Use the unique factorization for the integers' theorem (Section 4.3) and the definition of logarithm to prove that log3 (7) is irrational.

Answers

Answer 1

It is demonstrated that log3 (7) is irrational using unique factorization for integers theorem and the definition of logarithm.

Explain the term  unique factorization theorem?Every integer bigger than 1 is either a prime number by itself or the result of a singular combination of prime numbers, based on the fundamental theorem of arithmetic (FTA), Often known as the unique factorization theorem or even the unique-prime-factorization theorem.

If a contradiction is rational, then log3(7) = a/b for some a,b∈R .

In which, b≠0 will be true.

As a result, 7 = 3ᵃ/ᵇ according to the definition of logarithms.

7 = 1*7 is unique according to the unique factorization theorem.

Thus, it is demonstrated that log3 (7) is irrational using unique factorization for integers theorem and the definition of logarithm.

To know more about the unique factorization theorem, here

https://brainly.com/question/12971919

#SPJ4


Related Questions

19) A parking garage charges the rates in the table below. What is the rate of change? Don't forget your units.

Answers

The rate of change is not constant.

What is rate of change ?

A rate of change is a measurement of how one quantity alters in proportion to another. The dependent variable y must be present if independent variable x is. rate of change = y-to-x conversion of change. Change rates may be positive or negative.

We know that the rate of change in a function is given by :-

(change in dependent variable) / (change in independent variable)

Let x denotes the Number of hours and y denotes the Cost of parking .

Here , x- independent variable

y- dependent variable

Now, rate of change = ( change in y) / ( change in x)

                                  = (14-10)/(3-1) = 2

Here , the rate of change = $ 2 per hour.

Again rate of change =  ( change in y) / ( change in x)

                                    = (16-14)/(5-3) = 1

Here , the rate of change = $ 1 per hour.

Since both rate of changes are not equal , it means the rate of change is not constant.

To learn more about the rate of change from the given link

https://brainly.com/question/25184007

#SPJ4

Please help me I just look at the photo I am so confused

Answers

Answer:

Grandma=P

Wagon=TH

Library= PL

Step-by-step explanation:

its pretty simple

CAN SOMEONE HELP WITH THIS QUESTION?✨

Answers

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

The equation of the form y = A[tex]2^x[/tex] + K  from the graph above is

y = (-5/3) . [tex]2^x[/tex] - (2/3)

What are coordinates in a graph?

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

y = [tex]2^x[/tex]

From the graph, we see that,

x = 0, y = -1

x = 1, y = -4

Now,

The equation in the form of y = A.[tex]2^x[/tex]  + K can be written as,

Taking (0, -1) we get,

-1 = A x 1 + K

-1 = A + K ______(1)

Now,

Taking (1, -4) we get,

-4 = A x 2 + K

-4 = 2A + K _____(2)

From (1) and (2) we get,

A = K - 1 putting in (2) we get,

-4 = 2(K - 1) + K

-4 = 2K - 2 + K

-4 = 3K - 2

3K = -4 + 2

3K = -2

K = -2/3

Now,

A = K - 1

A = -2/3 - 1

A = (-2 - 3) / 3

A = -5/3

Now,

The equation is y = (-5/3) . [tex]2^x[/tex] - (2/3)

Thus,

The equation of the form y = A[tex]2^x[/tex] + K  from the graph above is

y = (-5/3) . [tex]2^x[/tex] - (2/3)

Learn more about coordinates here:

https://brainly.com/question/13118993

#SPJ1

Graham Auto Parts has current sales of $42,700, EBIT of $9,700, net income of $6,600, interest expense of $1,360, and dividends paid of $1,925. Assume the net profit margin, debt-equity ratio, and dividend payout ratio are held constant. Sales are expected to increase by $8,000 next year. What is the projected change to retained earnings for next year?

Answers

Retained profits for the upcoming year: 5551.

Retained earnings: What is it?

The amount of profit a business keeps after paying all of its direct and indirect expenses, income taxes, and dividends to shareholders is known as retained profits. This is the percentage of the company's equity that may be utilized, for example, to fund the purchase of new machinery, research and development, and marketing.

RE=[tex]RE_{0}[/tex]-NI-D

Reserved Earnings

RE stands for initial retained income.

Net income is referred to as NI.

the dividend D

Graham Auto Parts now has $42,700 in sales, $9,700 in EBIT, $6,600 in net income, $1,360 in interest expenditure, and $1,925 in dividends paid. and a $8,000 rise in revenue is anticipated for the following year.

8000/42700 = 0.1873536 is the sales growth rate as a result. Its proportion is 18.73536%.

Now project net income = 6600 * 1.1873536

7837

dividends = 1925*1.1873536 = 2286

7837 - 2286 = 5551

retained earnings for next year 5551

To know more about retained earnings click the link:

brainly.com/question/28495052

#SPJ1

test the pair of events b and d for independence based on the following table. a b c total d 0.12 0.04 0.24 0.40 e 0.09 0.03 0.18 0.30 f 0.09 0.03 0.18 0.30 total 0.30 0.10 0.60 1.00 Are A and D independent or dependent and why? Select the correct answer below and fill in the answer boxes to complete your choice. A) A and D are dependent because P(AnD) equals P(A)P(D): P(AOD) = and P(AJP(D) = B) A and D are dependent because P(AnD) does not equal P(A)P(D): P(AnD) = and P(A)P(D) = C) A and D are independent because P(AnD) does not equal P(A)P(D): P(AnD) = and P(A)P(D) = D) A and D are independent because P(AOD) equals P(A)P(D): P(AnD) = and P(A)P(D) =

Answers

There must be no chance that d and e will happen. If the two occurrences cannot coexist, we can infer that they are not independent.

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

What is the probability formula?

P(A) = n(A)/n(S)

Where P(A) is the likelihood that an event "A" will occur and n(A) is the number of positive outcomes. The total number of occurrences in the sample space is denoted by n(S).

We must have a similar probability for both events in order for them to be independent. Because of the table, we may test for independence by knowing the likelihood that e and d will occur. When we are told that occurrences d and e are mutually exclusive, the entire table of values becomes somewhat of a red herring. The chance of d given e and the probability of d given d are both equal to zero if two events are mutually incompatible. There must be no chance that d and e will happen. If the two occurrences cannot coexist, we can infer that they are not independent. There is a chance for it.

to learn more about probability visit:

https://brainly.com/question/29381779

#SPJ4

For what value of X is the parallelogram a rhombus?

Answers

Answer:

x = 8

Step-by-step explanation:

a rhombus has all equal sides so this means that you must set them equal to each other

8x - 5 = 5x + 19

now subtract 5x to both sides

3x = 24

x = 8

that is your answer

A can of campbell's chicken Noodles Soup has a diameter of 30 millimeters and a height of 5 inches Find the volume of the can in cubic millimeters

Answers

The volume of the can of campbell's chicken Noodles Soup in cubic millimeters is 89,725.5 cubic millimeters

What is the volume of the can?

Volume of a cylinder = πr²h

Convert inch to millimeters:

1 inch = 25.4 millimeters5 inch = 127 millimeters

Height of the cylinder = 5 inches = 127 millimeters

Radius = diameter / 2

= 30 millimeters / 2

= 15 millimeters

Volume of a cylinder = πr²h

= 3.14 × 15² × 127

= 3.14 × 225 × 127

= 89,725.5 cubic millimeters

Consequently, the can of campbell's chicken Noodles Soup has a volume of 89,725.5 cubic millimeters

Read more on volume of a cylinder:

https://brainly.com/question/9554871

#SPJ1

Ver en español
The volume of this cylinder is 1,570 cubic inches. What is the radius?

Use ​ ≈ 3.14 and round your answer to the nearest hundredth.

Answers

Therefore ,the radius of the given cylinder is 10 inches

What is volume ?

A three-dimensional space's occupied volume is measured. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume definition and length definition are connected.

Here,

The volume of the cylinder is 1570 cubic inches

Volume of the cylinder = 1570 cubic inches

Volume of cylinder = π[tex]r^{2}[/tex]h

Where r is the radius of cylinder

h is the height of cylinder

So,

Volume of the cylinder = 1570 cubic inches

=> 1570 = π[tex]r^{2}[/tex]h

=> 1570 = 3.14*[tex]r^{2}[/tex]*5

=> 1570/3.14 = [tex]r^{2}[/tex]*5

=> 500=[tex]r^{2}[/tex]  *5

=> 500/5 =[tex]r^{2}[/tex]

=>100 =[tex]r^{2}[/tex]

=>r=10 inches

Therefore the radius of the given cylinder is 10 inches.

