If a function has a positive average rate of change over
an interval, does that mean that the function must be increasing over that
interval? Explain.

Answers

Answer 1

Step-by-step explanation:

Yes, an positive average rate of change means that our endpoint of the interval is greater than the initial point of our interval. By definition, a function, f is increasing over an interval [a,b], if f(b)> f(a)

Answer 2

Yes, a positive average rate of change means that our endpoint of the interval is greater than the initial point of our interval.

What is the average rate of change?

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

Yes, a positive average rate of change indicates that the endpoint of our period is higher than the interval's starting point. A function f is rising over the range [a,b] by definition if f(b)> f. (a)

Therefore, the positive average rate of change over an interval must be increasing over that interval.

To know more about the average rate of change follow

https://brainly.com/question/8728504

#SPJ2


Related Questions

math help !!!!!!!!!!!!!!!

Answers

The values of b, h and k are (c) b = 2, h = -2 and k = -9

How to determine the values of b, h and k?

The logarithmic function is given as:

f(x) = log₂(x + 2) - 9

A logarithmic function is represented as:

f(x) = logb(x - h) + k

By comparing both equations, we have

b = 2

h = -2

k = -9

Hence, the values of b, h and k are (c) b = 2, h = -2 and k = -9

Read more about logarithmic function at

https://brainly.com/question/13473114

#SPJ1

1. If x = 1 and y = 7, evaluate x+y/4 ​

Answers

Answer:

2

Step-by-step explanation:

given x=1 and y=7

now, given expression ,

x+y/4

by putting the values of the x and y ,we get

x+y/4

= 1+7/4

= 8/4

= 2 (Ans.)

Find two consecutive numbers such that the sum of four times the first and triple the second is 157. (linear function)

Answers

So, 22, 23 are the two numbers.

What is linear and polynomial function?

There are two distinct but related ideas that are referred to as linear functions: A polynomial function of degree 0 or 1 is referred to as a linear function in calculus and related fields if its graph is a straight line.

Consecutive numbers are preceding and following, hence we need two numbers so that

X+1=Y

or

X- Y = -1

In addition, we are aware of

4x + 3y = 157

Let's increase the top equation by 3 times.

We get

3x - 3y = -3

Then we combine that with the bottom equation.

4x + 3y = 157

      7x= 154

       x = 22

Afterward, we substitute x into the initial equation,

22+1 = 23

So, 22, 23 are the two numbers.

To know more about linear function or polynomial function visit:

https://brainly.com/question/11536910

#SPJ4

A teacher gave her class two tests. 50% of the class passed the first
test, but only 25% of the class passed both tests. What percentage of
those who passed the first test also passed the second test? %
25
100
50
12.5

Answers

Answer: 50

Step-by-step explanation:

50% of the class passed the first test, so that 25% that passed both test has to be part of the 50% that passed the first test. 25% that passed both is 50% of the 50% that passed the first test. Hopefully that makes sense.

A professional basketball team won 48 games and lost 32. what fraction of the games did the team win?

Answers

Answer:

48/80 = 6/10

Step-by-step explanation:

 48 wins

+ 32 lost

= 80 total games

Then the fraction of the games win is:

48/80

= 6/10

Answer:3/5 of the games

Step-by-step explanation: The total number of games played by the team is 48+32 = 80 games. out of hose 80, they won 48 so they won 48/80 games. We can simplify this by dividing both sides by 8 to get 6/10. Which is 60%. Finally we can simplify again by dividing the fraction by 2/2 to get 3/5.

what expression is equivalent to 6+3(n-4)-8+2n

Answers

Answer:

Step-by-step explanation:

Comment

Begin by removing the brackets.

6+3(n-4)-8+2n

6 + 3n - 12 - 8 + 2n                 Collect like terms

3n + 2n + 6 - 12 - 8                 Combine

5n - 14

Answer

5n - 14

there were 7 cantaloupes for every 8 watermelons in the garden. If there were 98 cantaloupes, how many watermelons were in the garden?

