what is total area of the regions between the curves y=6x^2-9x and y=3x

Answers

Answer 1

The total area of the regions between the curves is 8 square units

Calculating the total area of the regions between the curves

From the question, we have the following parameters that can be used in our computation:

y = 6x² - 9x and y = 3x

With the use of graphs, the curves intersect ar

x = 0 and x = 2

So, the area of the regions between the curves is

Area = ∫6x² - 9x - 3x

This gives

Area = ∫6x² - 12x

Integrate

Area =  2(x - 3)x²

Recall that x = 0 and x = 2

So, we have

Area =  2(0 - 3) * 0² - 2(2 - 3) * 2²

Evaluate

Area =  8

Hence, the total area of the regions between the curves is 8 square units

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Related Questions

For the science fair Carol wanted to see how many minutes of videos she watched were ads. She watched
6 videos with each video lasting 9 minutes. After watching the videos she calculated that she had watched 3 minutes of
ads over all the videos. How many minutes were not ads?

Answers

Answer:

51 mins were not ads

Step-by-step explanation:

1 video = 9 mins

6 videos = x

x = 9×6 = 54 mins

mins of ads = 3 mins

mins that were not ads = total mins of videos – total mins of ads

= 54 – 3 = 51 mins

if this helped pls give brainliest

What is the probability he will roll a 5?

Answers

Answer:

hurt himself if he is 5 pieces away from jail in monopoly and this is his 9th time

Step-by-step explanation:

help me with the question please

help me with the question please

Answers

Answer:

I think it would be reflection because those triangles look very similar if not im sorry

Step-by-step explanation:

Brainlist maybe?

Can someone tell me the answer plz I’ll give brainlist and points

Can someone tell me the answer plz Ill give brainlist and points

Answers

Answer:

4502

Step-by-step explanation:

5323 -821 =4502

4502+821= 5323

A music website claims the mean length of their songs is 3.75 minutes. Suppose the length of songs from this website follows a Normal distribution with standard deviation 0.5 minutes. If 7 songs from this website are randomly selected, then there is about a 90% probability that the sample mean will fall in which interval

Answers

The confidence interval is from 3.44 to 4.06 minutes.

According to the statement

we have given that the mean length of songs is 3.75 minutes and standard deviation 0.5 minutes and the sample size n is 7. and the confidence interval is 90%

and we have to find the mean interval.

So, We know that the

A confidence interval is defined as the range of values that we observe in our sample and for which we expect to find the value that accurately reflects the population.

And A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample.

We know that the z value for 90% confidence interval is 1.64.

so, The formula to calculate margin of error is

MOE = Z*standard deviation/ (n)^1/2

put the values in it

MOE = Z*standard deviation/ (n)^1/2

MOE = 1.64*0.5/ (7)^1/2

MOE = 1.64*0.189

MOE = 0.310

And to find the interval the formula is

Confidence interval = sample mean ± margin of error

Confidence interval = 3.75 ± 0.310

Confidence interval = (4.06,3.44)

So, The confidence interval is from 3.44 to 4.06 minutes.

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Hector solves and equation by subtracting 8 from both sides of the equation. Then he multiples both sides of the equation by 3. The result is m=15. What was the original equation? How do you know?

Answers

Given:

The result is \(m=15\).

To find:

The original equation.

Solution:

We need to apply the opposite operations from bottom to top in the resultant equation to get the original equation.

It means opposite operation of last operation will be applied first.

We have,

\(m=15\)

Divide both sides by 3.

\(\dfrac{m}{3}=5\)

Add 8 on both sides.

\(\dfrac{m}{3}+8=5+8\)

\(\dfrac{m}{3}+8=13\)

Therefore, the original equation is \(\dfrac{m}{3}+8=13\).

9. Which pair of steps can be used to completelysolve this equation?4x - 5 = 17

Answers

In order to solve the equation

First step Add 5 to both sides

4x-5+5=17+5

4x=22

Second step Divide both sides by 4

\(\begin{gathered} \frac{4x}{4}=\frac{22}{4} \\ x=\frac{22}{4}=\frac{11}{2} \end{gathered}\)

the correct answer is D.

Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding 48.

Answers

The probability of selecting none of the correct six integers, when the order in which they are selected doesnot matter is 0.43.

According to thr question.

We have to find the probability of selecting none of the correct six integers from the positive integers not exceeding 48.  

Let E be the event of selecting 6 numbers from 40 and S be the sample space of all integers not exceeding 48.

Now,

The total number of ways of selecting 6 numbers from 48

\(= ^{48} C_{6}\)

\(= \frac{48!}{6!\times 42!}\)

\(= \frac{48\times 47\times46\times45\times44\times43\times42!}{6!\times\ 42!}\)

= 8835488640/6!

And, the total number of ways of selecting 6 incorrect numbers from 42

= \(^{42} C_{6}\)

\(= \frac{42\times41\times40\times39\times38\times37\times36!}{6!\times36!}\)

= 3776965920/6!

Therefore, the probability of selecting none of the correct six integers, when the order in which they are selected does not matter is given by

\(= \frac{^{42C_{6} } }{^{48} C_{6} }\)

\(= \frac{\frac{3776965920}{6!} }{\frac{8835488640}{6!} }\)

= 3776965920/8835488640

= 0.427

≈ 0.43

Hence, the probability of selecting none of the correct six integers, when the order in which they are selected doesnot matter is 0.43.

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8.40 Cats, Part II. Exercise 8.26 presents regression output from a model for predicting the heart weight
(in g) of cats from their body weight (in kg). The coefficients are estimated using a dataset of 144 domestic
cat. The model output is also provided below.
(Intercept)
body wt
Estimate Std. Error
-0.357
4.034
0.692
0.250
t value Pr(>|t|)
-0.515
16.119
0.607
0.000
s = 1.452
R² = 64.66%
Radi = 64.41%
(a) We see that the point estimate for the slope is positive. What are the hypotheses for evaluating whether
body weight is positively associated with heart weight in cats?
(b) State the conclusion of the hypothesis test from part (a) in context of the data.
(c) Calculate a 95% confidence interval for the slope of body weight, and interpret it in context of the data.
(d) Do your results from the hypothesis test and the confidence interval agree? Explain.

Answers

Both of these results provide evidence in support of a positive association between body weight and heart weight in cats.

How to solve the problem?

(a) The hypotheses for evaluating whether body weight is positively associated with heart weight in cats are:

Null hypothesis: The slope of the linear regression line is zero, indicating that there is no association between body weight and heart weight in cats.

Alternative hypothesis: The slope of the linear regression line is positive, indicating that there is a positive association between body weight and heart weight in cats.

(b) The p-value associated with the slope coefficient is 0.000, which is less than the significance level of 0.05. Therefore, we reject the null hypothesis and conclude that there is evidence of a positive association between body weight and heart weight in cats.

(c) A 95% confidence interval for the slope of body weight is (3.548, 4.520). This means that we are 95% confident that the true slope of the population regression line falls within this interval. In other words, if we were to repeat the study many times and calculate a 95% confidence interval for each study, 95% of the intervals would contain the true value of the population slope. Specifically, we are 95% confident that the true increase in heart weight per kg increase in body weight is between 3.548 g and 4.520 g.

(d) Yes, the results from the hypothesis test and the confidence interval agree. The p-value of 0.000 indicates that the slope of the regression line is significantly different from zero, while the confidence interval for the slope does not include zero, indicating that the slope is significantly different from zero at the 95% confidence level. Both of these results provide evidence in support of a positive association between body weight and heart weight in cats.

