Answer:
56
Step-by-step explanation:
Best way to tell is to convert them all to either decimals, fractions, or percentages. I usually convert to decimals. So, 75% is 0.75. 0.9 is already a decimal. And 4/5 is 0.8.
So 0.75, or 75%, is now clearly the smallest. In order from least to greatest, they go 75%, 4/5, and 0.9.
Rather than memorize sines and cosines of various common triangles, I prefer to remember the simple derivation of those formulas…
Imagine that the wall is a mirror, so you have one ladder leaning against the wall and you also have the reflection of that ladder leaning behind it. Now the ladder is 6m long, its reflection is 6m long, and if the distance between their bases is also 6m then you have a 60–60–60 equilateral triangle. And, good news, the problem says that the base angle is 60 degrees. So the real part in front of the mirror is half of the equilateral triangle, which means the distance from the base to the mirror is 3m. And then the height is sqrt(36–9) = sqrt(27) = 3*sqrt(3).
Looking at Pascal's Triangle, specifically at the row that starts with 1, 10, etc we see the value 210 in the 4th slot (start the count at 0) since 10-6 = 4
Or you can use the combination formula nCr to get the same result
nCr = (n!)/(r!*(n-r)!)
10C4 = (10!)/(4!(10-4)!)
<span>10C4 = (10!)/(4!*6!)
</span><span>10C4 = (10*9*8*7*6!)/(4!*6!)
</span><span>10C4 = (10*9*8*7)/(4!)
</span><span>10C4 = (10*9*8*7)/(4*3*2*1)
</span>10C4 = 210
Either way, the final answer is Choice C) 210
Answer:
2323
Step-by-step explanation:
Mental math means to find a way to do this problem in your head without using paper, pencil or a calculator.
The question says there are 23 classes and each class is to collect 101 items.
The equation would be 23 x 101.
To do this in your head real quick, make the numbers easier to multiply.
Make the 101 items 100. That means you are telling each class to collect 1 less item or 23 less items total.
You can do this in your head real quick. 23 classes collecting 100 items is 2300 items.
You had each class collect 100 items instead of 101. That mean you didn't collect 23 items. So if you add those back in, you will get
2323 items.
