The base of a rectangular prism is 20 cm 2 . If the height of the prism is 5 cm, what is its volume

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 composite figure has an area of 142 square yards

The composite figure has one square, right triangle, two rectangles

Area of square = side × side

=8×8

=64 yards

Area of triangle =1/2×8×6

=24 square yards

Area of 1st rectangle = 3×6

=18 square yards

Area of 2 nd rectangle = 9×4

=36 square yards

Total area is sum of square, rectangles and triangle

total area = 64+24+18+36

=142 square yards

Hence, the composite figure has an area of 142 square yards

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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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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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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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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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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

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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The area of the original figure is 1/9 times the area of the new figure

The perimeter of the original figure is 1/2 times the perimeter of the new figure

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

The figures

The areas of the new figures is calculated as

Area = Old area * scale factor

So, we have

Area Figure 1 = (1 * 3) * 3

Area Figure 1 = 9

The perimeter of the new figures is calculated as

Perimeter = Old Perimeter * scale factor

So, we have

Perimeter Figure 2 = (4 * 4 + 4 * (2 + 3)) * 1/2

Perimeter Figure 2 = 18

See attachment for the dilates figures

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Answer: 226.795 paperclips

Step-by-step explanation:

    First, we need to know how many grams are in a pound.

[tex]\boxed{\text{1 pound = 453.59 grams}}[/tex]

    Next, we will divide 453.59 grams by the 2 grams per paper clip to see how many paper clips would balance the scale with one pound.

     453.59 / 2 = 226.795 paperclips

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.

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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The value of P in the equation (10011 base 2 + P + 11100 base 2 + 101 base 2 = 1001111 base 2) is 11011 base 2.

The value of P in the equation is found as follows from the given equation:

10011 base 2 + P + 11100 base 2 + 101 base 2 = 1001111 base 2

Hence;

P = 1001111 base 2 - (10011 base 2 + 11100 base 2 + 101 base 2)

Summing the values in the bracket: 10011 + 11100 + 101 = 110100

Then the value of  P will be:

P = 1001111 base 2 - 110100 base 2

P = 11011 base 2

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Answer:

e

Step-by-step explanation:

g

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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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. :((

[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]

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

Answer:

3 2/5 +(3/2+3/5)×6/5÷3/2-10 1/2× 2/2

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]

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 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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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.

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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Answer:

  9

Step-by-step explanation:

You want the number of non-congruent rectangles that can be drawn on a 4 × 4 geoboard.

A rectangle will have right-angle corners and opposite sides the same length. The attachment shows the 9 rectangles we believe exhaust the possibilities for a grid of 4 dots by 4 dots.

<95141404393>

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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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.

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