A carpenter built a square table with side length x. Next, he will build a rectangular table by tripling one side and halving the other. The area of the rectangular table is represented by the expression (3 x)(one-half x).

A square with sides x. A rectangle with side one-half x and side 3 x.

What is the simplified expression for the area of the rectangular table?

Three-halves x squared
Three-halves x
Five-halves x squared
Five-halves x

a. Sketch the region of integration in the XY-plane.

b. Reverse the order of integration.

c. Evaluate the integral.

(a) The integral is a double integral, which means that the region of integration is a region in the XY plane. The region of integration is defined by the limits of integration for x and y. However, since the limits of integration are not given, it's not possible to sketch the region of integration in the XY plane.

(b) The integral is already written with the order of integration reversed.

(c) Without the limits of integration, it is not possible to evaluate the integral. The limits of integration are necessary to determine the region of integration, and thus the range of values for x and y over which the integral is to be taken. Without this information, it is not possible to carry out the evaluation of the integral.

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The mean of y-values is referred to as [tex]\bar{y}[/tex]. So, option b is the correct choice.

A variable in a set of sample data in statistics is symbolized by the little Latin letter x. If a letter has a horizontal bar above it, it means the variable it is placed over is considered the average or mean.

We would add all of the sample data points, divide by the sample size, and then compute the x-bar, or sample mean. This is given by [tex]\bar{x}=\frac{x_1+x_2+x_3+\cdots\cdots+x_n}{n}[/tex] where n is referred to as the sample size and [tex]\bar{x}[/tex] is the sample mean.

Therefore, the central tendency of the data is represented by this [tex]\bar{x}[/tex] or the x bar. Therefore, the mean of y-values is represented by y bar or [tex]\bar{y}[/tex].

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When the train stops at Tucson in return trip, distance he travelled is 2378 miles and distance left for the train to travel is 1408 miles

Distance is a measure of how far away two objects or points are from one another. In physics or daily life, the term "distance" can refer to a physical distance or an estimate based on other criteria (for example, "two counties over").

|AB| can be used to denote the distance between two points. In most situations, the distance from point B to point A can easily be used in place of the distance from point A to point B.

A distance metric or function is a way to explain what it means for elements of a space to be "far apart from" or "close to" each other. It is a generalisation of the idea of physical distance in mathematics.

If the train stops at Tucson in return trip, distance he travelled is,

d = 1893 + (1893 - 1408)

d = 2378 miles

And, miles the train have left to travel is

⇒ 1893 + 1893 - 2378

= 3786 - 2378

= 1408 miles

Thus, When the train stops at Tucson in return trip, distance he travelled is 2378 miles and distance left for the train to travel is 1408 miles.

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1. The complete table is shown below.

2. The graph is attached below.

3. the function h(x) is an odd function.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

m(x)=[tex]x^4[/tex]

and, h(x)= [tex]1/4 (x-6)^4[/tex]

So, the -6' in the h(x) there is Horizontal transformation on right side by 6 units, i.e., (x, y)--->(x +6, y)

and, 1/4 in h(x) shows there is Vertical stretch in h(x).

So, (x,  y)--->(x, y/4)

Now, Points on m(x)    points on h(x)

            (x, y)                      (x+6, y/4)

            (-2, 16)                   (4, 4)      

            (-1, 1)                      (5, 1/4)      

            (0, 0)                     (6, 4)      

            (2, 16)                    (8, 4)      

2. The graph is attached below.

3. Replace h(x) by h(-x) we get

h(-x) = [tex]1/4 (x-6)^4[/tex]

h(-x) = [tex]1/4 (-x-6)^4[/tex] will give an odd function.

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Answer:

y = [tex]\frac{8}{p+q+4}[/tex]

Step-by-step explanation:

py + qy = - 4y + 8 ( add 4y to both sides )

py + qy + 4y = 8 ← factor out y from each term on the left side

y(p + q + 4) = 8 ← divide both sides by p + q + 4

y = [tex]\frac{8}{p+q+4}[/tex]

The value of x is 1 and the value of y is 3, this can be obtained using the substitution method.