To know more about Volume , visit

https://brainly.com/question/23477586

#SPJ1

You want to buy a $181,000 home. You plan to pay 15% as a down payment, and take out a 30 year fixed loan for the rest.
Round all answers to the nearest cent as needed.

a) How much is the loan amount going to be?
$


b) What will your monthly payments be if the interest rate is 4.5%?
$


c) What will your monthly payments be if the interest rate is 5.5%?
$
Submit QuestionQuestion 4

Answers

Answer:

a)  $153,850

b)  $779.54

c)  $873.54

Step-by-step explanation:

Part a)

[tex]\begin{aligned}\textsf{Loan amount}&=\textsf{Cost of property}-\textsf{Down payment}\\&=181000-(181000 \times 0.15)\\&=181000-27150\\&=153850\end{aligned}[/tex]

Therefore, the loan amount is $153,850.

Part b)

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Monthly Payment Formula}\\\\$PMT=\dfrac{Pi\left(1+i\right)^n}{\left(1+i\right)^n-1}$\\\\where:\\\\ \phantom{ww}$\bullet$ $P =$ loan amount \\\phantom{ww}$\bullet$ $i =$ interest rate per month (in decimal form) \\\phantom{ww}$\bullet$ $n =$ term of the loan (in months) \\\end{minipage}}[/tex]

Given:

P = $153,850i = 0.045 per year = 0.045/12 per monthn = 30 years = 360 months

Substitute the given values into the  Monthly Payment formula and solve for PMT:

[tex]\implies \sf PMT=\dfrac{153850 \cdot \frac{0.045}{12}\left(1+\frac{0.045}{12}\right)^{360}}{\left(1+\frac{0.045}{12}\right)^{360}-1}[/tex]

[tex]\implies \sf PMT=\dfrac{153850 \cdot 0.00375\left(1.00375\right)^{360}}{\left(1.00375\right)^{360}-1}[/tex]

[tex]\implies \sf PMT=779.5353492[/tex]

Therefore, the monthly payments would be $779.54.

Part c)

Given:

P = $153,850i = 0.055 per year = 0.055/12 per monthn = 30 years = 360 months

Substitute the given values into the Monthly Payment formula and solve for PMT:

[tex]\implies \sf PMT=\dfrac{153850 \cdot \frac{0.055}{12}\left(1+\frac{0.055}{12}\right)^{360}}{\left(1+\frac{0.055}{12}\right)^{360}-1}[/tex]

[tex]\implies \sf PMT=873.5433786[/tex]

Therefore, the monthly payments would be $873.54.

At the local bunny-hop, Mr. Meyering jumps 20 inches on his first jump and then 10 inches with his second jump. If the distances form a geometric sequence, what is the total distance Mr. Meyering jumps if he completes infinitely many jumps?

Hint: Use S= a1/1- r and remember that |r| must be less than 1.

Answers

At the local bunny-hop, the sum of geometric sequences showing the jumps performed by Mr. Meyering is 40

How to find the sum of the jumping records of Mr. Meyering

The Sequences of the jump include

20, 10, ...

The common ratio, r is calculated from

first term, a * common ratio, r = second term

20 * r = 10

20r = 10

r = 10/20

r = 1/2

hence r < 1

The sum of gp to infinity for r < 1 is

Sum = a/ (1 - r)

Sum = 20 / (1 - 1/2)

Sum = 20 / 1/2

Sum = 20 * 2

Sum = 40

Learn more about geometric sequences at:

https://brainly.com/question/24643676

#SPJ1

10.
A
group of friends went to lunch. The bill,/before)
sales tax and tip, was $37.50. A sales tax of 8%
was added. The group then tipped 18% on the
amount after the sales tax was added.
What was
the amount, in dollars, of the sales tax?
What was the total amount the group paid,
including tax and tip?

