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mina [271]
2 years ago
9

The results of rolling a 6-sided die 120 times are given in the table below.

Mathematics
1 answer:
Bas_tet [7]2 years ago
5 0

Step-by-step explanation:

According to the results of rolling a 6-sided die 120 times, we have:

Rolling a 2:

Experimental = 15/120 = 1/8 = 0.125 = 12.5%

Theoretical = 20/120 = 1/6 = 0.1667 = 16.67%

Rolling a 1:

Experimental = 18/120 = 3/20 = 0.15 = 15%

Theoretical = 20/120 = 1/6 = 0.1667 = 16.67%

Rolling a 1 or 6:

Experimental = 18/120 + 20/120 = 38/120 = 19/60= 0.3167 = 31.67%

Theoretical = 20/120 + 20/120 = 40/120 = 1/3 = 0.3333 = 33.33%

Step-by-step explanation:

1. First of all, let's recall what is the difference between experimental and theoretical probability of an event.

The experimental probability is the result of an experiment, and the theoretical probability is based on the mathematical model developed in the theory of probability.  In simple words, the most important difference is that the experimental probability is based on what actually happens and the theoretical probability on what is expected to happen.

The accuracy of the results of the experiments depends directly on the sample size of the experiment and the accuracy is greater when the sample size is larger.

For this particular event the theoretical probability is the same for rolling each number of the die, 1/6 or 16.67%

Now, let's complete the answer this way:

Rolling a 2:

Experimental = 15/120 = 1/8 = 0.125 = 12.5%

Theoretical = 20/120 = 1/6 = 0.1667 = 16.67%

Rolling a 1:

Experimental = 18/120 = 3/20 = 0.15 = 15%

Theoretical = 20/120 = 1/6 = 0.1667 = 16.67%

Rolling a 1 or 6:

Experimental = 18/120 + 20/120 = 38/120 = 19/60= 0.3167 = 31.67%

Theoretical = 20/120 + 20/120 = 40/120 = 1/3 = 0.3333 = 33.33%

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Read 2 more answers
Fill in the blanks in the following proof.
NARA [144]

Answer:

Table :

     Statements                 Reasons

1)ΔEGC≅ΔEGB                 Given

2)EB = EC                          Corresponding Parts of Congruent

                                          Triangles are Congruent

3) BC = BE                         Given

4) By 2 and 3                      EB≅EC≅BC

5)∠BEC = 60°                     ΔBEC is an equilateral triangle

Step-by-step explanation:

We are given that BE = BC  ---1

We are also given that ΔEGC≅ΔEGB

So, BE = CE(Corresponding Parts of Congruent Triangles are Congruent) ---2

Now By 1 and 2

BE=BC=CE

In ΔBEC

BE=BC=CE

Since all sides are equal . So, it is an equilateral triangle

All angles of equilateral triangle are also equal i.e. 60°

So, ∠BEC = 60°

Hence proved

Table :

     Statements                 Reasons

1)ΔEGC≅ΔEGB                 Given

2)EB = EC                          Corresponding Parts of Congruent

                                          Triangles are Congruent

3) BC = BE                         Given

4) By 2 and 3                      EB≅EC≅BC

5)∠BEC = 60°                     ΔBEC is an equilateral triangle

7 0
3 years ago
What postulate or theorem can be used to prove that these two triangles are congruent?
kati45 [8]

Answer:

AAS postulate can be used to prove that these two triangles are congruent

Step-by-step explanation:

Let us revise the cases of congruence  

  1. SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ
  2. SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and including angle in the 2nd Δ
  3. ASA ⇒ 2 angles and the side whose joining them in the 1st Δ ≅ 2 angles and the side whose joining them in the 2nd Δ
  4. AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles and one side in the 2nd Δ
  5. HL ⇒ hypotenuse and leg of the 1st right Δ ≅ hypotenuse and leg of the 2nd right Δ  

In the given figure

∵ There is a pair of vertically opposite angles

∵ The vertically opposite angles are congruent ⇒ (1)

∵ There are two angles have the same mark

∴ These marked angles are congruent ⇒ (2)

∵ There are two sides have the same mark

∴ These two marked sides are congruent ⇒ (3)

→ From (1), (2), and (3)

∴ The two triangles have 2 angles and 1 side congruent

→ By using case 4 above

∴ The two triangles are congruent by the AAS postulate of congruency.

AAS postulate can be used to prove that these two triangles are congruent

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