The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another.

The given equations are:

x + 2y = 7 and 3x -2y = -3

In the given equation x + 2y = 7 isolate the value of x:

x = 7 - 2y

Substitute the value of x in 3x -2y = -3:

3( 7 - 2y) - 2y = -3

21 - 6y - 2y = -3

21 + 3 = 8y

24 = 8y

y = 3

Substitute the value of y in equation to find the value of x:

x + 2(3) = 7

x + 6 = 7

x = 1

Hence, the value of x is 1 and the value of y is 3.

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Answer:

Step-by-step explanation: Umm multiply 80 by 2 and divied 78 after add 10

Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution.

A quadratic equation is a second-order polynomial equation in one variable that goes like this: x ax2 + bx + c=0, where a 0.Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution.Real or complicated solutions are both possible.

Option A , x = 7/5 and x= -1

Formula: Let ax² + bx + c = 0 be the quadratic equation,

x = [-b±√(b²-4ac)]/2a

The given quadratic equation be

5x² -2x = 7

⇒ 5x² -2x - 7 = 0  

a = 5, b = -2 and c = -7

Therefore x = [-b±√(b²-4ac)]/2a

x=[-(-2) ±

√((-2)²-4*5*(-7))]/2*5

x =[2 ± √144)]/10

x =[2 ± 12)]/10

x = (2+12)/10 and x = (2-12)/10

x = 14/10 = 7/5 and x= -12/10 = -1

Therefore,the correct answer is Option A , x = 7/5 and x= -1.

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By analyzing the graph, we can see that the transformed function, F(x), is the one in option D.

F(x) = 2*x^2 + 3

On the graph, we can see the graphs of both equations, F(x) and G(x), where G(x) = x^2

First, we can see that the vertex of the quadratic of F(x) is at the point (0, 3).

So first we have a translation of 3 units upwards, we also can see that the parabola of F(x) is narrower (horizontally) than the one of G(x), then we must have a scale factor larger than 1 multiplying the function.

Then we have something like:

F(x) = k*G(x) + 3 = k*x^2 + 3

Where k > 1.

The only option that has this form is option D.

F(x) = 2*x^2 + 3

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The perimeter of trapezoid JKLM is

9 + √(2) + √(5) units.

Option D is the correct answer.

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as 1/2 x the sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

First, we find the lengths of each side of the trapezoid.

JK = distance between points J and K

JK = √((4 - 4)² + (-4 - (-7))²) = √(9) = 3

LM = distance between points L and M

LM = √((3 - 3)² + (-8 - (-2))²) = √(36) = 6

KL = distance between points K and L

KL = √((3 - 4)² + (-2 - (-4))²) = √(5)

JM = distance between points J and M

JM = √((3 - 4)² + (-8 - (-7))²) = √(2)

Now,

We can add up the lengths of each side to find the perimeter.

Perimeter = JK + KL + LM + JM

Perimeter = 3 + √(5) + 6 + √(2)

Perimeter = 9 + √(2) + √(5)

Therefore,

The perimeter of trapezoid JKLM is

9 + √(2) + √(5) units.

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The solution for the given system of equations is (-2, -2).

What is addition method?

Using the Addition Method to Solve Systems of Equations in Two Variables. The addition method, also known as the elimination method, is a third strategy for resolving linear equation systems. With this approach, we add two terms that share the same variable but have opposing coefficients, resulting in a sum of zero.

Given:

The system of equations,

3x + 7y = -20          ..(1)

-3x + 6y = -6            ..(2)

We have to solve this system of equations using addition method.

Adding equation (1) and (2)

      3x + 7y = -20

 +  -3x + 6y = -6

__________________

       0 + 13y = -26

13y = -26

  y = -2

Plug y = 2 in equation (1), we get

3x + 7(-2) = -20

3x - 14 = -20

3x = -20 + 14

3x = -6

x = -2

Hence, the solution for the given system of equations is (-2, -2).

