Step-by-step explanation:
First, find the degrees of freedom:
df = n − 1
df = 49
To find the p-value manually, use a t-score table. Find the row corresponding to 49 degrees of freedom. Then find the α column that corresponds to a t-score of 1.421. You'll find it's between α = 0.10 (t = 1.299) and α = 0.05 (t = 1.677). Interpolating, we get an approximate p-value of 0.084. For a more accurate answer, you'll need to use a calculator.
9514 1404 393
Answer:
1) f⁻¹(x) = 6 ± 2√(x -1)
3) y = (x +4)² -2
5) y = (x -4)³ -4
Step-by-step explanation:
In general, swap x and y, then solve for y. Quadratics, as in the first problem, do not have an inverse function: the inverse relation is double-valued, unless the domain is restricted. Here, we're just going to consider these to be "solve for ..." problems, without too much concern for domain or range.
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1) x = f(y)
x = (1/4)(y -6)² +1
4(x -1) = (y-6)² . . . . . . subtract 1, multiply by 4
±2√(x -1) = y -6 . . . . square root
y = 6 ± 2√(x -1) . . . . inverse relation
f⁻¹(x) = 6 ± 2√(x -1) . . . . in functional form
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3) x = √(y +2) -4
x +4 = √(y +2) . . . . add 4
(x +4)² = y +2 . . . . square both sides
y = (x +4)² -2 . . . . . subtract 2
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5) x = ∛(y +4) +4
x -4 = ∛(y +4) . . . . . subtract 4
(x -4)³ = y +4 . . . . . cube both sides
y = (x -4)³ -4 . . . . . . subtract 4
Answer:
Step-by-step explanation:
Answer:
5,5,7,*9,11,*12,16,23
Step-by-step explanation:
Since, the data has an even amount of numbers once, you put your numbers in order you place your pointer fingers from the 1st to last number & continue to move closer. There is an even amount of numbers so you would have to add the 2 numbers up & then divide them by 2.
9+11=20 divided by 2=10
