The teacher has to take 10 questions at a time from 12 questions.
Total ways = 12C10 = 12!/(10!)(12-10)! = 12 x 11 / 2 = 66
The teacher can make 66 different exams
Answer:
196
Step-by-step
Step 1: the last number of 38,416 is 6. <u>6 is not a perfect square.</u>
Step 2: because 6 is not a perfect square, split the number up and add each digit together:
3 + 8 + 4 + 1 + 6 =<u> 22</u>
<u>2 + 2 </u>= 4
Step 3:
the digital root of 38,416 is 4.
4 is in the list of digital roots that are always perfect squares. We can conclude that 38,416 could be a perfect square!
Step 4: find all the factors:
1 x 38,416 2 x 19,208 4 x 9,604 7 x 5,488 8 x 4,802 14 x 2,744 16 x 2,401 28 x 1,372 49 x 784 56 x 686 98 x 392 112 x 343 <em><u>196 x 196</u></em>
Underlined above is the factor combination that makes 38,416 a perfect square. A number can only be a perfect square if the product of two exactly the same numbers is equal to the original number.
Answer:
X° + 2x° + 45° = 180°
X = 45°, 2x = 90°
Step-by-step explanation:
Since the angles in a triangle sums up to 180
And the angles in this particular triangle is measured as 2x° + x° + 45° = 180
With this equation, we can find the value of x and 2x
2x + x + 45 = 180
3x + 45 = 180
3x = 180 - 45
3x = 135
Now divide both sides by 3
3x/3 = 135/3
X = 45
Therefore, the angles of that triangle are x° = 45, 2x°= 45 × 2 = 90° and the third angle which was given to us as 45°