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No, His answer is not reasonable.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Tarren estimates that the product of 10 and 4 is about 120.

Now, We know that;

The product of 10 and 4 is,

⇒ 10 × 4 = 40

Thus, His answer is not reasonable.

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Answer:

d

Step-by-step explanation:

I think the a answer is d

We can compute the integral of the velocity function's absolute value. In other words, the area under the velocity function's curve's absolute value equals the distance a particle travels.

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Answer:

27540

Step-by-step explanation:

yes

Given that tan alpha = -24/10 and pi < alpha < 2pi, we can use the trigonometric identities to find the value of sin alpha.

To what does sin equate?

In contrast to the cosine of an angle, which corresponds to the ratio of the nearby side to the hypotenuse, the sine of an angle is the ratio of the opposite side to the hypotenuse.

Since tan alpha = -24/10, we know that sin alpha / cos alpha = -24/10

We can find the value of cos alpha by using the fact that pi < alpha < 2pi, so 0 < alpha - pi < pi.

Therefore, cos alpha = cos (alpha - pi) = -cos (alpha - pi)

We can substitute this into the equation above:

sin alpha / (-cos (alpha - pi)) = -24/10

We can then solve for sin alpha:

sin alpha = (-24/10) * (-cos (alpha - pi))

We can simplify the expression, but we cannot determine the exact value of sin alpha without knowing the value of alpha.

Note that tangent is negative in the second and third quadrant, so the angle is in the third quadrant.

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On using the exterior angle theorem the value of ∠G  is obtained as option D: 88 degrees.

What is exterior angle theorem?

The measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle, according to the external angle theorem.

The measure of ∠F = (6x - 10)°

The measure of ∠E = 38°

The measure of ∠G = (7x + 18)°

But, in the given image it can be seen that the ∠G lies outside the triangle.

Apply the exterior angle theorem to solve the value for x.

According to the exterior angle theorem, the equation will be -

∠F + ∠E = ∠G

Substitute the values into the equation -

(6x - 10)° + 38° = (7x + 18)°

Simplify the equation -

6x - 10 + 38 = 7x + 18

Collect the like terms -

6x - 7x = 18 + 10 - 38

-x = -10

x = 10

So, the value of x is obtained to be 10°.

Substitute the value of x in ∠F and ∠G -

∠F = (6x - 10)°

∠F = (6(10) - 10)°

∠F = (60 - 10)°

∠F = 50°

∠G= (7x + 18)°

∠G= (7(10) + 18)°

∠G= (70 + 18)°

∠G= 88°

Therefore, the values of angles are ∠F = 50° and ∠G= 88°.

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If we assume that each student's heart creates the same amount of energy as a single person, the energy created would be enough to drive the truck for 192000 meters.

If we assume that each student's heart creates the same amount of energy as a single person, we can estimate the total amount of energy created by the class.

If one person's heart creates enough energy to drive a truck for 32 kilometers,

Then six people's hearts would create enough energy to drive the truck for 32 x 6 = 192 kilometers.

In meters, it would be 192 x 1000 = 192000 meters.

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Every day your heart creates enough energy to drive a truck for 32 kilometers. If you combined the energy that is created by all the students in your math class for a week, how many meters could the truck drive?

Number of students is 6

Answer: x belongs to (0, 0.4444)

Step-by-step explanation:

one of the most common forms of the equation of lines called slope-intercept form along with derivation.

The linear equation y = mx + c is a line with m as slope, m and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.

The slope, m, represents the steepness of a line. The slope of the line is also termed as gradient, sometimes. The y-intercept, b, of a line, represents the y-coordinate of the point where the graph of the line intersects the y-axis.

