Answer:
a.) f(x) =
where 90 < x < 120
b.) 
c.) 
d.) 
Step-by-step explanation:
Let
X be a uniform random variable that denotes the actual charging time of battery.
Given that, the actual recharging time required is uniformly distributed between 90 and 120 minutes.
⇒X ≈ ∪ ( 90, 120 )
a.)
Probability density function , f (x) =
where 90 < x < 120
b.)
P(x < 110) = 
= ![\frac{1}{30}[x]\limits^{110}_{90} = \frac{1}{30} [ 110 - 90 ] = \frac{1}{30} [ 20] = \frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B30%7D%5Bx%5D%5Climits%5E%7B110%7D_%7B90%7D%20%20%3D%20%5Cfrac%7B1%7D%7B30%7D%20%5B%20110%20-%2090%20%5D%20%3D%20%5Cfrac%7B1%7D%7B30%7D%20%5B%2020%5D%20%3D%20%5Cfrac%7B2%7D%7B3%7D)
c.)
P(x > 100 ) = 
= ![\frac{1}{30}[x]\limits^{120}_{100} = \frac{1}{30} [ 120 - 100 ] = \frac{1}{30} [ 20] = \frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B30%7D%5Bx%5D%5Climits%5E%7B120%7D_%7B100%7D%20%20%3D%20%5Cfrac%7B1%7D%7B30%7D%20%5B%20120%20-%20100%20%5D%20%3D%20%5Cfrac%7B1%7D%7B30%7D%20%5B%2020%5D%20%3D%20%5Cfrac%7B2%7D%7B3%7D)
d.)
P(95 < x< 110) = 
= ![\frac{1}{30}[x]\limits^{110}_{95} = \frac{1}{30} [ 110 - 95 ] = \frac{1}{30} [ 15] = \frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B30%7D%5Bx%5D%5Climits%5E%7B110%7D_%7B95%7D%20%20%3D%20%5Cfrac%7B1%7D%7B30%7D%20%5B%20110%20-%2095%20%5D%20%3D%20%5Cfrac%7B1%7D%7B30%7D%20%5B%2015%5D%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
Answer:
79° is the measure of the required angle
since it is the vertically opposite angle of AOB.
The required proof is given in the table below:
![\begin{tabular}{|p{4cm}|p{6cm}|} Statement & Reason \\ [1ex] 1. $\overline{BD}$ bisects $\angle ABC$ & 1. Given \\ 2. \angle DBC\cong\angle ABD & 2. De(finition of angle bisector \\ 3. $\overline{AE}$||$\overline{BD}$ & 3. Given \\ 4. \angle AEB\cong\angle DBC & 4. Corresponding angles \\ 5. \angle AEB\cong\angle ABD & 5. Transitive property of equality \\ 6. \angle ABD\cong\angle BAE & 6. Alternate angles \end{tabular}](https://tex.z-dn.net/?f=%20%5Cbegin%7Btabular%7D%7B%7Cp%7B4cm%7D%7Cp%7B6cm%7D%7C%7D%20%0A%20Statement%20%26%20Reason%20%5C%5C%20%5B1ex%5D%20%0A1.%20%24%5Coverline%7BBD%7D%24%20bisects%20%24%5Cangle%20ABC%24%20%26%201.%20Given%20%5C%5C%0A2.%20%5Cangle%20DBC%5Ccong%5Cangle%20ABD%20%26%202.%20De%28finition%20of%20angle%20bisector%20%5C%5C%20%0A3.%20%24%5Coverline%7BAE%7D%24%7C%7C%24%5Coverline%7BBD%7D%24%20%26%203.%20Given%20%5C%5C%20%0A4.%20%5Cangle%20AEB%5Ccong%5Cangle%20DBC%20%26%204.%20Corresponding%20angles%20%5C%5C%0A5.%20%5Cangle%20AEB%5Ccong%5Cangle%20ABD%20%26%205.%20Transitive%20property%20of%20equality%20%5C%5C%20%0A6.%20%5Cangle%20ABD%5Ccong%5Cangle%20BAE%20%26%206.%20Alternate%20angles%0A%5Cend%7Btabular%7D)
ANSWER: 783,840,183.9627281873
EXPLANATION:
Just use your calculator lol
Prime factorization is finding wich prime numbers multiply together to make the original number
ex.. 2*3=6
2 and 3 are factors