Answer:
Option (A).
Step-by-step explanation:
Option (A).
All whole numbers are integers.
True.
Option (B).
Whole numbers and integers have no element in common.
False. All whole numbers are integers. Therefore, whole numbers are contained in integers on Venn diagram.
Option (C).
All integers are whole numbers.
False. All whole numbers are integers.
Option (D).
Some whole numbers are integers.
False. All whole numbers are integers.
ANSWER
b=11
EXPLANATION
The given quadratic equation is
We expand to get:
We simplify further by combining the x terms.
This is the standard form.
Comparing to
We have b=11
(cos(x) + cos(y))^2 + (sin(x) - sin(y))^2 Remove the brackets
cos^2(x) + cos^2(y) + 2cos(x)*cos(y) + sin^2(x) - 2(sin(x)*sin(y) + sin^2(y) Combine these two in bold to make 1 because sin^2(x) + cos^2(x) = 1
1 + cos^2(y) + 2cos(x)*cos(y) - 2*sin(x)*cos(y) + sin^2(y)
These two in bold also make 1
2 + 2cos(x)*cos(y) - 2*sin(X)*sin(y) Bring out a common factor of 2
2 +2(cos(x)*cos(y) - sin(x)*sin(y) )
but cos(x+y ) = cos(x)*cos(y) - sin(x)*sin(y)
2 + 2* cos(x + y) is your final answer.
A) The empirical rule tells you the probability of being within 1 standard deviation of the mean is 68%.
b) The probability that the sample mean falls within 3 standard deviations* of the mean is 99.7%.
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* The standard deviation of the sample mean is 1/√9 = 1/3 of the standard deviation of an individual sample. Hence the same limits (90-110) now cover 3 standard deviations of the sample mean.