Answers

Answer:

14×7=98 so multiply the same into 14×8=112

Answer:

112 watermelons

Step-by-step explanation:

7/8 = 7÷7/8÷7 = 1/1.14285714286

1 x 98/ 1.14285714286 x 98

98/112

Determine the area between the curves by integrating over the x-axis or y-axis.

x=y^2

x=-|y|+12

Answers

When [tex]y\ge0[/tex] (above and on the [tex]x[/tex]-axis), we have [tex]|y|=y[/tex]. The parabola [tex]x=y^2[/tex] intersects with [tex]x=-|y|+12[/tex] in this region when

[tex]y^2 = -y + 12 \implies y^2 + y - 12 = (y-3)(y+4) = 0 \implies y=3[/tex]

On the other hand, when [tex]y<0[/tex] (below the [tex]x[/tex]-axis, we have [tex]|y|=-y[/tex], and so the curves intersect when

[tex]y^2 = -(-y) + 12 \implies y^2 - y - 12 = (y - 4)(y+3) = 0 \implies y=-3[/tex]

The area between the curves is then given by the definite integral,

[tex]\displaystyle \int_{-3}^3 (-|y| + 12) - y^2 \, dy[/tex]

The integrand is symmetric about the [tex]x[/tex]-axis, so the integral is equivalent to

[tex]\displaystyle 2\int_0^3 12 - y - y^2 \, dy = 2 \left(12y - \frac{y^2}2 - \frac{y^3}3\right)\bigg|_0^3 = \boxed{45}[/tex]

7. If F is a right angle, find the slope of line FH.

Answers

Answer:

1/2

Step-by-step explanation:

Find the slope, m,  between E and F      m = (7-3)/(2-4) = -2

  perpindicular  = - 1/m  =  1/2  = slope FH

On Wednesday, 1/3 of the students in Mr. Short's homeroom had drama practice, and 1/4 of his other homeroom students had band practice. If 6 students had band practice, how many students are in Mr. Short's homeroom?

Answers

Answer:

36

Step-by-step explanation:

Honestly, I'd work this out visually (see image) by drawing a rectangle and dividing it up. But if you need to show the math, here's how to do it:

Let x = the number of students in the homeroom

1/3 x have drama

1/4 (x - 1/3x) have band, and we are told 6 students have band, so

1/4 (x - 1/3 x) = 6

1/4 (2/3 x) = 6    

2/12 x = 6          

1/6 x = 6            

6 × 1/6 x = 6 × 6

1 x = 6 × 6            

x = 36

Answer:

36

Step-by-step explanation:

Let n be the total number of students in Mr. Short's homeroom. Then, working backward, we see that 

6 = 1/4(1 - 1/3)n = 1/4(2/3)n = 1/6n,$

so n = 6 x 6 = 36 students.

The average (mean) mass of an apple is 14g. The total mass of the
apple basket is 182g. So, how many apples are there in the basket?

Answers

The mean is the total mass (182g) divided by how many apples there are.
182/x = 14
We can rearrange this by multiplying both sides by x to get 182 = 14x
Then dividing both sides by 14 to get x equal to 182/14 which is 13
So there are 13 apples

Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:

Answers

The five number summary and interquartile range for the data-set is given by:

Minimum: 48Lower quartile: 54.Median: 63.5.Upper quartile: 74Maximum: 80.Interquartile range: 20

How to find the five number summary and interquartile range of the data-set?

The five number summary is composed by the minimum and maximum value, and the first quartile, median and third quartile. As for each of these data, they are explained below.

The minimum value is the smallest value from the data-set, as the maximum value is the greatest value of the data-set.The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference of the third quartile and the first quartile.

In this problem, we have that:

The minimum value is the smallest value, of 48.The maximum value is the smallest value, of 80.The data-set has even cardinality, hence the median is the mean of the middle elements, which are 63 and 64, hence the median is of 63.5.The first quartile is the median of the five elements of the first half, hence it is of 54.The third quartile is the median of the five elements of the second half, hence it is of 74.The IQR is the difference between the quartiles, hence 74 - 54 = 20.