We know that, the equation of a line in point slope form, where (x1, y1) is the point and slope m is:

(y – y1) = m(x – x1)

Here, (x1, y1) = (0, c)

Substituting these values, we get;

y – c = m(x – 0)

y – c = mx

y = mx + c

Therefore, the point (x, y) on the line with slope m and y-intercept c lies on the line if and only if y = mx + c

Slope Intercept Form Formula

As derived above, the equation of the line in slope-intercept form is given by:

y = mx + c

Here,

(x, y) = Every point on the line

m = Slope of the line

c = y-intercept of the line

Usually, x and y have to be kept as the variables while using the above formula

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Tthe probability that the difference in the diameters of the two ball bearings is less than 0.06 mm is 0.0478

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

Mean = 11.5

Standard deviation = 0.05

Let the diameters be X and Y

So, we have

P(|X - Y| < 0.06)

Using this information, we have

P(|X - Y| < 0.06) = P( -0.06 < X - Y < 0.06)

= P(X - Y < 0.06) - P(X - Y < -0.06)

= 0.0478

Hence, the probability is 0.0478

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It would take 28.6 years for the value of the account to reach $390.

The equation reads A(t) = Ao (2) Where

A(t) = 3902, Ao = 230, and t =?, k = 7 years

Hence, 3902 = 230 × (2)

^t/7

We divide 230 on both sides (3902/230 = 230) (2)

^t/7/230

16.965217391 = (2) (2)

^t/7

Calculate the ln of both sides:

16.965217391 = ln (2)t/7

ln 16.965217391 = t/7 ln (2) (2)

In 16.965217391/ln 2 = t/7

t = 4.0874628413× 7

t = 28.612239889 years

Approximately = 28.6 years

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The value of b in the Line JK passes through points J(–4, –5) and K(–6, 3) is

b = –21

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The slope, m of the linear function is calculated using the points J(–4, –5) and K(–6, 3)

m = (y₀ - y₁) / (x₀ - x₁)

m = (3 + 5) / (-6 + 4)

m = (8) / (-2)

m = -4

equation passing through point K(–6, 3)

(y - y₁) = m'  (x - x₁)

y - 3 = -4(x + 6)

y - 3 = -4x - 24

y = -4x - 24 + 3

y = -4x - 21

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The rotation of figure R about its center will produce the image of R as given in option C.

Rotation is a type of rigid transformation which involves turning a given figure or object at a an angle about a reference point to produce an image. This process can be used to explain the question given.

Some other types of rigid transformation are; dilation, translation, reflection.

All these have their distinct procedures and would be applied as expected or stated in the question.

When figure R is rotated about the center at 180 degrees, it would produce an image of R as shown in option C.

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Answer:

e

Step-by-step explanation:

Answer:

The completed table is given below and the equation for the given situation is 15=4a+0.50s.

Given that, it costs $0.50 to download an individual song and $4 to download an album.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Jada has $15 to spend downloading music.

Let s be number of songs and a be number of albums

So an equation for the given situation is 15=4a+0.50s

From table, in row 1

Given number of songs is 6

15=4a+0.50(6)

⇒ 15=4a+3

⇒ 4a=12

⇒ a=3

From table, in row 2

Given number of albums is 1

15=4(1)+0.50s

⇒ 0.50s=11

⇒ s=11/0.50

⇒ s=22

From table, in row 3

Given number of albums is 30

15=4a+0.50(30)

⇒ 15-15=4a

⇒ a=0

Hence, the completed table is given below and the equation for the given situation is 15=4a+0.50s.

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Step-by-step explanation:

The domain and the range of the graphed relation are given as follows:

The domain of a function is composed by the set that contains all possible values assumed by the input of the function. Hence, considering the graph of the function, the domain is given by the values of x of the graph.

As the graph contains open circles at both the ends of the domain, the domain is composed by an open interval.

The range of a function is composed by the set that contains all possible values assumed by the output of the function. Hence, considering the graph of the function, the range is given by the values of y of the graph.

The graph assumes a minimum value of -6, hence the lower bound is closed, however the upper bound at y = 4 is open, as the only point the graph reaches y = 4 is on the open circle.

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Answer:[tex]\sqrt{61}[/tex]

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]\sqrt{5^{2} +6^{2} } =\sqrt{25+36}=\sqrt{61}[/tex]

The distance between A and B = [tex]\sqrt{61}[/tex]