Answer:
5 31/30 or 181/30
Step-by-step explanation:
$3.60 for 2 cups would be $1.80 for one cup.
$3.60 for 2
$5.40 for 3
$7.20 for 4
$9 for 5
$10.80 for 6
$12.60 for 7
$14.40 for 8
Answer:
1.) mean
2.) H0 : μ = 64
3.) 0.0028
4) Yes
Step-by-step explanation:
Null hypothesis ; H0 : μ = 64
Alternative hypothesis ; H1 : μ < 64
From the data Given :
70; 45; 55; 60; 65; 55; 55; 60; 50; 55
Using calculator :
Xbar = 57
Sample size, n = 10
Standard deviation, s = 7.14
Test statistic :
(xbar - μ) ÷ s/sqrt(n)
(57 - 64) ÷ 8 / sqrt(10)
Test statistic = - 2.77
Pvalue = (Z < - 2.77) = 0.0028 ( Z probability calculator)
α = 10% = 0.1
Reject H0 ; if P < α
Here,
P < α ; Hence, we reject the null
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: