What is the volume (in terms of pi) for a cylinder with a radius of 3 inches

Malcolm has been watching a roulette-style game at a local charity bazaar. The game has only ten numbers on the wheel, and every

Mariana [72]

Answer:

Malcolm is showing evidence of gambler's fallacy.

This is the tendency to think previous results can affect future performance of an event that is fundamentally random.

Step-by-step explanation:

Since each round of the roulette-style game is independent of each other. The probability that 8 will come up at any time remains the same, equal to the probability of each number from 1 to 10 coming up. That it has not come up in the last 15 minutes does not increase or decrease the probability that it would come up afterwards.

5 0

3 years ago

A student solved the following problem and made an error: Triangles ABC and DEF. Angles A and F are congruent and measure 135 de

nignag [31]

The first false statement in the proof as it stands is in Line 5, where it is claimed that a line of length 2.83 is congruent to a line of length 4.47. This mistake cannot be corrected by adding lines to the proof.

_____

The first erroneous tactical move is in Line 4, where the length of DE is computed, rather than the length of FD. This mistake can be corrected by adding lines to the proof.

A correct SAS proof would use segment FD in Line 4, so it could be argued that the first mistake is there.

7 0

3 years ago

The vertices of a triangle are A(2,5), B(1, 2), and C(3, 1). Find the coordinates of the image after a dilation with respect

Dmitry_Shevchenko [17]

The coordinates of the image after a dilation with respect to the origin is A'' (2,10), B" (0,4), C" (4,2) .

<h3>How does dilation work?</h3>

Dilation of a figure will leave its sides get scaled (multiplied) by same number. That number is called the scale factor of that dilation.

Its also called scaling of a figure, but due to the involvement of coordinates, it involves a center of a dilation, which is like a pinned point that stays at the same place after dilation.

Its like we enlarge or shorten the size of the figure (or keep it same, when scale factor = 1).

The vertices of a triangle are A(2,5), B(1, 2), and C(3, 1).

A' = 2(2.5) = (4,10)

B' = 2(1,2) = (2,4)

C' = 2(3,1) = (6,2)

Translation of 2 units left means change in x

A'' = (4-2,10) = (2,10)

B" = (2-2,4) = (0,4)

C" = (6-2,2) = (4,2)

Translation of 1 units up means change in y

Learn more about vertices ;

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7 0

2 years ago

Would appreciate the help 24 points

andre [41]

Answer:

13) Rectangle

14) parallelogram

15) co ordinates areD (0,a) andE (c,b)

16) co ordinates are D(0,b) and E(a,0)

17)(-1,1) (4,1) (-1,4)

18)(0,0) (a,0) (a,a) (0,a)

Step-by-step explanation:

<h3>13)</h3><h3>Rectangle</h3>

The opposite sides of a rectangle are parallel and equal

left height = right height

(by using distance formula)

(0,3),(2,-2) = (5,5),(7,0)

√(2-0)²+(-2-3)² = √(7-5)²+(0-5)²

√(2)²+(-5)² = √(2)²+(-5)²

√4+25 = √(2)²+(-5)²

√29 = √29 hence equal

<h3>14)</h3><h3>parallelogram</h3>

The opposite sides of a rectangle are not equal

left height = right height

(by using distance formula)

(0,0),(3,-4) = (3,4),(7,0)

√(3-0)²+(-4-0)² = √(7-3)²+(0-4)²

√(3)²+(-4)² = √(5)²+(-4)²

√9+16 = √(25)+(16)

√(25) ≠√41

5 ≠ √41

<h3>15)</h3><h3>co ordinates are D(0,a) and E(c,b)</h3><h3>16)</h3><h3>co ordinates are D(0,b) and E(a,0) </h3>

since rhombus have equal opposite sides

6 0

3 years ago

Given: mAngleEDF = 120°; mAngleADB = (3x)°; mAngleBDC = (2x)° Prove: x = 24 3 lines are shown. A line with points E, D, C inters

N76 [4]

Answer:

" Vertical angles are congruent " ⇒ 2nd answer

Step-by-step explanation:

* <em>Look to the attached figure </em>

- There are three lines intersected at point D

- We need to find the missing in step 3

∵ Line FA intersects line EC at point D

- The angles formed when two lines cross each other are called

vertical angles

- Vertical angles are congruent (vertical angles theorem)

∴ ∠ADC and ∠FDE are vertical angles

∵ Vertical angles are congruent

∴ ∠EDF ≅ ∠ADC

∴ m∠EDF ≅ m∠ADC

∵ m∠EDF = 120° ⇒ given

∵ m∠ADC = m∠ADB + m∠BDC

∴ m∠ADB + m∠BDC = 120°

∵ m∠ADB = (3x)° ⇒ given

∵ m∠BDC = (2x)° ⇒ given

∴ 3x + 2x = 120 ⇒ add like terms

∴ 5x = 120 ⇒ divide both sides by 5

∴ x = 24

Column (1) Column (2)

m∠EDF = 120° given

m∠ADB = 3 x given

m∠BDC = 2 x given

∠EDF and ∠ADC are vertical angles defin. of vert. ∠s

∠EDF is congruent to ∠ADC vertical angles are

congruent

m∠ADC = m∠ADB + m∠BDC angle add. post.

m∠EDF = m∠ADC defin. of cong.

m∠EDF = m∠ADB + m∠BDC substitution

120° = 3 x + 2 x substitution

120 = 5 x addition

x = 24 division

∴ The missing reason is " vertical angles are congruent "

- From the explanation above ∠ADC and ∠FDE are vertical

angles then they are congruent according to vertical angle

theorem

6 0

3 years ago

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