Answer:
The value of E [Z] is 0.50.
Step-by-step explanation:
The expected value is computed using the formula:
![E(X)=\sum x\cdot P(X= x)](https://tex.z-dn.net/?f=E%28X%29%3D%5Csum%20x%5Ccdot%20P%28X%3D%20x%29)
Denote the three dices as follows:
X₁ = a four-sided die
X₂ = a six-sided die
X₃ = a 12-sided die
Define the indicator variables as follows:
![I_{1}=\left \{ {{1;\ X_{1}=4} \atop {0;\ X_{1}\neq 4}} \right. \\\\I_{2}=\left \{ {{1;\ X_{2}=4} \atop {0;\ X_{2}\neq 4}} \right. \\\\I_{3}=\left \{ {{1;\ X_{3}=4} \atop {0;\ X_{3}\neq 4}} \right.](https://tex.z-dn.net/?f=I_%7B1%7D%3D%5Cleft%20%5C%7B%20%7B%7B1%3B%5C%20X_%7B1%7D%3D4%7D%20%5Catop%20%7B0%3B%5C%20X_%7B1%7D%5Cneq%204%7D%7D%20%5Cright.%20%5C%5C%5C%5CI_%7B2%7D%3D%5Cleft%20%5C%7B%20%7B%7B1%3B%5C%20X_%7B2%7D%3D4%7D%20%5Catop%20%7B0%3B%5C%20X_%7B2%7D%5Cneq%204%7D%7D%20%5Cright.%20%5C%5C%5C%5CI_%7B3%7D%3D%5Cleft%20%5C%7B%20%7B%7B1%3B%5C%20X_%7B3%7D%3D4%7D%20%5Catop%20%7B0%3B%5C%20X_%7B3%7D%5Cneq%204%7D%7D%20%5Cright.)
The probability of rolling a 4 in the three dices are as follows:
![P(X_{1}=4)=\frac{1}{4}\\\\P(X_{2}=4)=\frac{1}{6}\\\\P(X_{3}=4)=\frac{1}{12}](https://tex.z-dn.net/?f=P%28X_%7B1%7D%3D4%29%3D%5Cfrac%7B1%7D%7B4%7D%5C%5C%5C%5CP%28X_%7B2%7D%3D4%29%3D%5Cfrac%7B1%7D%7B6%7D%5C%5C%5C%5CP%28X_%7B3%7D%3D4%29%3D%5Cfrac%7B1%7D%7B12%7D)
Compute the value of E [Z] as follows:
![E(Z)=E(I_{1})+E(I_{2})+E(I_{3})](https://tex.z-dn.net/?f=E%28Z%29%3DE%28I_%7B1%7D%29%2BE%28I_%7B2%7D%29%2BE%28I_%7B3%7D%29)
![=(1\times\frac{1}{4})+(1\times\frac{1}{6})+(1\times\frac{1}{12})\\\\=\frac{3+2+1}{12}\\\\=\frac{6}{12}\\\\=\frac{1}{2}\\\\=0.50](https://tex.z-dn.net/?f=%3D%281%5Ctimes%5Cfrac%7B1%7D%7B4%7D%29%2B%281%5Ctimes%5Cfrac%7B1%7D%7B6%7D%29%2B%281%5Ctimes%5Cfrac%7B1%7D%7B12%7D%29%5C%5C%5C%5C%3D%5Cfrac%7B3%2B2%2B1%7D%7B12%7D%5C%5C%5C%5C%3D%5Cfrac%7B6%7D%7B12%7D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%3D0.50)
Thus, the value of E [Z] is 0.50.
These are three solutions
(0,-2)
(1,3)
(2,8)
Step-by-step explanation:
Solution file attached
9514 1404 393
Answer:
arc AC = 63°
Step-by-step explanation:
Arc BC is twice the measure of inscribed angle BAC, so is ...
arc AC = 2×89° = 178°
The remaining arc of the circle is the difference between 360° and the sum of the other two.
arc AC = 360° -119° -178°
arc AC = 63°
Answer:
i. Term =
+ ![\frac{b_{2}h }{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bb_%7B2%7Dh%20%7D%7B2%7D)
ii. Coefficient = ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
iii. Constant = ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
iv. Factor = ![\frac{h}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bh%7D%7B2%7D)
Step-by-step explanation:
A trapezoid is a quadrilateral which has its base parallel to the opposite side. It's area can be determined by;
Area of trapezium =
(
+
)h
Where
is the measure of length of its fist base,
is the measure of its second base and h is its height.
Considering the given question,
Term =
+ ![\frac{b_{2}h }{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bb_%7B2%7Dh%20%7D%7B2%7D)
Coefficient = ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
Constant = ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
Factor = ![\frac{h}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bh%7D%7B2%7D)