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Use conservation of energy to determine the unknown energies.

Use conservation of energy to determine the unknown energies.

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You roll a 66-sided die two times. What is the probability of rolling a number greater than \(3\) and then rolling a number less than \(4\)? Write your answer as a percentage. ____ `%`
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There are 99 college students running for student government class president. The candidates include 77 education majors.\newlineIf 66 of the candidates are randomly chosen to give the first 66 speeches, what is the probability that all of them are education majors?\newlineWrite your answer as a decimal rounded to four decimal places.
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In an experiment, the probability that event A A occurs is 27 \frac{2}{7} , the probability that event B B occurs is 79 \frac{7}{9} , and the probability that events A A and B B both occur is 19 \frac{1}{9} .\newlineAre A A and B B independent events?\newlineChoices:\newline(A) yes\text{yes}\newline(B) no\text{no}
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At a science museum, visitors can compete to see who has a faster reaction time. Competitors watch a red screen, and the moment they see it turn from red to green, they push a button. The machine records their reaction times and also asks competitors to report their gender.\newlineThe probability that a competitor reacted in over 0.70.7 seconds is 0.60.6, the probability that a competitor was female is 0.40.4, and the probability that a competitor reacted in over 0.70.7 seconds and was female is 0.30.3.\newlineWhat is the probability that a randomly chosen competitor reacted in over 0.70.7 seconds or was female?\newlineWrite your answer as a whole number, decimal, or simplified fraction.\newline______
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A restaurant server claims that \(28\)% of the time he leaves candy with the bill, the customer tips well. \newlineIf the server's claim is true, and one day he leaves candy with \(4\) customers' bills, what is the probability that exactly \(3\) of those customers will tip well?\newlineWrite your answer as a decimal rounded to the nearest thousandth.
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There is a spinner with `50` equally likely sections, numbered from `1` to `50`. You have the opportunity to spin it. If the number is odd, you win $`11`. If the number is even, you win nothing. If you play the game, what is the expected payoff?\(\$\)_____
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There are two different raffles you can enter.\newlineIn raffle A, one ticket will win a `$720` prize, and the other tickets will win nothing. There are 1,0001,000 in the raffle, each costing `$11`.\newlineRaffle B is for a `$370` prize. Out of 125125 tickets, each costing `$5`, one ticket will win the prize, and the other tickets will win nothing.\newlineWhich raffle is a better deal?\newlineChoices:\newline[A]Raffle A\text{[A]Raffle A}\newline[B]Raffle B\text{[B]Raffle B}
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XX is a normally distributed random variable with mean 4949 and standard deviation 2525.\newlineWhat is the probability that XX is between 2424 and 7474??\newlineUse the 0.68−0.95−0.9970.68-0.95-0.997 rule and write your answer as a decimal. Round to the nearest thousandth if necessary.\newline____
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XX is a normally distributed random variable with mean 6565 and standard deviation 88.\newlineWhat is the probability that XX is between 6262 and 6868??\newlineWrite your answer as a decimal rounded to the nearest thousandth.\newline____
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Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 4343 and standard deviation 33, the bottom 30%30\% of the values are those less than ______.
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