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3 years ago

What is the value of the expression i0•i1•i2•i3•i4

2 answers:

8 0

$\bf \stackrel{1}{i^0}\cdot \stackrel{i}{i^1}\cdot \stackrel{-1}{i^2}\cdot \stackrel{-i}{i^3}\cdot \stackrel{1}{i^4}\implies i\cdot i\cdot 1\implies i^2\implies -1$

adoni [48]3 years ago

4 0

I hope you are trying to write

$i^0*i^1*i^2*i^3*i^4$

Now, $i^0=1$ Because any number to exponent 0 always result 1.

$i^1=i$ Any number to exponent 1 will result the same number.

$i^2= -1$ By using the property of imaginary number.

$i^3= i^2*i =(-1)*i= -i$

$i^4=i^2*i^2=(-1)*(-1)=1$

Now we can plug in these values in the given expression to get the value of the expression. So,

$i^0*i^1*i^2*i^3*i^4$

= $1*i*(-1)*(-i)*1$

= $i^2$

=-1

So, -1 is the correct choice.

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A math professor notices that scores from a recent exam are normally distributed with a mean of 61 and a standard deviation of 8

Alexeev081 [22]

Answer:

a) 25% of the students exam scores fall below 55.6.

b) The minimum score for an A is 84.68.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 61 and a standard deviation of 8.

This means that $\mu = 61, \sigma = 8$

(a) What score do 25% of the students exam scores fall below?

Below the 25th percentile, which is X when Z has a p-value of 0.25, that is, X when Z = -0.675.

$Z = \frac{X - \mu}{\sigma}$

$-0.675 = \frac{X - 61}{8}$

$X - 61 = -0.675*8$

$X = 55.6$

25% of the students exam scores fall below 55.6.

(b) Suppose the professor decides to grade on a curve. If the professor wants 0.15% of the students to get an A, what is the minimum score for an A?

This is the 100 - 0.15 = 99.85th percentile, which is X when Z has a p-value of 0.9985. So X when Z = 2.96.

$Z = \frac{X - \mu}{\sigma}$

$2.96 = \frac{X - 61}{8}$