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

Consequently, there are 5 elements in A B'.

Given the following definitions:

U = {1, 2, 3, 4, 5, 6, 7}A = {1, 2, 4, 5}B = {1, 3, 5, 7}

The complement of a set B is the set of all elements that belong to the universal set U but not to B.

A’ = {x | x ∈ U and x ∉ A} = {3, 6, 7}B’ = {x | x ∈ U and x ∉ B} = {2, 4, 6}

The union of sets A and B is the set of all elements that belong to set A or set B, or both.

A ∪ B = {x | x ∈ A or x ∈ B}

= {1, 2, 3, 4, 5, 7}A ∪ B'

= {x | x ∈ A or x ∈ B’}

= {1, 2, 4, 5, 6}

Therefore, the number of elements in A ∪ B' is 5.

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Solution

We have the following equation given:

18a X 32 b = 32 b x 18a

And we can see that the solution is:

b. Commutatitative property of multiplication

since the order of the factors not alter the result

The missing value 'x' in the two-way relative frequency table is 0.36.

To convert the two-way table to a two-way relative frequency table, we need to calculate the relative frequencies for each category. Relative frequency is calculated by dividing the frequency of a particular category by the total count in that row or column.

Let's denote the missing value as 'x'. To find the value of 'x', we need to ensure that the sum of the relative frequencies in each row and each column adds up to 1.

First, let's calculate the relative frequencies for each category:

Likes hockey: The total count in this row is 12 + 18 = 30.

Relative frequency of "Likes hockey" = 12/30 = 0.4

Relative frequency of "Doesn't like hockey" = 18/30 = 0.6

Likes baseball: The total count in this column is 12 + 14 = 26.

Relative frequency of "Likes baseball" = 12/26 ≈ 0.4615

Relative frequency of "Doesn't like baseball" = 14/26 ≈ 0.5385

To ensure that the relative frequencies add up to 1, we can set up the following equations:

0.4 + x = 1 (sum of relative frequencies in the "Likes hockey" row)

0.4615 + 0.5385 + x = 1 (sum of relative frequencies in the "Likes baseball" column)

Simplifying the equations, we have:

x = 0.6 (1 - 0.4) = 0.6 * 0.6 = 0.36

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The new angular speed, ω₂, is four times the initial angular speed, ω₁.

To solve this problem, we can use the conservation of angular momentum. The initial and final angular momenta should be equal:

I₁ω₁ = I₂ω₂

Where I₁ and I₂ are the initial and final moments of inertia, respectively.

Assuming the particles are connected in a circular arrangement, the moment of inertia can be calculated using:

I = n * m * r²

Where n is the number of particles and r is the distance from the center of rotation.

Now we have:

(n * m * L²)ω₁ = (n * m * (0.5L)²)ω₂

Simplifying the equation, we get:

ω₂ = 4ω₁

So the new angular speed, ω₂, is four times the initial angular speed, ω₁.

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A system of small particles, each with mass m, is connected by light strings of length L. The system is rotating at an initial angular speed ω₁. If the strings are shortened to 0.5L, what is the new angular speed, ω₂?

The domain value that corresponds to a range value of 4 is,

⇒ x = 1/2

Given that;

Function is,

y = 4x + 2

Since, the equation equal to the range value:

4 = 4x + 2

Then, we can solve for "x":

4 - 2 = 4x

2 = 4x

x = 1/2

Now that we have the value of "x", we can find the corresponding value of "y" by substituting it into the given equation:

y = 4x + 2

y = 4(1/2) + 2

y = 4 + 2

y = 6

Therefore, the domain value that corresponds to a range value of 4 is,

⇒  x = 1/2

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Answer:

(60-40)+80

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Expected Value = (Probability of winning) x (Amount won) + (Probability of losing) x (Amount lost)

In this case, the probability of winning is 1/6 (since there is only one way to roll a 3 out of six possible outcomes), and the probability of losing is 5/6 (since there are five other outcomes that do not result in a win).

The amount won is $15, and the amount lost (i.e., the cost of playing the game) is $3.

Therefore, the expected value is:

Expected Value = (1/6) x $15 + (5/6) x (-$3)

Expected Value = $2.50 - $2.50

Expected Value = $0

Answer:

0.43x250,000 = 107,500 teenagers.

Step-by-step explanation:

43% of students spend 1 hr on HW< and there are 25,000 students.

43% is basically just 43/100, so 0.43x250,000 is 107,500 students.

The statement that completes the blank is (c) the null hypothesis is true.

In sampling techniques, the expected count of a variable is dependent on the null hypothesis.