Answers

Answer:

The total amount of the sales tax: $3.00

The total amount paid: $47.25

Step-by-step explanation:

Tip (In $): 6.75

Sales tax: 3.00

The total amount of food (before additional fees): 37. 50

So, to find the amount (in dollars) of the sales tax and tip, we must use this formula:

Amount = whole number * part percent/100

So, plugging in the numbers to the formula, it would look like this:

37.50 * 18 / 100
That is how to find the tip, you would do the same to find the sales tax. Then, when you get both amounts, you add them to 37.50 (the total before the fees) and get $47.25.

zero and negative exponents result from applying properties of exponents. for example, zero indicates that the same number of repeated factors of a non-zero base was found in both the numerator and denominator of an expression.

Answers

The question is incomplete , I am answering it with my general knowledge,

Zero exponent

Simplifying an expression with a 0 as the exponent does not need consideration of the base value.

Any non-zero number multiplied by 0 has the value 1.

x0 = 1, where x = 0 and x = 1, 2, 3, and so forth.

Negative exponent

For any positive integer m and non-zero number a,

a⁻ⁿ=1/a⁻ⁿ

This rule states that if the exponent is negative, it can be made positive by writing the same number in the denominator and writing one for the numerator.

When a number is positive, the exponent shows how many times it has been multiplied by itself.

On the other hand, the negative exponent indicates how many times we must divide the base number. The negative exponent, then, tells us how many times to multiply the reciprocal of the base, to put it another way.

To learn more about exponents

brainly.com/question/26659533

#SPJ4

For each system of equations, which operation will eliminate one of the variable? 2x+7y=32 and 2x+y=8

Answers

By subtraction, the variable x will eliminate and we will find out the value of y in the given system of equations.

What is the equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

The equation must be constrained with some constraints.

As per the given system of equations,

2x + 7y = 32 and 2x + y = 8

Subtract both equations from each other,

(2x + 7y) - (2x + y) = 32 - 8

2x + 7y - 2x - y = 24

2x - 2x + 7y - y = 24

6y = 24

y = 4

Hence "By subtraction, the variable x will eliminate and we will find out the value of y in the given system of equations".

For more about the equation,

brainly.com/question/10413253

#SPJ1

Which expression is equivalent to (3+4i)(2−3i)

Answers

The expression that is equivalent to the given value would be = 18-i . That is option C.

What is an equivalent expression?

An equivalent expression is defined as the type of expression that is similar to a given value when simplified.

The given expression = ( 3 + 4i) ( 2 - 3i)

Expand the given expression by removing the brackets as follows:

= =2(3+4i)−3i(3+4i)

=(6+8i)−(9i−12)

= (6+12)+i(8−9)

=18−i.

Learn more about multiplication equation here:

https://brainly.com/question/28552292

#SPJ1

Combine the radicals

Answers

The combination of radical 5√27 - 17√3 is -2 √3, so option D is correct.

What are radicals?

The opposite of an exponent, denoted by the symbol "√" and also known as the root, is a radical. The number before the symbol or radical is regarded as an index number or degree.

Given:

5√27 - 17√3

Simplify the value under roots,

5√(3 × 3 × 3) - 17√3

5 × 3 √3 - 17√3

√3 (15 - 17)

-2 √3

Therefore, the combination of radical 5√27 - 17√3 is -2 √3.

To know more about Radicals:

https://brainly.com/question/8020018

#SPJ1

A series of rigid motions maps ANEM onto ACDE. Based on this information, which of the following is a true statement? OA) There isn't enough information to make a statement about ANEM and ACDE B) ACDE is half the area of ANEM. C) All corresponding pairs of angles and sides of ANEM and ACDE are congruent. OD) The corresponding pairs of angles of ANEM and ACDE are congruent, but the corresponding sides aren't. Question 9 (5 points)​

Answers

All the corresponding pairs of angles and sides of ΔNEM and ΔCDE are congruent.

What is rigid motion?

A geometric figure is moved by rigid motions, but its size and shape remain unchanged. It generates visuals that make sense.

Rigid transformation comes in four different varieties.

1. translate 2. reflect. 3. Rotation 4. Gliding reflection

Here,

We have a series of rigid motion maps ΔNEM  onto ΔCDE.

We have to find the correct statement, so we concluded that all the corresponding pairs of angles and sides of ΔNEM and ΔCDE are congruent.

Hence, ΔNEM and ΔCDE are congruent.

To learn more about the rigid motion from the given link

https://brainly.com/question/25965367

#SPJ1

What is the probability that out of 125 babies born, at least 50 will be girls? Assume that boys and girls are equally probable, and round your answer to the nearest tenth of a percent.

Answers

When boys and girls are equally likely, the likelihood that at least 50 of 125 infants born will be females is 0.40.

What is probability?

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

total number of sample=125

number of girls=50

Probability that out of 125 babies born, at least 50 will be girls,

=50/125

=0.40

The probability that out of 125 babies born, at least 50 will be girls is 0.40 when boys and girls are equally probable.

To know more about probability,

https://brainly.com/question/11234923

#SPJ1

(4, -22) and (9,-57)

Answers

Y=-7x+6 is the answer for your problem

What is the domain of the graph? *
{-5,-4,-3,-1,0,2,4}
All real numbers
{-5,-4,-3,-1}
{-4,0,2,4}

Answers

The domain of the graph is {-5,-4,-3,-1}.

How can I determine a graph's domain?

Graphs can be used as another tool for determining the domain and range of functions. The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph represents the possible output values, or range.Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.

To know more about domain check the below link:

https://brainly.com/question/26098895

#SPJ4

what is 122222×2222221÷12​

Answers

Answer:

The result of the calculation is approximately 22535940185.17

Step-by-step explanation:

To solve this problem, we can use the order of operations. First, we perform the multiplication:

122222 * 2222221 = 2704312822242

Then, we perform the division:

2704312822242 / 12 = 22535940185.17

In how many ways can a committee of five Democrats and four
Republicans be formed from a group of twelve Democrats and twelve
Republicans?

Answers

Answer:

392040 ways

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

Find the combination of 4 of 12 and 5 of 12:

C(12, 4) × C(12, 5) = 12!/(4!8!) × 12!/(5!7!) = 495 × 792 = 392040

Suppose a triangle with the vertices (-1, 4), (-1, -2) and (2, -2) were dilated, with the center of dilation at the origin and with a scale factor of 2. Which of these would be a vertex of the dilated figure? Select the three correct answers. A. (-2, -4) B. (-2, 8) C. (-1, -4) D. (-1, 4) E.

Answers

New coordinates become (-2,8) (-2,-4) and (4,-4)

What do you mean by scale factor?

Magnification is defined as the scale ratio of a given original object and a new object that is a representation of it but of a different size (larger or smaller).

The new figure obtained is similar to the original figure

The expansion description should state how much the shape was expanded.

Suppose a triangle with the vertices (-1, 4), (-1, -2) and (2, -2) were dilated, with the center of dilation at the origin and with a scale factor of 2.

As we know, if (x,y) point dilated by scale factor a then new coordinates become (ax, ay)

So, if triangle having vertices (-1, 4), (-1, -2) and (2, -2) were dilated, with the center of dilation at the origin and with a scale factor of 2 then new coordinates become (-2,8) (-2,-4) and (4,-4)

Therefore, new coordinates become (-2,8) (-2,-4) and (4,-4)

To learn more about the scale factor from the given link.

https://brainly.com/question/25722260

#SPJ1

what is the value of p?

Answers

The value of p, using the exterior angle property is 53°.

What is the exterior angle property of a triangle?

The exterior angle property of a triangle states that the sum of the measures of the two non-adjacent angles of a triangle is equal to the measure of the exterior angle of the triangle. This means that if a triangle has three interior angles, the measure of any non-adjacent angle of the triangle must be equal to the measure of the exterior angle of the triangle. This property is useful in solving for unknown angles when the measures of two angles are known. For example, if two angles of a triangle measure 30° and 45°, then the measure of the third angle must be 105°, which is the same measure of the exterior angle.

The Exterior angle is = Sum of the Interior opposite angles.

By using the exterior angle property, we can get the following:

p+p-13°=p+40°

=>p=40°+13°

=>p=53°

The value of p is 53°

To learn more about the exterior angle property of the triangle, visit the link below:

https://brainly.com/question/14256482

#SPJ1

Elizaveta painted 35 m2 of wall space. This represents 20% of the total area.
What is the total area of the walls to be painted?

Answers

The total area of the space will be equal to 175 square meters.

What is the percentage?

