How many different combinations of two can be made from 80 people?

1 answer:

3 0

Plugging directly into the combination formula, the answer is $\binom{80}{2}=\frac{80!}{2!78!}=\frac{80\cdot 79}{2\cdot 1}=40\cdot 79=\boxed{3160},$ where we have cancelled out common factors.

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2. Use the following picture for this question:

Art [367]

Answer:

a. $24\sqrt{3}$ and 41.6

b. 52.1

Step-by-step explanation:

Considering the left side triangle the blue dotted side is the side "opposite" to the angle given and the side 24 is the side that is "adjacent" to the angle given. The trigonometric ratio tan relates opposite to adjacent. Also, let the blue dotted side be y.

<u>Note:</u> the exact value of tan 60 is $\sqrt{3}$

Thus, we can write $Tan(60)=\frac{y}{24}\\y=24*Tan(60)\\y=24*\sqrt{3} \\y=24\sqrt{3}$

Approximate value (rounded to nearest tenth): $24\sqrt{3} =41.6$

Considering the triangle to the right, the side "opposite" to the angle given (53 degrees) is 41.6 (just found in part (a)) and the side "hypotenuse" (side opposite to 90 degree angle) is x. The trigonometric ratio sine relates opposite and hypotenuse.

Thus we can write and solve:

$Sin(53)=\frac{41.6}{x}\\x=\frac{41.6}{Sin(53)}=52.1$

4 0

3 years ago

Henry wants to paint the ceilings and the walls of his living room. One gallon of paint covers 450 ft squared. The rooms is 24 f

Mamont248 [21]

If you would like to know how many gallons of paint will Henry need to paint his living room, you can calculate this using the following steps:

the ceiling: 24 ft * 18 ft = 432 ft squared
walls: 2 * 24 ft * 9 ft + 2 * 18 ft * 9 ft = 2 * 24 * 9 + 2 * 18 * 9 = 432 + 324 = 756 ft squared

432 ft squared + 756 ft squared = 1188 ft squared

1 gallon of paint ... 450 ft squared
x gallons of paint = ? ... 1188 ft squared

1 * 1188 = 450 * x
1188 = 450 * x /450
x = 1188 / 450
x = 2.64 gallons of paint

The correct result would be 2.64 gallons of paint.

6 0

3 years ago

12.6 pounds equals how many ounces

Stells [14]

201.6 ounces
Hope this helps and please mark me as brainlest and like

4 0

3 years ago

Andre paid $13 for 3 books. Diego bought 12 books priced at the same rate.

yKpoI14uk [10]

X = $ 52 for the 12 books Diego bought

7 0

3 years ago

(2.3 x 10^5)(3.4 x 10^9) Answer in scientific notation!? asap please

wel

If the numbers supposed to be multiplied together the answer is 7.82 x 10^14

7 0

3 years ago