Given the function
. The above function can be written as

a)Now, the function
has minimum value since the coefficient of
is
.
b) The minimum value of the function occurs at
and its value is

c)The minimum value of the function occurs at
.
An=a1r^(n-1)
given
a5=1/24
a10=1/768
we know that
a5=1/24=a1r^(5-1) and
a10=1/768=a1r^(10-1)
so
1/24=a1r^4
1/768=a1r^9
(a1r^9)/(a1r^4)=r^5=(1/768)/(1/24)=1/32
r^5=1/32
take 5th root of both sides
r=1/2
we have
a5=a1r^4=1/24
evaluate r^4 or (1/2)^4
1/16
a1(1/16)=1/24
times both sides by 16/1
a1=16/24
a1=2/3
the first term is 2/3
Answer:

Step-by-step explanation:
Notice that there is a right angle triangle formed with sides as follows:
hypotenuse is the actual 1500 ft string. The acute angle 43 degrees is opposite to the segment that represents the height of the kite from the ground. Therefore, the trigonometric ratio that we can use to find that opposite side to the given angle, is the sine function as shown below:

Answer:
Two tailed
Step-by-step explanation:
Given that a security expert claims that exactly 13% of all homeowners have a home security alarm.
Here we have to check whether the contention of security expert is correct or not
The test is to be done for the proportion of homeowners who have a home security alarm to total homeowners.
Let p be the proportion.
For this we set up hypotheses as:

This is a two tailed test
Because alternate is for not equal to. If alternate is for > or < we say one tailed and if not equal to we say two tailed.
Answer:
All work but I’d pick the 3rd one
Step-by-step explanation: