The average value of the function y = x² – 1 on [0, 12] is

Answers

Answer 1

Answer:

47.

Step-by-step explanation:

1) the rule:

[tex]f_{avr}=\frac{1}{b-a} \int\limits^b_a {f(x)} \, dx ,[/tex]

where a;b are 0 and 12, f(x)=x²-1.

2) according to the rule above:

[tex]f_{avr}=\frac{1}{12-0} \int\limits^{12}_0 {(x^2-1)} \, dx=\frac{1}{12}(\frac{x^3}{3}-x)|^{12}_0=48-1=47.[/tex]


Related Questions

Help Me with this please

Answers

Answer:

B) Δ+5

Step-by-step explanation:

Means that Austin has $5 more than Mark

Hope this helps

A sector of a circle has a central angle of 45 ∘ . Find the area of the sector if the radius of the circle is 18 cm. cm2

Answers

Answer:

1,090

Step-by-step explanation:

3. Suppose a retail business sale its commodities at a margin of 25% on all items purchased and sold. Moreover the company uses 5% commission as selling expense and Birr 12,000 as a Fixed Cost, then Find the Breakeven revenue for the retail business after developing the equation ​

Answers

The Breakeven revenue for the retail business is Birr 12,500

What is breakeven?

Breakeven is the point at which the revenue is equals to the cost, hence the profit is zero.

Revenue = Cost

Let x represent the number of items sold, hence:

Revenue = (100% + 25%) of x = 1.25x

Cost = 5% of x + 12000 = 0.05x + 12000

At breakeven:

1.25x = 0.05x + 12000

x = 10000

Hence:

Revenue = 1.25(10000) = Birr 12,500

The Breakeven revenue for the retail business is Birr 12,500

Find out more on breakeven at: https://brainly.com/question/9212451

The following bond was quoted in The Wall Street Journal:
Bonds
NJ 4.125% 35
Current yield Volume
2.3%
5
Close
109.875%
Net change
+1.125%
Four bonds were purchased yesterday, and 4 bonds were purchased today. How much more did the 4 bonds cost today? (Do not
round intermediate calculations. Round your answer to the nearest cent.)
Increased cost

Answers

Answer:

$100 answers your question

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER

Answers

Ok I see it

Angle MKP is 95° because
120-25= 95
And it’s obtuse because 95 is greater than 90

Hope this helps :)

State six ordered pairs for this function
f(x)=.5x+3

Answers

(0,3) - The y-int, after you can just add 5 to the y-coord for each added 1 to the x-coord.

(1,8)

(2,13)

(3,18)

(4,23)

(5,28)

The equation x2 + 4y2 = 36 represents which conic section?

ellipse

circle

hyperbola

parabola

Answers

Answer: The answer is ellipse

Jacob wants to determine the principal amount still owed on his mortgage loan. He knows that the interest portion of his last monthly payment was $391.42. If he is paying interest at the rate of 11½%, what was the outstanding balance of the loan before that last payment was made?

Answers

If the interest rate is 11½%. The outstanding balance of the loan before that last payment was made is:$40,843.83.

Loan Oustanding balance

First step is to find the annual interest

Annual interest= $391.42 x 12

Annual interest= $4,697.04

Second step is to calculate the outstanding balance

Outstanding balance=Annual interest/Interest rate

Oustanding balance= $4,697.04/ 11½%,

Outstanding balance =$40,843.826

Outsatnding balance= $40,843.83 (Approximately)

Therefore the outstanding balance of the loan before that last payment was made is:$40,843.83.

Learn more about loan outstanding balance here:https://brainly.com/question/2279877

Write the standard equation of the circle with the center ​(-14​,-5​) that passes through the point ​(​-7,​5).