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Elizaveta painted 35 square meters of wall space. This represents 20% of the total area.

The total area will be calculated as,

20% of area = 35 square meters

100% of the area = ( 35 x 100) / 20

100% of the area = 175 square meters

Therefore, the total area of the space will be equal to 175 square meters.

To know more about percentages follow

https://brainly.com/question/24304697

#SPJ1

Elizaveta painted 35 m2 of wall space. This represents 20% of the total area.

What is the total area of the walls to be painted?f ^(4) 2

Question 1
Match the sample description with the type of sample that was taken.
Names of all high school students are placed on slips of paper in a box and 10 are chosen.________

Fifteen students are randomly selected from each grade level.______

A high school is divided into classrooms and one classroom is selected._______

All high school students eating lunch at 11 am.______

All students in the school are listed in alphabetical order and every 50th name is chosen._______

Answers

The sampling types in this problem are given as follows:

Names of all high school students are placed on slips of paper in a box and 10 are chosen -> Random.Fifteen students are randomly selected from each grade level -> Stratified.A high school is divided into classrooms and one classroom is selected -> Cluster.All high school students eating lunch at 11 am -> Convenient.All students in the school are listed in alphabetical order and every 50th name is chosen -> Systematic.

What are the sampling types?

The sampling types used in this problem are defined as follows:

Random: all options are listed as options and then some are selected.Convenient: all the options are at some place such as the cafeteria then some are selected.Systematic: one of each n elements is chosen.Cluster: options are divided into groups, and then one group is selected.Stratified: options are divided into groups, and then a proportion of each group is chosen.

More can be learned about the types of sampling at https://brainly.com/question/9910540

#SPJ1

The length and width of a rectangle are consecutive integers. The perimeter of the
rectangle is 86 inches. Find the length and width of the rectangle.

Answers

The rectangle has the consecutive integers of 21 inches and 22 inches for its width and length respectively.

What are consecutive integers

Consecutive integers are numbers that follow in a particular order, usually just one after the for example, 1, 2, 3,... and so on.

Let the width of the rectangle be represented by x so that the length will be x + 1 as they consecutive integers

The perimeter of the rectangle will have the equation;

x + x + x + 1 + x + 1 = 86 inches

4x + 2 = 86 inches {collect like terms}

4x = (86 - 2) inches {subtract 2 from both sides of the equation}

4x = 84 inches

x = (84/4) inches {divide through by the coefficient of x}

x = 21 inches

Therefore, the rectangle has width of 21 inches and length of 21 + 1 = 22inches.

Learn more about rectangle here:https://brainly.com/question/19819849

#SPJ1

Find the average rate of change of g(x) = 3x² - 8x from x= 1 to x = 6.
Simplify your answer as much as possible.

Answers

The average rate of change of g(x) = 3x² - 8x from x= 1 to x = 6 is 13.

What is the average?

The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

Given:

g(x) = 3x² - 8x

The intervals, x = 1 to x = 6

Calculate the values of g(6) and g(1) as shown below,

g(6) = 3 × 6² - 8 × 6

g(6) = 3 × 36 - 48

g(6) = 108 - 48

g(6) = 60

And, g(1) = 3 × 1² - 8 × 1

g(1) = 3 - 8

g(1) = -5

Calculate the average rate of change as shown below,

The average rate of change = [g(6) - g(1)] / x₂ - x₁

The average rate of change = [60 - (-5)] / 6 - 1

The average rate of change = 65 / 5

The average rate of change = 13

To know more about average:

https://brainly.com/question/28123159

#SPJ1

10. A bag contains marbles: 5 purple, 6 blue, 8 yellow, 1 green. You will draw a
marble, keep it, and then draw another. What is the probability that you will
draw a purple and a green? SHOW YOUR WORK. Make sure to simplify your
answer if using a fraction. If using a percent, round to the nearest hundredth
after you change it to a percent.

Answers

Answer:

1st darw

[tex] p(purple)= \frac{5}{20} \\ = \frac{1}{4} [/tex]

[tex]p(green) = \frac{1}{20} [/tex]

2nd draw

[tex]p(purple) = \frac{4}{18} \\ = \frac{2}{9} [/tex]

[tex]p(green) = 0[/tex]

Question

What is the net signed area between f(x) = 2x-6 and the x-axis over the interval [-8,5]? Do not include any units in

your answer

Provide your answer below:

Answers

The net signed area of f(x) = 2x - 6 on the interval [-8, 5] is - 21 units.

