Which of the following is the average rate of change over the interval [-5, 10] for the function g(x) = log2 (x+6)-3

A.4/5
B.5/4
C.4/15
D.15/4

Answers

Answer 1

It's answer is option(C) i.e, 4/15

What is Average rate of change?

The average rate of function f  over the interval a≤x≤b is given by ,

(f(b) - f(a)) / (b - a)

It is the average amount by which the function changed per unit throughout that time period.

In this question the equation is given,

g(x) = log2 (x+6)-3

Solve this eq. by putting the values [-5, 10],

let, interval [-5, 10] = [a, b]

Then solve for g(a) and g(b), we know g(a) = g(-5),

g(-5) = log₂(-5+6) - 3

       = log₂1 - 3

       = 0 - 3

g(-5) = -3

Now, for g(b) = g(10)

g(10) = log₂(10+ 6) - 3

        = log₂16 - 3

        = 4 - 3

g(10) = 1

Now put these values in average rate formula,

Average rate = (g(b) - g(a)) / (b - a)

                      = (1 - (-3)) / (10 - (-5))

                      = (1 + 3) / (10 + 5)

                      = 4 / 15

Therefore, the average rate is 4/15 i.e, option(C)

To read more about Average rate.

https://brainly.com/question/24313700

#SPJ13

Answer 2

Answer: C. 4/15. I took the test and got it right.

Step-by-step explanation:


Related Questions

Please explain how you got the question because i have no idea how to plug in the numbers

Answers

Given sequence:

[tex]\frac{1}{2},\text{ }1,\text{ }\frac{3}{2},2[/tex]

To find the 109th term, we need to first determine whether the sequence follows an arithmetic progression or a geometric progression.

Check

The sequence is arithmetic if the successive terms of the sequence are formed by adding or subtracting a value.

The sequence is geometric if the successive terms of the sequence are formed by multiplying or dividing by a value.

We have that:

first term = 1/2

second term = 1

third term = 3/2

Taking the difference of the second term from the first term:

[tex]\begin{gathered} =\text{ 1-}\frac{1}{2} \\ \text{ = }\frac{1}{2} \end{gathered}[/tex]

Taking the difference of the third term from the second term:

[tex]undefined[/tex]

what is the correct algebraic reprentation for a translation 5 units right and 4 units down?

Answers

We want to write the correct algebraic representation for a translation 5 units right and 4 units down.

Which means 5 units along the positive x axis and 4 units along the negative y axis.

So, we have;

[tex](x,y)\rightarrow(x+5,y-4)[/tex]

Therefore, the correct algebraic

Complete the order pairs below so they satisfy the equation Y=-3x+2Complete the order pairs (0,__) (7,__) (__,17)

Help!!

Answers

The ordered pairs which satisfy the equation are  (0,2) , (7,19) (-5,17) .

Finding the values of the variables that result in equality is the first step in solving a variable equation.

The values of the unknown variables that fulfil the equality are the equation's solutions, also known as the variables for which the equation must be solved. The two forms of equations are identity equations and conditional equations. All feasible values of the variables share the same identity. Only specific instances where the values of the variables coincide can result in the truth of a conditional equation. Two phrases are combined into one by using the equals sign ("="). The "left hand side" and "right hand side" of the equation refer to the expressions on each side of the equals sign. It's typical.

At x = 0 the value of y from the equation is :

y = 2

At x = 7 , y =-19

at y=17 , x= -5

Therefore the ordered pairs are :(0,2) , (7,19) (-5,17) .

To learn more about equation visit:

https://brainly.com/question/10413253

#SPJ1

this is geometry please help

Answers

Answer: 1st one is sometimes

2nd one is always

3rd one I think is always

4th one is always

Step-by-step explanation:

1st one the sum must equal 90 so either one could be greater

2nd one vertical angles always equal each other

3rd one if B is the midpoint it would be AB BC

4th one it will always equal 180

The average speed, s, in miles per hour that a student walks the 3 miles from home to school varies inversely as the number of hours, h that the student walks.The formula is given by s = 3/hAs the number of hours it takes the student to walk from home to school increases, what happens to the speed?