This means that, if the null hypothesis is true, then the expected count is what is expected to be seen in the sample.

This in other words, means that the complete statement is:

The expected count of females who are not pierced is what we would expect to see in the sample if the null hypothesis is true.

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Answer:

Let's choose the three odd consecutive numbers 1, 3, and 5.

3^2=9

1•5=5

9-5=4

Let's try the same thing, but with the numbers 101, 103, and 105.

103^2=10609

101•105=10605

10609-10605=4

So, yes, the square of the second number out of three consecutive odd numbers is four greater than the product of the first and the third numbers.

Pick 3 consecutive odd numbers:

3, 5, 7

Square the 2nd number: 5 ^ 2 = 25

Multiply the first and 3rd:

3 x 7 = 21

25-21 = 4

This is true.

Try another set of numbers:

9, 11, 13

11^2 = 121

9 x 13 = 117

121-117 = 4

Again it’s true.

Answer: 1) NO. the zeros are: 2 and -7

              2) (x + 5)² has a middle term when in expanded form

             3) Factoring provides the Intercept form: y = a(x - p)(x - q)

Step-by-step explanation:

1) y = (x - 2)(x + 7)

To find the zeros, set the factors equal to zero:

0 = x - 2        0 = x + 7

x = 2              x = -7

The zeros are 2 and -7.  

The student did not set the factors equal to zero.

2) (x + 5)² = (x + 5)(x + 5)

               = x² + 5x + 5x + 25

               = x² + 10x + 25       ≠  x² + 25

3) The Intercept form of a quadratic equation is: y = a(x - p)(x - q) where p and q are the x-intercepts.  Notice that the intercept form IS the factored form. Set the factors equal to zero to find the x-intercepts.

y = x² - 4x + 3

y = (x - 1)(x - 3)     --> Intercept form

0 = (x - 1)(x - 3)    --> finding the zeros (aka x-intercepts)

0 = x - 1       0 = x - 3

x = 1            x = 3       -->    zeros are 1 and 3

1.The zeroes are 2,-7

2.\(x^2 + 25\neq ( x + 5)^{2}\)

3. So, factoring can help to find the x-intercepts

1.We have y = (x - 2)(x + 7)

For zeroes of y , Put y=0

(x - 2)(x + 7) =0

x=2,-7

So, the zeroes of y = (x - 2)(x + 7) are 2 and -7.

2. We have \(x^2 + 25\)

\(x^2 + 25= x^2 + 5^{2}\)

And

\((x+ 5)^{2} \\=x^{2} +5^{2} +10x\\=x^{2} +25 +10x\\\neq x^{2} +25\)

So, \(x^2 + 25\neq ( x + 5)^{2}\)

3.We have the quadratic function \(y = x^2 - 4x + 3\)

\(y=x^2 - 4x + 3\\=(x-3)(x-1)\\\)

For x-intercept put y=0, we get

\((x-3)(x-1)=0\\x=3,x=1\)

So, factoring can help to find the x-intercepts of the graph of the quadratic function \(y = x^2 - 4x + 3.\)

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The value of x is approximately 49.4 units.

What is volume ?

Volume is a measure of the amount of space occupied by a three-dimensional object. It is typically expressed in cubic units such as cubic meters, cubic centimeters, or cubic feet. Volume is a fundamental concept in mathematics and physics, and it is an important property for describing the size, capacity, or amount of material contained within an object.

Let's start by defining some variables:

r: radius of the cone

h: height of the cone

V: volume of the cone

A right cone has a circular base, and its volume can be calculated as follows:

V = (1/3) * π * r² * h

If the diameter of the base is 12 units, then the radius is half of that:

r = 6 units

We also know that the volume is 2767 units³, so we can write:

2767 = (1/3) * π * 6² * h

Simplifying:

h = (2767 * 3) / (π * 6²)

h ≈ 49.15 units

Now, we need to find the value of x. We can use the Pythagorean theorem to relate x, r, and h:

x² = r² + h²

Substituting the values we have:

x² = 6² + 49.15²

x ≈ 49.4 units

Therefore, the value of x is approximately 49.4 units.

In summary, we used the formula for the volume of a cone to relate the radius and height of the cone to its volume. Then, we used the Pythagorean theorem to relate the unknown value of x to the known values of r and h. Finally, we substituted the known values to find the approximate value of x.

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Your complete question is :-The volume of the right cone below is 2767 units³. Find the value of x if it's diameter is 12

The required statistical parameters has been computed as follows:

Range = 15.

Standard deviation, SD = 4.4441.

Variance = 19.75.

