The volume of a cylinder is 180π cubic meters. The height of the cylinder is 11.25 meters. What is the radius of the cylinder?

The segments AB and CD are, parallel, perpendicular or neither, depending on the slopes obtained from the coordinates on the segments as follows;

Parallel lines or line segments are line segments that have the same slope.

1. The slope of the segment [tex]\overline{AB}[/tex] is; (3 - 13)/(0 - (-2)) = -10/2 = -5

The slope of the segment [tex]\overline{CD}[/tex] is;  (3 - 0)/(10 - (-5)) = 3/15 = 1/5

The slope of  [tex]\overline{AB}[/tex] is the negative inverse of the slope of  [tex]\overline{CD}[/tex] therefore;

[tex]\overline{AB}[/tex] ⊥  [tex]\overline{CD}[/tex],   [tex]\overline{AB}[/tex] is perpendicular to  [tex]\overline{CD}[/tex]

2. The slope of the segment [tex]\overline{AB}[/tex] is; (1 - 7)/(-6 - 3) = -6/-9 = 2/3

The slope of the segment [tex]\overline{CD}[/tex] is;  (-1 - (-5))/(0 - (-6)) = 4/6 = 2/3

The slope of  [tex]\overline{AB}[/tex] is the same as the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] ║ [tex]\overline{CD}[/tex],   [tex]\overline{AB}[/tex] is parallel to [tex]\overline{CD}[/tex]

3. The slope of the segment [tex]\overline{AB}[/tex] is; (4 - 2)/(-2 - (-6)) = 2/4 = 1/2

The slope of the segment [tex]\overline{CD}[/tex] is;  (-7 - 11))/(5 - (-1)) = -18/6 = -3

The slope of [tex]\overline{AB}[/tex] is different from and not the negative inverse of the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neither parallel or perpendicular

4. The slope of the segment [tex]\overline{AB}[/tex] is; (3 - 8)/(2 - (-3)) = -5/5 = -1

The slope of the segment [tex]\overline{CD}[/tex] is;  (2 - 6)/(-8 - (-4)) = -4/(-4) = 1

The slope of  [tex]\overline{AB}[/tex] is the negative inverse of the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] ⊥ [tex]\overline{CD}[/tex]

5. The slope of the segment [tex]\overline{AB}[/tex] is; (2 - (-1))/(-4 - (-8)) = 3/4

The slope of the segment [tex]\overline{CD}[/tex] is;  (6 - (-3))/(12 - 0) = 9/12 = 3/4

The slope of  [tex]\overline{AB}[/tex] is the same as the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] ║  [tex]\overline{CD}[/tex]

6. The slope of the segment [tex]\overline{AB}[/tex] is; (-1 - 5)/(3 - 6) = -6/-3 = 2

The slope of the segment [tex]\overline{CD}[/tex] is;  (7 - (-5))/(-4 - 2)) = 12/(-6) = -2

The slope of  [tex]\overline{AB}[/tex] is different from and not the negative inverse of the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] and  [tex]\overline{CD}[/tex] are neither parallel nor perpendicular.

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Answer:  Garnier's Opera House is a revival of the Baroque style.

The true similarity statement are using Right Triangle Altitude Theorem :

ΔABD similar to ΔBCD

ΔABC similar to ΔADB

ΔABC similar to ΔBDC

Two triangles are said to be similar if the triangles are of the same shape but different size. The angles of the triangle will be equal and the sides are proportional.

By the Right Triangle Altitude Theorem,

If the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then the triangles formed by the division are similar to each other and both are similar to the original triangle.

Using this,

ΔABD similar to ΔBCD

ΔABC similar to ΔADB

ΔABC similar to ΔBDC

Hence the true statements are ΔABD similar to ΔBCD, ΔABC similar to ΔADB, ΔABC similar to ΔBDC.

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The complete question is given below.

Answer:

  C)  a = b  ⇒  b = a

Step-by-step explanation:

You want to identify the statement that represents the symmetric property of equality.

