explanation:

the explicit formula for a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = - 4 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{12}{-4}[/tex] = - 3 , then

[tex]a_{n}[/tex] = - 4 [tex](-3)^{n-1}[/tex]

Sean works at a book shop. He finds that when a book is chosen from the shop at random, the following probabilities are correct: P(non-fiction) = 0.37 P(paperback) = 0.23 P(both non-fiction and paperback) = 0.18 - Work out P(neither non-fiction nor paperback) as a decimal.​

Answers

Answer:

0.22

Step-by-step explanation:

Add all the probabilities together then subtract it from 1

[tex]0.37+0.23+0.18=0.78[/tex]

[tex]1-0.78=0.22[/tex]

The total cost for my brother's bowling party was $140 It cost $50 to reserve a bowling lane plus the cost of renting shoes for the 9 people attending.
How much is the cost of renting shoes per person?

Answers

Answer:

10

Step-by-step explanation:

140-50 = 90 90/9 =10

.•*
689
Four friends buy cinema tickets using this offer.
Cinema tickets
Buy 3 tickets and get a ticket free
They each pay £7.05
How much does a ticket cost?
t
+

Answers

Answer:

7.04*4=x

x/3=how much the tickets cost

Step-by-step explanation:

If each of the four friends pays $7.04, the equation would be set up like this: 7.04*4=28.16. This means the total cost for tickets is 28.16. If the total cost for three tickets is 28.16, just divide the total cost by how many tickets were purchased. 28.16/3=9.39. This means one ticket cost 9.39.

Answer:-

[tex]\longrightarrow \sf £ \:9.4 [/tex]

Solution:-

[tex]\leadsto[/tex]Money paid by 1 friend = £ 7.05

[tex]\leadsto[/tex]Money paid by 4 friend = £ 7.05 × 4

[tex] \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad[/tex]= £ 28.2

This is equal to cost of 3 tickets

[tex]\leadsto[/tex] Cost of 3 tickets = £ 28.2

[tex]\leadsto[/tex] Cost of 1 ticket = £ 28.2 ÷ 3

[tex]\quad\quad\quad\quad\quad\quad\quad\quad\quad[/tex]=£ 9.4

Thus , each ticket cost £ 9.4 .

A recipe uses 2 cups of milk to make 12 servings. If the same amount of milk is used for each serving, how many servings can be made from two pints?

Answers

Answer:

24

Step-by-step explanation:

2 cups = 1 pint

2 cups = 12 serving

1 pint = 12 serving

2 pint = 12 x 2

2 pint = 24 serving

Which product is negative?

−3⋅5⋅(−6)⋅4

−3⋅4⋅(−2)⋅(−7)

−4⋅(−6)⋅(−3)⋅(−5)

−7⋅(−3)⋅(−9)⋅0

Answers

Answer:

c i hope I was not too late

What is the volume of the shape?

Answers

The volume of the triangular prism = [tex]V = (base-area)*height[/tex]

Thus the volume is [tex]\\V = (\frac{1}{2} *3*4) * 7 = 6 * 7 = 42[/tex].

Thus the volume is 42 cubic km.

Hope that helps!

what is the answer?

Answers

Answer:

A. P(3/4)

Step-by-step explanation:

(07. 04 LC)


Mellie is conducting a test on mold spores on bread. She uses 6 slices of bread to compare two strains of mold. She applies one strain to the left side of the bread and one strain to the right side. She flips a coin to decide which strain goes on the right side of the bread. The mold spores that appear on each side are counted and she records them in a table.


Bread Number of Spots for Strain 1 Number of Spots for Strain 2

1 30 19

2 21 17

3 15 15

4 13 12

5 6 9

6 8 4

If Mellie is to perform an appropriate t-test to determine if there is a mean difference between the number of spots per piece of bread produced by the two strains, how many degrees of freedom should she use?


a

4


b

5


c

6


d

10


e

12

Answers

Considering the t-test applied, the number of degrees of freedom is given by:

d. 10.

What is the number of degrees of freedom of a t-test?

For a sample of size n, the number of degrees of freedom is given by:

df = n - 1

When there are m samples, the amount of degrees of freedom is m multiplied by the sum of degrees of freedom of each sample.

In this problem, there are 2 samples with 6 - 1 = 5 df, hence:

2 x 5 = 10.

Option d is correct.

More can be learned about a t-test at https://brainly.com/question/13873630

An isosceles triangle has an angle that measures 112°. What measures are possible for the other two angles? Choose all that apply. 14, 84, 34, 20

Answers

34° is possible for the other two angles.

180°-112°=68°
68°/2= 34°

4. There is no triangle with sides 8, 6 and 14 True or False

please help it's urgent ​

Answers

Answer:

True

Step-by-step explanation:

Any two sides of a triangle is greater than the third side.

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