Answers

[tex]\begin{gathered} \text{The given formula is} \\ \\ s\text{ =}\frac{3}{h} \\ \text{Because there is an inverse relationship betwe}en\text{ the distance walked and the time} \end{gathered}[/tex]

If the number of hours it takes the student to walk home increases, then the speed decreases

Let us see an example

if h = 1

and we increase h to be = 3

[tex]\begin{gathered} \text{when h =1} \\ \text{The sp}eed,\text{ s =}\frac{3}{1}=3milesperhour \end{gathered}[/tex][tex]\begin{gathered} \text{When h increases to 3} \\ s\text{ =}\frac{3}{3}=1mileper\text{ hour} \end{gathered}[/tex]

3miles/hour is more than 1 mile/hour so hence the speed will decrease when the time increases

The answer is option A, the speed decreases

In \triangle NOP,△NOP, \overline{PN}\cong \overline{OP} PN ≅ OP and \text{m}\angle P = 50^{\circ}.m∠P=50 ∘ . Find \text{m}\angle O.m∠O.

Answers

The value of the measure of ∠O will be 65°

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In ΔNOP;

PN ≅ OP

So, ∠O = ∠N

And, Measure of ∠P = 50°

Now,

In the ΔNOP;

The sum of all the three angles are 180°.

The value of the measure of ∠O = x

We get;

∠O + ∠N + ∠P = 180°

Substitute ∠P = 50° and ∠O = ∠N = x we get;

x + x + 50 = 180

2x + 50 = 180

2x = 180 - 50

2x = 130

x = 65

Thus, The value of the measure of ∠O will be 65°.

Learn more about the triangle visit:

https://brainly.com/question/1058720

#SPJ1

3. Find the volume of the
cylinder. Round to the nearest
tenth. Diameter = 15. Hight = 11

Answers

Answer:

518.4

Step-by-step explanation:

the volume of a cylinder is area of base x height

the radius is half of the diameter = 7.5

area of base = 2πr = 2xπx7.5 = 47.124

volume = 47.124 x 11 = 518.4

What are the solutions to the equation 3|x + 5| - 2 = 13 ?

Answers

To solve the absolute value equation;

[tex]3|x+5|-2=13[/tex]

Note that the left side of the equation is an absolute value. The first step is to remove the absolute value sign, and then the next step is to solve while using the positive and negative value of the number on the right side of the equation.

This is shown below;

[tex]\begin{gathered} 3|x+5|-2=13 \\ \text{remove the absolute value sign;} \\ We\text{ now have;} \\ 3(x+5)-2=13 \\ 3(x+5)=13+2 \\ 3x+15=15 \\ \text{Subtract 15 from both sides;} \\ 3x+15-15=15-15 \\ 3x=0 \\ \text{Divide both sides by 3} \\ \frac{3x}{3}=\frac{0}{3} \\ x=0 \end{gathered}[/tex]

Let us now solve for the equation when the right side is -13.

[tex]\begin{gathered} 3(x+5)-2=-13 \\ 3(x+5)=-13+2 \\ 3x+15=-11 \\ \text{Subtract 15 from both sides;} \\ 3x+15-15=-11-15 \\ 3x=-26 \\ \text{Divide both sides by 3;} \\ \frac{3x}{3}=-\frac{26}{3} \end{gathered}[/tex]

ANSWER:

[tex]\begin{gathered} x=0, \\ OR \\ x=-\frac{26}{3} \end{gathered}[/tex]

The last option is the correct answer

.shvsguvsguvsguvsguss

Answers

Answer:

what is that ? What do you mean

Answer:

m

Step-by-step explanation:

help me pleaseeeeeeeeeeeeeeeeeeeeeee




thank you

Answers

Answer:

Domain: A, [1, 7]

Range: [-4, 2]

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

Solve for the unknown: K/2+3=5

Answers

Solve for K:

[tex]\frac{K}{2}+3=5[/tex]

Subtracting 3 to each member of the equation:

[tex]\frac{K}{2}+3-3=5-3[/tex]

Operating:

[tex]\frac{K}{2}=2[/tex]

Now we multiply by 2:

[tex]2\cdot\frac{K}{2}=2\cdot2[/tex]

Simplifying and operating:

[tex]K=4[/tex]

