In 1980, the average cost of a pack of cigarettes was $0.88. In 2000, the average cost was $5.31 per pack.

What is the average rate of change of the cost of a pack of cigarettes? What is another name for the average rate of change?

Round your answer to the nearest cent.

Answers

Answer 1

Answer:

The average rate of change of the cost of a pack is 22 cents per year.

Another name for the average rate of change is slope.

Step-by-step explanation:

The average rate of change of the cost of a pack ([tex]r[/tex]), in monetary units per year, is equal to the change in the average cost of a pack ([tex]\Delta c[/tex]), in monetary units, divided by the change in time ([tex]\Delta t[/tex]), in years. Then, the average rate of change is:

[tex]r = \frac{\$\,5.31-\$\,0.88}{2000-1980}[/tex]

[tex]r = \$\,0.22\,\frac{1}{yr}[/tex]

The average rate of change of the cost of a pack is 22 cents per year.

Another name for the average rate of change is slope.


Related Questions

find the exact value of tan(165°) using a difference of two angles

Answers

Answer:  [tex]-2+\sqrt{3}[/tex]

=========================================================

Work Shown:

Apply the following trig identity

[tex]\tan(A - B) = \frac{\tan(A)-\tan(B)}{1+\tan(A)*\tan(B)}\\\\\tan(225 - 60) = \frac{\tan(225)-\tan(60)}{1+\tan(225)*\tan(60)}\\\\\tan(165) = \frac{1-\sqrt{3}}{1+1*\sqrt{3}}\\\\\tan(165) = \frac{1-\sqrt{3}}{1+\sqrt{3}}\\\\[/tex]

Now let's rationalize the denominator

[tex]\tan(165) = \frac{1-\sqrt{3}}{1+\sqrt{3}}\\\\\tan(165) = \frac{(1-\sqrt{3})(1-\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})}\\\\\tan(165) = \frac{(1-\sqrt{3})^2}{(1)^2-(\sqrt{3})^2}\\\\\tan(165) = \frac{(1)^2-2*1*\sqrt{3}+(\sqrt{3})^2}{(1)^2-(\sqrt{3})^2}\\\\\tan(165) = \frac{1-2\sqrt{3}+3}{1-3}\\\\\tan(165) = \frac{4-2\sqrt{3}}{-2}\\\\\tan(165) = -2+\sqrt{3}\\\\[/tex]

----------------------

As confirmation, you can use the idea that if x = y, then x-y = 0. We'll have x = tan(165) and y = -2+sqrt(3). When computing x-y, your calculator should get fairly close to 0, if not get 0 itself.

Or you can note how

[tex]\tan(165) \approx -0.267949\\\\-2+\sqrt{3} \approx -0.267949[/tex]

which helps us see that they are the same thing.

Further confirmation comes from WolframAlpha (see attached image). They decided to write the answer as [tex]\sqrt{3}-2[/tex] but it's the same as above.

The height of an object dropped from the top of a 144-foot building is given by ℎ(. How long will it take the object to hit the ground?)=―162+144

Answers

Answer:

Step-by-step explanation: h(t) = -16t2 + 144

h(1) = -16(12) + 144 = 128 ft

h(2) = -16(22) + 144 = 80 ft

h(2) - h(1) = 80 - 128 = -48 ft

It fell 48 ft between t = 1 and t = 2 seconds.

It reaches the ground when h(t) = 0

0 = -16t2 + 144

t = √(144/16) s = 3s

It reaches the ground 3s after being dropped.

2 men can build a wall in 10 days. in how many days will 8 men build the wall?​

Answers

Step-by-step explanation:

8 men can do 60 man days of work by dividing 60 man days by the 8 men, which gives us 60/8 = 7 1/2 da

I need to know the answer and explaining how to do it please

Answers

Answer:

Its 0.11

Step-by-step explanation:

When you divide any number by 10, you just move the decimal place one to the left, as for this number 1.1, you move it one place to the left which makes it 0.11. Mathmatically, to check your work you can do 0.11 x 10 to get 1.1

Mark brainliest and helpful

Find:P(large or blue)

Answers

Answer:

7/10

Step-by-step explanation:

Total number = 17+3+8+12 = 40

The ones that are large are 17 and 8

The ones that are blue are 17 and 3

Do not count the 17 twice

P(large or blue) = (17+3+8)/40

                          = 28/40

                         =7/10

find the area of the circle use 3.14 for pi d=4 m

Answers

Answer:

The area of circle is 12.56m sq.

