Answer: The point estimate of the population mean is <u>25</u>.
The margin of error for the confidence interval is <u>3</u> .
Step-by-step explanation:
The confidence interval for population mean is given by :-
, here
is the point estimate of the population mean and E is the margin of error .
As per given , we have
Lower bound of CI =
(1)
Upper bound of CI =
(2)
Add (1) and (2) , we get

Subtract (1) from (2) , we get

Hence, the point estimate of the population mean is <u>25</u>.
The margin of error for the confidence interval is <u>3</u> .
Problem 16
<h3>Answer: i</h3>
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Work Shown:
The exponent 41 divided by 4 leads to
41/4 = 10 remainder 1
The "remainder 1" means that
i^(41) = i^1 = i
The reason why I divided by 4 is because the pattern shown below
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
repeats itself over and over. So this is a block of four items repeated forever.
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Problem 18
<h3>Answer: 1</h3>
------------------
Work Shown:
Divide 3136 over 4 to get
3136/4 = 784 remainder 0
Therefore,
i^3136 = i^0 = 1
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Problem 20
<h3>Answer: i</h3>
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Work Shown:
Combine i^6*i^7 into i^13. We add the exponents here
Now divide by 4 to find the remainder
13/4 = 3 remainder 1
So, i^13 = i^1 = i
THe LCD is x(x^2 - 4)
so multiplying through by this we get:-
2x(x + 2) + 7x = 5(x^2 - 4)
2x^2 + 4x + 7x = 5x^2 - 20
3x^2 - 11x - 20 = 0
(3x + 4)(x - 5 ) = 0
so x = 5 , -4/3
Its the second choice
Answer : x = 25
5 x=32−7
5 x = 25
25x = 625
x=625/25
x=25
good luckkk
Answer:
y = root under 24 (evaluate it if necessary)
or y = 2 root 6
Step-by-step explanation:
Let the reference angle be x
for the triangle in left,
b = 6-4 = 2
Now,
taking x as refrence angle,
cosx = b/h
or, cosx = 2/h
again,
for the bigger triangle,
taking x as reference angle,
cosx = b/h
or, cosx = b/6
As we can see base of bigger triangle is equal to hypotenuse of triangle at the left,
Let's suppose its a
so, cosx = a/6 = 2/a
now,
a/6 = 2/a
or, a² = 12
now,
for bigger triangle, using pythagoras theorem,
h² = p²+b²
or, 6² = y² + a²
or, 36 = y² + 12
or, y² = 24
so, y = root under 24