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2 years ago

Which expression is equivalent to i 233

2 answers:

5 0

Start with second, third and fourth degree of imaginary unit i:

$i^2=-1, \\ i^3=i^2\cdot i=-1\cdot i=-i, \\ i^4=i^2\cdot i^2=-1\cdot (-1)=1$ .

Since 233=232+1=4·58+1, then $i^{233}=i^{4\cdot 58+1}=(i^4)^{58}\cdot i^1=1^{58}\cdot i=i$ .

Answer: $i^{233}=i$

natta225 [31]2 years ago

5 0

Answer:C

Step-by-step explanation:

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1 year ago

From past experience, a company has found that in carton of transistors: 92% contain no defective transistors 3% contain one def

jasenka [17]

Answer:

$E(X) = 0*0.92 + 1*0.03 +2*0.03 +3*0.02 = 0.1500$

In order to find the variance we need to find first the second moment given by:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i)$

And replacing we got:

$E(X^2) = 0^2*0.92 + 1^2*0.03 +2^2*0.03 +3^2*0.02 = 0.3300$

The variance is calculated with this formula:

$Var(X) = E(X^2) -[E(X)]^2 = 0.33 -(0.15)^2 = 0.3075$

And the standard deviation is just the square root of the variance and we got:

$Sd(X) = \sqrt{0.3075}= 0.5545$

Step-by-step explanation:

Previous concepts

The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.

The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).

Solution to the problem

LEt X the random variable who represent the number of defective transistors. For this case we have the following probability distribution for X

X 0 1 2 3

P(X) 0.92 0.03 0.03 0.02

We can calculate the expected value with the following formula:

$E(X) = \sum_{i=1}^n X_i P(X_i)$

And replacing we got:

$E(X) = 0*0.92 + 1*0.03 +2*0.03 +3*0.02 = 0.1500$

In order to find the variance we need to find first the second moment given by:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i)$

And replacing we got:

$E(X^2) = 0^2*0.92 + 1^2*0.03 +2^2*0.03 +3^2*0.02 = 0.3300$

The variance is calculated with this formula:

$Var(X) = E(X^2) -[E(X)]^2 = 0.33 -(0.15)^2 = 0.3075$

And the standard deviation is just the square root of the variance and we got:

$Sd(X) = \sqrt{0.3075}= 0.5545$

8 0

2 years ago

A square has an area of 50 square feet what is the perimeter of the square rounded to the nearest foot

dezoksy [38]

Answer:

28 feet

Step-by-step explanation:

area of a square = side times side; the sides are equal

50 = side times side or 50 = side^2

sqroot of 50 = sqroot of side^2

7 feet is about the size of the side of the square so using that information..

2 length + 2 width or 4 side

4 times 7 = 28

the perimeter is 28 feet

8 0

2 years ago