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salantis [7]
3 years ago
11

P(King or black card)?

Mathematics
1 answer:
Pavlova-9 [17]3 years ago
4 0

Answer:

7/13

Step-by-step explanation:

If we are looking at a standard deck of playing cards, we have 52 cards total.

*13 of each suit (there are 4 suits; spades, clubs, hearts, and diamonds)

*2 kinds of colors-black or red. Half the deck is black and half the deck is red. There are 26 reds and 26 blacks.

*There is 1 king of each suit and since there are 4 suits, then there are 4 kings.

We can make other observations.

P(King or black card)

=P(King)+P(black card)-P(king and black card)

(We are subtracting out anything that counted twice in the "and" part)

=4/52 +   26/52         -    2/52

Notes:

-P(king)=4/52 comes from there being 4 kings in all in a deck of 52 playing cards.

-P(black card)=26/52 comes from that half the deck is black (and the other half is red) in a deck of 52 playing cards. Technically, we could have just said this equal 1/2 here instead. I will leave as 26/52 for now so I can have a common denominator already setup.

-P(king and black card)=2/52 comes from there being 2 black cards that are kings in a deck of 52 playing cards.  We have to get rid of these 2 from the 4+26 since if we don't we would have counted them twice)

Let's simplify:

=(4+26-2)/52

=(30-2)/52

=28/52

Let's reduce:

=(28/4)/(52/4)

=7/13

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2) Brian purchased pens for 75 cents each and pencils for 40 cents each he bought total of 22 writing utensils for $11.95. How m
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Answer:

13 pencils.

Step-by-step explanation:

Let x be the pens and y be the pencils

Given:

Brian purchased pens for 75 cents each and pencils for 40 cents each he bought total of 22 writing utensils for $11.95.

Total pens and pencils is 22

So, x+y=22----------------(1)

And he bought all utensils for $11.95. and each pen for 75 cents and pencils for 40 cents.

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solve equation 1 and equation 2 for x and y.

From equation 1.

x+y=22

y=22-x----------------(3)

put y value in equation 2.

0.75x+0.4(22-x)=11.95

0.75x+0.4\times 22-0.4x=11.95

0.75x+8.8-0.4x=11.95

0.75x-0.4x=11.95-8.8

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x=\frac{3.15}{0.35}

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Suppose that your business is operating at the 4.5-Sigma quality level. If projects have an average improvement rate of 50% annu
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Answer:

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Step-by-step explanation:

If we ignore the fact that "6-sigma" quality means the error rate corresponds to about -4.5σ (3.4 ppm) and simply go with ...

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and

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the ratio of these error rates is about 0.000290372. We're multiplying the error rate by 0.5 each year, so we want to find the power of 0.50 that gives this value:

  0.50^t = 0.000290372

  t·log(0.50) = log(0.00290372) . . . . take logarithms

  t = log(0.000290372)/log(0.50) ≈ -3.537045/-0.301030

  t ≈ 11.75

It will take about 11.75 years to achieve Six Sigma quality (0.99 ppb error rate).

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<em>Comment on Six Sigma</em>

A 3.4 ppm error rate is customarily associated with "Six Sigma" quality. It assumes that the process may have an offset from the mean of up to 1.5 sigma, so the "six sigma" error rate is P(z ≤ (1.5 -6)) = P(z ≤ -4.5) ≈ 3.4·10^-6.

Using that same criteria for the "4.5-Sigma" quality level, we find that error rate to be P(z ≤ (1.5 -4.5)) = P(z ≤ -3) ≈ 1.35·10^-3.

Then the improvement ratio needs to be only 0.00251699, and it will take only about ...

  t ≈ log(0.00251699)/log(0.5) ≈ 8.6 . . . . years

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Step-by-step explanation:

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Step-by-step explanation:

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