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8.40 Cats, Part II. Exercise 8.26 presents regression output from a model for predicting the heart weight(in

Given points A(1,0,4), B(2, -3,2), and C(-7, -2,0) (a) Find the magnitude of AB. (b) Find a unit vector in the direction of AB. (c) Write a vector equation for the line through the po

Answers

The magnitude of AB is sqrt(14), the unit vector in the direction of AB, and  the vector equation for the line through points A and B is: r = <1, 0, 4> + t<1/sqrt(14), -3/sqrt(14), -2/sqrt(14)>

(a) To find the magnitude of AB, we first need to find the vector AB. This can be done by subtracting the coordinates of A from the coordinates of B:
AB = <2-1, -3-0, 2-4> = <1, -3, -2>
The magnitude of AB is then:
|AB| = sqrt(1^2 + (-3)^2 + (-2)^2) = sqrt(14)
So, the magnitude of AB is sqrt(14).
(b) To find a unit vector in the direction of AB, we divide the vector AB by its magnitude:
AB/|AB| = <1/sqrt(14), -3/sqrt(14), -2/sqrt(14)>
This is the unit vector in the direction of AB.
(c) To write a vector equation for the line through the points A and B, we need a direction vector and a point on the line. We already have the direction vector, which is AB. We can use point A as the point on the line. Therefore, the vector equation for the line through points A and B is:
r = <1, 0, 4> + t<1/sqrt(14), -3/sqrt(14), -2/sqrt(14)>
where r is the position vector of any point on the line and t is a parameter that can take on any real value.

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Does the table below represent a function? Explain why or why not.

Does the table below represent a function? Explain why or why not.

Answers

Answer:

No.

Step-by-step explanation:

An input can't have 2 outputs. But, an output can have an 2 inputs.

Hope this helped!

What is the median of the data

44,13,36,52,19,27,33

Answers

Answer:33

Step-by-step explanation:

does anybody have the answers to the ukmt junior maths challenge 1998
PLS HELP ME

Answers

Answer: did u mean to put ukmt

Step-by-step explanation:

a distribution of values is normal with a mean of 164.8 and a standard deviation of 92.6. find p42, which is the score separating the bottom 42% from the top 58%.

Answers

The raw score which is the score separating the bottom 42% from the top 58% is 183.32.

The given variable is a normal distribution variable.

Mean of the variable is given by = µ = 164.8

Standard deviation of the variable is given by = s = 92.6

Let the p42 or the score separating the bottom 42% from the top 58% be x.

z = (x - 164.8)/92.6

So, P(Z < z) = 0.42

We know that normal distribution table that P(Z < -0.21) = 0.42

So, z = - 0.21

(x - 164.8)/92.6 = 0.21

x - 164.8 = 0.21*92.6

x - 164.8 = 18.52

x = 18.52 + 164.8

x = 183.32

Hence the required raw score will be 183.32.

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What is the arc measure of minor arc AB on circle P in degrees?

What is the arc measure of minor arc AB on circle P in degrees?

Answers

Answer:

74

Step-by-step explanation:

This is called a central angle, meaning that what ever te angle measure is, is the same to its ark measure.

So to find that inside angle measure you have to subtract 360 by 286

whitch is 74

74 is your inside angle and the angle for ark AB

If the diameter of a circle is 46 centimeters long, how long is the radius of the circle?
OA. 184 centimeters
OB B. 11.5 centimeters
OC. 92 centimeters
OD. 23 centimeters

Answers

Answer:

r = 23

Step-by-step explanation:

Using the formula

d = 2r

Solving for r

r = d / 2 = 46 / 2 = 23

Identify the highlighted part of circle O shown below

Central angle
Secant
Inscribed angle
Chord

Identify the highlighted part of circle O shown below Central angle Secant Inscribed angle Chord

Answers

Answer:

Chord

Step-by-step explanation:

Notice that the highlighted part is the line segment that joins the points J and E on the circle, which is known as a chord.

How does confidence interval affect margin of error.

Answers

the width of the confidence interval is twice the margin of error. The lower bound of the confidence interval is the observed score minus the margin of error;

need answer with work out!!

need answer with work out!!

Answers

The volume of the figure is the sum of the volume of the square prism and the volume of the square pyramid which is 67.2cm³

What is the volume of the figure?

To calculate the volume of the figure, we need to find the volume of the square prism and the volume of the square pyramid.

