What is the average rate of change of the function f(x)= 4x^2 + 3x on the interval [1,5]

The scatterplot that represents Bryson's data is the scatterplot that is downward sloping.(Check the graph attached)

What is negative correlation?

To know more about negative correlation check the below link:

https://brainly.com/question/16913516

#SPJ4

Answer:

A. 2x⁴ - 11x³ + 7x² + 5x - 3

Step-by-step explanation:

Given (2x² - 3x + 1)(x² - 4x - 3)

Multiply both polynomials by distributing the terms 2x², -3x, 1, to every term you have in the second polynomial respectively.

Thus,

2x²(x² - 4x - 3) -3x(x² - 4x - 3) +1(x² - 4x - 3)

Open the parentheses by multiplying

2x⁴ - 8x³ - 6x² - 3x³ + 12x² + 9x + x² - 4x - 3

Pair like terms

2x⁴ - 8x³ - 3x³ - 6x² + 12x² + x² + 9x - 4x - 3

2x⁴ - 11x³ + 7x² + 5x - 3

The right answer is: A. 2x⁴ - 11x³ + 7x² + 5x - 3

Answer:64

8 to the power of 8 is 16777216. This is what you would find when multiplying 8 times itself 8 times. 8 to the power of 6, or 8 times itself 6 times is 262144. 16777216 divided by 262144 is 64.

I hope this helped & Good Luck <3 !!!

Answer:

I disagree.............................................................................

Step-by-step explanation:

System state space model is: y = [1  0] x. y = 4 is an equilibrium point.  x(t) = P∧(Dt)P−1 x(0) is the state transition matrix. The system is stable. The transfer function of the system is U(s)X(s) = [(s-2)²+ 4]⁻¹ [(s-2)  -2; 2  (s-2)] [0 2].

(a) i) System state space model:

x = [y  y']T;

dx/dt = [0  2; -1  1]x + [0  2]T u;

y = [1  0] x

Here, x represents the state vector.

ii) The equilibrium point(s) of the system if u is a constant value equal to 4: dy/dt = 0

Thus, 2y = 8 or y = 4. Therefore, y = 4 is an equilibrium point.

(b) The state transition matrix for autonomous linear systems is derived as follows:

If A is diagonalizable, then there exist an invertible matrix P and diagonal matrix D such that A = PDP−1.

Thus, x(t) = P∧(Dt)P−1 x(0) is the solution where exp(Dt) is calculated from the diagonal entries of D and t is the time of propagation.

(c) i)The stability of the system is determined by the eigenvalues of the system matrix A. If all the eigenvalues have a negative real part, the system is stable. If one of the eigenvalues has a positive real part, the system is unstable. And, if one eigenvalue has a zero real part, the system is marginally stable. Since the system has two eigenvalues with negative real parts, it is stable.

ii) The transfer function of the system is given as follows:

U(s) → X(s): X(s) = (sI − A)−1 B U(s)Y(s) → X(s): Y(s) = CX(s) = C(sI − A)−1 B U(s)

Thus, substituting the values of A, B, and C we get,Y(s) = [1 -1] [(s-2)²+ 4]⁻¹ [(s-2)  -2; 2  (s-2)] [0 2]

U(s)X(s) = [(s-2)²+ 4]⁻¹ [(s-2)  -2; 2  (s-2)] [0 2]

To know more about system state space model, visit:

https://brainly.com/question/32598929

#SPJ11

If an invertible symmetric n×n matrix A has a nonzero vector v in R^n such that Av is orthogonal to v, then it means that the dot product of Av and v is equal to zero. In other words, Av . v = 0. Using th peroperties of the dot product, we can rewrite this equation as:
v . A^T v = 0

Since A is symmetric, A^T = A, and we can rewrite the equation as:
v . A v = 0
This equation can be further simplified using the properties of the dot product:
v . A v = (A v) . v = 0
From this equation, we can see that the eigenvalues of A must be either positive or negative. If the eigenvalues of A are all positive, then v . A v > 0, which contradicts the equation v . A v = 0. Similarly, if the eigenvalues of A are all negative, then v . A v < 0, which also contradicts the equation v . A v = 0.
Therefore, the only way for there to exist a nonzero vector v in R^n such that Av is orthogonal to v is if the eigenvalues of A are both positive and negative. In other words, A must have both positive and negative

eigenvalues.

Read more about nonzero vector v  here:https://brainly.com/question/30301934

#SPJ11

Answer:

i think the answer would be 95 degree. im not absolutley positive though

Step-by-step explanation:

i added 35 and 50 and got the sum of 85 then i subtracted 85 from 180 and got 95

feedback is appreciated.

