Given a scalene triangle with whole number angle measurements, what is the greatest sum possible of the two smallest angles?

Mathematics

1 answer:

Olegator [25]1 year ago

7 0

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define scalene triangle

A Scalene Triangle is any triangle with unequal sides. This means that, in a scalene triangle, all of the three sides and angles are different lengths, just like in the illustration below. This also means that each angle has to be different.

STEP 2: Get the greatest sum possible of the two smallest angles

Since the measures of the angles of the triangle are different whole numbers , for the sum of the two angles to be the least possible, one of the angles must be smallest whole number i.e 1°

Now, the next smallest angle will be the next angle of a whole number that is not 1 degree, i.e, 2 degrees.

Thus, the greatest possible sum of the measures of two smallest angles will be:

$1^{\circ}+2^{\circ}=3^{\circ}$

Hence, the greatest sum possible of the two smallest angles is 3 degrees

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A group of 30 students from your school is part of the audience for a TV game show. The total number of people in the audience i

s344n2d4d5 [400]

Answer:

5.3%

Step-by-step explanation:

The final probability is calculated by means of the quotient of the specific combinations and the total of total combinations

Let's start with the specific ones,

First the number of combinations of 4 of the 30 students getting a spot, i.e .:

A combinations are equal to:

nCx = n! / x! * (n-x)!

Replacing:

30C4 = 30! / (4! * 26!) = 27405

Segundo the number of combinations of the other audience members filling the other 4 (8-4) spots n = 110, 140 - 30

110C4 = 110! / (4! * 106!) = 5773185

Now the total combinations of possible 8 contestants from the audience

140C8 = 140! / (8! * 132!) = 2.98 * 10 ^ 12

Finally, the probability is equal to:

P = (30C4 * 110C4) / 140C8

replacing:

P = 27405 * 5773185 / 2.98 * 10 ^ 12

P = 0.053

Therefore the probability is 5.3%

4 0

3 years ago

Which simplified fraction is equal to 0.53? 1) 24/45 2) 8/15 3) 48/90 4) 5/9

Shalnov [3]

To express a decimal number (with a finite decimal expression) in a fraction, you work like this: the numerator is the number without decimale separator (you simply pretend it's not there), while the denominator will be $10^n$ , where n is the number of digits after the decimal separator.