If a = b and b = c, then a = c. This is the transitive property of equality.

If a = b, then ac = bc. This is the multiplication property of equality.

If a = b, then b = a. This is the symmetric property of equality.

a(b +c) = ab +ac. This is the distributive property of multiplication over addition.

Answer: the real zero of this equation is 5/3.

[tex]\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( ~~ \cfrac{\pi \theta }{180}-\sin(\theta ) ~~ \right) ~~ \begin{cases} r=radius\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=5\\ \theta =80 \end{cases} \\\\\\ A=\cfrac{5^2}{2}\left( ~~ \cfrac{\pi (80) }{180}-\sin(80^o ) ~~ \right)\implies A=\cfrac{25}{2}\left(\cfrac{4\pi }{9}- \sin(80^o) \right) \\\\\\ A=\cfrac{50\pi }{9}-\cfrac{25\sin(80^o)}{2}\implies A\approx 5.1~cm^2[/tex]

The simplified form of trigonometric functions by trigonometric formulas are listed below:

Case 1: 0.5√(2 - √3)

Case 2: (0.5√2) / (1 + 0.5√2)

Case 3: sin 6x

Case 4: sin θ

In this problem we must simplify and evaluate trigonometric functions by means of trigonometric formulas. The first two expressions must be simplified and evaluated by of half angle formulas:

Case 1

sin 15° = √[(1 - cos 30°) / 2]

sin 15° = √[(1 - √3 / 2) / 2]

sin 15° = √[(2 - √3) / 4]

sin 15° = 0.5√(2 - √3)

Case 2

tan 22.5° = sin 45° / (1 + cos 45°)

tan 22.5° = (0.5√2) / (1 + 0.5√2)

The last two expressions are simplified and evaluated by double angle formulas:

Case 3

2 · sin 3x · cos 3x

sin 6x

Case 4

2 · sin 0.5θ · cos 0.5θ

sin θ

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The area of the composite figure is equal to 521.080 square milimeters.

In this problem we have the representation of a composite figure, whose area should be found. This figure is the consequence of the combination of  three figures: a semicircle, a rectangle and a triangle. The area formulas for each case are introduced below:

Semicircle

A = 0.5π · r²

Where r is the radius, in milimeters.

Rectangle

A = b · h

Triangles

A = 0.5 · b · h

Where:

Now we proceed to compute the area of the composite figure:

A = 0.5π · (10 mm)² + (20 mm) · (14 mm) + 0.5 · (12 mm) · (14 mm)

A = 50π mm² + 280 mm² + 84 mm²

A = 521.080 mm²

The statement is absent. Complete statement is introduced below:

Find the area of the figure.

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The amount it would cost to put a new floor in the closet is $76.00

From the question, we are to calculate how much it would cost to put a new floor in the closet

From the given information,

A closet in the house is 2 yards by 1 yard.

To determine how much it would cost to put a new floor in the closet,

First,

We calculate the area of the closet

Area of the closet = 2 yard × 1 yard

Area of the closet = 2 square yards

Now,

From the given information,

The flooring costs $38.00 per square yard

Thus,

The amount it would cost to put a new floor in the closet is

2 × $38.00

= $76.00

Hence,

The amount it would cost is $76.00

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The correct groupings for each probability are given below as follows:

The possibility of two events occurring simultaneously and at the same time is known as joint probability.

Joint probability is the likelihood that event Y will take place at the same time as event X.

An example of a joint probability is the probability that you eat at the restaurant and have no commute

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The length of MN to the nearest tenth is 11.4 units

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

cos E = 4/7

MP = 20

Because the triangles are similar triangles, we have

cos M = cos E = 4/7

So, we have

cos M = MN/MP

This gives

MN/MP = 4/7

So, we have

MN/20 = 4/7

Evaluate

MN = 20 * 4/7

So, we have

MN = 11.4

Hence, the length is 11.4

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Answer:

The areas R and S are equal.

Step-by-step explanation:

Since, the tangent line to the curve y = x³ at point A(a, a³) is given by y = 3a²(x - a) + a³. This line intersects the curve at point B(a, a³), and we can find the x-coordinate of point B by setting y = 3a²(x - a) + a³ equal to x³ to get the equation x³ - 3a²x + 3a³ - a³ = 0. Using the fact that x = a is a root of this equation, we can factor it as (x - a)³ = 0, which implies that the curve and the tangent line are tangent at point B.

The slope of the tangent line at point B is 3a², so the equation of the tangent line at point B is y = 3a²(x - a) + a³. This line intersects the curve at another point C, and we can find the x-coordinate of point C by setting y = 3a²(x - a) + a³ equal to x³ to get the equation x³ - 3a²x + 3a³ - a³ = 0. Using the fact that x = a is a root of this equation, we can factor it as (x - a)³ = 0, which implies that the curve and the tangent line are tangent at point C.

The region bounded by the curve and the tangent line at point A is a triangle with base a - (a - a) = 0 and height a³ - a³ = 0, so its area is 0. The region bounded by the curve and the tangent line at point B is a triangle with base a - a = 0 and height a³ - a³ = 0, so its area is also 0. Therefore, the areas R and S are both equal to 0, which means they are equal to each other.

The 95% confidence interval for the mean is [3.23, 8.76].

The confidence of interval of the mean is calculated as follows;

Confidence interval = σ ± (t-value  x   μ)

where;

The standard error is calculated as follows:

μ = std / √n

μ = 5 / √15

μ = 1.29

Based on this value we will check the distrbution table, for the t-value of 95% confidence;

=  2.145.

Confidence interval = σ ± (t-value  x   μ)

= 6 ± (2.145 x 1.29)

= [3.23, 8.76]

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An inequality for each of the constraints (one for frames, one for hours for assembly, and 2 non-negative inequalities describing the products is:

x + y ≤ 300

x1 + y3 ≤ 360

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal.

Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

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The transformations of the given functions is vertical shift 2 units down.

Given that, the function is f(x)=-eˣ to f(x)=-eˣ-2.

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Parent Function: f(x)= −eˣ

Horizontal Shift: None

Vertical Shift: Down 2 Units

Reflection about the x-axis: None

Vertical Compression or Stretch: None

Therefore, the transformations of the given functions is vertical shift 2 units down.

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The probability values are P(A) = 0.722 and P(B) = 0.50

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

A fair die

The sample space of the events are

A = Sum is greater than 5

B = Sum is an even number

From the sample space of the sum of outcomes, we have

n(A) = 26

n(B) = 18

So, we have

P(A) = 26/36 = 0.722

n(B) = 18/36 = 0.50

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The value of x in the heptagon is 38.6 degrees.

An heptagon is a polygon with 7 sides. A regular heptagon is an heptagon with all sides equal to each other.

Therefore,  sum of angles in an heptagon is equal to 900 degrees.

Let's find each angle of the heptagon.

each angle in the regular heptagon = 900 / 7

each angle in the regular heptagon = 128.57 degrees

Therefore, each angle of a square is 90 degrees.

Hence,

x = 128.57 - 90

x = 38.5714285714

Finally,

x = 38.6 degrees

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hmm im not sure, but I'm going to try to help you!! but I think it is B or D. Maybe but I'm not too sure. though. :((

The requried, intersection points are (√5, 5), (-√5, 5), (√2, 2), and (-√2, 2).

To find the intersection points of the parabola y = x² and the circle with radius √6 and center at (0,4), we need to solve the system of equations:

x² + (y - 4)² = 6 (equation of circle)

y = x² (equation of parabola)

We can substitute y = x² into the equation of the circle and obtain a quadratic equation in x:

x² + (x² - 4)² = 6

x⁴ - 7x² + 10 = 0

This equation can be factored as:

(x² - 5)(x² - 2) = 0

Therefore, the solutions for x are x = ±√5 and x = ±√2. To find the corresponding values of y, we can substitute these values of x into the equation of the parabola:

y = x²

For x = √5, we have y = (√5)² = 5, and for x = -√5, we have y = (-√5)² = 5.

For x = √2, we have y = (√2)² = 2, and for x = -√2, we have y = (-√2)² = 2.

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The other interval is (-1.1, 0.9)

In a graph of any function, values of f(x) are represented by the values on the y-axis for the different input values on x-axis.

For the given graph, values of f(x) are less than zero.

That means interval in which the values of the function are negative for the different values of x.

Negative values of the given function are in the intervals (-∞, -3), (-1.1, 9).

Therefore, from the given options, Option (4) will be the answer.

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The complete question is

F(x)<0 over (-∞, -3) and what other interval?

O (-2.4, - 1.1)

O (-3, - 1.1)

O (-1.1, 2)

O (-1.1, 0.9)

The measure of angle TDC in the triangle is 32 degrees.

The tangent CD forms a right angle with the radius CT of the circle. This forms a right angle triangle.

Therefore, the sum of angles in the triangle is 180 degrees.

Hence,

∠C = 90 degrees

Therefore,

3x + 14 + 8x + 10 + 90 = 180

11x + 114 = 180

11x = 180 - 114

11x = 66

divide both sides by 11

x = 66 / 11

x = 6

Therefore,

∠TDC = 3x + 14 = 3(6) + 14 = 18 + 14 = 32 degrees.

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Answer: The height is 4.5 in

Step-by-step explanation:

       We can use the given formula for volume, transform it to solve for height (h), and then substitute our given values to solve.

Given formula:

[tex]\displaystyle V=\pi r^2h[/tex]

Transformed to solve for height:

[tex]\displaystyle h=\frac{V}{\pi r^2}[/tex]

Substitute given points:

[tex]\displaystyle h=\frac{(8\; \text{cubic inches})}{\pi (0.75\; \text{inches})^2}[/tex]

Square:

[tex]\displaystyle h=\frac{(8\; \text{cubic inches})}{\pi (0.5625)}[/tex]

Multiply:

[tex]\displaystyle h=\frac{8}{1.767146}[/tex]

Divide:

[tex]\displaystyle h=4.527[/tex]

Round to the nearest tenth:

[tex]\displaystyle h=4.5[/tex]

Result:

The total cost of the jeans and shirts  = 5(x + y)

Let's use variables (x and y) to show the total cost of one pair of jeans and one T-shirt, respectively.

Let x = the cost of one pair of jeans.

Let y = e the cost of one T-shirt.

Given:

Maria bought 3 pairs of jeans and 4 T-shirts, all at the same price. That is:

3x = cost of Maria's jeans

4y = cost of Maria's T-shirts

Joan bought 2 pairs of jeans and 1 T-shirt, all at the same price. That is:

2x = cost of Joan's jeans

y = cost of Joan's T-shirt

To find the total cost of all they bought, add up the costs:

Total cost = Maria's cost + Joan's cost

Total cost = 3x + 4y + 2x + y

Total cost = 5x + 5y

So the total cost is 5 times the sum of the cost of one pair of jeans and one T-shirt.

Simplify the expression by factoring out a common factor of 5, and we get:

Therefore, total cost = 5(x + y)

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Answer: 226

Step-by-step explanation:

The angle is half of the arc angle

so mDGF is 2 times as big as the angle

mDGF=113*2

mDGF=226

Answer:

e

Step-by-step explanation:

g

The proportion equivalent with Two-thirds would be 6/9.

Since we know that the proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We are given that the  proportion with Two-thirds

If you actually divide it’ll make since , so first  we want to divide the 2 , then you want to multiply the third of the two

2/3 x 3/3

6/9

thus, the answer will be 6/9.

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Answer:

1/3

Step-by-step explanation:

p(event) = (number of desired outcomes)/(total number of outcomes)

total number of outcomes = 13 + 15 + 17 = 45

number of desired outcomes = 15

p(can of tomato soup) = 15/45 = 1/3

Answer:

3 2/5 +(3/2+3/5)×6/5÷3/2-10 1/2× 2/2