Write the polynomial in standard form. Then name the polynomial based on its degree and number of
terms.
y-7y3 + 15y9

Answers

Answer:

[tex]15y^9 - 7y^3 + y[/tex]

Nonic polynomial

Step-by-step explanation:

Given

[tex]y - 7y^3 + 15y^9[/tex]

Required

Write in standard form

The standard form of a polynomial is:

[tex]ay^n + by^{n-1} + ......... + k[/tex]

So, we have:

[tex]y - 7y^3 + 15y^9[/tex]

The standard form is:

[tex]15y^9 - 7y^3 + y[/tex]

And the name is: Nonic polynomial (because it has a degree of 9)

If f(x) = x2 + 7x and g(x) = 3x - 1, what is f(g(x))?

Answers

Answer:

f(g(x)) = 9x^2 + 15x - 6

Step-by-step explanation:

We are using function g(x) = 3x - 1 as the input to function f(x) = x^2 + 7x.

Starting with f(x) = x^2 + 7x, substitute g(x) for x on the left side and likewise substitute x^2 + 7x for each x on the right side.  We obtain:

f(g(x)) = (3x - 1)^2 + 7(3x - 1).

If we multiply this out, we get:

f(g(x)) = 9x^2 - 6x + 1 + 21x - 7, or

f(g(x)) = 9x^2 + 15x - 6

..............................

Answers

Answer:

[tex]x=17[/tex]

Step-by-step explanation:

[tex](6x+10)(x+17)(4x-34)[/tex]

[tex]6x+10+x+17+4x-34=180[/tex]

Add:- [tex]6x+x+4x=11x[/tex]

and [tex]10+17-34=-7[/tex]

So, [tex]11x-7=180[/tex]

Add 7 to both sides:-

[tex]11x=187[/tex]

Divide both sides by 11:-

[tex]\frac{11x}{11}=\frac{187}{11}[/tex]

[tex]x=17[/tex]

OAmalOHopeO

The firm had 15 billion VND of earnings before interest and tax (EBIT), corporate tax is 20%. The market price of stock is 60.000đ. Knowing that net income will be held 40% before using it for dividend. How much of the net income can be divided for shareholders?

Answers

Answer:

was assigned with this problem (the reference text is attached):

Which of the following, if included in a student's paper, would NOT be an example of plagiarism?

1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).

2. Baseball is rather surprisingly known as "America's Favorite Pastime."

3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).

4. All of these are plagiarism.

The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):

Which of the following, if included in a student's paper, would NOT be an example of plagiarism?

1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).

2. Baseball is rather surprisingly known as "America's Favorite Pastime."

3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).

4. All of these are plagiarism.

The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):

Which of the following, if included in a student's paper, would NOT be an example of plagiarism?

1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).

2. Baseball is rather surprisingly known as "America's Favorite Pastime."

3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).

4. All of these are plagiarism.

The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):

Which of the following, if included in a student's paper, would NOT be an example of plagiarism?

1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).

2. Baseball is rather surprisingly known as "America's Favorite Pastime."

3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).

4. All of these are plagiarism.

The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):

Which of the following, if included in a student's paper, would NOT be an example of plagiarism?

1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).

2. Baseball is rather surprisingly known as "America's Favorite Pastime."

3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).

4. All of these are plagiarism.

The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):

Which of the following, if included in a student's paper, would NOT be an example of plagiarism?

1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).

2. Baseball is rather surprisingly known as "America's Favorite Pastime."

3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).

4. All of these are plagiarism.

The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):

Which of the following, if included in a student's paper, would NOT be an example of plagiarism?

When A = 200, solve the equation x2 - 40x + A=0 using the quadratic formula. Show all your working and give your answers correct to 2 decimal places.​

Answers

Answer:

Solution given:

equation is:

x²-40x+A=0

when A=200

equation becomes

x²-40x+200=0

Comparing above equation with ax²+bx+c=0 we get

a=1

b=-40

c=200

By using quadratic equation formula

x=[tex]\displaystyle \frac{-b±\sqrt{b²-4ac}}{2a}[/tex]

substituting value

x=[tex]\displaystyle \frac{-*-40±\sqrt{(-40)²-4*1*200}}{2*1}[/tex]

x=[tex]\displaystyle \frac{40±\sqrt{800}}{2}[/tex]

x=[tex]\displaystyle \frac{40±20\sqrt{2}}{2}[/tex]

taking positive

x=[tex]\displaystyle \frac{40+20\sqrt{2}}{2}[/tex]

x=34.14

taking negative

x=[tex]\displaystyle \frac{40-20\sqrt{2}}{2}[/tex]

x=5.86

x=34.14 or 5.86

which is an example of an algebraic expression


A.4(3+8)
B.18^2
C. 3-a
D. 12•4

Answers

Answer:

C: 3-a

Step-by-step explanation:

The answer is C because an algebraic expression needs to have a variable in it. The variable is "a," so the answer has to be C.

Answer:

Option C : as in algebraic expression there must a variable and constant.

What is the correct answer?

