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2 years ago

BRAINLIEST AND 20 POINTS PLZ HELP ASAP

Mathematics

2 answers:

DanielleElmas [232]2 years ago

5 0

Answer:

Step 1: It should be m∠m + m∠n + m∠o = 180° (sum of angles in a triangle)

Step-by-step explanation:

He made the mistake in Step 1: m∠m + m∠n + m∠p = 180°

It should be m∠m + m∠n + m∠o = 180°

Then only, he can equate it with m∠o + m∠p in step 3.

So, m∠p is the exterior angle and m∠m and m∠n are the two remote interior angles.

m∠o is the adjacent angle to m∠p. They form a linear pair.

Hence, the correct answer is Step 1.

Rom4ik [11]2 years ago

5 0

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Suppose we write the numbers $1,2,3,4,5,6$, and then color each number red or blue. The coloring is called factorific if there i

Oxana [17]

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The probability that his coloring is factorific is 0.28125

Step-by-step explanation:

For calculate the probability is necessary to identify the total number of ways to color the six number. This can be calculate with the rule of multiplication as:

2*2*2*2*2*2=64

Because we have 2 options to color every number.

For know the number of ways in which the coloring is factorific, first we need to identify the divisors of each number:

1: the divisor is 1

2: The divisors are 2 and 1

3: The divisors are 3 and 1

4: The divisors are 4, 2 and 1

5: The divisors are 5 and 1

6: The divisors are 6, 3 and 1

From these information we analyse that for made a factorific coloring, is necessary that the number 1 is color blue. Additionally if the number 4 is color blue, the number 2 needs to be color blue and if the number 6 is blue, the number 3 needs to be blue.

So, the number of ways in which we can create a factorfic number is determined by the following cases:

The number 2 is blue and the number 3 is blue: In this case we have 1 option for number 1, one for number 2 and 1 for number 3. Taking into account that the number 2 and 3 are blue, if the number 4 and 6 are blue or red doesn't change the fact that the coloring is going to be factorific. So, we have two options for number 3 and 2 options for number 6. Finally the color of the number 5 is independent of the colors of number 2 and 3, so we also have 2 options for coloring number 5 and the coloring is going to be factorific. Then the number of ways for this situation is calculate as:

1 * 1 * 1 * 2 * 2 * 2 = 8

number 1 number 2 number 3 number 4 number 5 number 6

At the same way we can calculate the following cases:

The number 2 is blue and the number 3 is red: If the number 3 is red, the coloring is only going to be factorific is number 6 is red. Then the number of ways for this situation is calculate as:

1 * 1 * 1 * 2 * 2 * 1 = 4

number 1 number 2 number 3 number 4 number 5 number 6

The number 2 is red and the number 3 is red: If the number 2 and 3 are red, the coloring is only going to be factorific is number 4 and 6 are red. Then the number of ways for this situation is calculate as:

1 * 1 * 1 * 1 * 2 * 1 = 2

number 1 number 2 number 3 number 4 number 5 number 6

The number 2 is red and the number 3 is blue: If the number 2 is red, the coloring is only going to be factorific is number 4 is red. Then the number of ways for this situation is calculate as:

1 * 1 * 1 * 1 * 2 * 2 = 4

number 1 number 2 number 3 number 4 number 5 number 6

If we sum all the cases, we obtain 18 ways to make a factorific coloring. So the probability can be calculated as:

$P= \frac{18}{64} = 0.28125$

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