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Answer:
(27.3692 ; 44.6308)
Step-by-step explanation:
Mean, xbar = 36
Standard deviation, s = 11
Sample size, n = 12
Tcritical at 0.2, df = 12 - 1 = 11 ; Tcritical = 2.718
Confidence interval :
Xbar ± Margin of error
Margin of Error = Tcritical * s/sqrt(n)
Margin of Error = 2.718 * 11/sqrt(12) = 8.6308
Confidence interval :
Lower boundary : 36 - 8.6308 = 27.3692
Upper boundary : 36 + 8.6308 = 44.6308
(27.3692 ; 44.6308)
Answer:
x = ±4
Step-by-step explanation:
Step 1: Write out quadratic
2x² - 5 = 27
Step 2: Add 5 to both sides
2x² = 32
Step 3: Divide both sides by 2
x² = 16
Step 4: Take the square root of both sides
x = ±4
∴ x can equal -4 or 4
Average rate of change of the function 
Solution:
Given function: 
from x = 1 to x = 5
Substitute x = 1 and x = 5 in f(x).
Let us find the average rate of change of the function.
Average rate of change
Here a = 1 and b = 5.
Substitute f(5) and f(1).
Average rate of change of the function
248 to 370 gems
set up two equations
132=(1/2)x+8 x=248
193=(1/2)x+8 x=370