Answer: K = 4

Hii i forgot how to multiply fractions and I'm a bit rusty since the pandemic

Answers

Solution

The area of a rectangle is given as length(l) x width(w)

length = 2 1/4

width = 1 1/2

Hence substituting these values into the formula

[tex]\begin{gathered} \text{Area = 2}\frac{1}{4}\times1\frac{1}{2} \\ \text{Area = }\frac{(4\times2)+1}{4}\times\frac{(2\times1)+1}{2} \\ \text{Area = }\frac{9}{4}\times\frac{3}{2} \\ \text{Area = }\frac{27}{8}in^2 \\ \text{Area = 3}\frac{3}{8}in^2 \end{gathered}[/tex]

pls help: find the probability of rolling a die five times and getting at least one three

Answers

The probability of getting at least one 3 when a die is rolled 5 times is 0.59 .

What is probability?

The area of mathematics known as probability deals with numerical estimates of how likely an event is to occur.

A die is rolled 5 times.

The sample space is [tex]6^{5}=7776[/tex].

Probability of getting no 5 is [tex]\frac{5}{6}[/tex].

Probability of getting at least one 5 = 1- probability of getting no 5

                                                                 [tex]1-(\frac{5}{6}) ^{5} \\\\\frac{7776-3125}{7776}\\ \\\frac{4651}{7776}\\ \\0.59[/tex]

Hence Probability of getting at least one 5 is 0.59.

To learn more about the probability from the given link

https://brainly.com/question/25839839

#SPJ13

An English teacher at a high school can teach six classes. There are 43 students enrolled in English I, 51 in English II, and 53 in English III. Use the Webster method to determine the apportionment of students to the courses to determine the number of sections needed per course.

Answers

Given:

Heigh school teach = 6 classes

Enrolled student

English 1 = 43

English 2 =51

English 3 =53

Apportionment student is:

[tex]\begin{gathered} =\frac{\text{English}1+\text{English}2+\text{English}3}{6} \\ =\frac{43+51+53}{6} \\ =\frac{147}{6} \\ =24.5 \end{gathered}[/tex]

I'm doing topic about classifying numbers can you please help me with these problems?

Answers

According to this question we have to classify what type of number is 10.

The number 10 should be considered as a natural number, real number, rational number, integer number, whole number because of the following reason:

It is a rational and a integer number because because it can be expressed as the quotient of two integers 10/1

Also, it is a natural number because natural numbers are numbers which are used for counting and ordering, and 10 is an example of them.

Also, it is a real number. Real numbers are any number on the real line. So, 10 it is on the real line so, is considered a real number.

Also it is a whole number because it is a natural number.

Solve the following equation for all values of x:2 +3−28=9+27

Answers

[tex]x^2+3x-28=9x+27\Rightarrow x^2-6x-55=0\Rightarrow(x-11)(x+5)=0^{}[/tex][tex]x=11\text{ and x=-5}[/tex]

there are 4 swimmers in a race. there will be 1st, 2nd and 3rd place prize awarded. In how many different ways can the prizes be awarded?

Answers

From the problem we will have that:

[tex]\begin{gathered} _4P_3=\frac{4!}{(4-3)!}\Rightarrow_4P_3=\frac{24}{(1)} \\ \\ \Rightarrow_4P_3=24 \end{gathered}[/tex]

There will be 24 possible ways to award the 3 prizes between 4 people.

A particular fruit's weights are normally distributed, with a mean of 406 grams and a standard deviation of 27 grams.The heaviest 14% of fruits weigh more than how many grams?Give your answer to the nearest gram.

Answers

Given

mean of 406 grams and a standard deviation of 27 grams.

Find

The heaviest 14% of fruits weigh more than how many grams?

Explanation

given

mean = 406 gms

standard deviation = 27 gms

using standard normal table ,

[tex]\begin{gathered} P(Z>z)=14\% \\ 1-P(Zso , [tex]\begin{gathered} x=z\times\sigma+\mu \\ x=1.08\times27+406 \\ x=435.16 \end{gathered}[/tex]

Final Answer

Therefore , The heaviest 14% of fruits weigh more than 435.16 gms

Solve the formula v = pi r2 h solve for r

Answers

[tex]v=\pi r^2h[/tex]Explanation

We can do the following steps to solve the given expression for r.