Mathematically, the range of a data set can be calculated by using this formula;

Range = Highest number - Lowest number

Range = 36 - 21

Range = 15.

Mathematically, the mean for these data sets would be calculated by using this formula:

Mean = [F(x)]/n

F(x) = 22 + 29 + 21 + 24 + 27 + 28 + 25 + 36

F(x) = 212.

Mean = 212/8

Mean = 26.5

Next, we would calculate the standard deviation by using this formula:

SD = √(1/n × ∑(xi - u₁)²)

SD = √(1/5 × ∑(22 - 26.5)² + 1/5 × ∑(29 - 26.5)² + 1/5 × ∑(21 - 26.5)² + 1/5 × ∑(24 - 26.5)² + 1/5 × ∑(27 - 26.5)² + 1/5 × ∑(28 - 26.5)² + 1/5 × ∑(25 - 26.5)² + + 1/5 × ∑(36 - 26.5)²)

Standard deviation, SD = 4.4441.

In Statistics, the standard deviation of a data sample is the square root of the variance and this is given by this mathematical expression:

Variance = δ²

Variance = 4.4441²

Variance = 19.75.

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Answer:

1

Step-by-step explanation:

4-3=1 denominator never changes may i be marked brainliest?

The expressiοn (x+1)(x+2) has the greatest vaIue οf 30 when x=4.

An aIgebraic expressiοn is a mathematicaI phrase that cοntains variabIes, cοnstants, and mathematicaI οperatiοns. It may aIsο incIude expοnents and/οr rοοts. AIgebraic expressiοns are used tο represent quantities and reIatiοnships between quantities in mathematicaI situatiοns, οften in the cοntext οf prοbIem-sοIving.

Tο evaIuate the expressiοn (x+1)(x+2) when x=4, we simpIy substitute 4 intο the expressiοn, which gives us (4+1)(4+2).

SοIving this expressiοn, we first perfοrm the additiοns inside the parentheses tο get (5)(6).

Then, we muItipIy the twο numbers tο get 30.

when x=4, the expressiοn (x+1)(x+2) evaIuates tο 30, which is its greatest vaIue. This is because the quadratic expressiοn x² + 3x + 2 increases as x increases, and it reaches its maximum vaIue when x=4.

Therefοre, the expressiοn (x+1)(x+2) has the greatest vaIue οf 30 when x=4.

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An exponential function is a function in which the independent variable x appears as an exponent.

a is the y-intercept.

b is the rate of change and common ratio.

The function is exponential growth when b > 1.

The function is exponential growth when b < 1.

y-intercept is the initial value of the function when x is equal to 0.

Asymptote is the line that the function approaches but does not cross.

In Mathematics, an exponential function is typically represented by the following mathematical expression:

f(x) = a(b)^x

Where:

Based on the given exponential function y = a(b)^x, we can logically deduce that the y-intercept is represented by a, b is the rate of change, and common ratio.

In conclusion, an asymptote is a line which the graph of a given function approaches, but it would neither touch nor cross.

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Answer:

Step-by-step explanation:

that implies a simple multiplication:

snow = (3/4)(6) = 4.5 inch

and note the units elimination in the operation as well:

= [inch/hour][hour] = inch

My fault if im wrong :(

Answer:

\(5y^3/5y^-2\) = \(y^5\)

Step-by-step explanation:

\(5y^3/5y^-2\)

as 5 is both in numerator and denominator it will get cancelled so we have now expression

\(y^3/y^-2\)

we will use  law of indices wherein if there is

\(a^x/a^y = a^(x-y)\)

which means that if the base is same in numerator and denominator then we have to subtract the power of denominator from numerator to get the reduced form using this concept

here power in numerator is 3 and power in denominator  is -2

hence we will be subtracting -2 from 3

\(y^3/y^-2 = y^(3-(-2) = y^(3+2) = y^5\)

Thus,

\(5y^3/5y^-2\) = \(y^5\)

Answer:

b) 2(x-6)(x+9)

Step-by-step explanation:

2x^2+6x-108

Factor out the 2, common factor!!!

2 (x^2 +3x -54)

Now time to factor, what to numbers multiply to get -54 and add to get 3

6,9 look good

what combination???

9,-6 because 9-6 = 3 and 9x-6=-54

so

2(x-6)(x+9)

From what I'm use to you put the 2 back in by dividing the numbers but in this case you dont need to.

The values of the piecewise function {h(x)} for different values of {x} is given above.