The volume of a square prism is given as;

V = L³

l = length of the sides;

V = 4³

V = 64cm³

The volume of the square pyramid is given as;

V = 1/3lh

l = length of baseh = height of pyramid

V = 1/3 * 4 * 2.4

V = 3.2cm³

The volume of the figure is 64cm³ + 3.2cm³ = 67.2cm³

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How to simplify radicals with variables and exponents?

Answers

Radicals expression with variables and exponents can be simplify by:

Separate the number and variablesTry to find variables with even exponentsTry to breakdown the number into any factors that are perfect squareTry to rewrite both number and variables into square exponent Separate the squared factors into individual radicalsTake the square root of each radicalSimplify and multiply

To help us understand each step better, we will take an example of a radical expression with variables and exponents of: \(\sqrt{16a^{3}b^6c^5 }\)

First, we need to separate the number and variables:

\(\sqrt{16a^3b^6c^5}=\sqrt{16} \sqrt{a^3b^6c^5}\)

Next, we will try to find variables with even exponents:

\(\sqrt{16} \sqrt{a^3b^6c^5} = \sqrt{16} \sqrt{a.a^2.b^6.c^4.c^}\)

Remember that:

(xᵃ)ᵇ = xᵃᵇ; then:

\(\sqrt{16}\sqrt{a.a^2.b^6.c^4.c} =\sqrt{16}\sqrt{a.a^2.(b^3)^2.(c^2)^2.c}\)

We try to breakdown any number into any factor that are perfect square:

\(\sqrt{16}\sqrt{a.a^2(b^3)^2.(c^2)^2.c} = \sqrt{4 .4} \sqrt{a.a^2(b^3)^2.(c^2)^2.c}\)

We will rewrite both number and the variables into a square exponents:

\(\sqrt{4 .4} \sqrt{a.a^2(b^3)^2.(c^2)^2.c} = \sqrt{4^2} \sqrt{a.a^2(b^3)^2.(c^2)^2.c}\)

We will separate the squared factors into individual radicals:

\(\sqrt{4 ^2} \sqrt{a.a^2(b^3)^2.(c^2)^2.c} = \sqrt{4^2} \sqrt{a^2} .\sqrt{(b^3)^2} \sqrt{(c^2)^2} \sqrt{a.c}\)

We take the square root of each radical into:

\(\sqrt{4^2} \sqrt{a^2} .\sqrt{(b^3)^2} \sqrt{(c^2)^2} \sqrt{a.c} = 4|a|.|b^3|.c^2\sqrt{ac}\)

We just need to simplify our last equation into:

\(4|a|.|b^3|.c^2\sqrt{ac} = 4|ab^3|c^2\sqrt{ac}\)

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If you bisect an angle that is 128 degrees, what size are the two new angles?

Answers

Answer:

64 is the answer

hope you like tjis

stay at home stay safe

Answer:

Each angles measures 64 degrees

Step-by-step explanation:

Bisect means divide in half

128/2 = 64

Each angles measures 64 degrees

how do u do this pls help me understand

how do u do this pls help me understand

Answers

Answer:

10.8

Step-by-step explanation:

5 times what gives 6? 5 times 1.2

So now you just do 9 times 1.2 which is 10.8

Answer:

10.8

Step-by-step explanation:

5*x=6

5*1.2=6

9*1.2=r

r=10.8

You want to put a 2 inch thick layer of topsoil for a new 15 ft by 12 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order

Answers

The order approximately 1.1111 cubic yards of topsoil from the dirt store.

The volume of topsoil required in cubic feet.

The area of the garden is:

The area of the garden is found by multiplying the length and width of the garden. In this case, the garden is 15 feet by 12 feet, so the area is 15 ft x 12 ft = 180 sq ft.