Answers

Answer:

Option D

Only the equation in option D matches with the table

Answered by GAUTHMATH

The to your question answer is D

What is the volume of the cylinder below?


Height 4
Radius 7

Answers

Answer:

V ≈ 615.75

r Radius 7

h Height 4

express 111 as a sum of two primes​

Answers

Answer:

2 + 109 = 111

Step-by-step explanation:

.............

Can someone please help me with this math problem

Answers

We have [tex]f\left(f^{-1}(x)\right) = x[/tex] for inverse functions [tex]f(x)[/tex] and [tex]f^{-1}(x)[/tex]. Then if [tex]f(x) = 2x+5[/tex], we have

[tex]f\left(f^{-1}(x)\right) = 2f^{-1}(x) + 5 = x \implies f^{-1}(x) = \dfrac{x-5}2[/tex]

Then

[tex]f^{-1}(8) = \dfrac{8-5}2 = \boxed{\dfrac32}[/tex]

rewrite the following statements into algebraic expression
the sum of x and y
5 is subtracted from y​

Answers

x+y

5-y

i really hope this is it.

The average weekly assignment score of students in a statistics class is 7 out of 10 points. The professor proposes new incentives to boost the score of the students (like providing internship contacts etc.) He hopes that the results of running this incentives plan for a trial during the next couple of weeks will enable him to conclude that the incentives he offers increase the average weekly assignment score of students. What is the null hypothesis.
A. The average weekly score is strictly more than or equal to 7.
B. The average weekly score is less than our equal to 7.
C. The average weekly score is strictly less than 7.
D. The average weekly score is strictly more than 7.

Answers

Answer:

B. The average weekly score is less than or equal to 7.

Step-by-step explanation:

The average weekly assignment score of students in a statistics class is 7 out of 10 points. Test if it has increased.

This means that at the null hypothesis it is tested that the mean score of the students has not increased, that is, it still is of at most 7, so:

[tex]H_0: \mu \leq 7[/tex]

And thus, the correct answer is given by option b.

relationship between the two number
b 70.908
7.908
Which one is greater

Answers

Answer:

70.908 is greater than 7.908 .

I hope your day goes nice

Answer:

70.9 0 8 is Greater

both are different because of different placement of point.

Question 4 plz show ALL STEPS

Answers

Part (a)

Locate x = -1 on the x axis. Draw a vertical line through this x value until you reach the f(x) curve. Then move horizontally until you reach the y axis. You should arrive at y = 4. Check out the diagram below to see what I mean.

Since f(-1) = 4, this means we can then say

g( f(-1) ) = g( 4 ) = 4

To evaluate g(4), we'll follow the same idea as what we did with f(x). However, we'll start at x = 4 and draw a vertical line until we reach the g(x) curve this time.

Answer:  4

==========================================================

Part (b)

We use the same idea as part (a)

f(-2) = 5

g( f(-2) ) = g(5) = 6

Answer:  6

==========================================================

Part (c)

Same idea as the last two parts. We start on the inside and work toward the outside. Keep in mind that g(x) is now the inner function for this part and for part (d) as well.

g(1) = -2

f( g(1) ) = f(-2) = 5

Answer:   5

==========================================================

Part (d)

Same idea as part (c)

g(2) = 0

f( g(2) ) = f( 0 ) = 3

Answer:  3

How to find Joint and Combined variation?

Answers

Answer:

W is multiplied by 8

Step-by-step explanation:

If W varies jointly with x, y, and z, we can say that

W = k (xyz), with k being a constant for our original equation. We are asked what will happen to W if x, y, and z are each doubled. To figure this out, we can go back to our equation,

W = k (xyz)

First, we can double x, meaning that we multiply it by 2. Doing this, we get

W = k (2x * y * z)

Then, we can double y and z in a similar fashion, resulting in

W = k (2x * 2y * 2z)

W = 8 * k (xyz)

The new W, after all the doubling, is equal to 8 * k * x * y * z. The old W is equal to k * x * y * z. It can be determined that the new W is equal to 8 * the old W, so W is multiplied by 8

Calls to a customer service center last on average 2.3 minutes with a standard deviation of 2 minutes. An operator in the call center is required to answer 76 calls each day. Assume the call times are independent.
What is the expected total amount of time in minutes the operator will spend on the calls each day?
What is the standard deviation of the total amount of time in minutes the operator will spend on the calls each day? Give your answer to four decimal places.
What is the approximate probability that the total time spent on the calls will be less than 166 minutes? Give your answer to four decimal places. Use the standard deviation as you entered it above to answer this question.
What is the value c such that the approximate probability that the total time spent on the calls each day is less than c is 0.95? Give your answer to four decimal places. Use the standard deviation as you entered it above to answer this question.

