Answer:
I would say C
Step-by-step explanation:
because I think that 15 is the slope and the 35 is the y intercept. I could be wrong but that would be my guess
Answer:
The expected number of appearance defects in a new car = 0.64
standard deviation = 0.93(approximately)
Step-by-step explanation:
Given -
7% had exactly three, 11% exactly two, and 21% only one defect in cars.
Let X be no of defects in a car
P(X=3) = .07 , P(X=2) = .11 , P(X=3) = .21
P(X=0 ) = 1 - .07 - .11 - .21 = 0.61
The expected number of appearance defects in a new car =
E(X) =
=
= 0.64
= variation of E(X) =
= 
=
= 0.8704
standard deviation =
=
= 0.93(approximately)
J. -8 is the correct answer
If you're talking about inequality graphs, you shade the area where any point in the shaded area can solve the inequality, if I remember correctly. I can't exactly show you how much to shade.
Answer:
General Formulas and Concepts:
<u>Pre-Calculus</u>
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Integration
- Integrals
- Definite/Indefinite Integrals
- Integration Constant C
Integration Rule [Reverse Power Rule]: 
Integration Rule [Fundamental Theorem of Calculus 1]: 
U-Substitution
- Trigonometric Substitution
Reduction Formula: 
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 (trigonometric substitution).</em>
- Set <em>u</em>:

- [<em>u</em>] Differentiate [Trigonometric Differentiation]:

- Rewrite <em>u</em>:

<u>Step 3: Integrate Pt. 2</u>
- [Integral] Trigonometric Substitution:
![\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \int\limits^a_b {cos(u)[1 - sin^2(u)]^\Big{\frac{3}{2}} \, du](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5Ea_b%20%7B%281%20-%20x%5E2%29%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%20%5C%2C%20dx%20%3D%20%5Cint%5Climits%5Ea_b%20%7Bcos%28u%29%5B1%20-%20sin%5E2%28u%29%5D%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%20%5C%2C%20du)
- [Integrand] Rewrite:
![\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \int\limits^a_b {cos(u)[cos^2(u)]^\Big{\frac{3}{2}} \, du](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5Ea_b%20%7B%281%20-%20x%5E2%29%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%20%5C%2C%20dx%20%3D%20%5Cint%5Climits%5Ea_b%20%7Bcos%28u%29%5Bcos%5E2%28u%29%5D%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%20%5C%2C%20du)
- [Integrand] Simplify:

- [Integral] Reduction Formula:

- [Integral] Simplify:

- [Integral] Reduction Formula:
![\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg|\limits^a_b + \frac{3}{4} \bigg[ \frac{2 - 1}{2}\int\limits^a_b {cos^{2 - 2}(u)} \, du + \frac{cos^{2 - 1}(u)sin(u)}{2} \bigg| \limits^a_b \bigg]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5Ea_b%20%7B%281%20-%20x%5E2%29%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7Bcos%5E3%28u%29sin%28u%29%7D%7B4%7D%20%5Cbigg%7C%5Climits%5Ea_b%20%2B%20%5Cfrac%7B3%7D%7B4%7D%20%5Cbigg%5B%20%5Cfrac%7B2%20-%201%7D%7B2%7D%5Cint%5Climits%5Ea_b%20%7Bcos%5E%7B2%20-%202%7D%28u%29%7D%20%5C%2C%20du%20%2B%20%5Cfrac%7Bcos%5E%7B2%20-%201%7D%28u%29sin%28u%29%7D%7B2%7D%20%5Cbigg%7C%20%5Climits%5Ea_b%20%5Cbigg%5D)
- [Integral] Simplify:
![\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg| \limits^a_b + \frac{3}{4} \bigg[ \frac{1}{2}\int\limits^a_b {} \, du + \frac{cos(u)sin(u)}{2} \bigg| \limits^a_b \bigg]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5Ea_b%20%7B%281%20-%20x%5E2%29%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7Bcos%5E3%28u%29sin%28u%29%7D%7B4%7D%20%5Cbigg%7C%20%5Climits%5Ea_b%20%2B%20%5Cfrac%7B3%7D%7B4%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B2%7D%5Cint%5Climits%5Ea_b%20%7B%7D%20%5C%2C%20du%20%2B%20%5Cfrac%7Bcos%28u%29sin%28u%29%7D%7B2%7D%20%5Cbigg%7C%20%5Climits%5Ea_b%20%5Cbigg%5D)
- [Integral] Reverse Power Rule:
![\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg| \limits^a_b + \frac{3}{4} \bigg[ \frac{1}{2}(u) \bigg| \limits^a_b + \frac{cos(u)sin(u)}{2} \bigg| \limits^a_b \bigg]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5Ea_b%20%7B%281%20-%20x%5E2%29%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7Bcos%5E3%28u%29sin%28u%29%7D%7B4%7D%20%5Cbigg%7C%20%5Climits%5Ea_b%20%2B%20%5Cfrac%7B3%7D%7B4%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B2%7D%28u%29%20%5Cbigg%7C%20%5Climits%5Ea_b%20%2B%20%5Cfrac%7Bcos%28u%29sin%28u%29%7D%7B2%7D%20%5Cbigg%7C%20%5Climits%5Ea_b%20%5Cbigg%5D)
- Simplify:

- Back-Substitute:

- Simplify:

- Rewrite:

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

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e