Since we want a 2 inch thick layer of topsoil, we need to convert the thickness to feet:

2 inches = 2/12 feet = 0.1667 feet

The volume of topsoil required in cubic feet is therefore:

180 sq ft × 0.1667 ft = 30 cubic feet

To convert this to cubic yards, we divide by 27 (since there are 27 cubic feet in a cubic yard):

The dirt store sells topsoil by the cubic yard, so we need to convert our answer from cubic feet to cubic yards. Since there are 27 cubic feet in a cubic yard (3 feet x 3 feet x 3 feet)

30 cubic feet ÷ 27 = 1.1111 cubic yards

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Solve by substitution method 2x+7y=11 and x-3y=5​

Answers

Answer:

Step-by-step explanation:

\(x = \frac{68}{13}\)

\(y = \frac{1}{13}\)

To solve the system of equations by substitution method, we can use one equation to solve for x or y, and then substitute that expression into the other equation to solve for the other variable.

From the second equation, we have:

x - 3y = 5

Solving for x, we get:

x = 3y + 5

Now we can substitute this expression for x into the first equation and solve for y:

2x + 7y = 11

2(3y + 5) + 7y = 11

6y + 10 + 7y = 11

13y = 1

y = 1/13

Now that we have solved for y, we can substitute this value back into one of the original equations to solve for x:

x - 3y = 5

x = 3y + 5

x = 3(1/13) + 5

x = 5 6/13

Therefore, the solution to the system of equations is:

x = 5 6/13 and y = 1/13.

Jessie's school has 570 students. Thirty percent of the students are eighth-graders. One-third of eighth-graders walk to school. How many eighth-graders walk to school?

Answers

Answer:

57

Step-by-step explanation:

10% of 570 = 57 (dividing by 10). Times that by 3, which is 171. Now divide 171 by 3, equals 57 (the answer).

the use of numeric data to demonstrate a point are known as? group of answer choices inform persuade statistics entertain

Answers

Numeric data can be used to present facts, show relationships between variables, and support an argument.

Numeric data is a powerful tool that can be used to present facts, demonstrate relationships between variables, and support an argument. It is often used to provide evidence for a particular point of view, and it can be used to persuade an audience or inform them about a particular topic. Numeric data can be presented in various forms such as graphs, tables, and charts, and when used effectively, it can be a very effective tool for conveying information. It is important to understand how to interpret numeric data correctly, as it can be used to draw false conclusions if the data is misinterpreted.

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HELPP!!
describe the pattern. then write the next 3 numbers
729,243,81,27

Answers

Answer: it's being devided by 3  heres is an equation \(\frac{729}{3^{n-1} }\)  the next 3 numbers are 9,3,1

Which of the following best describes the graph above?
A.
neither a relation nor a function
B.
function only
C.
relation only
D.
both a relation and a function

Which of the following best describes the graph above? A. neither a relation nor a function B. function

Answers

Answer:

Option C

Step-by-step explanation:

To test a graph whether it represents a function or relation we conduct a vertical line graph.

If the vertical line intersect the graph at two different points, graph represents a relation only.

By analyzing the given graph with the vertical line test,

Since, a vertical line (x = -4) intersect the graph at two points (y = -1 and y = 5),

Given graph represents a relation only.

Option C is the answer.

Which of the following best describes the graph above? A. neither a relation nor a function B. function

a town has 10,000 two-child families.

Answers

Answer:

Step-by-step explanation:

if its asking how many people there are it would be 40,000

Mother, Father, 2 kids=4

4 x 10,000= 40,000

Find (f0f)(81)
f(x)=sqrt{x}​,g(x)=(x−7)^2

Answers

From the given function f(x) the value of expression f(f(81)) is equal to 3.

Let's see how to find the answer to the question:

Find (f0f)(81)

In the given question, we need to find the value of (f0f)(81). This notation means (f◦f)(81).

Given that f(x)= sqrt(x) and g(x) =\((x - 7)^2\).

We know that to find (f◦f)(x), we need to evaluate f(f(x)).

This means we need to first evaluate f(x), and then evaluate f(f(x)).

To find (f◦f)(81), we need to find f(f(81)).

Using the function f(x), we find f(81):

f(81) = sqrt(81) = 9

Now, we use the function f(x) again to find f(f(81)):

f(f(81)) = f(9)

= sqrt(9)

= 3

Thus, we have found that

(f◦f)(81) = f(f(81))

= 3

Hence, the value of (f0f)(81) is 3.

Therefore, the value of (f0f)(81) is 3.

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