An algebraic expression is a made up of terms both constants and variables. For example, we can write -

2x + 3y + z

5x + y

x + 8y

Given is the relation as -

y = {- x² - 6x - 9          for   x < - 2}

y = {x/3 - 4              for x > - 2}

The given function is a piecewise function. We can write the values for different values of {x} as -

{x} = - 4

y{4} = - (-4)² - 6(-4) - 9 = - 1

{x} = - 3

y{-3} = - (-3)² - 6(-3) - 9 = - 0

{x} = - 1

y{-1} = -1/3 - 4= -4.3

{x} = 0

y{-1} = 0/3 - 4 = - 4

Therefore, the values of the piecewise function {h(x)} for different values of {x} is given above.

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Answer:

17

Step-by-step explanation:

fhxc. t thug g h y yxhxg yxtzt

Answer:

V=1/3*pi*radius(to the power of two)*height

Answer: 14 in squared

Answer:

30,016

Step-by-step explanation:

Answer: 6003.2

Step-by-step explanation:

Answer:

6613.87

Step-by-step explanation:

multiply by 2205

Answer:

30 degrees

Step-by-step explanation:

Answer:

The animal farm should buy 1.775 bags of soybeans and 1.575 bags of oats

\(Cost = 51.275\)

Step-by-step explanation:

The given parameters can be summarized as:

\(\begin{array}{cccc}{} & {x} & {y} & {Total} & {Protein} & {70} & {21} & {168} &{Fats}& {9} & {7} & {27} & {Minerals} & {7} & {1} & {14}& {Cost} & {21} & {7} & {} \ \end{array}\)

Where: x = Soybeans and y = Oats.

So, the system of equations are:

\(70x + 21y = 168\)

\(9x +7y = 27\)

\(7x + y = 14\)

\(Cost = 21x + 7y\)

The best way to solve this, is using graph

Plot the following equations on a graph, and get the points of intersection:

\(70x + 21y = 168\)

\(9x +7y = 27\)

\(7x + y = 14\)

From the attached graph, we have:

\((x_1,y_1) = (1.636,2.545)\)

\((x_2,y_2) = (1.775,1.575)\)

\((x_3,y_3) = (2.023,1.256)\)

Substitute each of the values of x's and y's in the cost function to get the minimum cost:

\(Cost = 21x + 7y\)

\((x_1,y_1) = (1.636,2.545)\)

\(Cost = 21 * 1.636 + 7 * 2.545\)

\(Cost = 52.171\)

\((x_2,y_2) = (1.775,1.575)\)

\(Cost = 21 * 1.775 + 7 * 1.575\)

\(Cost = 48.3\)

\((x_3,y_3) = (2.023,1.256)\)

\(Cost = 21 * 2.023 + 7 * 1.256\)

\(Cost = 51.275\)

The values of x and y that gives the minimum cost is:

\((x_2,y_2) = (1.775,1.575)\)

and the minimum cost is:

\(Cost = 48.3\)

Hence, the animal farm should buy 1.775 bags of soybeans and 1.575 bags of oats

Answer:

Step-by-step explanation:

we add 1 hour and 54 minutes to 17:30, then we add the 13 minute break and we have the end time of the movie

17:30 + 01:54 = 19:24

19:24 + 00:13 = 19:37 (your answer)

19:37

To calculate the time when the movie finished, we need to add the duration of the movie to the time when Sebastian started watching, taking into account the pause duration.

The movie duration is 1 hour and 54 minutes, which is equivalent to 1 hour + 54 minutes = 114 minutes.

Sebastian paused the movie for 13 minutes.

To find the total elapsed time, we add the movie duration and the pause duration:

114 minutes (movie duration) + 13 minutes (pause duration) = 127 minutes.

Now, we need to add the elapsed time of 127 minutes to the starting time of 17:30.

17:30 + 2 hours and 7 minutes (127 minutes) = 19:37.

Therefore, the movie finished at 19:37 on the 24-hour clock.

Answer:

is already in the simplest form. It can be written as 0.47138 in decimal form (rounded to 6 decimal places).

Find the GCD of numerator and denominator

GCD of 140 and 297 is 1

When you divide both the numerator and denominator by 1

The answer will remain the same

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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The ordered pairs for the equation y = -7x + 8 are (0, 8), (1, 1), and (-1, 15).

To find ordered pairs for the equation y = -7x + 8, we can substitute different values of x and solve for y.

Let's choose three values of x:

When x = 0, y = -7(0) + 8 = 8. So one ordered pair is (0, 8).

When x = 1, y = -7(1) + 8 = 1. So another ordered pair is (1, 1).

When x = -1, y = -7(-1) + 8 = 15. So another ordered pair is (-1, 15).

Therefore, the ordered pairs  are (0, 8), (1, 1), and (-1, 15).

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