The probability is always expressed as a part of the whole. So, it can be in terms of fraction or percentage. The numerator is the number of possible events while the denominator is the number of total events. Let x be the number of times you roll an odd number. So, the number of times you roll an even number would be 2x. The total rolls would then be x + 2x. Thus, the probability of rolling an odd number is
Probability = x/(2x + x) = x/3x = 1/3
The triangle inequality requires the third side be in the range
.. 12 -4 ≤ third side ≤ 12 +4
.. 8 ≤ third side ≤ 16 . . . . . . . . . your answer is the number(s) in this range
_____
Some define the triangle inequality using < rather than ≤. Be careful here.
Answer:
The integral is equal to 
for an arbitrary constant C.
Step-by-step explanation:
a) If 
then 
so the integral becomes 
. (the constant of integration is actually 5C, but this doesn't affect the result when taking derivatives, so we still denote it by C)
b) In this case 
hence 
. We rewrite the integral as 
.
c) We use the trigonometric identity 
is part b). The value of the integral is 
. which coincides with part a)
Note that we just replaced 5+C by C. This is because we are asked for an indefinite integral. Each value of C defines a unique antiderivative, but we are not interested in specific values of C as this integral is the family of all antiderivatives. Part a) and b) don't coincide for specific values of C (they would if we were working with a definite integral), but they do represent the same family of functions.
Simplifying
30c + -45d
Factor out the Greatest Common Factor (GCF), '15'.
15(2c + -3d)
Final result:
15(2c + -3d)
Let it be x
Using basic proportionality theorem
