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3 years ago

Solve the equation. Round to the nearest hundredth. Show work.

Mathematics

1 answer:

Burka [1]3 years ago

3 0

Answer:

$x=-0.75$

Step-by-step explanation:

The given equation is

$4^{-5x-7}=6^{2x-1}$

We take logarithm of both sides to base 10.

$\log(4^{-5x-7})=\log(6^{2x-1})$

$(-5x-7)\log(4)=(2x-1)\log(6)$

We expand the brackets to get;

$-5x\log(4)-7\log(4)=2x\log(6)-\log(6)$

Group similar terms;

$-7\log(4)+\log(6)=2x\log(6)+5x\log(4)$

$-7\log(4)+\log(6)=(2\log(6)+5\log(4))x$

$\frac{-7\log(4)+\log(6)}{(2\log(6)+5\log(4))}=x$

$x=-0.752478$

To the nearest hundredth.

$x=-0.75$

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3 years ago

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Vinvika [58]

Answer:

a) No.

b) Yes.

c) Yes.

Step-by-step explanation:

a) No.

As being without replacement, the probabilities of each color in each draw change depending on the previous draws.

This is best modeled by an hypergeometric distribution.

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3 years ago

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MatroZZZ [7]

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