Mathematics Middle School

Given the function h(x) = 3(5)x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.

Part A: Find the average rate of change of each section. (4 points)

Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)

i really just need an answer for B mostly

Answers

Answer 1

Part A: The average rate of change of section A is 12 and that of B is 300.

Part B: The average rate of change of Section B is 25 times greater than that of Section A due to the exponential nature of the function h(x).

Explaining the average rate of change for two sections and comparing their values in an exponential function context,

Part A:
For Section A: h(1) - h(0) = 3 [tex](5)^1[/tex]- 3 [tex](5)^0[/tex] = 15 - 3 = 12
For Section B: h(3) - h(2) = 3 [tex](5)^3[/tex] - 3 [tex](5)^2[/tex] = 375 - 75 = 300
Therefore, the average rate of change for Section A is 12 and for Section B is 300.Part B:
To find how many times greater Section B's rate of change is compared to Section A, we divide the average rate of change of Section B by the average rate of change of Section A: [tex]\frac{300}{12}[/tex] = 25 times greater.

One rate of change is greater than the other because of the exponential growth nature of the function. The function h(x) = 3 [tex](5)^x[/tex] is an exponential function, and the rate of change increases rapidly as x increases, leading to a much greater average rate of change for Section B than Section A.

The question is:

Given the function h(x) = 3 [tex](5)^x[/tex], Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.

Part A: Find the average rate of change of each section.

Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other.

Related Questions

Could someone please help me on this

Answers

The dependent variable would be b (affected by the change of n) and the independent variable would be n (affects b). The equation would be
b = 12n.

Classify the angles in questions 1-3 below. PLEASE HELP

Answers

A 90 degree angle or right angle is an L shape. Anything less than that, like < is an acute angle, and anything greater is an obtuse. A straight angle is literally straight, like this__
1. This is acute because it’s less than 90 degrees.

2. This is obtuse because it’s more than 90 degrees.

3. This is right because it’s exactly 90 degrees, indicated by the square in the angle measure’s place.

one number is 2 larger than another number. the sum of their squares is 100. find the numbers

Answers

x= first number
x+2= second number

x^2 + (x + 2)^2= 100
square the parentheses

x^2 + [(x + 2)(x + 2)]= 100
x^2 + x^2 + 2x + 2x + 4= 100
combine like terms

2x^2 + 4x + 4= 100
subtract 100 from both sides

2x^2 + 4x - 96= 0
factor

2(x−6)(x+8)=0
set each parentheses equal to 0

x-6= 0
x= 6

OR

x+8= 0
x= -8

CHECK:
x^2 + (x + 2)^2= 100
(6)^2 + (6 + 2)^2= 100
36 + (8)^2= 100
36 + 64= 100
100= 100

x^2 + (x + 2)^2= 100
(-8)^2 + (-8 + 2)^2= 100
64 + (-6)^2= 100
64 + 36= 100
100= 100


ANSWER: x= 6 or x= -8

Hope this helps! :)

The numbers are 6 and -8

let

the first number = x

One of the number is 2 larger than another number .Therefore, the second number will be as follows;

x + 2

Sum of there squares will be as follows:

x² + (x + 2)² = 100

Therefore,

x² + x² + 4x + 4 = 100

2x² + 4x + 4 - 100 = 0

2x² + 4x - 96 = 0

x + 2x - 48 = 0

let's find x

x - 6x + 8x - 48 = 0

x(x - 6) + 8(x - 6) = 0

(x - 6)(x + 8) = 0

x -6 = 0 and x + 8 = 0

x = 6 and x = -8

The numbers are 6 and -8.

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Is how many countries are in North America a statistical question

Answers

yes, because you could collect data to answer the question.

The question, "How many countries are in North America" is not a statistical question.

What are statistical Questions?

Statistical questions are defined as the questions which are answered by collecting data from many which will probably vary.

The given question is,

How many countries are in North America"How many countries are in North America.

Although the answers to this from the students may vary because they don't know, the answer to this question is a constant.

This is not something which varies.

Hence this is not a statistical question.