Answers

equation: (x + 14)² + (y + 5)² = 149

Given:

centre :  ​(-14​,-5​)point ​(​-7,​5)

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

Formula's:

(x-h)² + (y-k)² = r²centre : (h, k)radius : rdistance between points : [tex]\sf \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]

Find the radius:

[tex]\rightarrow \sf \sqrt{(-7-(-14))^2 + (5-(-5))^2}[/tex]

[tex]\sf \rightarrow \sqrt{\left(-7+14\right)^2+\left(5+5\right)^2}[/tex]

[tex]\sf \rightarrow \sqrt{149}[/tex]

Equation of circle:

(x-h)² + (y-k)² = r²(x-(-14))² + (y-(-5))² = (√149)²(x + 14)² + (y + 5)² = 149

Graph for clarification:

Answer:

[tex]\sf (x+14)^2+(y+5)^2=149[/tex]

Step-by-step explanation:

Standard equation of a circle:  [tex]\sf (x-a)^2+(y-b)^2=r^2[/tex]

(where (a, b) is the center and r is the radius of the circle)

Substitute the given center (-14, -5) into the equation:

[tex]\sf \implies (x-(-14))^2+(y-(-5))^2=r^2[/tex]

[tex]\sf \implies (x+14)^2+(y+5)^2=r^2[/tex]

Now substitute the point (-7, 5) into the equation to find r²:

[tex]\sf \implies ((-7)+14)^2+(5+5)^2=r^2[/tex]

[tex]\sf \implies (7)^2+(10)^2=r^2[/tex]

[tex]\sf \implies 149=r^2[/tex]

Final equation:

[tex]\sf (x+14)^2+(y+5)^2=149[/tex]

A researcher is studying the growth of bacteria. He starts with 260 of the bacteria. It grows continuously at a rate of 1% per hour. How many bacteria will there be in 6 hours?​

Answers

[tex]\bold{ANSWER:}[/tex]
276.0775

[tex]\bold{EXPLANATIONS:}[/tex]

I need help ASAP or im going to fail

Answers

45? Three non student tickets plus parking so 12*3 +9

Answer:

45

Step-by-step explanation:

Since it given that her parent and grandmother attend a soccer game. Thus, we can see that there is no students.

Also given that:

Student tickets: $6

Non-Student tickets : $12

Parking : $9

Thus,

Non- Student tickets:$ 12 (Parents and grandmother are not students)

Parking: $9 ( Since they attend a soccer game they need somewhere to park)

Parents = 2 person (Mom and Dad)

Grandmother = 1 person

1 + 2 = 3

Now,

Since Non-student tickets = $12

3 * 12 +9

36 + 9

45

Hence, the family spend $45 to attend the game.

~lenvy~

A fair dice is rolled.
Work out the probability of getting a number less than 6.
Give your answer in its simplest form

Answers

Answer: 5/6

Step-by-step explanation: If its a six sided die with numbers 1 - 6

A bookstore has 120 science fiction books. It has 30% fewer mysteries than science
fiction books. It has 25% more biographies than mysteries. How many biographies
are in the bookstore? Show your work.

Answers

Answer:

105

Step-by-step explanation:

Explanation is in photo

Find the slope of the line (2,-3) (4,-7)

Answers

hello!

Use the slope formula:-

[tex]\displaystyle\frac{y2-y1}{x2-x1}[/tex]

[tex]\displaystyle\frac{-7-(-3)}{4-2} =\frac{-7+3}{2} =\frac{-4}{2} =\bigstar{\boxed{\pmb{-2}}}[/tex]

note:-

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

CAN SOMEBODY SOLVE EQUATION IM LOST

Answers

Answer:

2

- x  -1

3  

Step-by-step explanation:

Sientific notation (please help!)

Answers

√5

You know that √4 = 2

so √5 > 2

2.5 * 2.5 = 6.25,

√6.25 = 2.5

so √5 in between 2 & 2.5

2 < n < 2.5

π/3

π/3 ≈ 3.14/3

3/3 = 1

4.5/3 = 1.5

π is in between 3 & 4.5

1 < n < 1.5

√3

√2.25 = 1.5

√4 = 2

√3 is in between

1.5 < n < 2

Hope this helped!

can someone help me with this please

Answers

Answer:

perspective

I hope this helps you

:)

2x+3y=8 find the solution using addition elimination method

Answers

Answer:

X equals 1, and Y equals 2

First, find the value of 2x, we have to assign one to make the problem work.

