Answer: A) 1260
Step-by-step explanation:
We know that the number of combinations of n things taking r at a time is given by :-
![^nC_r=\dfrac{n!}{(n-r)!r!}](https://tex.z-dn.net/?f=%5EnC_r%3D%5Cdfrac%7Bn%21%7D%7B%28n-r%29%21r%21%7D)
Given : Total multiple-choice questions = 9
Total open-ended problems=6
If an examine must answer 6 of the multiple-choice questions and 4 of the open-ended problems ,
No. of ways to answer 6 multiple-choice questions
= ![^9C_6=\dfrac{9!}{6!(9-6)!}=\dfrac{9\times8\times7\times6!}{6!3!}=84](https://tex.z-dn.net/?f=%5E9C_6%3D%5Cdfrac%7B9%21%7D%7B6%21%289-6%29%21%7D%3D%5Cdfrac%7B9%5Ctimes8%5Ctimes7%5Ctimes6%21%7D%7B6%213%21%7D%3D84)
No. of ways to answer 4 open-ended problems
= ![^6C_4=\dfrac{6!}{4!(6-4)!}=\dfrac{6\times5\times4!}{4!2!}=15](https://tex.z-dn.net/?f=%5E6C_4%3D%5Cdfrac%7B6%21%7D%7B4%21%286-4%29%21%7D%3D%5Cdfrac%7B6%5Ctimes5%5Ctimes4%21%7D%7B4%212%21%7D%3D15)
Then by using the Fundamental principal of counting the number of ways can the questions and problems be chosen = No. of ways to answer 6 multiple-choice questions x No. of ways to answer 4 open-ended problems
= ![84\times15=1260](https://tex.z-dn.net/?f=84%5Ctimes15%3D1260)
Hence, the correct answer is option A) 1260
Answer:
![\displaystyle m = \frac{1}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Coordinates (x, y)
- Slope Formula:
![\displaystyle m = \frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%20%3D%20%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
Point (2, 5)
Point (6, 7)
<u>Step 2: Find slope </u><em><u>m</u></em>
- Substitute in points [Slope Formula]:
![\displaystyle m = \frac{7-5}{6-2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%20%3D%20%5Cfrac%7B7-5%7D%7B6-2%7D)
- [Fraction] Subtract:
![\displaystyle m = \frac{2}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%20%3D%20%5Cfrac%7B2%7D%7B4%7D)
- [Fraction] Simplify:
![\displaystyle m = \frac{1}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
Answer:
25
Step-by-step explanation:
Answer:
f(5, 0) = 25
f(5, -3) = 61
Step-by-step explanation:
f(x, y) = x² - 3xy - y²
⇒ f(5, 0) = (5)² - 3(5)(0) - (0)²
= 25 - 0 - 0
= 25
⇒ f(5, -3) = (5)² - 3(5)(-3) - (-3)²
= 25 - 15(-3) - 9
= 25 + 45 - 9
= 61
Answer:
42
Step-by-step explanation:
A pentagon has an internal sum of 540.
93+166+127+112+x=540
x=42