Answers

Answer:

The expected total amount of time in minutes the operator will spend on the calls each day is of 174.8 minutes.

The standard deviation of the total amount of time in minutes the operator will spend on the calls each day is of 17.4356 minutes.

0.3085 = 30.85% approximate probability that the total time spent on the calls will be less than 166 minutes.

The value c such that the approximate probability that the total time spent on the calls each day is less than c is 0.95 is [tex]c = 203.4816[/tex]

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

n instances of a normally distributed variable:

For n instances of a normally distributed variable, the mean is:

[tex]M = n\mu[/tex]

The standard deviation is:

[tex]s = \sigma\sqrt{n}[/tex]

Calls to a customer service center last on average 2.3 minutes with a standard deviation of 2 minutes.

This means that [tex]\mu = 2.3, \sigma = 2[/tex]

An operator in the call center is required to answer 76 calls each day.

This means that [tex]n = 76[/tex]

What is the expected total amount of time in minutes the operator will spend on the calls each day?

[tex]M = n\mu = 76*2.3 = 174.8[/tex]

The expected total amount of time in minutes the operator will spend on the calls each day is of 174.8 minutes.

What is the standard deviation of the total amount of time in minutes the operator will spend on the calls each day?

[tex]s = \sigma\sqrt{n} = 2\sqrt{76} = 17.4356[/tex]

The standard deviation of the total amount of time in minutes the operator will spend on the calls each day is of 17.4356 minutes.

What is the approximate probability that the total time spent on the calls will be less than 166 minutes?

This is the p-value of Z when X = 166.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem:

[tex]Z = \frac{X - M}{s}[/tex]

[tex]Z = \frac{166 - 174.8}{17.4356}[/tex]

[tex]Z = 0.5[/tex]

[tex]Z = 0.5[/tex] has a p-value of 0.6915.

1 - 0.6915 = 0.3085.

0.3085 = 30.85% approximate probability that the total time spent on the calls will be less than 166 minutes.

What is the value c such that the approximate probability that the total time spent on the calls each day is less than c is 0.95?

This is X = c for which Z has a p-value of 0.95, so X = c when Z = 1.645. Then

[tex]Z = \frac{X - M}{s}[/tex]

[tex]1.645 = \frac{c - 174.8}{17.4356}[/tex]

[tex]c - 174.8 = 1.645*17.4356[/tex]

[tex]c = 203.4816[/tex]

The value c such that the approximate probability that the total time spent on the calls each day is less than c is 0.95 is [tex]c = 203.4816[/tex]

Which expression is the radical form of 1/5b

Answers

Answer:

1st option, ⁵√b

Step-by-step explanation:

b⅕

= ⁵√b (radical form)

Find the measure of the missing angles.

Answers

Answer:

b = 53

c = 53

Step-by-step explanation:

Alright so we already know that b and c are going to have the same angle measures. We can find b by subtracting 180 degrees to 127. Why you may ask? Its because when b and 127 are added together its obvious that it creates a straight line (supplementary angle). This means that two angles will sum up to 180 degrees. We can create an easy equation and solve for b.

127 + b = 180

b = 53 and c = 53

Best of Luck!

Maria is using a meter stick to determine the height of a door. If the smallest unit on the meter stick is centimeters, which measurement could Maria have used to most accurately record the height of the
door?

Answers

Answer:

2.31 m

Step-by-step explanation:

with marking down to centimeter length, one can only estimate accurately to the nearest  centimeter or hundredth of a meter.

Answer:2.31 meter

Step-by-step explanation: none

What is the equation of the line through (4, -3) and (0, -2)?
O A. y = -x + 2
B. Y= -1x – 2
O C. y= - 4x –
D. y = 4x + 2

Answers

Answer:

B

Step-by-step explanation:

Pull in -4 and 0 into the variable x. and the 4 and -2 in the variable y and solve to get an equal answer.

What is the dimension of the null space Null (A) of A = ​

Answers

Answer:

the nullity of a matrix A is the demision of its null space:nullity A = dim (n(A).

A state lottery sells instant-lottery scratch tickets. 12% of the tickets have prizes. Neil goes to the store and buys 10 tickets. What is the probability that exactly three of Neil's tickets will have prizes? ​

Answers

Answer:

The probability of success is .12

The probability of failure is .88

According to the binomial theorem the probability of 3 success is

10! / (3! * 7!) * .12^3 * .88^7 = .085

I will mark as brainliest:)

Answers

Hii I believe your option would be D. I hope it helps :)

Answer:

Point E.

.................

Raul is a manager at a local restaurant. He earns $18.50 per hour. How many hours per week does Raul
work if he earns $740 per week?

Answers

Answer: 40 hours
Just divide the total amount (740) by the rate per hour (18.50) and you get 40
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