[tex]2x = 2 * 1[/tex]

Now, find y.

[tex]3y = 3 * 2[/tex]

Find the results of the multiplication. Remember that anything times 1 is always the same number, the base number.

[tex]2 * 1 = 2[/tex]

[tex]3 * 2 = 6[/tex]

Now, add.

[tex]6 + 2 = 8[/tex]

________________________________________________________

Now, we go over what we learned.

________________________________________________________

What have we learned?

We learned how to make inequalities true by assigning values to substitutions.

Questions related to this topic? Ask me in the comments box.

Melissa deposits $5000 into an account that pays simple interest at a rate of 4% per year. How much interest will she be paid in the first 2 years?

Answers

Answer:

$400 is the intrest she will pay in the first 2 yrs

Step-by-step explanation:

principal (p) = 5000

time (t) = 2yrs

rate (r) = 4%

Now,

Intrest(I) = p×t×r/100

= 5000×2×4/100

= 400$

Which expression is equivalent to 4/5x + 1 4/5
A 1/5(4x +1)
B 2/5(2x + 3)
C 4/5 (x + 2)
D 5/4 (x + 1)

Answers

There is none, but the closest is C.

It should be: 4/5( x + 2.25)

4/5 x x = 4/5x

4/5 x 2.25 = 9/5 (or 1 4/5)

(4 x? = 9) ==> 2.25

Step-by-step explanation:

A) 4/5 x + 1/5

B) 4/5x + 6/5 (or 1 1/5)

C) 4/5x + 8/5 (or 1 3/5)

D) 5/4 x + 5/4 (or 1 1/4)

Hope this helps!

Use the quadratic formula to solve for x.
3x2 + 2x - 6 = 0

Answers

Answer:

x = 1/3 (sqrt(19) - 1) or x = (1/3 (-1 - sqrt(19)))

Step-by-step explanation:

Solve for x over the real numbers:

3 x^2 + 2 x - 6 = 0

Using the quadratic formula, solve for x.

x = (-2 ± sqrt(2^2 - 4×3 (-6)))/(2×3) = (-2 ± sqrt(4 + 72))/6 = (-2 ± sqrt(76))/6:

x = (-2 + sqrt(76))/6 or x = (-2 - sqrt(76))/6

Simplify radicals.

sqrt(76) = sqrt(4×19) = sqrt(2^2×19) = 2sqrt(19):

x = (2 sqrt(19) - 2)/6 or x = (-2 sqrt(19) - 2)/6

Factor the greatest common divisor (gcd) of -2, 2 sqrt(19) and 6 from -2 + 2 sqrt(19).

Factor 2 from -2 + 2 sqrt(19) giving 2 (sqrt(19) - 1):

x = 1/6(2 (sqrt(19) - 1)) or x = (-2 sqrt(19) - 2)/6

In (2 (sqrt(19) - 1))/6, divide 6 in the denominator by 2 in the numerator.

(2 (sqrt(19) - 1))/6 = (2 (sqrt(19) - 1))/(2×3) = (sqrt(19) - 1)/3:

x = (1/3 (sqrt(19) - 1)) or x = (-2 sqrt(19) - 2)/6

Factor the greatest common divisor (gcd) of -2, -2 sqrt(19) and 6 from -2 - 2 sqrt(19).

Factor 2 from -2 - 2 sqrt(19) giving 2 (-sqrt(19) - 1):

x = 1/3 (sqrt(19) - 1) or x = 1/6(2 (-1 - sqrt(19)))

In (2 (-sqrt(19) - 1))/6, divide 6 in the denominator by 2 in the numerator.

