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Sholpan [36]
2 years ago
11

Suppose we want to choose 6 letters, without replacement, from 15 distinct letters. (A) how many ways can this be done, if the o

rder of choices is not taken into consideration? (B) How many ways can this be done, if the order of choices is taken into consideration?
Mathematics
1 answer:
Olenka [21]2 years ago
7 0

Answer:

Below in bold.

Step-by-step explanation:

A.This is the number of combinations of 6 from 15

= 15C6

=  15! / (15-6)! 6!

= 5,005 ways.

B.  This is the number of permutaions of 6 from 15:

= 15! / (15-6)!

= 3,603,600 ways.

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A bag of skittles contains green and purple candies in the ratio of 3 green to 4 purple. If there are 24 purple candies in the b
Basile [38]

Answer:

Their would be 12 green skittles.

6 0
3 years ago
Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse
Drupady [299]

Answer:

a'(d) = \frac{d}{5} + \frac{3}{5}

a(a'(d)) = a'(a(d)) = d

Step-by-step explanation:

Given

a(d) = 5d - 3

Solving (a): Write as inverse function

a(d) = 5d - 3

Represent a(d) as y

y = 5d - 3

Swap positions of d and y

d = 5y - 3

Make y the subject

5y = d + 3

y = \frac{d}{5} + \frac{3}{5}

Replace y with a'(d)

a'(d) = \frac{d}{5} + \frac{3}{5}

Prove that a(d) and a'(d) are inverse functions

a'(d) = \frac{d}{5} + \frac{3}{5} and a(d) = 5d - 3

To do this, we prove that:

a(a'(d)) = a'(a(d)) = d

Solving for a(a'(d))

a(a'(d))  = a(\frac{d}{5} + \frac{3}{5})

Substitute \frac{d}{5} + \frac{3}{5} for d in  a(d) = 5d - 3

a(a'(d))  = 5(\frac{d}{5} + \frac{3}{5}) - 3

a(a'(d))  = \frac{5d}{5} + \frac{15}{5} - 3

a(a'(d))  = d + 3 - 3

a(a'(d))  = d

Solving for: a'(a(d))

a'(a(d)) = a'(5d - 3)

Substitute 5d - 3 for d in a'(d) = \frac{d}{5} + \frac{3}{5}

a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}

Add fractions

a'(a(d)) = \frac{5d - 3+3}{5}

a'(a(d)) = \frac{5d}{5}

a'(a(d)) = d

Hence:

a(a'(d)) = a'(a(d)) = d

7 0
2 years ago
The measure of angle 3 is 42°. <br><br> What is the measure of angle 1 in degrees?
Svetradugi [14.3K]

Answer:

Angle 1 is 48°

Step-by-step explanation:

So angle 1 + angle 2 + angle 3 = 180°

Angle 2 = 90°

Angle 3 = 42°

180 - 90 - 42 =  48°

3 0
2 years ago
I need help on this please!! 10th grade geometry!!
Over [174]

Answer:

D. 90tan50 degrees

Step-by-step explanation:

The tree is known as the opposite leg of the 50 degree angle, and the given 90 feet is the adjacent leg. Here, we use tan because SOHCAHTOA can help us remember tan means opposite over adjacent. Then, we do tan50 degrees = (the height of the tree)/90. To solve, multiply tan50 by 90. This gives us the height of the tree = 90tan50 degrees.

5 0
3 years ago
√18 is between _____. <br>8.9 and 9.1 <br>3.1 and 3.2 <br>4.2 and 4.3 <br>4.5 and 4.6
Eva8 [605]

Answer:

I think it is 8.9 and 9.1

Step-by-step explanation:

because

3.1 its way off so no

4.2 and 4.3 it ehh

but 4.5 and 4.6 it close

hope this helps

3 0
2 years ago
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