Find the value of the expression 1/2x + 3 if x = 12
2 answers:
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Answer: For 95% Confidence Interval:
Upper Limit = 110.2
Lower Limit = 97.8
95% Confidence Interval = [97.8, 110.2]
Step-by-step explanation:
Given that,
Mean(M) = 104
Standard Deviation(SD) = 10
Sample Size(n) = 10
Formula for calculating 95% Confidence Interval are as follows:
Standard error(SE) =
=
= 3.164
⇒ M ± × SE
= 104 ± (1.96)(3.164)
= 104 ± 6.20
∴ Upper Limit = 104 + 6.20 = 110.2
Lower Limit = 104 - 6.20 = 97.8
So,
95% Confidence Interval = [97.8, 110.2]
A graph shows the solutions to be
(x, y) = (-6, 312) or (6, 312)
To solve algebraically, remove a factor of 2 from the second equation and use that expression to substitute for y in the first equation.
10x^2 -(8x^2 +24) = 48
2x^2 = 72
x = ±√(72/2) = ±6
y = 8*36 +24 = 312
(x, y) = (-6, 312) or (6, 312)
To solve algebraically, remove a factor of 2 from the second equation and use that expression to substitute for y in the first equation.
10x^2 -(8x^2 +24) = 48
2x^2 = 72
x = ±√(72/2) = ±6
y = 8*36 +24 = 312