Step 1: We divide by πh from both sides.

[tex]\begin{gathered} v=\pi r^2h \\ \frac{v}{\pi h}=\frac{\pi r^2h}{\pi h} \\ \frac{v}{\pi h}=r^2 \end{gathered}[/tex]

Step 2: We apply square root to both sides of the equation.

[tex]\begin{gathered} \sqrt{\frac{v}{\pi h}}=\sqrt{r^2} \\ \sqrt{\frac{v}{\pi h}}=r \end{gathered}[/tex]Answer[tex]r=\sqrt{\frac{v}{\pi h}}[/tex]

Which best describes the relationship between the lines with equations 4x−8y=9 and 8x−7y=9?A. parallelB. same lineC. neither perpendicular nor parallelD. perpendicular

Answers

The given equations are,

4x-8y=9 and 8x-7y=9

The slopes can be determined as,

[tex]\begin{gathered} m_1=\frac{-a}{b}=\frac{-(4)}{-8}=\frac{1}{2} \\ m_2=\frac{-a}{b}=\frac{-(8)}{-7}=\frac{8}{7} \end{gathered}[/tex]

As, the slope are not equal nor their product is -1.

Thus, they are neither parallel nor perpendicular.

Thus, option (C) is correct.

Express x^2-3x+1 in the form (x-p)^2+q

Answers

By algebra properties, the equation x² - 3 · x + 1 in the form (x - p)² + q is equal to (x - 3 / 2)² - 5 / 4.

How to simplify a quadratic equation by completing the square

Completing the square is a method used to simplify quadratic equations of the form a · x² + b · x + c that are not perfect squares, where a part of it becomes into perfect square and is simplified. This can be found by using algebraic methods. The complete procedure is shown below:

x² - 3 · x + 1

(x² - 3 · x + 1) + 0

(x² - 3 · x + 1) + [9 / 4 + (- 9 / 4)]

(x² - 3 · x + 9 / 4) + [1 + (- 9 / 4)]

(x - 3 / 2)² - 5 / 4

The quadratic equation is equivalent to (x - 3 / 2)² - 5 / 4.

To learn more on quadratic equations: https://brainly.com/question/1863222

#SPJ1

Liam is comparing the costs of phone plans at two different companies to determine which plan to buy. Company A charges $50 each month plus an additional $10 per gigabyte of data used. Company B charges $60 each month plus an additional $8 per gigabyte of data used. The following equation represents the cost of the phone plans for the two companies when they are equal, where g represents the amount of gigabytes of data used. 50+10g+60+8g Complete each of the statements below with the correct answer choice.

The cost of the phone plans will be the same for company A and company B when
5?10?15?18? gigabytes of data are used.

If company A changes the cost of data per gigabyte to
20?24?50?8? , then the two phone plans will never have the same cost.

If company B's initial monthly cost Increases by $10?Decreases by $10
and the cost of data per gigabyte Remains the same? Decreases by $2? Increases by $2, then the cost of the two phone plans will always be the same.

Answers

1. Using equations, the cost of the phone plans will be the same for company A and company B when A. 5 gigabytes of data are used.

2. If company A changes the cost of data per gigabyte to D. 8, then the two phone plans will never have the same cost.

3. If company B's initial monthly cost B. Decreases by $10 and the cost of data per gigabyte B. Decreases by $2, then the cost of the two phone plans will always be the same.

What is an equation?

An equation is a mathematical statement that shows that two mathematical expressions are equal or equivalent in value.

Equations are represented using the equation sign (=) to establish the equality of two numerical values or mathematical expressions.

