Suppose we want to choose 5 objects, without replacement, from 15 distinct objects.
1 answer:
15444 ways we can choose 5 objects, without replacement, from 15 distinct objects.
Given that, suppose we want to choose 5 objects, without replacement, from 15 distinct objects.
<h3>What is a permutation?</h3>A permutation is a mathematical calculation of the number of ways a particular set can be arranged, where the order of the arrangement matters.
Now, = 13!/(13-5)!
= 13!/8! = 13x12x11x10x9= 1287 x 120 = 15,444
Therefore, 15444 ways we can choose 5 objects, without replacement, from 15 distinct objects.
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Answer:
It has amplitude of .
It is a horizontal shift of the parent function units left.
Step-by-step explanation:
We have the function, .
It is clear that the parent function is .
So, we see that,
The amplitude of the function f(x) is , which gives,
.
Also, g(x) is translated units to the left, which gives,
.
Further, the function is translated 1 unit downward, resulting in .
So, the correct options are,
It has amplitude of .
It is a horizontal shift of the parent function units left.
Answer:
200
Step-by-step explanation:
We have:
We can rearrange the numbers to obtain:
From the left, we can factor out a negative. So:
In other words, we want to find the sum of all the odd numbers from 1 to 99.
And the sum of all the even numbers from 2 to 100.
Let's do each one individually:
Odd Terms:
We have:
We can use the arithmetic series formula, where:
Where k is the number of terms, a is the first term, and x_k is the last term.
Since it's all the odd numbers between 1 and 99, there are 50 terms.
Our first term is 1 and our last term is 99. So, the sum of all the odd terms are:
Divide the fraction. Add within the parentheses:
Multiply:
So, the sum of all the odd terms is 2500.
Even Terms:
We have:
Again, we can use the above formula.
Our first term is 2, last term is 100. And since it's from 2-100, we have 50 even terms. So:
Divide and add:
Multiply:
We originally had:
Substitute them for their respective sums:
Multiply:
Add:
Multiply:
So, the sum of our sequence is 200.
And we're done!
Note: I just found a <em>way</em> easier way to do this. We have:
Let's group every two terms together. So:
We can see that they each sum to 1:
Since there are 100 terms, we will have 50 pairs, so 50 times 1. So:
Multiply:
Pick which one you want to use! I will suggest this one though...
Edit: Typo