Let's start from what we know.

Note that:

(sign of last term will be + when n is even and - when n is odd).
Sum is finite so we can split it into two sums, first

with only positive trems (squares of even numbers) and second

with negative (squares of odd numbers). So:

And now the proof.
1) n is even.
In this case, both

and

have

terms. For example if n=8 then:

Generally, there will be:

Now, calculate our sum:



So in this case we prove, that:

2) n is odd.
Here,

has more terms than

. For example if n=7 then:

So there is

terms in

,

terms in

and:

Now, we can calculate our sum:




We consider all possible n so we prove that:
Answer:
Step-by-step explanation:
A parameter describes a population, and a statistic describes a sample.
The first one is a statistic. A sample was surveyed.
The second one is a parameter. It describes the entire soccer team.
The third one is a statistic. A sample was surveyed.
The fourth one is a parameter. It describes the entire golf team.
Answer:
A. 64/125
B. 124/125.
Step-by-step explanation:
A). As the events ( germinate or not germinate) are independent we multiply the probabilities.
Prob(All seeds germinate) = 4/5*4/5*4/5 = 64/125.
B). Probability of at least one germinating = 1 - probability that none germinate
Probability of 1 seed not germinating = 1 -45 = 1/5.
So Prob(at least one germinating)
= 1 - (1/5 * 1/5 * 1/5)
= 1 - 1/125
= 124/125.
Answer:
first one should be $35.52
Second one $18.60
Step-by-step explanation:
Answer:
Options A, B and C are CORRECT PROPORTIONS
Step-by-step explanation:
Option A
3:5 = 6:10
The LHS must equal the RHS
3:5 is in it's lowest term.
6/10 will be in it's lowest term by dividing the numerator and denominator by 2.
6/10 = 3/5
Option B
3/6 and 5/10.
Diving 3/6 fractions by 3
= 1/2
Dividing 5/10 fraction by 5
= 1/2
Option C
Dividing 6/3 by 3 = 2
Dividing 10/5 by 5 = 2
Thats how you work through equivalent proportional fractions