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6 months ago

From a standard deck of 52 playing cards what are the ODDS IN FAVOR of selecting an ace then a face card WITH REPLACEMENT.

Mathematics

1 answer:

Murljashka [212]6 months ago

7 0

The odds in favor of selecting an ace then a face card is 3/52.

<h3>What is the probability?</h3>

Probability is used to determine the odds in favor of an event happening. The odds in favor of an event happening lies between 0 and 1. The greater the odds in favor of the event happening, the closer to one, the probability value would be. In a deck of cards, there are 13 aces and there are 12 face cards

The odds in favor of selecting an ace then a face card = (number of ace cards / total number of cards) x (number of face cards / total number of cards)

(13 / 52) x (12 / 52)

1/4 x 3/13 = 3/52

To learn more about probability, please check: brainly.com/question/13234031

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2 years ago

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Answer:

The value of x that maximizes the volume enclosed by this box is 0.46 inches

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Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The volume of the open-topped box is equal to

$V=LWH$

where

$L=(7-2x)\ in\\W=(2-2x)\ in\\H=x\ in$

substitute

$V=(7-2x)(2-2x)x$

Convert to expanded form

$V=(7-2x)(2-2x)x\\V=(14-14x-4x+4x^{2})x\\V=14x-14x^2-4x^2+4x^{3}\\V=4x^{3}-18x^{2} +14x$

using a graphing tool

Graph the cubic equation

Remember that

The domain for x is the interval -----> (0,1)

Because

If x>1

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the width is negative (W=2-2x)

The maximum is the point (0.46,3.02)

see the attached figure

therefore

The value of x that maximizes the volume enclosed by this box is 0.46 inches

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