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xenn [34]
1 year ago
8

What is the value of the expression below? (8^2/3)^1/2 A. 4 B. 1 C.2 D.8

Mathematics
1 answer:
CaHeK987 [17]1 year ago
4 0

The value of the given expression is 2. The correct option is C.2

<h3>Simplifying an Expression </h3>

From the question, we are to determine the value of the given expression

The given expression is

(8^2/3)^1/2

This can be properly written as

(8^{2/3})^{1/2}

First, clear the bracket by multiplying the powers

That is,
8^{\frac{2}{3}\times \frac{1}{2}  }

Simplifying, we get

8^{\frac{1}{3} }

This becomes

\sqrt[3]{8}

= 2

Hence, the value of the expression is 2. The correct option is C.2

Learn more on Simplifying an expression here: brainly.com/question/13009179

SPJ1

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The expected value of the points earned on a single roll in this game is \dfrac{1}{6} = 0.1667 .

Step-by-step explanation:

We are given that consider a game in which players roll a number cube to determine the number of points earned. If a player rolls a prime number, that many points will be added to the player’s total. Any other roll will be deducted from the player’s total.

Assuming that the numbered cube is a dice with numbers (1, 2, 3, 4, 5, and 6).

Here, the prime numbers are = 1, 2, 3 and 5

Numbers which are not prime = 4 and 6

This means that if the dice got the number 1, 2, 3 or 5, then that many points will be added to the player’s total and if the dice got the number 4 or 6, then that many points will get deducted from the player’s total.

Here, we have to make a probability distribution to find the expected value of the points earned on a single roll in this game.

Note that the probability of getting any of the specific number on the dice is   \dfrac{1}{6} .

      Numbers on the dice (X)                       P(X)

                      +1                                                 \frac{1}{6}

                      +2                                                \frac{1}{6}

                      +3                                                \frac{1}{6}

                      -4                                                 \frac{1}{6}

                      +5                                                \frac{1}{6}

                      -6                                                 \frac{1}{6}

Here (+) sign represent the addition in the player's total and (-) sign represents the deduction in the player's total.

Now, the expected value of X, E(X)  =  \sum X \times P(X)

   =  (+1) \times \frac{1}{6} +(+2) \times \frac{1}{6} +(+3) \times \frac{1}{6} +(-4) \times \frac{1}{6} +(+5) \times \frac{1}{6} +(-6) \times \frac{1}{6}

   =  \frac{1}{6} + \frac{2}{6} + \frac{3}{6} - \frac{4}{6} + \frac{5}{6} - \frac{6}{6}

   =  \frac{1+2+3-4+5-6}{6}

   =  \frac{11-10}{6}= \frac{1}{6}

Hence, the expected value of the points earned on a single roll in this game is  \frac{1}{6} = 0.1667 .

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