If 44% of a number is 120, find 11% of that number.
1 answer:
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Answer:
- (-1, -32) absolute minimum
- (0, 0) relative maximum
- (2, -32) absolute minimum
- (+∞, +∞) absolute maximum (or "no absolute maximum")
Step-by-step explanation:
There will be extremes at the ends of the domain interval, and at turning points where the first derivative is zero.
The derivative is ...
h'(t) = 24t^2 -48t = 24t(t -2)
This has zeros at t=0 and t=2, so that is where extremes will be located.
We can determine relative and absolute extrema by evaluating the function at the interval ends and at the turning points.
h(-1) = 8(-1)²(-1-3) = -32
h(0) = 8(0)(0-3) = 0
h(2) = 8(2²)(2 -3) = -32
h(∞) = 8(∞)³ = ∞
The absolute minimum is -32, found at t=-1 and at t=2. The absolute maximum is ∞, found at t→∞. The relative maximum is 0, found at t=0.
The extrema are ...
- (-1, -32) absolute minimum
- (0, 0) relative maximum
- (2, -32) absolute minimum
- (+∞, +∞) absolute maximum
_____
Normally, we would not list (∞, ∞) as being an absolute maximum, because it is not a specific value at a specific point. Rather, we might say there is no absolute maximum.
Answer:
2.87%
Step-by-step explanation:
We have the following information:
mean (m) = 200
standard deviation (sd) = 50
sample size = n = 40
the probability that their mean is above 21.5 is determined as follows:
P (x> 21.5) = P [(x - m) / (sd / n ^ (1/2))> (21.5 - 200) / (50/40 ^ (1/2))]
P (x> 21.5) = P (z> -22.57)
this value is very strange, therefore I suggest that it is not 21.5 but 215, therefore it would be:
P (x> 215) = P [(x - m) / (sd / n ^ (1/2))> (215 - 200) / (50/40 ^ (1/2))]
P (x> 215) = P (z> 1.897)
P (x> 215) = 1 - P (z <1.897)
We look for this value in the attached table of z and we have to:
P (x> 215) = 1 - 0.9713 (attached table)
P (x> 215) =.0287
Therefore the probability is approximately 2.87%
