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Sedbober [7]
3 years ago
13

In his suitcase, Jack has 3 shirts, 4 pants, 2 socks (pairs of socks), and 2 shoes (pairs of shoes). How many unique ways can Ja

ck get fully dressed? Show your work and explain.
Mathematics
1 answer:
kipiarov [429]3 years ago
8 0

Answer:

48

Step-by-step explanation:

the number of shirts are 3, number of pants 4, number of socks pairs 2 and 2 pairs of shoes.

first lets start with shirts and pants, number of unique combinations are,

(for each shirt there are 4 different pant combinations) = (3)(4)

=12

similiarly for each shirt pant pair there are 2 shoes and 2 socks pairs.

thus, total number of combinations are=

(12)(2)(2)

= 48

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I NEED HELP!! please show all work
PtichkaEL [24]

Take the logarithm of both sides. The base of the logarithm doesn't matter.

4^{5x} = 3^{x-2}

\implies \log 4^{5x} = \log 3^{x-2}

Drop the exponents:

\implies 5x \log 4 = (x-2) \log 3

Expand the right side:

\implies 5x \log 4 = x \log 3 - 2 \log 3

Move the terms containing <em>x</em> to the left side and factor out <em>x</em> :

\implies 5x \log 4 - x \log 3 = - 2 \log 3

\implies x (5 \log 4 - \log 3) = - 2 \log 3

Solve for <em>x</em> by dividing boths ides by 5 log(4) - log(3) :

\implies \boxed{x = -\dfrac{ 2 \log 3 }{ 5 \log 4 - \log 3 }}

You can stop there, or continue simplifying the solution by using properties of logarithms:

\implies x = -\dfrac{ \log 3^2 }{ \log 4^5 - \log 3 }

\implies x = -\dfrac{ \log 9 }{ \log 1024 - \log 3 }

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You can condense the solution further using the change-of-base identity,

\implies \boxed{x = -\log_{\frac{1024}3}9}

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2 years ago
How to find the radius of a circle when given two points?
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The base of the parallelogram is represented by b

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The simplified expression for the area of the parallelogram is A = 2x³ - 8x² - 6x + 24

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