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:21 members
Step-by-step explanation:
35 *60% =35 *(60/100)
=21
The transformation that changes the area of a shape is dilation (Option D)
Step by step explanation
Option A: Translation
A translation is a geometric transformation that moves every point of a figure, shape, or space by the same distance in a given direction. For this type, the image is congruent with the original shape.
Option B: Rotation
A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point. For this type, the image is congruent with the original shape.
Option C: Reflection
A reflection is a transformation where each point in a shape appears at an equal distance on the opposite side of a given line - the line of reflection. For this type, the image is congruent with the original shape.
Option D: Dilations
Dilation in math is a transformation that changes the size of a figure so it becomes larger or smaller without changing shape. This type changes the area since the area is the size of a figure.