(i'm not gonna beg for brainliest)

Answer:

2 X 4 = 8, 8 X 2 = 16

2 X 5 = 10, 10 X 2 = 20

5 X 4 = 20, 20 X 2 = 40

16 + 20 + 40 = 76 square yards

A regular hex decagon's measure of one internal angle is 7.5 degrees more than a regular dodecagon's measure of one interior angle.

We must ascertain the measure of each individual angle in each polygon in order to compare the differences in one inside angle between a regular hex decagon and a regular dodecagon.

The following formula can be used to determine the size of each interior angle in a regular polygon with n sides:

Interior Angle = (n - 2) x 180 / n

Regular hex decagon:

Interior Angle = (16 - 2) * 180 / 16

= 14 * 180 / 16

= 2520 / 16

= 157.5 degrees

Regular dodecagon:

Interior Angle = (12 - 2) * 180 / 12

= 10 * 180 / 12

= 1800 / 12

= 150 degrees

Difference = Measure of hexadecagon angle - Measure of dodecagon angle

= 157.5 degrees - 150 degrees

= 7.5 degrees

Therefore, the measure of one interior angle of a regular hex decagon is 7.5 degrees greater than the measure of one interior angle of a regular dodecagon.

Learn more about regular polygon click;

https://brainly.com/question/29722724

#SPJ1

Answer:

D. (90, 60)

Step-by-step explanation:

A proportional relationship is a relationship in which the ratios of two variables are equivalent.

If we take two points on the graph such as (45, 30) and (30, 20), we can see that they can both be simplified to the ratio 3:2. Using this we can find the correct answer. From looking at all the points we can see that only (90,60) would also form a ratio of 3:2, thus d would be the correct answer.

Answer:

2916 and 6724 respectively

Step-by-step explanation:

the steps on how to evaluate 54^2 and 82^2 using the formula for squaring a binomial are:

1. Write the binomial as a sum of two terms.

\(54^2 = (50 + 4)^2\)

\(82^2 = (80 + 2)^2\)

2. Square each term in the sum.

\(54^2 = (50)^2 + 2(50)(4) + (4)^2\\82^2 = (80)^2 + 2(80)(2) + (2)^2\)

3. Add the products of the terms.

\(54^2 = 2500 + 400 + 16 = 2916\\82^2 = 6400 + 320 + 4 = 6724\)

Therefore, the values  \(54^2 \:and \:82^2\)are 2916 and 6724, respectively.

Answer:

54² = 2916

82² = 6724

Step-by-step explanation:

A binomial refers to a polynomial expression consisting of two terms connected by an operator such as addition or subtraction. It is often represented in the form (a + b), where "a" and "b" are variables or constants.

The formula for squaring a binomial is:

\(\boxed{(a + b)^2 = a^2 + 2ab + b^2}\)

To evaluate 54² we can rewrite 54 as (50 + 4).

Therefore, a = 50 and b = 4.

Applying the formula:

\(\begin{aligned}(50+4)^2&=50^2+2(50)(4)+4^2\\&=2500+100(4)+16\\&=2500+400+16\\&=2900+16\\&=2916\end{aligned}\)

Therefore, 54² is equal to 2916.

To evaluate 82² we can rewrite 82 as (80 + 2).

Therefore, a = 80 and b = 2.

Applying the formula:

\(\begin{aligned}(80+2)^2&=80^2+2(80)(2)+2^2\\&=6400+160(2)+4\\&=6400+320+4\\&=6720+4\\&=6724\end{aligned}\)

Therefore, 82² is equal to 6724.

≈ 63.30 ft²

Heron formula

A = √p(p - a)(p - b)(p - c)

a = 9 ; b = 15 ; c = 20

p = (a + b + c)/2 = (9 + 15 + 20)/2 = 44/2 = 22

A = √22(22-9)(22-15)(22-20)

= √22×13×7×2

= √4004

≈ 63,27

≈ 63.30 ft²

The type of sampling that Huw is using is called Convenience Sampling.

Explanation:

Convenience sampling is a non-probability sampling technique where the sample is selected based on ease of access and availability. In Huw's case, he is administering the questionnaire to people who happen to be in the town centre, which is convenient for him. The sample is not selected randomly, and therefore does not accurately represent the population as a whole. Convenience sampling is often used in quick, informal surveys where the researcher does not have the resources or time to conduct a more rigorous, randomized sampling method.