More can be learned about five number summaries at brainly.com/question/17110151

#SPJ1

What is the shape of the cross section taken parallel to the base of a cylinder? circle rectangle triangle ellipse

Answers

The option A is correct. A circle is the shape of the cross section taken parallel to the base of a cylinder.

According to the statement

We have given that the cylinder and we have to tell that the which shape required for the cross section taken parallel to the base of a cylinder.

So, For this purpose,

We know that the

A cylinder is a three-dimensional solid, one of the most basic geometric shapes.

In this shape the surface formed by the points at a fixed distance from a  line segment, which is  known as the axis of the cylinder.

As the bases of cylinder are two identical circles which are parallel to the curved surface.

The curved surface when we open will be circle rather than the circle.

So, Due to this reason the answer is a circle.

Therefore, a circle is the shape of the cross section taken parallel to the base of a cylinder.

Learn more about base of cylinder here

https://brainly.com/question/76387

#SPJ1

Which set of radian angle measures is
equivalent to….

Answers

[tex]

\sin^{-1} \left(-\frac{1}{2} \right)=-\sin^{-1} \left(\frac{1}{2} \right)=\boxed{-\frac{\pi}{6}}[/tex]

Hello, I need help with this. Giving brainiliest

9^(a) = (sqrt(3))^(a +2)​

Answers

Answer:

2/3

Step-by-step explanation:

Let's solve your equation step-by-step.

9a=(√3)a+2

9a=1.732051a+2

Solve Exponent.

9a=1.732051a+2

log(9a)=log(1.732051a+2)(Take log of both sides)

a*(log(9))=(a+2)*(log(1.732051))

a=(log(1.732051)/log(9))*(a+2)

a=0.25*(a+2)

a=0.25a+0.5(Simplify both sides of the equation)

a−0.25a=0.25a+0.5−0.25a(Subtract 0.25a from both sides)

0.75a=0.5

0.75a/0.75=0.5/0.75

(Divide both sides by 0.75)

a=0.666667

a=2/3

0.666667=2/3

Hope this helps :)

Answer:

2/3

Step-by-step explanation:

9^a = sqrt(3)^a * sqrt(3)^2

9^a = 3^((a/2)+1)

3^(2a) = 3^((a/2)+1)

2a = (a/2)+1

1.5a=1

a=1/(3/2) = 2/3

THIS IS REALLY IMPORTANT I NEED IT DONE BY TODAY PLEASE

Answers

Answer:

15. 155°

16. 115°

Step-by-step explanation:

15.

Use the big triangle.

At the top, the supplement of 60° is 120°.

The angle measuring 120° and the angle measuring 35° are the remote interior angles to exterior angle x.

120° + 35° = x

x = 155°

16.

See picture below.

x = 115°

Answer:

  15)  x = 155°

  16)  x = 115°

Step-by-step explanation:

The theorem that relates an exterior angle of a triangle to the opposite (remote) interior angles is helpful for these problems. It says the exterior angle is equal to the sum of the remote interior angles.

15)

Remove the altitude line and consider the interior angle of the triangle next to the exterior angle marked 60°. That interior angle will be ...

  180° -60° = 120°

Then the angle we just found and the one marked 35° are "remote" to the exterior angle marked x. The theorem cited at the beginning tells us ...

  x = 35° +120°

  x = 155°

16)

Extend the left side of the "parallelogram" (the side with the arrow) upward until it meets the top horizontal line. This cuts off a triangle with an exterior angle marked x, an interior angle marked 50°, and another remote interior angle at the top edge of that triangle.

The opposite angles of a parallelogram are congruent, so the external angle to the triangle at the top edge will be x, and the adjacent interior angle in the triangle will be (180° -x).

The exterior angle (x) is equal to the sum of the remote interior angles (50° and (180° -x)), so we have ...

  x = 50 +(180 -x)

  2x = 230 . . . . . . add x, simplify

  x = 115 . . . . . . . divide by 2

The measure of the angles marked x is 115°.