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Dakota built a wall with bricks like this one:

Look at Dakota’s wall:

What is the length of the side of the brick labeled a? ____________

What is the length of the side of the brick labeled b? _____________

What is the total height of the wall? ____________

What is the total length of the wall? __________

Answers

I don't know if i'm right but I think the first question is 5 inches, the second question is 8 inches, the third question is 24 inches because there are three blocks and each are 8 inches so 8 x 3 = 24, and the last question is 45 inches because there are 9 bricks each 5 inches on the top so 9 x 5 = 45. (again I am not sure if this is correct but it is what I think)

Lisa is asked to draw a triangle with the following specifications:

two angles are complementary
the side between the two complementary angles has a length of 12 centimeters

Which of the following statements about this triangle is true?

A.
Exactly one triangle exists with the given conditions, and it must be an isosceles triangle.

B.
More than one triangle exists with the given conditions, and all instances must be right triangles.

C.
More than one triangle exists with the given conditions, and all instances must be isosceles triangles.

D.
Exactly one triangle exists with the given conditions, and it must be a right triangle.

Answers

B is correct.

Since two of the angles are complementary, adding up to 90°, the third angle must be 180-90=90°.

However, this does not mean only one triangle exists.  The only information we are given about the two angles is that they are complementary.  This could be 30 and 60; 45 and 45; or multiple other combinations.  This means there is more than one triangle that fits these criteria.

Final answer:

Triangles with two complementary angles must be right triangles. Since these angles add up to 90 degrees, the side between them is part of a right triangle. There can be many different right triangles that satisfy these conditions, but all must have a 90-degree angle. (Option D)

Explanation:

The question asks about the conditions that define a certain type of triangle. With two angles being complementary, they add up to 90 degrees. In geometry, a complementary pair of angles adds up to 90 degrees, which means that the two angles in question must be acute angles that add up to form a right angle. Therefore, the triangle with two complementary angles must be a right triangle.

Since the triangle can have many different dimensions for the other sides and angles while keeping the side between the complementary angles at 12 centimeters, we can infer that there are infinite variations of this triangle, each with different measures for the remaining side and angle. However, all those triangles must satisfy the condition of being right triangles.

Thus, the correct answer to this question is:

D. Exactly one triangle exists with the given conditions, and it must be a right triangle.

Use unit multipliers to convert 123 pounds per mile to ounces per centimeter. There are 5,280 feet in 1 mile. There are 16 ounces in 1 pound. There are approximately 2.54 cm in 1 inch. Enter your answer as a decimal rounded to the nearest hundredth. Just enter the number.

Answers

A unit multiplier is a conversion factor of value 1 that we can use to convert quantities.
We want to convert 123 pounds per mile to ounces per centimeter. 
First, we are going to express the quantity to convert as a fraction:
123 pounds per mile=[tex]123 \frac{pounds}{mile} [/tex]

Next, we are going to find our multipliers:
- We know for our problem that there are 5,280 feet in 1 mile, so our first multiplier will be: [tex] \frac{1mile}{5280ft} [/tex]
- We also know that there are 16 ounces in 1 pound, so our second multiplier will be: [tex] \frac{16ounces}{1pound} [/tex]
- We know that there are 12 inches in 1 foot, so our third multiplier will be: [tex] \frac{1ft}{12in} [/tex]
- We know that there are approximately 2.54 cm in 1 inch, so our fourth multiplier will be: [tex] \frac{1in}{2.54cm} [/tex]

Now we can put all our multipliers together:
[tex]123 \frac{pounds}{mile} * \frac{1mile}{5280ft}*\frac{16ounces}{1pound}* \frac{1ft}{12in}*\frac{1in}{2.54cm}=0.01 \frac{ounces}{cm} [/tex]

We can conclude that the answer is 0.01

A company says that the probability of finding an all-star card in a game pack is 12.5%. A student wants to determine the probability that, if he buys 6 game packs, 2 or more will have an all-star card.

To do this, he uses a random number table to pick 6 numbers from 1 to 8. He lets 1 represent a pack with an all-star card and 2 through 8 represent a pack without an all-star card. He repeats this for a total of 15 trials. The results are shown in the table.

561673 366468 314255 361362 838443 126285 257231 768551 652585 468113 123711 322764 487626 783134 384664

Select from the drop-down menus to correctly complete each statement.

To estimate the probability that 2 or more out of 6 packs will have an all-star card, the student must count the number of trials with BOX RIGHT HERE and divide by the number of trials.

This gives an estimated probability of about . BOX RIGHT HERE

PLEASE I NEED THIS ANSWERED I HOPE ITS CLEAR ENOUGH.

