Find the volume of the solid that results when the region enclosed by the given curves is revolved about the x-axis. Round the answer to at least two decimal places.
[tex]y=e^{x}, y=0,x=0,x=ln(3)[/tex]

Answer:

96 in²

Step-by-step explanation:

Length of Semiperimeter

[tex]\displaystyle s=\frac{1}{2}(a+b+c)=\frac{1}{2}(12+16+20)=\frac{1}{2}(48)=24[/tex]

Area of Triangle w/Heron's Formula

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{24(24-12)(24-16)(24-20)}=\sqrt{24(12)(8)(4)}=\sqrt{9216}=96[/tex]

Hence, the area of the triangle is 96 in².

According to the given information the lateral surface area of given cylinder is 725.34 in².

In mathematics, a cylindrical is indeed a three-dimensional solid that retains two parallel bases spaced apart by a curving surface. These bases frequently have a circular shape (like a circle), and also an axis links their respective centers.

A cylinder is a three-dimensional form having two parallel, round sides on either end, one side that curves, no vertices or edges.

As we know that the lateral surface area of cylinder (A) = 2πrh

Given

D = [tex]16\frac{1}{2}[/tex]in

h = 14in

r = D/2

 = 33/4 in

A = (2 × 3.14 × 33 × 14) / 4

   = 2901.36 /4

   = 725.34 in²

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The system of equations that can be used to find the length of each workout and the duration of each workout are as follows;

(a) 5·x + 3·y = 10

2·x + 6·y = 10

(b) Length of each Plan A workout: 1.25 hours

Length of each Plan B workout: 1.25 hours

A linear system of equation consists of two or more linear equations that share common variables.

(a) The number of Plan A workouts Mary trained on Wednesday = 5

Number of Plan B workouts she trained on Wednesday = 3

The total time (in hours) Mary trained both workouts on Wednesday = 10

Where x represents the length (in hours) of each of the Plan A workout, and B represents the time in hours of each of the Plan B workout, we get;

5·x + 3·y = 10

Similarly, the number of Plan A workouts trained on Thursday = 2

Number of Plan B workout trained on Thursday = 6

The duration of training of all workouts on Thursday = 10 hours

Therefore, we get;

2·x + 6·y = 10

The system of equations that could be used to find the length (in hours) of each type of workout can be presented as follows;

(b) The first equation from the system of equations indicates that we get;

5·x + 3·y = 10

3·y = 10 - 5·x

Plugging the value of y above into the second equation from the system of equations, we get;

2·x + 6·y = 10

2·x + 6 × ((10 - 5·x)/3) = 10

2·x + 2·(10 - 5·x) = 10

2·x + 20 - 10·x = 10

20 - 8·x = 10

8·x = 20 - 10 = 10

x = 10/8 = 1.25

y = (10 - 5·x)/3,

x = 1.25, therefore;

y = (10 - 5 × 1.25)/3 = 1.25

y = 1.25

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The length of the side is 12 units in simplest radical form with a rational denominator.

A triangle is said to be equilateral if all of its sides and angles are equal. An equilateral triangle is also known as an equiangular triangle since each of its angles has a value of 60 degrees.

Given:

The triangle given in the image is an equilateral triangle.

That means the angle measure of the triangle is 60° each.

And all the sides are equal.

To find the value of x:

Sin(60/2)° = opposite/ hypotenuse.

Sin30° = x/6

x = 6/Sin30°

[tex]x = \frac{6}{1/2}[/tex]

x = 6(2)

x = 12

Therefore, the value of x is 12 units.

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The complete question:

The triangle below is equilateral. Find the length of the side in simplest radical form with a rational denominator.

The image is given below.

Answer:

  20 cubic yards

Step-by-step explanation:

You want to know the volume in cubic yards of a layer of topsoil that is 6 inches deep over an area 31 feet by 34 feet.

You know that ...

Then the dimensions of the volume being applied are ...

  6 inches = 6/36 yards

  31 feet = 31/3 yards

  34 feet = 34/3 yards

The volume is the product of the dimensions of the space:

  V = LWH

  V = (31/3 yd)(34/3 yd)(6/36 yd) ≈ 19.519 yd³

About 20 cubic yards are needed to fill the garden.

Answer:

21.7% to win $3, thats ~1/5

Step-by-step explanation:

100/6 = 10.(6) % to roll for each number (let it be just ~10.7)

for rolling a 3 or a 1 u will get $3

10.7 + 10.7 = 21.7% to win $3, thats 1/5

If the temperature dropped at a constant rate, it would have dropped 4°C per hour. This can be calculated by taking the difference in temperature (24°C) and dividing it by the number of hours that passed (4 hours).

Answer:

5 seconds

Step-by-step explanation:

d = vt + 16t² , that is

vt + 16t² = d

substitute d = 480, v = 16 into the equation

16t + 16t² = 480 ( divide through by 16 )

t + t² = 30 ( subtract 30 from both sides )

t² + t - 30 = 0 ← in standard form

(t + 6)(t - 5) = 0 ← in factored form

equate each factor to zero and solve for t

t + 6 = 0 ⇒ t = - 6

t - 5 = 0 ⇒ t = 5

t > 0 , then t = 5

the object will hit the ground 5 seconds later

Answer:

-------------------------

As per given we have:

Substitute these into given equation and solve for t:

The first value of t is discarded as time can't be negative, so the answer is 5 seconds.

The solution set of the inequality is [3, ∝)

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

2x + 4 < 10

Subtract 4 from both sides of the inequality

So, we have the following representation

2x + 4 - 4 < 10 - 4

Evaluate the like terms

2x < 6

Divide both sides by 2

x < 3

When represented as an interval notation, we have

[3, ∝)

See attachment for the inequality of the solution set

Hence, the solution is [3, ∝)

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Answer: I do not have the capability to create a graph. However, I can tell you how to graph the parabola h(x) = -x^2 + 3.

A parabola is defined by its equation in the form y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = -1, b = 0, and c = 3.

The vertex of the parabola is the highest or lowest point on the graph and is given by the coordinates (-b/2a, c - b^2/4a). For this parabola, the vertex is (0, 3), since b = 0 and a = -1.

To find another point on the parabola, you can plug in any x-value and use the equation of the parabola to find the corresponding y-value. For example, if you plug in x = -2, you get:

h(-2) = -(-2)^2 + 3

h(-2) = 4 + 3

h(-2) = 7

So the point (-2, 7) is also on the parabola.

With the vertex and one other point on the parabola, you can now graph the parabola.

Step-by-step explanation:

Answer:

3% increase

Step-by-step explanation:

Answer: x=56

Step-by-step explanation: Question 2 shows a right angle that is equal to 90 degrees. Since you are already given 34, you just need to subtract 90-34.

Question 4 shows an 180 degree angle and so you need to do the same thing; 180-124

Answer:

2nd choice  y = 1/2x - 5

Step-by-step explanation:

y = 1/2x - 5  is the only function listed that if you graph it, it makes a straight line.   A linear function forms a straight line when it is plotted on a graph.

The first and last choices are number values of x.

The 3rd choice, if you graph it, makes a parabola.

Answer:

Second option:

[tex]y = \dfrac{1}{2}x -5[/tex]

Step-by-step explanation:

A linear function should have y as a function of x (or x as a function of y) and the degree of the function (the highest power has to be 1)

Both x and y must be present to make it a linear function

General slope intercept form is y = mx + b where m = slope, b = y-intercept

With these restrictions the second option is the correct one
[tex]y = \dfrac{1}{2}x -5[/tex]

This line is in slope intercept form y = mx + b where m = slope(in this case 1/2) and y-intercept b(in this cae -5)

Option 1:  x = 3 is a straight vertical line parallel to the y-axis. Such a line has a slope of ∞

Option 3 is a function with degree 2 and is a quadratic function

Option 4 : 3x - 6 = 4==> 3x = 6 + 4 = 10 or x = 10/3, again another vertical line with slope = ∞

Answer: The correct system of linear inequalities that represents this situation is:

X + Y ≤ 32 (to represent the maximum number of hours you can work)

7X + 8Y ≥ 256 (to represent the minimum amount of money you need to earn)

X ≥ 0, Y ≥ 0 (to represent that you can only work a non-negative number of hours at each job)

Where X represents the number of hours you spend tutoring and Y represents the number of hours you spend babysitting. The first inequality represents the maximum number of hours you can work, and the second inequality represents the minimum amount of money you need to earn. The last two inequalities represent that you can only work a non-negative number of hours at each job.

Step-by-step explanation:

Answer:

---------------------------

According to picture we observe:

The segment connecting the midpoints is the midsegment.

As per property of the midsegment, it is parallel to opposite side and is half of its measure.

It tells us that WB is parallel to AE and:

The statement that are true are :

a. Z is an element {y,z}

b. {6,7,8 } is a subset of {1,2,3,4......}

c. 3 is an element of {2,3}

d. r is not an element of {s,t,u}

What is set?

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

The objects in a set are called the elements (or members ) of the set; the elements are said to belong to the set (or to be in the set), and the set is said to contain the elements.

The following statements are true about the set

a. Z is an element {y,z}

b. {6,7,8 } is a subset of {1,2,3,4......}

c. 3 is an element of {2,3}

d. r is not an element of {s,t,u}

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Using Venn diagram, 49 students participated in only music, 29 students participated in only sports, and 156 students were involved in either music or sports.

Let's use a Venn diagram to represent the information given:

We know that there are 200 students in total, and we can use the information given to fill in the numbers in the Venn diagram.

a.

127 students were involved in music, including 78 who were also involved in sports, so 127 - 78 = 49 students participated in only music.

b.

78 students participated in both music and sports, so 78 - 49 = 29 students participated in only sports.

20 students did not participate in either activity.

c.

The total number of students involved in music or sports is the sum of the number of students in each circle: 49 + 29 + 78 = 156.

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On solving the provided question, we can say that from the graphs The curve preceding technolοgical advancement is called PPF0. PPF1 is the curve following technological advancement.

Mathematicians use graphs to logically convey facts or values using visual representations οr charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue tοgether the nodes, οften referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of expοnential growth. a logarithmic graph in the shape οf a triangle

The curve preceding technolοgical advancement is called PPF0. PPF1 is the curve following technοlogical advancement.

Priοr to technological advancement, the opportunity cost of treating HIV/AIDS rises as the wοrld deviates from its PPF. The pοtential cost of treating more HIV/AIDS cases falls as a result of technοlogical advancements since less other commοdities and services must be sacrificed in οrder to treat more HIV/AIDS patients. Alternatively, the world might treat mοre HIV/AIDS patients right now by forgoing the same number of other commοdities and services.

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The equation of the rational function with the given features is given as follows:

F(x) = [4(x² + 5x + 4)]/(x² - x - 6).

A rational function is a fraction, in which both the numerator and the denominator contain instances of the variable x.

Considering the x-intercepts, the numerator of the function is defined as follows:

y = a(x + 4)(x + 1)

y = a(x² + 5x + 4).

Considering the y-intercept at (0,4), the leading coefficient a is given as follows:

a = 4.

The vertical asymptotes determine the zeros of the denominator, which is given as follows:

(x + 2)(x - 3) = x² - x - 6.

Hence the function is defined as follows:

F(x) = [4(x² + 5x + 4)]/(x² - x - 6).

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Now , to find the area

Total area of figure = Area of first Triangle + Area of second triangle

The area of the triangle = ( 1/2 ) x Length x Base

Total area of figure = ( 1/2 ) x ( 36 x 15 ) + ( 1/2 ) x ( 15 x 8 )

= ( 1/2 ) x 540 + ( 1/2 ) x 120

= 270 + 60

= 330 inches²

Therefore , the value is 330 inches²

Hence , The area of the figure is 330 inches²

The value for the variable x in the parallelogram is equal to 7.

The parallelogram LMNO have two pairs of parallel sides hence LO = MN and LM = ON.

We shall evaluate for variable x as follows:

5x + 9 = x + 37

5x - x = 37 - 9 {collect like terms}

4x = 28

x = 28/4 {divide through by 4}

x = 7

Therefore, the value for the variable x in the parallelogram is equal to 7.

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The value of the variable x is 7

It is important to note that the opposite sides of a parallelogram are congruent or equal in length.

Then, for the parallelogram LMNO

NM is parallel to OL

Now, substitute the values, we get;

NM = OL

x + 37 = 5x + 9

collect like terms

x - 5x = 9 - 37

subtract the like terms

-4x = -28

Make 'x' the subject

x = 7

Hence, the value is 7

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Answer:

Chebyshev's inequality states that for any given dataset, at least 1 - 1/k^2 of the data will lie within k standard deviations from the mean.

When k = 3, at least 1 - 1/3^2 = 1 - 1/9 = 8/9 of the data will lie within 3 standard deviations from the mean.

So, for the temperature data, we can determine that at least 8/9 of the data will lie between 28.8 - 3 × 7.4 = 7°F and 28.8 + 3 × 7.4 = 50.6°F.

In other words, we can say that at least 8/9 of the temperatures recorded during the two months were between 7°F and 50.6°F.

the displacement is 23.14m and the velocity is 21.28m/s

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The given equation y  = 25t - 1.86t²

at t =  1

So the displacement y = 25-1.86 = 23.14

to find velocity dy/dt = 25- 2(1.86)t

v = 25 - 3.72 = 21.28m/s

Hence the displacement is 23.14m and velocity is 21.28m/s

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A) The rate of change in this situation is -$100 per week.

B) She will have $300 left in her account after five weeks.

At x=2, the function in the graph is approaches to infinity. This is satisfied by equation 1 that models the rational function, hence option 1 is the correct answer.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

From given graph we can see that

At x=2, the function in the graph is approaches to infinity.

It means function is not defined at x=2

We know that a rational function is undefined when denominator is equal to zero.

For equation 1:

f(x)= 2(x+2)/(x-2)

Equating the denominator:

x-2=0

x=2

It means function is not defined at x=2

The y-intercept is: y= -2

The function is passing through the point (1,-6).

When we substitute x=1

Hence, option 1 is true.

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No one bank is not always better. Factors such as the fees and the charges in one bank may differentiate it from another bank.

No, one bank is not always better than another. The best bank for an individual depends on a variety of factors, including their financial needs and preferences, location, and the fees and charges associated with different banks.

For example, one bank may have lower fees for checking accounts but higher fees for ATM withdrawals or international transactions, while another bank may have higher fees for checking accounts but lower fees for other services.

Other factors that might affect which bank has the better fee structure include the type of account, the minimum balance required to avoid fees, and the level of customer service provided by the bank. Ultimately, the best bank is the one that meets an individual's financial needs at the lowest cost.

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The shape of the distribution of the number of clase friends for the males is best characterized as Skewed to the higher values (right or positively skewed).

Construction of closed geometric shapes involves the usage of points, line segments, circles, and curves. These shapes are all around us. Circles, rectangles, triangles, and other shapes are examples of geometric shapes. Triangle-shaped slices make up the shape of a pizza

The basic shapes include the square, circle, triangle, and other simple shapes that cannot be further subdivided into the simpler shapes by general standards.

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