Adie is a cube with dots on each face. the faces have 1, 2, 3, 4, 5, or 6 dots. the table below is a computer simulation (from the software package minitab) of the results of rolling a fair die 20 times. data display row c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 1 5 2 2 2 5 3 2 3 1 4 2 3 2 4 5 4 5 3 5 3 4 (a) assume that each number in the table corresponds to the number of dots on the upward face of the die. is it appropriate that the same number appears more than once? why? no, the outcome of the die roll cannot repeat. no, each distinct number of dots cannot appear on more than one face of the die. yes, the outcome of the die roll can repeat. yes, each distinct number of dots can appear on more than one face of the die.

Yes, The outcome of the die roll can repeat.

Step-by-step explanation:

Since, it is a Random Experiment No. of dots on the face of die can appear more than once.

If No. in data shows no. of dots on die. we cay say.

From the given data,

No. 1 appears 2 times which is more than once.

No. 2 appears 6 times.

No. 3 appears 5 times.

No. 4 appears 4 times.

No. 5 appears 5 times.

No. 6 appears 0 times

If we repeat this computer simulation again. we get different set of dat. But in that No. can also repeats more than once.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.