Answers

Answer:

the first box is "two or more 1s"

the second box is "0.13"

Step-by-step explanation: Im a K12 Student

The probability that 2 or more out of 6 packs will have an all-star card is given by the equation P = 0.1333

What is Probability?

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability that 2 or more out of 6 packs will have an all-star card be P

The probability of finding an all-star card in a game pack is 12.5 %

The student has pointed that 1 represent a pack with an all-star card and 2 through 8 represent a pack without an all-star card

The test results are given in set A = { 561673, 366468, 314255, 361362, 838443, 126285, 257231, 768551, 652585, 468113, 123711, 322764, 487626, 783134, 384664 }

The number of trials that represent that 2 or more out of 6 packs have an all-star are = { 468113 , 123711 }

Therefore , the probability is given as

Probability that 2 or more out of 6 packs will have an all-star card P = 2/15

On simplifying the equation , we get

Probability that 2 or more out of 6 packs will have an all-star card P = 0.133

Hence , the probability is 13.33 %

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Help please........................

Answers

Dilation means multiply. (I don't know why they just don't say it).

You have the right answer. 2.5 * 2.5 = 6.25 Can't beat being right.

1. You have 60 in. of molding to use as a frame around a picture you are painting. The area of the painting is giving by the function y = 30x - x^2 where x is the width in inches. What width gives the maximum area for the painting? What is the maximum area?

2. You are trying to dunk a basketball. You need to jump 2.5 ft in the air in order to dunk the ball. The height that your feet are above the ground is given by the function h = -16t^2 + 12t. What is the maximum height your feet will be above the ground? Will you be able to dunk the basketball?

I need a lot of help with these problems. Please answer them to the best of your capabilities. I'M GOING INSANE!!! Thanks so much!

Answers

1) [tex]y = 30x - x^2 y = -x^2+30x (y = ax^2+b)[/tex]

[tex]x = -b/2a = -30/2(-1) = 15[/tex]

[tex]y = -(15)^2+20(15) y = -225+450 y = 225[/tex]

So, 15 as the width would give us the maximum area for the painting.
---------------------------------------------------------------------------------------------------------
2)  The maximum height your feet will be above the ground is 2.25 ft.
     No, you wouldn't be able to dunk the ball because the maximum height           you can jump is 2.25, but you need to jump 2.5 ft to dunk.

What is 4x-2x answer asap

Answers

4x - 2x is 2x. If we have 4 x's, and we take away 2 x's, we have 2 x's left. I hope this helps!

Here is an explanation:
[tex]4x-2x = 4(x) - 2(x) = (4-2)(x) = 2(x) = 2x. [/tex]
You could also think of this as:
( x + x + x + x ) - ( x + x ) = x + x + x + x - x - x

plz make ,....................

Answers

we know that
the length of rectangle is 5*(x+6) cm
the breadth of rectangle is (2x+6) cm
perimeter=192 cm
perimeter of a rectangle=2*[length+breadth]
so
192=2*[5*(x+6)+(2x+6)]----> 192/2=[5x+30+2x+6]---> 96=7x+36
7x=96-36-----> 7x=60--------> x=60/7 cm

the answer is
x=60/7 cm or 8.57 cm

What is the weight ( in grams) of a liquid that exactly fills a 163.5 millimeter container if the density of the liquid is 0.492 grams/millimeter?

Answers

Comment
The formula for density is [tex] \text{density} = \frac{m}{V} [/tex]

Givens
V = 163.5 mL
d = 0.492 grams / mL

Solution
m = d * V                   The formula has been rearranged.
m = 0.492 * 163.5
m = 80.442 grams. <<<<< Answer

Find the product of two numbers whose sum is 11 and difference is 3.

Answers

The two numbers are 7 and 4

Let the first number = x

let the second number = y

The sum of the numbers is 11, in algebra form x + y  = 11

The difference of the two numbers is 3, in algebra form, x - y = 3

To obtain the two unknown numbers, we solve the two equations;

from the first equation, x = 11 - y

substitute the value of x into the last equation;

(11 - y) - y = 3

11 - y - y = 3

11 - 2y = 3

2y = 11 - 3

2y = 8

y = 4

The value of x = 11 - 4 = 7

Thus, the two numbers are 7 and 4

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Final answer:

To find the product of two numbers with a sum of 11 and a difference of 3, solve the system of equations to find the numbers (7 and 4) and multiply them to get the product, which is 28.

