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3 years ago

2 Points

1 answer:

4 0

"An angle that forms a linear pair with one of the interior angle the triangle" is the best definition of an exterior angle of a triangle.

Option: C

Explanation:

When to the sum of the inward angles opposite outer angle of a triangle the sum of the inward angles opposite is equivalent thus understood as exterior angle of a triangle.

The Triangle outer angle theorem for more about is if at each vertex the equivalent angle is drawn, the outer angles always add up to 360°. In reality, this is valid for any convex polygon, not just triangles.

In the most easiest pattern , since any angle of triangle equivalent is 60′, the outer angle would be 120′. Therefore all exterior angles sum is:

120 + 120 + 120 = 360°.

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Scores on a final exam taken by 1200 students have a bell shaped distribution with mean=72 and standard deviation=9

SVETLANKA909090 [29]

Answer:

a. 72

b. 816

c. 570

d. 30

Step-by-step explanation:

Given the graph is a bell - shaped curve. So, we understand that this is a normal distribution and that the bell - shaped curve is a symmetric curve.

Please refer the figure for a better understanding.

a. In a normal distribution, Mean = Median = Mode

Therefore, Median = Mean = 72

b. We have to know that 68% of the values are within the first standard deviation of the mean.

i.e., 68% values are between Mean $\pm$ Standard Deviation (SD).

Scores between 63 and 81 :

Note that 72 - 9 = 63 and

72 + 9 = 81

This implies scores between 63 and 81 constitute 68% of the values, 34% each, since the curve is symmetric.

Now, Scores between 63 and 81 = $\frac{68}{100} \times 1200$

= 68 X 12 = 816.

That means 816 students have scored between 63 and 81.

c. We have to know that 95% of the values lie between second Standard Deviation of the mean.

i.e., 95% values are between Mean $\pm$ 2(SD).

Note that 90 = 72 + 2(9) = 72 + 18

Also, 54 = 63 - 18.

Scores between 54 and 90 totally constitute 95% of the values. So, Scores between 72 and 90 should amount to $\frac{95}{2} \%$ of the values.

Therefore, Scores between 72 and 90 = $\frac{95}{2(100)} \times 1200 = \frac{95}{200} \times 1200$

$\implies 95 \times 12$ = 570.

That is a total of 570 students scored between 72 and 90.

d. We have to know that 5 % of the values lie on the thirst standard Deviation of the mean.

In this case, 5 % of the values lie between below 54 and above 90.

Since, we are asked to find scores below 54. It should be 2.5% of the values.

So, Scores below 54 = $\frac{2.5}{100} \times 1200$

= 2.5 X 12 = 30.

That is, 30 students have scored below 54.

8 0

2 years ago

What are two events helped bring the renaissance?

vaieri [72.5K]

Answer:

The two major events that helped bring about the Renaissance were the Black Death and the development of banking systems

Step-by-step explanation:

5 0

3 years ago

Chin canned a number of quart jars and a number of pint jars of tomatoes from his garden. A pint is 16 ounces and a quart is 32

saveliy_v [14]

Chin canned a number of quart jars and a number of pint jars of tomato. She canned total of 40 quarts, now what equation model did Chin used in the scenario

let’s simplify the problem:
Pint = 16oz
quart = 32oz

what model best show to get 40quarts.
=> p + q = 40
=> 16p + 32q = 40

the equation model that Chin used to get 40 quarts is p + q.

6 0

3 years ago

What is the probability that five people selected at random have the same birthday month?

Arturiano [62]

Answer:

Step-by-step explanation:

Uuryrurururururururu

JK the answer is 49%

5 0

3 years ago

Translate the following phrase into an algebraic expression. Do not simplify. Use the variable names "x" or "y" to describe the

Rainbow [258]

Answer:

this would be 4x

Step-by-step explanation:

this is because when you carry over the dividend you have to divide it by 2 and assuming y is 8 the answer would be 4x

7 0

3 years ago