To solve this problem, we make use of the z statistic.
What we have to do here is to find for the z score using the given data and
from the standard probability tables for z, we locate the proportion of the
fish longer than 12 inches.
The formula for calculating the z score is:
z = (x – μ) / σ
where,
x = the sample value = 12 inches
μ = the sample mean = 11 inches
σ = 2 inches
so,
z = (12 – 11) / 2
z = 1 / 2
z = 0.5
Since we are looking for the values greater than 12, so
this is a right tailed test. Using the tables, the value of p at this value of
z is:
p (z = 0.5) = 0.3085
Therefore there is a 30.85% probability that the fish is
longer than 12 inches.
Answer:
Option 2: (1,0) is the correct answer
Step-by-step explanation:
Given inequality is:
y>-5x+3
In order to find which point is solution to the given inequality we'll put the point one by one in the inequality. If the point satisfies the inequality, then the point is the solution of the inequality.
Putting (0,3) in inequality
Putting (1,0) in inequality
Putting (-3,1) in inequality
Putting (-1,-2) in inequality
The inequality is true for (1,0)
Hence,
Option 2: (1,0) is the correct answer
Step-by-step explanation:
You have to do first and second derivatives :
y = a sin 3x + b cos 3x
dy/dx = 3a cos 3x - 3b sin 3x
d²y/dx² = - 9a sin 3x - 9b cos 3x
Next, you have to compare it :
let d²y/dx² = ky,
-9a sin 3x - 9b cos 3x = k(a sin 3x + b cos 3x)
-9(a sin 3x + b cos 3x) = k(a sin 3x + b cos 3x)
Therefore, k is equals to 9.
The sum of the angles of a triangle ALWAYS sum up to 180 degrees. So to find the other angle, you would take 180, subtract 90, and then subtract 26, to get 64.
The measure of the 3rd angle equals 64.
