Looks like the PMF is supposed to be

which is kinda weird, but it's not entirely clear what you meant...
Anyway, assuming the PMF above, for this to be a valid PMF, we need the probabilities of all events to sum to 1:

Next,





If

, then

, where we take the positive root because we know

can only take on positive values, namely 1, 2, and 5. Correspondingly, we know that

can take on the values

,

, and

. At these values of

, we would have the same probability as we did for the respective value of

. That is,

Part (5) is incomplete, so I'll stop here.
Answer:
<em>(8.21, -20.79)</em>
Step-by-step explanation:
Given the simultaneous equation;

From 2;
a = 29 + b ....3
Substitute 3 into 1;

Factorize
b = -18±√18²-4(-58)/2
b = -18±√324+232/2
b = -18±√556/2
b = -18±23.58/2
b = -18-23.58/2 and -18+23.58/2
b = -41.58/2 and 5.58/2
b = -20.79 and 2.79
Since a = 29 + b
when b = -20.79
a = 29 - 20.79
a = 8.21
<em>Hence the solution to the system of equation is (8.21, -20.79)</em>
Answer:a
Step-by-step explanation:
Answer:

General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]: ![\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bcf%28x%29%5D%20%3D%20c%20%5Ccdot%20f%27%28x%29)
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Integration
Integration Rule [Fundamental Theorem of Calculus 1]: 
Integration Property [Multiplied Constant]: 
U-Substitution
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>

<u>Step 2: Integrate Pt. 1</u>
<em>Identify variables for u-substitution.</em>
- Set <em>u</em>:

- [<em>u</em>] Differentiate [Basic Power Rule, Derivative Properties]:

- [Bounds] Switch:

<u>Step 3: Integrate Pt. 2</u>
- [Integral] Rewrite [Integration Property - Multiplied Constant]:

- [Integral] U-Substitution:

- [Integral] Exponential Integration:

- Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:

- Simplify:

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
<h2>
Hello!</h2>
The answer is: There are a total of 16 skits in the video.
<h2>Why?</h2>
From the statement, we know that the total length of the video is 101 minutes and it contains a 5-minute introduction, the rest of the minutes are short skits (which are 6 minutes long each one).
So, we need to write the following equations:
First equation:

Second equation:

Where,

So, replacing and substituting the second equation into the first equation we have:

So, there are a total of 16 skits in the video.
Let's prove it substituting "n" into the first equation:

Have a nice day!