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3 years ago

Rewrite 140 1/8 in radical form

Mathematics

2 answers:

Sergeeva-Olga [200]3 years ago

8 0

140^1/8 = \sqrt[8]{140}

julia-pushkina [17]3 years ago

3 0

$a \frac{x}{n}=\sqrt[n]{a^x} 140 \frac{1}{8} = \sqrt[8]{140^1} 140 \frac{1}{8} = \sqrt[8]{140} 

 
$

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Lucy offers to play the following game with Charlie: "Let us show dimes to each other, each choosing either heads or tails. If w

Darya [45]

Answer:

(a)Charlie is right

(b)$0

Step-by-step explanation:

(a)A game is said to be a fair game when the probability of winning is equal to the probability of losing. Mathematically, a game is said to be fair when the expected value is zero.

In the game, the possible outcomes are: HH, HT, TH and TT.

Charlie wins when the outcome is HH, TT

P(Charlie Wins)=2/4
P(Charlie Losses)=2/4

Lucy wins when the outcome is HT or TH

P(Lucy Wins)=2/4
P(Lucy Losses)=2/4

Therefore, the game is fair. Charlie is right.

(b)

If the outcome is HH, Lucy pays $3.

If the outcome is HT or TH, Lucy gets $2.

If the outcome is TT, Lucy pays $1.

The probability distribution of Lucy's profit is given below:

$\left|\begin{array}{c|c|c|c}$Profit(x)&-\$3&-\$1&\$2\\P(x)&1/4&1/4&2/4\end{array}\right|$

Expected Profit

$=(-3 \times \frac14)+(-1\times \frac14)+(2 \times \frac24)\\=$0$

Lucy's expected profit from the game is $0.

7 0

3 years ago

2^5×8^4/16=2^5×(2^a)4/2^4=2^5×2^b/2^4=2^c A= B= C= Please I'm gonna fail math

aleksley [76]

9514 1404 393

Answer:

a = 3, b = 12, c = 13

Step-by-step explanation:

The applicable rules of exponents are ...

(a^b)(a^c) = a^(b+c)

(a^b)/(a^c) = a^(b-c)

(a^b)^c = a^(bc)

___

You seem to have ...

$\dfrac{2^5\times8^4}{16}=\dfrac{2^5\times(2^3)^4}{2^4}\qquad (a=3)\\\\=\dfrac{2^5\times2^{3\cdot4}}{2^4}=\dfrac{2^5\times2^{12}}{2^4}\qquad (b=12)\\\\=2^{5+12-4}=2^{13}\qquad(c=13)$

_____

Additional comment

I find it easy to remember the rules of exponents by remembering that an exponent signifies repeated multiplication. It tells you how many times the base is a factor in the product.

$2\cdot2\cdot2 = 2^3\qquad\text{2 is a factor 3 times}$