Use the recursive formula to find the first five terms in the arithmetic sequence.

Answers

The first five terms of the given arithmetic sequence are:

54, 45, 36, 27, 18 (First option)

The arithmetic sequence is given as follows,

f(n) = f(n-1) - 9 ............ (1)

Also, f(1) = 54 .............. (2)

Now, for finding the first five term of this arithmetic sequence, we will substitute n as 1, 2, 3, 4, and 5 one by one. Using the above formula for the arithmetic sequence, we can deduce the first five terms.

f(1) is the first term of the sequence which is already provided as 54.

Now, putting n=2 in equation (1), we get,

f(2) = f(2-1) - 9

f(2) = f(1) - 9

Substitute f(1) = 54 from equation (2)

⇒ f(2) = 54 - 9

f(2) = 45

To find the third term of the arithmetic sequence, put n = 3 in equation (1)

f(3) = f(3-1) - 9

f(3) = f(2) - 9

⇒ f(3) = 45 - 9

f(3) = 36

Similarly, we can find the fourth and fifth terms of the arithmetic sequence by substituting n = 4 and n = 5 respectively.

∴ f(4) = f(3) - 9

⇒ f(4) = 36 - 9

f(4) = 27

Likewise, f(5) = f(4) - 9

⇒f(5) = 27 - 9

f(5) = 18

Thus, using the recursive formula, the first five terms of the arithmetic sequence are deduced to be:

54, 45, 36, 27, 18

Learn more about arithmetic sequence here:

brainly.com/question/15412619

#SPJ1

Find the missing length indicated.

Answers

The missing length indicated on the right triangle is 120 units

How to determine the missing length?

To start with:

The missing length in the right triangle can be represented with the variable x

Next, we have the following equivalent ratio from the given triangle

64 : x = x : 289 - 64

Express the ratio as a fraction

64/x = x/(289 - 64)

Evaluate the difference on the right-hand side

64/x = x/225

Cross multiply in the above equation

x * x = 64 * 225

This gives

x^2 = 64 * 225

Take the square root of x^2 (do not approximate)

x = 64 * 225

Take the square root of 64 and 225 (do not approximate)

x = 64 * 225

Evaluate the product of 8 and 5

x = 120

Based on the given parameters, the missing length indicated on the right triangle is 120 units

Read more about right triangles at:

https://brainly.com/question/2437195

#SPJ1

A newspaper article claimed: "the average cost of weekly groceries is $124.50." what statistical measurement are they most likely claiming?

Answers

The average cost of weekly groceries exists at $124.50." The statistical measurement exists they most probably claim exists mean.

What is mean?

The arithmetic mean of a given data exists as the totality of all observations divided by the number of observations.

For instance, a cricketer's scores in five ODI matches exist as follows:

12, 34, 45, 50, 24.

To estimate his average score in a match, we compute the arithmetic mean of data utilizing the mean formula:

Mean = Sum of all observations/Number of observations

Median

The value of the middlemost observation, acquired after organizing the data in ascending or descending order, exists named the median of the data.

For instance, consider the data: 4, 4, 6, 3, 2. Let's organize this data in ascending order: 2, 3, 4, 4, 6. There exist 5 observations.

Therefore, median = middle value i.e. 4.

Mode

The value which occurs most often in the provided data i.e. the observation with the highest frequency exists named a mode of data.

As per the circumstances we have given the average cost of groceries.

The mean exists also the average sum of data divided by the total number of data.

Therefore, the statistical measurement exists as the mean.

To learn more about mean refer to:

brainly.com/question/15323584

#SPJ4

Help please! What is the correct answer and how do I solve for R?

Answers

the correct answer is d, to solve for r divide both sides by 2piH

How many positive 3-digit numbers are divisible by 11?

Answers

Answer:

81

Step-by-step explanation:

If a number is divisible by 11, then you can make those numbers by multiplying 11 by any number. Like 33 is divisible by 11 because 3×11 is 33.

