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10 problems match “percentages”. Clear

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1. Unknown number from percentages ●○○○○ 10 ptsIf $15\%$ of $N$ is $45\%$ of $2003$, what is the value of $N$?
2. Male listeners in a radio survey ●○○○○ 10 ptsA radio station, KAMC, surveyed listeners. The results are in a two-way table with columns Listen, Don't Listen and Total, and rows Male, Female and Total. The known entries are: - Listen column: Total $136$, Female $58$ - Don't Listen column: Male $26$, Total $64$ - Total column: Female $96$, Total $200$ The other entries are unknown. What percentage of the males surveyed listen to the station?
3. Empirical rule: values within three deviations ●○○○○ 10 ptsThe values of a bell-shaped (normal) distribution have mean $89$ and standard deviation $14$. Using the empirical rule, find the approximate percentage of values between $47$ and $131$. Round to one decimal place.
4. Profit percent from pencil prices ●○○○○ 10 ptsThe cost price of 11 pencils is equal to the selling price of 10 pencils. Find the profit percent.
5. Markup rate from profit ratio ●○○○○ 10 ptsOn selling 20 units of an item, the profit is equal to the cost price of 5 units. Find the markup rate, as a percentage of the cost price.
6. Fish population by tag and recapture ●●○○○ 20 ptsA biologist wants to estimate the number of fish in a lake. On May 1 she catches a random sample of 60 fish, tags them, and releases them. On September 1 she catches a random sample of 70 fish and finds that 3 of them are tagged. To estimate the number of fish in the lake on May 1, she assumes that 25% of the May 1 fish are no longer in the lake on September 1 (because of death and emigration), that 40% of the fish in the lake on September 1 were not in the lake on May 1 (because of births and immigration), and that the tagged and untagged fish in the September 1 sample are representative of the whole population. What number does she calculate for the number of fish in the lake on May 1?
7. Smallest survey size with given percentages ●●○○○ 20 ptsA total of $n$ people were asked a question in a survey. Exactly $76\%$ of the $n$ people responded "yes" and exactly $24\%$ of the $n$ people responded "no". What is the smallest possible value of $n$?
8. Students who like to dance ●●○○○ 20 ptsOf the students attending a school party, $60\%$ are girls, and $40\%$ of the students like to dance. After these students are joined by $20$ more boys, all of whom like to dance, the party is now $58\%$ girls. How many students at the party now like to dance?
9. Cost price from loss and profit ●●○○○ 20 ptsSamy sold his dining table set at a loss of 20%. If he had sold it for $800 more, he would have received a profit of 5%. Find the cost price in dollars.
10. Maximum pencils with cashback ●●●○○ 50 ptsVasya's mother gave him exactly enough money to buy 30 pencils. All pencils cost the same. A store promotion works as follows: for a receipt for a set of 20 pencils, the factory returns 25% of the set's cost, and for a receipt for a set of 5 pencils, it returns 10% of the set's cost. The refunds can be spent on further purchases. What is the maximum number of pencils Vasya can buy?