Answer: 8
Step-by-step explanation: 112 divided by 8 is 14. I took the quiz.
You would use inches if you were in the United States. If you were not in the United States, you would use centimeters.
Answer:
B. the trials must be dependent
Step-by-step explanation:
The image for the question is attached.
The missing options are;
A. The probability of a success remains the same in all trials.
B. The trials must be dependent.
C. Each trial must have all outcomes classified into two categories.
D. The procedure has a fixed number of trials.
For a binomial distribution probability, the event must be repeated for a number of time (n) and the probability of success (q) must be the same during each trial.
Binomial distribution probability has two possible outcome: success (p) or failure (q). The event are also independent of each other.
The formula for a binomial distribution probability is given as:
P(X=x) = nCx (p ^ x) (q ^ (n-x))
From the above, we can see that the answer is:
B. the trials must be dependent
The given differential equation is
<em>x</em> ² (<em>y'</em> - <em>x</em> ²) + 3<em>xy</em> = cos(<em>x</em>)
Expanding and rearranging terms, we get
<em>x</em> ² <em>y'</em> + 3<em>xy</em> = cos(<em>x</em>) + <em>x</em> ⁴
Multiply both sides by <em>x</em>, which is motivated by the fact that (<em>x</em> ³)<em>'</em> = 3<em>x</em> ².
<em>x</em> ³ <em>y'</em> + 3<em>x</em> ²<em>y</em> = <em>x</em> cos(<em>x</em>) + <em>x</em> ⁵
The left side is the derivative of a product:
(<em>x</em> ³<em>y</em>)<em>'</em> = <em>x</em> cos(<em>x</em>) + <em>x</em> ⁵
Integrate both sides with respect to <em>x</em> :
∫ (<em>x</em> ³<em>y</em>)<em>'</em> d<em>x</em> = ∫ (<em>x</em> cos(<em>x</em>) + <em>x</em> ⁵) d<em>x</em>
<em>x</em> ³<em>y</em> = cos(<em>x</em>) + <em>x</em> sin(<em>x</em>) + 1/6 <em>x</em> ⁶ + <em>C</em>
Solve for <em>y</em>. Since <em>x</em> > 0, we can safely divide both sides by <em>x</em> ³.
<em>y</em> = cos(<em>x</em>)/<em>x</em> ³ + sin(<em>x</em>)/<em>x </em>² + 1/6 <em>x</em> ³ + <em>C</em>/<em>x</em>³