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3 years ago

14

Use the Fundamental Counting Principle to find the total number of outcomes for each situation. a) Choosing a bagel with one typ

e of cream cheese from the list shown in the table Hint: there are 4 bagel choices and 3 cream cheese choices

1 answer:

Sedbober [7]3 years ago

8 0

There are 1/7 choices

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Step-by-step explanation:

what is a rational number

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3 years ago

Let u= ln x and v=ln y. Write ln(x^3y^2) in terms of u and v.

amid [387]

<h2>Answer:</h2>

a. 3u + 2v

<h2>Step-by-step explanation:</h2>

To solve this problem, we need to apply some properties of logarithms. Properties are useful to simplify complicated expressions. Here we need to use a very useful property of logarithms called <em>the logarithm of a product is the sum of the logarithms, </em>that is:

$log_{b}(MN)=log_{b}(M)+log_{b}(N)$

From the function, it is then true that:

$ln(x^{3}y^{2})=ln(x^{3})+ln(y^{2})$

The other property we must use is Logarithm of a Power:

$log_{b}M^{n}=nlog_{b}M$

Then:

$ln(x^{3}y^{2})=ln(x^{3})+ln(y^{2}) \\ \\ ln(x^{3}y^{2})=3ln(x)+2ln(y)$

Since:

$u=ln(x) \\ v=ln(y)$

Then:

$ln(x^{3}y^{2})=3u+2v$

Finally, the correct option is:

a. 3u + 2v

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