Explanation:

To find the product of two numbers whose sum is 11 and whose difference is 3, we can let the two numbers be x and y, with x being the larger number. Therefore, we have two equations from the given information: x + y = 11 and x - y = 3.

Adding these two equations, we get:

2x = 14x = 7

Using x = 7 in the first equation, we have:

7 + y = 11y = 4

Now that we have both numbers, we can find their product:

Product = x * yProduct = 7 * 4Product = 28

The product of the two numbers is 28.

50 PIONTS AND BRANLIEST PWEASE HELP
The product of two rational numbers is positive. What can you conclude about the factors? Express your answer in two or more complete sentences.

Answers

If the product of two rational numbers is positive, then the two factors are either both positive rational numbers or both negative rational numbers. A positive times a positive makes a positive and a negative times a negative makes a negative.

|1 - 4x| > 7

A. {x|x < -1.5 ∪ x > 1.5}
B. {x|x < -1.5 ∪ x > 2}
C. {x|-1.5 < x < 2}

Answers

[tex]|1-4x| > 7\iff1-4x > 7\ \vee\ 1-4x < -7\ \ \ |-1\\\\-4x > 6\ \vee\ -4x < -8\ \ \ |:(-4)\\\\x < -1.5\ \vee\ x > 2\\\\Answer:\boxed{B.\ \{x:x < -1.5\ \cup\ x > 2\}}[/tex]

which of the following mesurments are greater than 130 fluid ounces. 5 quarts, 16 cups, 9 pints, 2 gallons or 1 gallon

Answers

9 pints i'm pretty sure i'm right hope i helped
130 fluid ounces to quarts is 4.06, so 5 quarts is larger.

130 fluid ounces to cups is 16.25, so 16 cups is smaller.

130 fluid ounces to pints is 8.13, so 9 pints is larger.

130 fluid ounces to gallons is 1.02, so 2 gallons is larger and 1 gallon is smaller. 

graph
[tex]y = |x| - 1[/tex]

Answers

Graph y = x  (black)

(0; 0); (2; 2)

Symmetry about the x-axis (green)

Translation down 1 unit (red)

a local parts shop buys a machine that costs $500,000. its value depreciates exponentially each year by 10%. what is the machines value after 5 years? round to nearest integer

Answers

Hello!

Answer:

$295.295

Explanation:

Of the statement, we have that the price of the machine decreased 10% every year exponentially, so in the first year it real value drops to 90% of the costs. For 5 years, It can be expressed and simplified by the following equation:

We can't use that the percent drop as a percent itself, so we are going to divide 90% by 100%, and it will give us an entire number.

[tex]\frac{90}{100}=0,9 \\ \\ Value=Costs.(0.9)^{years}[/tex]


By substituting we have:

[tex]Value=500000.(0.9)^{5}[/tex]

Value: $295.245


Have a nice day!



use the integer values of x from -3 to 13 to graph the equation y= -x

Answers

y = -x

This is an equation of the straight line, therefore we need only two points to the graph.

for x = -3 we have y = -(-3) = 3 → (-3; 3)

for x = 0 we h→ve y = -0 = 0 → (0; 0)

The graph in the attachment

Write an algebraic expression for the word expression

The sum of 15 and the product of 5 and v

use parentheses

Answers

5(v) + 15

Hope this helps!

solve the equation 30t - 4 = 1 for t

Answers


[tex]30t - 4 = 1 \\ 30t = 5 \\ t = \frac{5}{30} \\ t = \frac{1}{6} [/tex]

Answer : t = 1/6, or in decimal form, 0.17

Hope this helps. - M

Answer:

A) 1/6

Step-by-step explanation:

Help please! Don’t understand!

Answers

[tex]6+2-(-1)+(-8)=8+1-8=1[/tex]
Hi there! The answer is 1.

[tex]6 + 2 - ( - 1) + ( - 8) = [/tex]
Keep in mind that the sum of a plus and a minus ends up in a minus. So
+ - = -

Keep in mind that the sum of a minus and a minus ends up in a plus.
- - = +

[tex]6 + 2 + 1 - 8 = [/tex]
Now add from left to right.

