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21 problems match “arithmetic mean”. Clear

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1. Sum of squares from means ●○○○○ 10 ptsReal numbers $x$ and $y$ have an arithmetic mean of 18 and a geometric mean of $\sqrt{92}$. Find $x^2+y^2$.
2. Positive x in a sequence of squares ●○○○○ 10 ptsThe numbers $1^2$, $x^2$, $3^2$ are consecutive terms of an arithmetic sequence. Find the positive value of $x$. Round to two decimal places.
3. Middle term of an arithmetic sequence ●○○○○ 10 ptsIn the arithmetic sequence $3^2, x, 3^4$, find the value of $x$.
4. Average of integers between two fractions ●○○○○ 10 ptsWhat is the average of all the integer values of $M$ such that $\frac{M}{56}$ is strictly between $\frac{3}{7}$ and $\frac{1}{4}$?
5. Smallest of five consecutive integers ●○○○○ 10 ptsThe mean (average) of 5 consecutive integers is 9. What is the smallest of these 5 integers?
6. Positive difference from an average ●○○○○ 10 ptsThe average of the numbers 23 and $x$ is 27. What is the positive difference between 23 and $x$?
7. Average speed over equal times ●○○○○ 10 ptsShyam travels at 40 km/h for half of the total time and at 30 km/h for the other half. What is Shyam's average speed, in km/h?
8. Greatest integer in a set of five ●○○○○ 10 ptsFive positive integers have an average of 15. What is the greatest possible value of one of these integers?
9. Smallest average of distinct even integers ●○○○○ 10 ptsWhat is the smallest possible average of four distinct positive even integers?
10. Largest of four integers from triple averages ●●○○○ 20 ptsDewa writes down a list of four integers. He calculates the average of each group of three of the four integers. These averages are $32, 39, 40, 44$. What is the largest of the four integers?

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