Answer:

Essential Elegance Candle

Step-by-step explanation:

Ratios are Lavender:Vanilla

For the Essential elegance candle the ratio is 3:6 which can be simplified to 1:2 whereas the Glory Candle is 4:10 which can be simplified to 2:5 on either one the vanilla is the bigger number but in terms of ratio it would be the essential elegance since 1/2>2/5

Using the percentage concept, it is found that 40% of Alberto’s income is used to pay for his rent and groceries.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

\(P = \frac{a}{b} \times 100\%\)

In this problem:

Then, the percentage is given by:

\(P = \frac{1280}{3200} \times 100\% = 40\%\)

More can be learned about the percentage concept at https://brainly.com/question/10491646

Answer:I think it’s B but I’m not so sure

Step-by-step explanation:

Answer:

A.Domain:{x\x is a real number }

Range:{y\y>5}

Asymptote :y=5

Step-by-step explanation:

We are given that a function

We have to find the domain, range and asymptote of h(x).

It is exponential function therefore, it is defined for all values of x.

Hence, domain  of h(x)={x| x is a real number}

Substitute x=0 then we get

(a^0=1)

Hence, range of h(x)={y|y>5}

For exponential function,

Horizontal asymptote: when

Apply limit

Hence, the horizontal asymptote y=5.

Answer:

70% of the people at the fair are students

165 people are on the ride

Step-by-step explanation:

In order to find a percentage, take the fraction given, 385/550, and divide the numerator, 385, and divide it by the denominator, 550. Once completing this, we get 0.7

Next, we multiply the result by 100, and get 70, thus, 385 is 70% of 550.

To find how many people 30% of 550 is, we take the percentage and put it in a fraction with the denominator being 100(changes with size of fraction like a decimal, 300 would be over a denominator of 1000)

With 30/100, we then multiply by 550 with the equation looking like this:

30/100*550/1

Once we finish multiplying(typically using a calculator, although you can do it manually) we get 165, the value of how many people are on rides out of the total 550.

Answer:

a) \(SA = 522.9~cm^2\)

b) \( V_{cone} = 670.2~cm^3 \)

c) \( V_{empty} = 1340.4~cm^3 \)

Step-by-step explanation:

a)

For a cone,

\( SA = \pi r (L + r) \)

where L = slant height

\( L = \sqrt{r^2 + h^2} \)

We have r = 8 cm; h = 10 cm

\(L = \sqrt{(8~cm)^2 + (10~cm)^2}\)

\(L = \sqrt{164~cm^2}\)

\(SA = (\pi)(8~cm)(\sqrt{164~cm^2} + 8~cm)\)

\(SA = 522.9~cm^2\)

b)

\( V_{cone} = \dfrac{1}{3}\pi r^2 h \)

\( V_{cone} = \dfrac{1}{3}(\pi)(8~cm)^2(10~cm) \)

\( V_{cone} = 670.2~cm^3 \)

c)

\( V_{cylinder} = \pi r^2 h \)

empty space = volume of cylinder - volume of cone

\( V_{empty} = V_{cylinder} - V_{cone} \)

\( V_{empty} = \pi r^2 h - \dfrac{1}{3}\pi r^2 h \)

\( V_{empty} = (\pi)(8~cm)^2(10~cm) - \dfrac{1}{3}(\pi)(8~cm)^2(10~cm) \)

\( V_{empty} = 1340.4~cm^3 \)

Net rendering is a method of rendering a computer-generated animation or image on multiple computers over a network.

Net rendering is a method of rendering a computer-generated animation or image on multiple computers over a network. This technique allows a user to take advantage of the computing power of multiple computers to render a scene. To do this, the user would divide the scene into several parts, assigning each part to a different computer. The computers would then render each part of the scene independently, and then the results are combined into a single image. This process can significantly reduce the time required to render a scene, as the workload is distributed over multiple computers. For example, if it would normally take a single computer 10 minutes to render a scene, net rendering could reduce that time to 2 minutes.

Learn more about significantly here:

https://brainly.com/question/14789537

#SPJ1

The value of x is approximately 44.31km

Firstly, we should know that 1 mile is not the same as kilometres, therefore:

1 mile = 1.60934 km.

Since the difference of x and y gives us 27, we represent it as:

x - y = 27 (in km)

But x is given in miles, so we have

1.60934x - y = 27km

Also the question says the distance x is same as y, then we replace y with x in the above equation:

1.60934x - x = 27

0.60934x = 27

x = 27/0.60934

Therefore x = 44.31km

Learn more about distance here:

https://brainly.com/question/26550516

#SPJ1

Answer:

-15.6 or -15 3/5

Step-by-step explanation:

The y-intercept is (0, 4).

