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mel-nik [20]
3 years ago
6

How can I rewrite this in exponential form and then evaluate it?

Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
6 0

QUESTION:- EVALUATE THE EXPRESSION

EXPRESSION:-

{( \sqrt[6]{27 {a}^{3}  {b}^{4} } )}^{2}

<h3>ANSWER-></h3>

{( \sqrt[6]{27 {a}^{3}  {b}^{4} } )}^{2}  \\ {( {27 {a}^{3}  {b}^{4} } )}^{ \frac{2}{6} }  \\ {({27 {a}^{3}  {b}^{4} } )}^{ \frac{ \cancel{2}}{ \cancel6 {}^{ \:  3} } } \\ {(27)}^{ \frac{1}{3} }  {a}^{ \frac{3}{3} }  {b}^{ \frac{4}{3} } \\{(3)}^{ \frac{ \cancel3}{ \cancel3} }  {a}^{ \frac{ \cancel3}{ \cancel3} }  {b}^{\frac{3 + 1}{3} } \\3a {b}^{ \frac{ \cancel3}{ \cancel3} }  {b}^{ \frac{1}{3} } \\ ANSWER->3ab \sqrt[3]{b}  \:  \:  \:  \:  \: or \: \: 3a {b}^{ \frac{4}{3} }

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if tom spins the spinner 80 times work out an estimate for the number of times the spinner will land on 3 please help me
NNADVOKAT [17]

Answer:

The estimated number of times the spinner will land on 3 is 20.

Step-by-step explanation:

The complete question is:

A four-sided spinner is provided. If Tom spins the spinner 80 times then work out an estimate for the number of times the spinner will land on 3.

Solution:

Assume that the four-sided spinner is unbiased.

That is all the four outcomes are equally likely to be selected.

The probability that the spinner lands on any of the four numbers is:

P(1) = P (2) = P (3) = P (4) = 0.25

It is provided that Tom spins the spinner <em>n</em> = 80 times.

The spinner can land on any of the four numbers independently.

The random variable <em>X</em>, defined as the number of times the spinner lands on 3, follows a Binomial distribution with parameters <em>n</em> = 80 and <em>p</em> = 0.25.

The expected value of <em>X</em> is:

E(X)=np

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Thus, the estimated number of times the spinner will land on 3 is 20.

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F:[1/2,infinity)—&gt;[3/4,infinity) <br> f(x)=x^2-x+1 <br> find the inverse of f(x);please explain
dexar [7]

Answer:

f^{-1}(x)=\frac{1}{2}+\sqrt{x-\frac{3}{4}}

Step-by-step explanation:

y=x^2-x+1

We want to solve for x.

I'm going to use completing the square.

Subtract 1 on both sides:

y-1=x^2-x

Add (-1/2)^2 on both sides:

y-1+(-1/2)^2=x^2-x+(-1/2)^2

This allows me to write the right hand side as a square.

y-1+1/4=(x-1/2)^2

y-3/4=(x-1/2)^2

Now remember we are solving for x so now we square root both sides:

\pm \sqrt{y-3/4}=x-1/2

The problem said the domain was 1/2 to infinity and the range was 3/4 to infinity.

This is only the right side of the parabola because of the domain restriction. We want x-1/2 to be positive.

That is we want:

\sqrt{y-3/4}=x-1/2

Add 1/2 on both sides:

1/2+\sqrt{y-3/4}=x

The last step is to switch x and y:

1/2+\sqrt{x-3/4}=y

y=1/2+\sqrt{x-3/4}

f^{-1}(x)=1/2+\sqrt{x-3/4}

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3 years ago
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