14C3 = 14! / 11!3!
<span>= 14 x13 x12 / 3x2x1 </span>
<span>= 2184 / 6 </span>
<span>= 364 different combinations </span>
<span>The first movie can be any of 14 </span>
<span>As you have already seen one the second movie can be any of the 13 remaining </span>
<span>As you have already seen two the third movie can be any of the 12 remaining. </span>
<span>Therefore there are 14 x 13 x 12 = 2184 PERMUTATIONS of movies you can see. </span>
<span>However among those 2184 different permutations will be instances where you have watched the same three movies but just in a different order. </span>
<span>eg ET, The Piano, Harry Potter = ET Harry Potter The Piano = The Piano, ET, Harry Potter = The Piano Harry Potter ET = Harry Potter ET The Piano = Harry Potter The Piano ET. </span>
<span>For each set of three films there are 3! or 3x2x1 or SIX different ways they can be arranged in. </span>
<span>Therefore we need to DIVIDE the above 2184 permutations by 6 to get the number of COMBINATIONS of different films that can be watched. </span>
<span>2184 / 6 = 364</span>
Applying the Pythagorean theorem, the missing lengths in the right triangles are:
1. √19 ≈ 4.4
2. √96 ≈ 9.8
3. √60 ≈ 7.7
4. √231 ≈ 15.2
5. √21 ≈ 4.6
6. √24 ≈ 4.9
<h3>What is the Pythagorean Theorem?</h3>
The Pythagorean theorem is a formula that can be used to find the leg of a right triangle, and is given as: c² = a² + b², where a and b are the smaller legs and c is the longest leg/hypotenuse.
1. missing leg = √(10² - 9²) = √19 ≈ 4.4
2. missing leg = √(11² - 5²) = √96 ≈ 9.8
3. missing leg = √(8² - 2²) = √60 ≈ 7.7
4. missing leg = √(16² - 5²) = √231 ≈ 15.2
5. missing leg = √(5² - 2²) = √21 ≈ 4.6
6. missing leg = √(7² - 5²) = √24 ≈ 4.9
Learn more about the Pythagorean theorem on:
brainly.com/question/343682
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The "given series" should be for 
, not 
, so that
In the limit (which should say 
, not 
), we have
Answer:
3^16
Step-by-step explanation:
12^8 * 9^12
Rewrite 12 as 3*4 and 9 as 3*3
(3*4)^8 * (3*3)^12
We know that (ab)^c = a^c * b^c
3^8 4^8 3^12 3^12
We can write 4 as 2^2
3^8 2^2^8 3^12 3^12
We know a^b^c = a^(b*c)
3^8 2^(2*8) 3^12 3^12
3^8 2^(16) 3^12 3^12
We also know that a^b *a^c *a^d = a^(b+c+d)
2^(16) 3^8 3^12 3^12
2^(16) 3^(8+12+12)
2^16 3^(32)
But we need 6 ^16 so we will need a 3^16 3^32 = 3^16 * ^16 (16+16=32)
2^16 *3^16 *3^16
Remember a^b*c^b = (ac)^b
(2*3)^16 3^16
6^16 3^16
Answer:
23 degrees
Step-by-step explanation:
First, subtract 9 from 29 to find the temperature at 9 A.M. The temperature at 9 A.M. was 20 degrees. The temperature from 5 A.M. doubled to get to the temperature at 9 A.M., so divide 20 by 2. The temperature at 5 A.M. was 10 degrees. The temperature from midnight to 5 A.M. fell 13 degrees, so add 13 to get the temperature at midnight. 13+10=23. It was 23 degrees at midnight.
