|Ω| = 6 - number of all results
A = {1, 3} → |A| = 2 - number of (a) results
P(A) = 2/6 = 1/3
Answer:
![\left\{\begin{array}{l}y\ge -x-6\\ \\ y\le 2x+4\end{array}\right.](https://tex.z-dn.net/?f=%20%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7Dy%5Cge%20-x-6%5C%5C%20%5C%5C%20y%5Cle%202x%2B4%5Cend%7Barray%7D%5Cright.)
Step-by-step explanation:
The diagram shows shaded region which boundary is bounded with two lines.
<u>Equation of the 1st line:</u>
This line passes through the points (-6,0) and (0,-6), so its equation is
![\dfrac{x-(-6)}{0-(-6)}=\dfrac{y-0}{-6-0}\\ \\\dfrac{x+6}{6}=\dfrac{y}{-6}\\ \\y=-x-6](https://tex.z-dn.net/?f=%5Cdfrac%7Bx-%28-6%29%7D%7B0-%28-6%29%7D%3D%5Cdfrac%7By-0%7D%7B-6-0%7D%5C%5C%20%5C%5C%5Cdfrac%7Bx%2B6%7D%7B6%7D%3D%5Cdfrac%7By%7D%7B-6%7D%5C%5C%20%5C%5Cy%3D-x-6)
<u>Equation of the 2nd line:</u>
This line passes through the points (-2,0) and (0,4), so its equation is
![\dfrac{x-(-2)}{0-(-2)}=\dfrac{y-0}{4-0}\\ \\\dfrac{x+2}{2}=\dfrac{y}{4}\\ \\y=2x+4](https://tex.z-dn.net/?f=%5Cdfrac%7Bx-%28-2%29%7D%7B0-%28-2%29%7D%3D%5Cdfrac%7By-0%7D%7B4-0%7D%5C%5C%20%5C%5C%5Cdfrac%7Bx%2B2%7D%7B2%7D%3D%5Cdfrac%7By%7D%7B4%7D%5C%5C%20%5C%5Cy%3D2x%2B4)
The origin belongs to the shaded region, so it must satisfy both inequalities, so
correct inequality is ![-x-6\le y](https://tex.z-dn.net/?f=-x-6%5Cle%20y)
correct inequality is ![2x+4\ge y](https://tex.z-dn.net/?f=2x%2B4%5Cge%20y)
Note that signsare with notion "or equal to" because lines are solid.
Answer:
![\left\{\begin{array}{l}-x-6\le y\\ \\2x+4\ge y\end{array}\right.\Rightarrow \left\{\begin{array}{l}y\ge -x-6\\ \\ y\le 2x+4\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7D-x-6%5Cle%20y%5C%5C%20%5C%5C2x%2B4%5Cge%20y%5Cend%7Barray%7D%5Cright.%5CRightarrow%20%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7Dy%5Cge%20-x-6%5C%5C%20%5C%5C%20y%5Cle%202x%2B4%5Cend%7Barray%7D%5Cright.)
<span>The answer would be 20.
The question is asking you to find the value of the expression for when c = 100, so we have to put 100 where c is in the equation. Given that fact, we start with c/5, then put the 100 in for c.
c/5 = ??
100/5 = 20. </span>
We know that formular for volume of pyramid=area of base ×height
the area of the base is 1/2×base×height
=1/2×15×14
=105cm²
the given volume is 270cm³
∴height=volume÷base area
=270cm³÷105cm²
=
![\frac{18}{7}](https://tex.z-dn.net/?f=%20%5Cfrac%7B18%7D%7B7%7D%20)
=
Answer: I can answer 20
I think....the answer... Is......2 1/2