                                           Company A     Company B

Fixed charge                             $50                 $60

Variable charge per gigabyte  $10                    $8

The equation to represent when the two plans are equal:

50 + 10g = 60 + 8g

10g - 8g = 60 - 50

2g = 10

g = 5

Learn more about equations at https://brainly.com/question/2972832

#SPJ1

Kai took five tests this semester. His scores are listed below. 92, 88, 90, 96, 84What is the mean absolute deviation of Kai's test scores?4.03.22.01.6

Answers

the mean can be calculate with this equation:

[tex]m=\frac{x_1+x_2+\cdots}{n}[/tex]

So in our problem will be:

[tex]\begin{gathered} m=\frac{92+88+90+96+84}{5} \\ m=90 \end{gathered}[/tex]

What are the solutions to the equation 6x2 - x - 40 = 0? A. x = -8/3, x = -5/2B. x = -8/3, x = 5/2 С. x = -2, x = 3 D. x = -6, x = 2

Answers

[tex]\begin{gathered} \text{ Given that } \\ 6x^2-x-40=0 \end{gathered}[/tex][tex]\begin{gathered} \text{ Therefore} \\ 6x^2-16x+15x-40=0 \\ \text{Hence,} \\ 2x(3x-8)+5(3x-8)=0 \\ \text{Thus} \\ (2x+5)(3x-8)=0 \\ \text{ therefore} \\ 2x+5=0;3x-8=0 \\ \text{this implies that} \\ x=\frac{8}{3};x=-\frac{5}{2} \end{gathered}[/tex]

Answer please and thanks

Answers

A percentage of 100 · [p' - exp(- 4000 · k)] / p' of carbon-14 has decayed and lost in last 4000 years.

How to determine the remaining percentage of carbon-14 in ancient pollen

In this question we have the case of simple decay of a radioactive isotope (carbon-14) in time, which is represented by the following exponential formula:

p(t) = p' · exp(- k · t)

Where:

p' - Initial amount of pollen.p(t) - Current amount of pollen.k - Decay constant.t - Time, in years.

If we know that t = 4000 years, then percentage of lost carbon-14 is:

p = 100 - 100 · p(t) / p'

p = 100 - [100 · exp(- 4000 · k)] / p'

p = 100 · {1 - [exp(- 4000 · k)] / p'}

p = 100 · [p' - exp(- 4000 · k)] / p'

An amount of 100 · [p' - exp(- 4000 · k)] / p' per cent has been decayed and lost.

To learn more on isotope decay: https://brainly.com/question/21501209

#SPJ1

McMichael Inc. collects 25% of its sales on account in the month of the sale and 75% in the month following the sale. If sales on account are budgeted to be $523,000 fo September and $465,000 for October, what are the budgeted cash receipts from sales on account for October?

Answers

The budgeted cash receipts from sales on account for October is $479500.

Define sale.

A sale is a deal in which two or more parties exchange goods or services for cash or other assets. A sale in the financial markets is an arrangement involving the cost of a security and its delivery for agreed-upon payment between a buyer and a seller. Sales in general business operations refer to any exchanges of money or value for the right to possess a good or get a service. Sales, in the context of accounting, refers to the income generated by a corporation via the selling of goods or services (net sales).

Given Data

McMichael Inc. collects 25% of its sales on account in the month of the sale and 75% in the month.

If sales on account are budgeted to be $523,000 to September and $465,000 for October.

We can respond as follows based on the data provided in the question:-

25% of sales from October plus 75% of sales from September equal the budgeted cash receipts from sales.

Sales revenue budgeted for in cash is

($523,000 (25%)) + ($465,000  (75%))

130750 + 348750

479500

The budgeted cash receipts from sales on account for October is $479500.

To learn more about sales, visit:

https://brainly.com/question/15375944

#SPJ13

Use f(x) = 4x – 2 and g(x) = 5 – x^2 to evaluate the expression.(a)(f o g)(-2)(b)(g o f)(-2)

Answers

Given the functions:

[tex]\begin{gathered} f(x)=4x-2 \\ g(x)=5-x^2 \end{gathered}[/tex]

We will find (f o g)(-2)

So, first, we will find the function (f o g)(x) as follows:

[tex]\begin{gathered} \mleft(f\circ g\mright)(x)=f\lbrack g(x)\rbrack=4(5-x^2)-2 \\ (f\circ g)(x)=20-4x^2-2 \\ (f\circ g)(x)=18-4x^2 \end{gathered}[/tex]

Now, substitute with x = -2

so,

[tex](f\circ g)(-2)=18-4\cdot(-2)^2=18-4\cdot4=18-16=2[/tex]

so, the answer to the part (a) (f o g)(-2) = 2

b) (g o f)(-2)

We will find (g o f)(x) as follows:

[tex](g\circ f)(x)=g\lbrack f(x)\rbrack=5-(4x-2)^2[/tex]

Substitute with x = -2

So,

[tex]\begin{gathered} (g\circ f)(-2)=5-(4\cdot-2-2)^2 \\ =5-(-8-2)^2 \\ =5-(-10)^2 \\ =5-100 \\ =-95 \end{gathered}[/tex]

So, the answer to the part (b): (g o f)(-2) = -95

A train can travel 225 kilometers in 3 hours. At this rate, how many kilometers can the train travel in 7 hours?

