What exponential function is the best fit for the data in the table?
2 answers:
Answer: fourth option
Explanation:
1) the pair x = 3 f(x) = 0, leads you to probe this:
f(3) = 0 = A [4 ^ (3 - 1) ] + C = 0
=> A [4^2] = - C
A[16] = - C
if A = 1/4
16 / 4 = 4 => C = - 4
That leads you to the function f(x) = [1/4] 4 ^( x - 1) - 4
2) Now you verify the images for that function for all the x-values of the table:
x = 2 => f(2) + [1/4] 4 ^ (2 - 1) - 4 = [1/4] 4 - 4 = 4 / 4 - 4 = 1 - 4 = - 3 => check
x = 3 => f(3) = [1/4] 4^ (3 - 1) - 4 = [1/4] 4^2 - 4 = 16 / 4 - 4 = 4 - 4 = 0 => check
x = 4 -> f(4) = [1/4] 4^ (4-1) - 4 = [1/4] 4^(3) - 4 = (4^3) / 4 - 4 = 4^2 - 4 = 16 - 4 = 12 => check.
Therefore, you have proved that the answer is the fourth option.
Explanation:
1) the pair x = 3 f(x) = 0, leads you to probe this:
f(3) = 0 = A [4 ^ (3 - 1) ] + C = 0
=> A [4^2] = - C
A[16] = - C
if A = 1/4
16 / 4 = 4 => C = - 4
That leads you to the function f(x) = [1/4] 4 ^( x - 1) - 4
2) Now you verify the images for that function for all the x-values of the table:
x = 2 => f(2) + [1/4] 4 ^ (2 - 1) - 4 = [1/4] 4 - 4 = 4 / 4 - 4 = 1 - 4 = - 3 => check
x = 3 => f(3) = [1/4] 4^ (3 - 1) - 4 = [1/4] 4^2 - 4 = 16 / 4 - 4 = 4 - 4 = 0 => check
x = 4 -> f(4) = [1/4] 4^ (4-1) - 4 = [1/4] 4^(3) - 4 = (4^3) / 4 - 4 = 4^2 - 4 = 16 - 4 = 12 => check.
Therefore, you have proved that the answer is the fourth option.
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Answer: 95.45 %
Step-by-step explanation:
Given : The distribution is bell shaped , then the distribution must be normal distribution.
Mean :
Standard deviation :
The formula to calculate the z-score :-
For x = 13
For x = 19
The p-value =
In percent,
Hence, the percentage of data lie between 13 and 19 = 95.45 %
Well... we know that... there are 365 days in a year, unless is a leap-year, but we'll use 365 anyway
and each day has 24hrs, each hr has 60 minutes
so. let us use those ratios
so.. multiply and simplify, cancelling out any like-units atop and bottom
notice, all we do, is use the ratios, in a way, that if we need one unit to be changed, we flip the ratio
for example, to toss away "year" unit, since in the first fraction is at the bottom, then we put it on the top on the ratio, year/year = 1, effectively cancelling the unit
and each day has 24hrs, each hr has 60 minutes
so. let us use those ratios
so.. multiply and simplify, cancelling out any like-units atop and bottom
notice, all we do, is use the ratios, in a way, that if we need one unit to be changed, we flip the ratio
for example, to toss away "year" unit, since in the first fraction is at the bottom, then we put it on the top on the ratio, year/year = 1, effectively cancelling the unit