Of course, 33 is too small, we are looking for 3-digit numbers...

see image.

1 + 7x = 5x + 25 solve for X

Answers

Answer:

x = 12

Step-by-step explanation:

1 + 7x = 5x + 25 ( subtract 5x from both sides )

1 + 2x = 25 ( subtract 1 from both sides )

2x = 24 ( divide both sides by 2 )

x = 12

Answer:

12

Step-by-step explanation:

Start by subtracting both sides by 5x:

[tex]1+7x-5x=25\\1+2x=25[/tex]

Subtract 1 from both sides

[tex]2x=24[/tex]

Divide both sides by 2

[tex]x=12[/tex]

Check

[tex]1+7(12)=5(12)+25\\1+84=60+25\\85=85[/tex]

Therefore x = 12

At the beginning of the summer, sarah has $250. she takes a summer job and saves $150 per week. felicia has $1,650 at the beginning of the summer. she travels during the summer and spends $200 per week. at the end of which week do sarah and felicia have the same amount of money?

Answers

Answer:

Week 4

Step-by-step explanation:

Victoria has $250 and saves $150 each week, hence have increments $150 each week

250+150 (first week)

= 400

second week = 400 + 150 = 550

third week = 550 + 150 = 700

fourth week = 700 + 150 = $850

Felicia on the other hand has $1,650 and spends $200 each week, hence has decrements of $200 each week.

1650+200 (first week)

= 1450

second week = 1450 - 200 = 1250

third week = 1250 - 200 = 1050

fourth week = 1050 + 200 = $850

100 points to whoever can answer this!

Answers

Answer:

10724.29

Step-by-step explanation:

mean means average

so to find an average you add everything together then divide it by the amount of variables

m = (10150 + 10211 + 10424 + 10769 + 10884 + 11155 + 11477)/7

m = 75070/7

m = 10724.2857143

m = 10724.29

Find the average rate of change of the function a(x) = πx2 where a is the area of a circle with radius x as the radius changes from x=4 to x=6.

Answers

The average rate of change of the given function is 10π.

Given function

a = πx^2

Where a is the area of a circle with radius x

The radius changes from x = 4 to x = 6.

Calculating the average rate of change of function:

The method of finding the average rate between the function value over a certain interval is called the average rate of change.

The formula is given by :

Average = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

Where f(a) and f(b) are the function value over the limit a and b.

Average = [tex]\frac{f(6)-f(4)}{6-4}[/tex]

= [tex]\frac{\pi (6)^{2} -\pi (4)^{2} }{6-4}[/tex]

= [tex]\frac{\pi (36-16)}{2}[/tex]

= [tex]\frac{20\pi }{2}[/tex]

= 10π

The average rate of change of the given function is 10π.

Find out more information about average rate of change here

brainly.com/question/8792759

#SPJ4

The pair of triangles below have
two corresponding parts marked
as congruent. What additional
information is needed for a AAS
congruence correspondence?

Answers

Answer:

option c

Step-by-step explanation:

option c is a correct answer

A soap company started a promotion in which each packet of detergent powder will have 20% extra powder at the
same price, Jenna buys a 2 kg packet of the detergent powder. How much total detergent powder will be in the packet?

Answers

2.4kg.,

..

hope it helps

Answer is 2.4 kg total detergent powder
Step by step
She buys 2kg of powder plus 20% extra powder
2 x 20%
2 x .20 = .4
Add the .4 to the original 2kg
Total 2.4 kg
Problem solved

Combine the like terms to create an equivalent expression. 9+a-5b-2=

Answers

❄ Hi there,

let us combine the like terms and create an equivalent expression –

[tex]\large\begin{gathered} \sf{9+a-5b-2} \\\sf{9-2+a-5b}\\\sf{7+a-5b} \end{gathered}[/tex]

That's as far as we can go.

A repeated-measures study comparing two treatments with n = 4 participants produces md = 2 and ss = 75 for the difference scores. what is the estimated standard error for the sample mean difference?

Answers

The estimated standard error for the sample mean difference is  2.5 .

According to the question

A repeated-measures study comparing two treatments

n = 4

MD(mean difference) = 2

SS (sum of square) = 75

Now,

error for the sample  

Formula for standard error

[tex]S^{2} = \frac{SS}{n-1}[/tex]

by substituting the value

[tex]S^{2} = \frac{75}{4-1}[/tex]

[tex]S^{2} = \frac{75}{3}[/tex]

S² = 25

S = 5 (s is never negative)

Standard error of the estimate for the sample mean difference

As

The standard error of the estimate is the estimation of the accuracy of any predictions.

The formula for standard error of the mean difference

standard error of the mean difference  =[tex]\frac{standard\\\ error}{\sqrt{n} }[/tex]  

standard error of the mean difference = [tex]\frac{5}{\sqrt{4} }[/tex]  

standard error of the mean difference = 2.5

Hence, the estimated standard error for the sample mean difference is  2.5 .

To know more about estimated standard error here:

https://brainly.com/question/14524236

#SPJ4

Given f(x)=abx+c. How would increasing the value of a change the graph?

Answers

Increasing the value of a increases the initial value of our exponential, and also increases the rate of growth of the function.

How would increasing the value of a change the graph?

Y assume we have an exponential equation of the form:

y = a*b^x + c

In this case, a is what we know as the "initial value" of the exponential.

Notice that when we evaluate in x = 0, we get:

y = a*b^0 + c

y = a + c

So increasing a will increase the initial value of what we are representing, but it will also increase the "rate" at which our function increases when x increases.

if you want to learn more about exponential functions:

https://brainly.com/question/11464095

#SPJ1

Other Questions
Sociologist andrew cherlin suggests that the u. s. s high divorce rates may be in part a reflection of a broad sense of ____ unique to american culture You should develop your social media budget before you create your social media plan.a) trueb) false need heeeelp please What happened to individuals who refused to enlist in the war due to religious reasons? Tina just started enjoying the game of peekaboo which stage of cognitive development is tina in? The bar graph shows the rents paid per month for apartments in an urban neighborhood. The curve shows that the rents are normally distributed. Estimate the percent of apartments residents who pay less than $650 per month. A. 99%B. 25%C. 68%D. 30% 30. You want to simulate an experiment to draw cards out of a deck. Youplan to draw 35 cards (with replacement), and list which card you drew. Howmany times would you expect to draw a face card?681210 Let x, y, z be three natural numbers such that x < y < z. If GCF(x, y, z) = 3, GCF (y, z) = 15, LCM (x, y, z) = 3150, and x is even number greater than 10, then find the values of x, y and z. Find the value of x.answer choicesA. 70B. 65C. 30D. 40 A car coasts 62. 2 meters along a hill that makes a 28. 3 angle with the ground. if the car's mass is 1234 kg, then what is the change in potential energy? Complete the proofs, ASAP!!! (Geometry) When running for office, when is a political candidate most likely to benefit from the media agenda-setting role? The major differenc ebetween the use of scrubber and the use of fluidiozed - bed combustions as pollution control measures in power plants is? In the circle below, O is the center and mGl= 145. What is the measure of the central angle ZGOR? H G 0 145 I Solve for n.7+2n = 11 Chemical reactions can be detected by: _________a) color change from reactants to products b) the production of a precipitate c) a change in temperature d) an increase of surface area Which of the following detail is NOT how the Time Traveller is described when he first sits down to dinner in The Time Machine:A. Clean lab coatB. Bloody socksC. Dazzled by lightD. Haggard appearance Find both the scalar projection compvuand the vector projection projvuof the vectoru=1,1,1onto the vectorv=1,0,1. answer:. . . . . . . . . . . . . . . . . . . . how a person's cultural bias can impact Aboriginal and/or Torres Strait Islander UrgentDuring an experiment, distilled water was placed in a sealed container and the container was heated gradually. Describe this system when it reaches phase equilibrium.