[tex]8 + 1 - 8 = [/tex]
Add once more

[tex]9 - 8 = [/tex]
Subtract

[tex]1[/tex]
Hence, the answer is 1.
~ Hope this helps you!

Please help me.I need this answered

Answers

For the first one each side would be 2.05. Because 2.05 x4 = 8.2. I hope this helps.
1. 8.2•8.2= 67.24.
2. 0.5(9•11)= 49.5.
3. pi•(17/12)^2= about 289/144pi.
4. 3.75•7.6= 28.5.
5. (42•20)+(10•22)= 840+220= 1,060.
6. 0.5(10.667•3.2)+(10.667•15)= 170.667+160= 330 and two thirds.

Jack or three protein bars for a total of $4.26. Which equation could be used to find the cost c in dollars of each protein bar?

Answers

Jack bought 3 protein bars for $4.26. The individual cost of the protein bars can be determined by the following:

(total cost / quantity bought) = c

$4.26 / 3 = $1.42

The cost of an individual protein bar is $1.42.
Jack bought 3 protein bars for a total of $4.26?

First, set up your equation. I'll let "b" represent the value of each individual bar:

3b = 4.26

Now, divide the total value by the number of bars for the answer:

b = $1.42

to the nearest whole number, how many times larger is the volume of Earth compared to the volume of our moon? use a radius of 1079 miles for the moon and 3,959 miles for the Earth.

Answers

Well, that would be 3,959 divided by 1079, which is 4 (when rounded up to nearest whole number. Original answer 3.6691)

The volume of Earth is about 49 times larger than the volume of the Moon, based on their provided radii.

To the nearest whole number, the volume of Earth is approximately 49 times larger than the volume of the Moon.

Given that the volumes of spheres are proportional to the cubes of their diameters, and using the radii provided (1079 miles for the Moon and 3959 miles for Earth), we can calculate the volume ratio:

Volume of Earth: [tex](3959)^3[/tex]

Volume of Moon: [tex](1079)^3[/tex]

Volume of Earth compared to the Moon,  = [tex](3959^3) / (1079^3)[/tex] ≈ 49.

There volume of the earth is 49 times larger.

write the function for the graph below

Answers

This is a function y=√x that was moved 2 units to the right.
y=√(x-2)

The function f(x) is given by the set of ordered pairs.
{(1,0), (-10,2), (0,6), (3,17), (-2,-1)}
which equation is true?
f(-10)=1
f(2)=-10
f(0)=6
f(1)=-10

Answers

Answer: f(0) = 6.

Explanation:

Ther ordered pairs are: (x,y) or (x, f(x) )

So, (1,0) means that f(1) = 0 which denies the fourth choice.

(-10,2) means that f(-10) = 2 which denies the first choice

(0,6) means that f(0) = 6, which is the third choice. So, that is the true equation.

Answer:  the correct option is (C) f(0) = 6.

Step-by-step explanation:  We are given the function f(x) by the following set of ordered pairs :

{(1,0), (-10,2), (0,6), (3,17), (-2,-1)} .

We are to select the TRUE equation.

We know that

in the ordered pairs, the first element stands for the independent variable x and the second element stands for the dependent variable f(x).

So, the equations that comes from the given ordered pairs are

[tex]f(1)=0,~~f(-10)=2,~~f(0)=6,~~f(3)=17,~~f(-2)=-1.[/tex]

Thus, the only true equation is f(0) = 6.

Option (C) is CORRECT.

A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs 20 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in pounds can be represented by f x( ) = 20x + 4. What is the range of the function for this situation? Please explain.

Answers

The range of the function would be from 0 to 244.

The range of the function is the possible output values for the function. In this case, it is from zero to the highest possible weight. Since there are 6 pairs of weight plates, we can input 12 for x to get the maximum.

20(12) + 4 = 244

Name the point with the given coordinates (4 -2)

Answers

The point with the given coordinates (4 -2) is h.

What are the coordinates of midpoint of the line segment AB?

Suppose we've two endpoints of a line segment as:

A(p,q), and B(m,n)

Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:

[tex]x = \dfrac{p+m}{2}[/tex]

and

[tex]y = \dfrac{q+n}{2}[/tex]

We are given that;

The graph of four points

Now,

One point is k with (-4,2)

One point is g with (2,4)

One point is h with (4,-2)

One point is j with (-2,-4)

Therefore, by the midpoint the answer will be h(4,-2).

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