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9 problems match “geometric 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. Geometric mean of three numbers ●○○○○ 10 ptsFind the geometric mean of $3$, $6$ and $12$.
3. Arithmetic mean from geometric and harmonic means ●●○○○ 20 ptsFind the arithmetic mean of two positive numbers whose geometric mean is 4 and whose harmonic mean is $\frac{16}{5}$.
4. Harmonic mean from the other means ●●○○○ 20 ptsFind the harmonic mean of two positive numbers whose arithmetic mean is $\frac{15}{2}$ and whose geometric mean is $6$.
5. Average growth rate from yearly returns ●●○○○ 20 ptsA sum of money grew over 4 years by 25%, 12%, -4% and 10%, one rate per year. Find the average annual growth rate as a percentage. Round to two decimal places.
6. Two numbers from mean conditions ●●●○○ 50 ptsFind two numbers whose arithmetic mean exceeds their geometric mean by $\frac{1}{2}$ and whose harmonic mean is $\frac{25}{26}$ less than their arithmetic mean.
7. Two numbers from their means ●●●○○ 50 ptsTwo positive numbers have an arithmetic mean that exceeds their geometric mean by $2$, and their geometric mean exceeds their harmonic mean by $1.6$. Find the two numbers.
8. Two numbers from three means ●●●○○ 50 ptsFind two positive numbers whose arithmetic mean exceeds their geometric mean by $2$ and whose harmonic mean is $3.6$ less than their arithmetic mean. Give them in increasing order.
9. Combined growth rate of two funds ●●●○○ 50 ptsFund A was worth $2.5m in 2000 and grew by 8%, -3%, -5%, 2% and 9% in the following five years. Fund B was worth $3.5m in 2000 and grew by 2%, 4%, -10%, 3% and 18% in the following five years. Find the average annual growth rate of the two funds taken together, as a percentage. Round to two decimal places.