Which expression is equivalent to 3.5 B +4.5+0.5 B -0.5-1.5 B?

Kelsie works at a bicycle shop as a salesperson. She records the number of bicycles she sells daily. Here is the probability dis

Andru [333]

Answer:

a) $E(B)= \sum_{i=1}^n B_i P(B_i) =0*0.3+1*0.5+2*0.15+ 3*0.05=0.95$

b) $E(T)= \sum_{i=1}^n T_i P(T_i) =10*0.3+20*0.5+30*0.15+ 40*0.05=19.5$

c) $E(B^2)= \sum_{i=1}^n B^2_i P(B_i) =0^2 *0.3+1^2 *0.5+2^2 *0.15+ 3^2 *0.05=1.55$

And the variance is given by:

$Var(B) = E(B^2) -[E(B)]^2 = 1.55- [0.95]^2 =0.6475$

And the deviation would be $Sd(B) = \sqrt{0.6475}=0.8047$

$E(T^2)= \sum_{i=1}^n T^2_i P(T_i) =10^2 *0.3+20^2 *0.5+30^2 *0.15+ 40^2 *0.05=445$

And the variance is given by:

$Var(T) = E(T^2) -[E(T)]^2 = 445- [19.5]^2 =64.75$

And the deviation would be $Sd(T) = \sqrt{64.75}=8.047$

Step-by-step explanation:

Previous concepts

In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".

The variance of a random variable Var(X) is the expected value of the squared deviation from the mean of X, E(X).

And the standard deviation of a random variable X is just the square root of the variance.

Solution to the problem

Part a

For this case we have the following info:

B 0 1 2 3

____________________________________

T 10 20 30 40

____________________________________

P 0.3 0.5 0.15 0.05

____________________________________

And we can calculate the expected value for the random variable B like this:

$E(B)= \sum_{i=1}^n B_i P(B_i) =0*0.3+1*0.5+2*0.15+ 3*0.05=0.95$

Part b

Similar to part a we can find the expected value for the random variable T like this:

$E(T)= \sum_{i=1}^n T_i P(T_i) =10*0.3+20*0.5+30*0.15+ 40*0.05=19.5$

Part c

In order to find the variance for B we need to calculate the second moment given by:

$E(B^2)= \sum_{i=1}^n B^2_i P(B_i) =0^2 *0.3+1^2 *0.5+2^2 *0.15+ 3^2 *0.05=1.55$

And the variance is given by:

$Var(B) = E(B^2) -[E(B)]^2 = 1.55- [0.95]^2 =0.6475$

And the deviation would be $Sd(B) = \sqrt{0.6475}=0.8047$

Similar for the random variable T we have:

$E(T^2)= \sum_{i=1}^n T^2_i P(T_i) =10^2 *0.3+20^2 *0.5+30^2 *0.15+ 40^2 *0.05=445$

And the variance is given by:

$Var(T) = E(T^2) -[E(T)]^2 = 445- [19.5]^2 =64.75$

And the deviation would be $Sd(B) = \sqrt{64.75}=8.047$

7 0

4 years ago

A wheel of 0.5 m radius rolls without slipping on a horizontal surface. The axle of the wheel advances at constant velocity, mov

neonofarm [45]

Answer:

$\omega = 8\,\frac{rad}{s}$

Step-by-step explanation:

The translation speed of the wheel is:

$v=\frac{20\,m}{5\,s}$

$v=4\,\frac{m}{s}$

The angular speed of the wheel is:

$\omega = \frac{4\,\frac{m}{s} }{0.5\,m}$

$\omega = 8\,\frac{rad}{s}$

4 0

3 years ago

You have two strands of decorative lights. Strand A changes color every

VLD [36.1K]

Answer:

Both strands will change color at 126 seconds.

Step-by-step explanation:

In this case, find the least common mutiple or LCM.

EXAMPLE OF LCM:

There are two integers a and b marked as LCM ( a, b ), the LCM is the smallest positive integer that can be divisible by both a and b.

So LCM(18,42) =

$18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198 ...\\42, 84, 126, 168, 210, 252, 294 ...$

The LCM is 126, it is the least common multiple.

8 0

4 years ago

How do I do this. it's a proof. so no work. just how do you do this.

Elena L [17]

JMK’s angle is part of the right angle of JMN. The measurements there is 28°. A right angle is 90° so subtract 90 and 28 to get your angle measurement of JMK.

A small hint for the STR one is the fact that the straight lines are 180°. So Look at the line RTS. RTS is 180° by adding both the measurement of STR and STP. Simply subtract 180° with 118 to get STR.

3 0

3 years ago

2+2y = -10 6х +8y = -48 help please

irina1246 [14]

Answer:

x = 0 and y = -6

5 0

3 years ago

Which expression is equivalent to 3.5 B +4.5+0.5 B -0.5-1.5 B?￼

Which expression is equivalent to 3.5 B +4.5+0.5 B -0.5-1.5 B?