What is the net signed area?

The definite integral can be used to calculate the net signed area, which is the area above the x-axis less the area below the x-axis.

Given, f(x) = 2x - 6 and the x-axis over the interval [-8 , 5].

∴ The net signed area is,[tex]\[ \int_{-8}^{5} 2x -6 \,dx \][/tex].

[tex]= \[ \int_{-8}^{5} 2x \,dx \ - \ \int_{-8}^{5} 6 \,dx \][/tex].

= (5)² - (-8)² - {(5×6) - (-8×6)}.

= 25 - 64 - 30 + 48.

= - 21 units.

learn more about net signed area here :

https://brainly.com/question/22867526

#SPJ1

Every day a school bus driver passes the same traffic light twice, once before school and once after. Each time he passes the light, he records If it is red, green, or yellow.
Here is a summary of the data he got after 200 days.

Traffic light before school Traffic light after school Number of day
red red 25
red green 21
red yellow 17
green red 16
green green 31
green yellow 27
yellow red 22
yellow green 28
yellow yellow 13

Suppose the driver will continue recording the colors for 150 more days.
In how many of these 150 days will the light be red exactly once? Use the data to make a prediction.

Answers

Answer:

Step-by-step explanation: the amswer is B trust me

Other Questions
yury is opening a financial consulting service for high-income retirees in his area. this target market is used to paying for quality and associates high quality with high prices. in this instance, yury should probably not use a penetration pricing strategy because How has programming changed in the past 50 years? until the early there were only neglible amounts of free oxygen in the atmosphere.A: MesozicB CenozoicC ProterozoicD Precambian When a members deviant behavior leads to a positive change in the group norm, it suggests that some deviant behavior can be functional for groups.a. trueb. false A side of the triangle below has been extended to form an exterior angle of 156. Find the value of x. Please select the word from the list that best fits the definition number of people living in an area at a particular time. Please post an answer to the following question: You are a delegate at the Philadelphia Convention in 1787. Do you feel the United States should revise the Articles of Confederation or start over with a new government? Justify your response with two historical facts. Your response should be 3-5 sentences. (BIG POINTS) Question 8What is the value of having AWS Cloud services accessible through an Application Programming Interface (API)? A. Cloud resources can be managed programmaticallyB. AWS infrastructure use will always be cost-optimizedC. All application testing is managed by AWSD. Customer-owned, on-premises infrastructure becomes programmable if he don't go out more, he will____unsociable*turn into*grow up PS bisects QPR . Complete the proof that PSR PSQ . What factors led cities in the u. S. To boom in the late 1800s and what effects did the boom have?. A dice game involves rolling 2 dice. If you roll a 2, 3, 4, 10, 11, or a 12 you win $5. If you roll a 5, 6, 7, 8, or 9 you lose $5. Find the expected value you win (or lose) per game. A roll of paper that is 3 feet wide can be cut to any length. a. If we cut a length of 2.5 feet, what is the perimeter of the paper? b. Complete the table with the perimeter for each given side length. Then, write a rule for a function, P, that gives the perimeter of the paper in feet when the side length in feet is L, use a function notation A cable running from the top of a telephone pole creates a horizontal pull of 889 Newtons (N). A support cable running to the ground is inclined 71 from the horizontal.Find the tension in the support cable. Give answer to the nearest whole number. the ledger of tamarisk company at teh end of the current year shows accounts receivable 77000 credit sales 810000 and sales returns and allowances 3700 prepare journal entries for each saperate scenario below process costing is typically used for businesses that make large quantities of identical items. T/F is a parallel to b? Explain using angels and measurements. Angel measrment should be part of your explanation. true or false? choosing to not use the marketing hub blog tool to host your blog will make your marketing hub campaign reporting less comprehensive. Question 1-7Similar triangles MRC and WYC are shown where MR = 14, CR=28, WY = 6, and MW = 17.88.What is the length of YC? Several processes are involved in generating rainfall or snow. First, water is ______ from oceans and moves into the atmosphere. Next, the moisture condenses into clouds which cool and release rain or snow as ______.