Answer:
The standard error of the mean = 5.14 mins
Step-by-step explanation:
Number of random sample (n) = 20
Mean(X) = 31.25 mins
Standard deviation (α) = 23.7 mins
Standard error of mean =
standard deviation / √sample size
= 23.7/√20
= 23.7/4.4721
= 5.14 mins
Answer:
Distance of home plate to 1st base is equal to home plate to 3rd base
Step-by-step explanation:
Let's first assign each position:
A: home base
B: 1st base
C: 2nd base
D: 3rd base
The information given:
'It’s the same distance from the second base to the first base from the second base to third-base' tells us BC = CD
'the angle formed by the first base second base and Homeplate has the same measure as the angle formed by the base second base home plate' tells us angle(BCA) = angle(DCA)
Check for congruency between triangle ABC and ADC
BC = CD - side congruency (S)
angle(BCA) = angle(DCA) - angle congruency (A)
CA = CA - side congruency (S)
So triangle ABC and ADC fullfill the criteria of congruence property as SAS.
Since both triangle are congruent, another side of the triangles AB and AD must be the same too.
AB = home plate to 1st base
AD = home plate to 3rd base
Therefore we can conclude that the distance of home plate to 1st base is equal to home plate to 3rd base
Answer:
6.5500
Step-by-step explanation:
Note that f(x) as given is <em>not</em> invertible. By definition of inverse function,
which is a cubic polynomial in 
with three distinct roots, so we could have three possible inverses, each valid over a subset of the domain of f(x).
Choose one of these inverses by restricting the domain of f(x) accordingly. Since a polynomial is monotonic between its extrema, we can determine where f(x) has its critical/turning points, then split the real line at these points.
f'(x) = 3x² - 1 = 0 ⇒ x = ±1/√3
So, we have three subsets over which f(x) can be considered invertible.
• (-∞, -1/√3)
• (-1/√3, 1/√3)
• (1/√3, ∞)
By the inverse function theorem,
where f(a) = b.
Solve f(x) = 2 for x :
x³ - x + 2 = 2
x³ - x = 0
x (x² - 1) = 0
x (x - 1) (x + 1) = 0
x = 0 or x = 1 or x = -1
Then 
can be one of
• 1/f'(-1) = 1/2, if we restrict to (-∞, -1/√3);
• 1/f'(0) = -1, if we restrict to (-1/√3, 1/√3); or
• 1/f'(1) = 1/2, if we restrict to (1/√3, ∞)
