Study the diagram of circle B. Points C, R, and V lie on circle B. The radius, BC¯¯¯¯¯¯¯¯, and the diameter, VR¯¯¯¯¯¯¯¯, are dra
wn. Arc CR has a measure of 90∘. If m∠VBC=(3x+4)∘, what is the value of x?
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Answer:
<em>95% of confidence interval for the Population</em>
<em>( 6.1386 , 6.8614)</em>
Step-by-step explanation:
<u><em>Step( i ):-</em></u>
<em>Given random sample size 'n' =85</em>
<em>Mean of the sample size x⁻ = 6.5 years</em>
<em>Standard deviation of Population = 1.7 years</em>
<em>Level of significance = 0.95 or 0.05</em>
<u><em>Step(ii):-</em></u>
<em>95% of confidence interval for the Population is determined by</em>
<em></em><em></em>
<em></em><em></em>
<em>( 6.5 - 0.3614 , 6.5 + 0.3614 )</em>
<em>( 6.1386 , 6.8614)</em>
<u><em>Conclusion</em></u><em>:-</em>
<em>95% of confidence interval for the Population</em>
<em>( 6.1386 , 6.8614)</em>
Given that <span>3 cards are dealt without replacement in a </span><span>standard deck of 52 cards.
Part A:
There are 4 queens in a standard deck of 52 card, thus the probability that the first card is a queen is given by 4 / 52 = 1 / 13.
Since, the first card is not replaced, thus there are 3 queens remaining and 51 ards remaining in total, thus the probability that the second card is a queen is given</span> by 3 / 51 = 1 / 17
Similarly the probability that the third card is a queen is given by 2 / 50 = 1 / 25.
Therefore, the probability that <span>all three cards are queens is given by
Part B:
Yes the probability of drawing a queen of heart is independent of the probability of drawing a queen of diamonds because they are separate cards and drawing one of the cards does not in any way affect the chance of drawing the other card.
Part C:
Given that the first card is a queen, then there are 3 queens remaining out of 51 cards remaining, thus the number of cards that are not queen is 51 - 3 = 48 cards.
Therefore, </span>if the first card is a queen, the probability that the second card will not be a queen is given by 48 / 51 = 16 / 17
Part D:
<span>Given that the first two card are queens, then there are 2 queens remaining out of 50 cards remaining.
Therefore, </span>if two of the three cards are queens ,<span>the probability that you will be dealt three queens</span> is given by 2 / 50 = 1 / 25 = 0.04
Part E:
<span>Given that the first two card are queens, then there are 2 queens remaining out of 50 cards remaining, thus the number of cards that are not queen is 50 - 2 = 48 cards.
Therefore, </span>if two of the three cards are queens ,the probability that the other card is not a queen is given by 48 / 50 = 24 / 25 = 0.96
Part A:
There are 4 queens in a standard deck of 52 card, thus the probability that the first card is a queen is given by 4 / 52 = 1 / 13.
Since, the first card is not replaced, thus there are 3 queens remaining and 51 ards remaining in total, thus the probability that the second card is a queen is given</span> by 3 / 51 = 1 / 17
Similarly the probability that the third card is a queen is given by 2 / 50 = 1 / 25.
Therefore, the probability that <span>all three cards are queens is given by
Part B:
Yes the probability of drawing a queen of heart is independent of the probability of drawing a queen of diamonds because they are separate cards and drawing one of the cards does not in any way affect the chance of drawing the other card.
Part C:
Given that the first card is a queen, then there are 3 queens remaining out of 51 cards remaining, thus the number of cards that are not queen is 51 - 3 = 48 cards.
Therefore, </span>if the first card is a queen, the probability that the second card will not be a queen is given by 48 / 51 = 16 / 17
Part D:
<span>Given that the first two card are queens, then there are 2 queens remaining out of 50 cards remaining.
Therefore, </span>if two of the three cards are queens ,<span>the probability that you will be dealt three queens</span> is given by 2 / 50 = 1 / 25 = 0.04
Part E:
<span>Given that the first two card are queens, then there are 2 queens remaining out of 50 cards remaining, thus the number of cards that are not queen is 50 - 2 = 48 cards.
Therefore, </span>if two of the three cards are queens ,the probability that the other card is not a queen is given by 48 / 50 = 24 / 25 = 0.96