An alternate method to find the x-intercepts is to factor the quadratic equation.

The vertex is (-2, 0).

The graph of the equation is illustrated below.

One of the most common types of equations is a quadratic equation, which is an equation of the form ax² + bx + c = 0. In this case, we have the equation x² + 4x + 4 = 0, and we need to find the x-intercepts.

To find the x-intercepts, we can use the quadratic formula, which is given by:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = 4, and c = 4, so we can substitute these values into the formula:

x = (-4 ± √(4² - 4(1)(4))) / 2(1) x = (-4 ± √(0)) / 2 x = -2

Therefore, the x-intercept is -2. We can check this by plugging in x = -2 into the equation and verifying that it equals zero:

(-2)² + 4(-2) + 4 = 0

In this case, we can see that the equation can be factored as:

(x + 2)² = 0

Taking the square root of both sides, we get:

x + 2 = 0

x = -2

This gives us the same x-intercept as before.

To find the vertex of the parabola represented by the equation, we can use the formula:

x = -b / 2a

and then substitute this value of x into the equation to find the y-coordinate of the vertex. In this case, we have:

x = -4 / 2(1) x = -2

Substituting x = -2 into the equation, we get:

(-2)² + 4(-2) + 4 = 0

Since the coefficient of x² is positive (i.e., a = 1 > 0), the parabola opens upwards and the vertex is a minimum.

To graph the parabola, we can plot the vertex at (-2, 0) and use the x-intercept we found earlier at (-2, 0). Since the equation is symmetric about the vertical line through the vertex, we know that there is another point on the graph that is the same distance from the vertex but on the other side of the line. Therefore, we can plot the point (-3, 0) as well. We can also find the y-intercept by setting x = 0 in the equation:

0² + 4(0) + 4 = 4

Using this information, we can sketch the parabola by connecting the points (-3, 0), (-2, 0), and (0, 4), and noting that the parabola is symmetric about the line x = -2.

To know more about equation here

https://brainly.com/question/10413253

#SPJ1

Rounded up to the nearest whole number, the answer is 5626.

Hence, the correct option is (C) 5626.

Given that the planning value for the population proportion is p* = 0.25,

we need to determine the size of the sample that should be taken to provide a 95% confidence interval with a margin of error of 0.1.

To determine the minimum required sample size (n), use the following formula:`n = (p*(1-p) * (Z² / E²))`

Where p is the planning value for the population proportion, Z is the value from the standard normal distribution for the desired confidence level (in this case, Z = 1.96 for a 95% confidence level), and E is the desired margin of error. Substituting these values, we have:`n = (0.25*(1-0.25) * (1.96² / 0.1²))`

Simplifying:`n = (0.25*0.75 * 384.16 / 0.01)`

Evaluating:`n = 5625`Therefore, the minimum sample size required is 5625.

Rounded up to the nearest whole number, the answer is 5626.

Hence, the correct option is (C) 5626.

To know more about confidence interval, visit:

https://brainly.com/question/32546207

#SPJ11

Applying the trapezoid midsegment theorem, the length of the midsegment of a trapezoid whose bases are 27 and x a+ 8 is determined as: (x + 35) / 2.

According to the trapezoid midsegment theorem, the length of the midsegment of a trapezoid is equal to the sum of the two bases divided by two.

The formula for finding the length of the midsegment of a trapezoid is therefore:

Length of midsegment = (sum of the two bases) / 2.

Given the length of the bases of a trapezoid as 27 and x + 8 respectively, therefore, according to the trapezoid midsegment theorem, we have the equation below:

Length of the midsegment = (27 + x + 8) / 2

Simplify by combining like terms:

Length of the midsegment = (x + 35) / 2

Therefore, the answer is, (x + 35) / 2.

Learn more about the midsegment of a trapezoid on:

https://brainly.com/question/7412602

#SPJ1

Using the concepts of domain and range of functions, we have that:

10. The range is y ≥ 2.

11. The domain is all real numbers, the range is y ≤ 3, and it is a function.

12. The domain is (-4,3], and the range is (-5,5).

Hence, for these problems:

10. The range is y ≥ 2.

11. The domain is all real numbers, the range is y ≤ 3, and it is a function.

12. The domain is (-4,3], and the range is (-5,5).

In item 11, we have that it is a function because it has no vertically aligned points, that is, each value of x is associated with only one value of y.

In item 12, the open intervals are due to the open circles at the extremes of the domain and the range on the graph.

More can be learned about the domain and the range of functions at https://brainly.com/question/10891721

#SPJ1