(2 (-sqrt(19) - 1))/6 = (2 (-sqrt(19) - 1))/(2×3) = (-sqrt(19) - 1)/3:

Answer:  x = 1/3 (sqrt(19) - 1) or x = (1/3 (-1 - sqrt(19)))

Simplify the expression with nested parentheses.
4 30+ 26+6 −33

Answers

Answer:

not sure if the 4 is seperate but if it is then (30+26)+(6-33)

Step-by-step explanation:

What is the limit on the number of members in a limited liability company? There is no limit to the number of members in a limited liability company.

Answers

Hmm that is a weird question is it already ans

i kneed help

Which of the following is an example of symbolism in a political communication?

A campaign ad that uses the American flag to show the candidate is patriotic
A website that explains where candidates stand on the issues of their party's platform
A news channel that actively advocates for a particular candidate
A radio program where local politicians are interviewed about important local issues

Answers

Answer:

Here :D

Step-by-step explanation:

The option that is an example of symbolism in a political communication is; A radio program where local politicians are interviewed about important local issues.

What is Symbolism in Communication?

In symbolism in communication, we are trying to use a means or medium to pass across a message to an audience consciously or unconsciously.

Now, for political communication, the politicians are trying to talk about important issues with respect to the elections. Thus, from the given options, the only one that is an example of symbolism in a political communication is A radio program where local politicians are interviewed about important local issues.

Read more about Symbolism at; https://brainly.com/question/15816956

#SPJ2

Easy math 2 questions

Answers

I only know question 1: 8 inches.

Also, don't delete this.

It's helpful to certain people with the same problem.

Answer:

For problem 11, Q is 16 degrees

For problem 12 I think it is 8 inches

Step-by-step explanation:

A new computer repair company offers house calls to their customers. They use the function f(h) = 45h + 80 to calculate the total repair bill, f(h), for h number of hours worked. A. What does 45 represent in the function? < B. What does 80 represent in the function? > C. Find h if f(h) = 215. What does this value of h mean in the context of the problem? <​

Answers

The function f(h) = 45h + 80  of the computer repair is a linear function

45 represents the hourly rate80 represents the base costThe value of h means 3 hours

What 45 and 80 represents?

A linear function is represented as:

f(h) = mh + c

Where:

m represents the rate; m = 45b represents the base cost or y-intercept; y = 80

By comparison;

45 represents the hourly rate and 80 represents the base cost

How to calculate h?

We have:

f(h) = 45h + 80  

When f(h) = 215, the function becomes

45h + 80 = 215

Subtract 80 from both sides

45h = 135

Divide both sides by 45

h = 3

Hence, the value of h means 3 hours

Read more about linear functions at:

https://brainly.com/question/15602982

40 points for this question!!!

Answers

Answer:

Never

Step-by-step explanation:

It should be never since as the value of x increases, so does y.

If the y value increases as x increases, the function is said to be increasing.

If the y value decreases as x increases, the function is said to be decreasing.

I NEED HALP PWEASE AND PWEASE DONT IGNORE ME EVERONE DOES THAT WHEN I PUT A QUESTION UP IM GIVING BRAINLYS OUT

Answers

Answer:

The order goes:

B

A

D

C

Step-by-step explanation:

Based on the clues joe has the least so he would be B

Terrell has the most so his would be A

Jimmy has half so he would be D

and Justin is C last option

Answer:

Clue 1:  1,4 = B

Clue 2: 1,6 = A

Clue 3: 2,4 = C

Clue 4 : 4,5 = D

Solve the system of equations.​
−4x+3y=−2
y=x−1​

Answers

(-1,-2)

x= -1

y= -2

Have a wonderful day :)

Hope this helps ....... :))))

A movie is 9.75 seconds long.

Describe a situation related to this movie that could be a represented by the expression 9.75 / 2.5

Answers

Answer:

Step-by-step explanation: Maybe you could try:

A movie is 9.75 seconds long and each 2.5 seconds there is an ad so how many ads are there during the movie?

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