Answers

Answer: 1575

Step-by-step explanation: You can multiply 225x7 and you will get 1,575

The radius of a circular pond is increasing at a constant rate, which can be modeled by the function r(t) = 5t, where tis time in months. Thearea of the pond is modeled by the function A(1) = 1+?. The area of the pond with respect to time can be modeled by the compositionA(r(t).Which function represents the area with respect to time?OAA(r(t) = 5x52OBA(r(t) = 25m€2O cA(r(E) = 10x92O D.A(-(t)) = 51t?

Answers

Explanation

We are asked to find the function that represents the area with respect to time A(r(t))

Given that

[tex]\begin{gathered} r(t)=5t \\ \\ A(r)=\pi r^2 \end{gathered}[/tex]

what we will simply do will be to put in the value of r(t) into the equation of A(r)

Thus

[tex]\begin{gathered} A(r)=[\pi\times(5t)^2] \\ \\ A(r)=\pi\times25t^2 \\ \\ A(r)=25\pi t^2 \end{gathered}[/tex]

Thus, the answer is option B

First six non zero multiples of 21

Answers

Answer:

21, 42, 63, 84, 105, 126

Step-by-step explanation:

21, 42 ,63 ,84,105,126
Other Questions
Calculate the simple interest earned. Round to the nearest cent.P = $4200, r = 7%, t = 1 year Tickets to a baseball game cost $3 for a childs ticket and $5 for an adult ticket. At the last game, $521 was collected when 139 people attended the game. Which value could replace x in the table so that a single-variable equation can be written and solved to determine the number of childs tickets, c, sold? ABC is congruent to DEF. what is the length of AB and what is angle EDF? What is 157.8- (3^2+ 6) times 3Please show your work Need help with question 2 related to literal C of question 1 Clytie looked at her social studies test. She received a grade of 85%. If there were 33 questions on the test, how many did Clytie get right? ANSWER PLEASE. FIRST ANSWER WILL BE BRAILIEST!!! DUE TODAY PLEASE HELP!!! WORTH 25 points!!! Consider photographing a football stadium fully lit with stadium lights compared toa football stadium lit by nothing but candlelight. What is the main differencebetween these two lighting situations?(1 point)O the light intensityO the light qualityO the shadow of the lightO the position of the light any assumption we have made about a person, an issue, or a topic before we have heard all the facts is a(n) . Were colonial methods of protest against these British laws effective? Hans is a software salesman. His base salary is $1700, and he makes an additional $70 for every copy of History is Fun he sells. Let P represent his total pay (in dollars), and let N represent the number of copies of History is Fun he sells. Write an equation relating P to N. Then use this equation to find his total pay if he sells 26 coples of History Is Fun. what was mendeleevs predictions for germanium What is 7 to the power of two? What is the gcf of 12 and 86? the shorter leg of a right triangle is 7 m shorter than the longer leg. the hypotenuse is 7 m longer than the longer leg. find the side lengths of the triangle. length of the shorter leg:length of the longer leg:length of the hypotenuse: Hello! I need help Why do you think Eisenhower made his Address on Little Rock speech? Below are the times (in days) it takes for a sample of 5 customers from Tony's computer store to pay their invoices. Choose one of the prompts listed below. Write a five-sentence paragraph usingchronological order and including a topic sentence to explain the steps that you would take to complete one of the following tasks,a, Preparing for a testb. Preparing to host a party or an eventC. Getting ready for workd. Cleaning your room of your homee, Building a snowman, sandcastle, or sculpturef, Creating a budget jalisa feels inferior to the people around her, but she tries to act like she is powerful and in control. adler would say that jalisa is . group of answer choices which two items are part of the implementation phase of the strategic marketing process?