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Svetlanka [38]
4 years ago
13

If each coded item in a catalog begins with 3 distinct letters followed by 4 distinct nonzero digits, find the probability of ran

domly selecting one of these coded items with the first letter a vowel and the last digit even.
Mathematics
1 answer:
laila [671]4 years ago
3 0

Answer: 10/117

Step-by-step explanation:

3 distinct letters and 4 distinct nonzero digits

For letters: A → Z = 26 options

For numbers: 1 → 9 = 9 options

As we have 26 options for letters and 9 for numbers and they have to be distinct, for the total of codes we have

Total of codes: 26.25.24.9.8.7.6

For the particular code asked, we have 5 options of vowels and 4 options of even numbers, so

5.25.24.8.7.6.4

probability: <u>5.25.24.8.7.6.4</u> =    <u>10</u>

                   26.25.24.9.8.7.6     117

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If we know that line AB is equal to line AD, then this means that ∠ADB has to be equal to ∠ABD in order to form a closed triangle. All angle measures of a triangle add up to 180°, so use the equation: 2(35) + x = 180.

70 + x = 180

Subtract 70 from both sides to isolate x:

180 - 70 = 110

110 = x

Hope this helped.

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Step-by-step explanation:

value of d = 90° ( as it's a perpendicular)

e = 49° ( vertically opposite angle)

as, sum of all angles on a straight line is 180°

so,

48° + f = 180°

f = 180 - 49 = 131°

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Step-by-step explanation:

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3 years ago
Public opinion in the large city of Bedrock is that 60 percent of the residents are in favor of increasing taxes to fund alterna
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Answer: 0.8461

Step-by-step explanation:

Let p be the proportion of residents are against the increase of taxes to fund alternatives to drug addiction treatment.

As per given , we have p=0.40

A random sample is taken with size : n= 400

Expecting sample proportion : \hat{p}=\dfrac{150}{400}=0.375

Now , the probability that more than 150 of the residents surveyed will be against increasing taxes if a random sample of 400 residents are surveyed will be :

P(p>0.375)=P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}>\dfrac{0.375-0.40}{\sqrt{\dfrac{0.40(0.60)}{400}}})

=P(z>\dfrac{0.375-0.40}{\sqrt{\dfrac{0.40(0.60)}{400}}})\ \ [\because\ z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}]

=P(z>-1.02)=P(z-z)=P(Z

\approx0.8461  [By z-table]

Hence, the approximate probability that more than 150 of the residents surveyed will be against increasing taxes if a random sample of 400 residents are surveyed is 0.8461 .

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4 years ago
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