To determine the probability that the spinner does not land on sectors Q or R, we first need to find the angle measures of these sectors, and then the total angle for the entire circle.
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Total angle in a circle: \[ 360 \text{ degrees} \]
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Central angle of sector R: \[ 31 \text{ degrees} \]
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Central angle of sector Q: \[ 225 \text{ degrees} \]
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Total angle of sectors Q and R: \[ 31 + 225 = 256 \text{ degrees} \]
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Angle not covered by sectors Q and R: \[ 360 - 256 = 104 \text{ degrees} \]
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Probability that the spinner does not land on Q or R: The probability \( P \) is the angle not landing on these sectors divided by the total angle in a circle: \[ P = \frac{104}{360} \]
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Now, simplify this fraction: Find the greatest common divisor (GCD) of 104 and 360.
\[ 104 = 2^3 \times 13 \ 360 = 2^3 \times 3^2 \times 5 \] The GCD is \( 2^3 = 8 \).
Now, divide both the numerator and denominator by their GCD: \[ \frac{104 \div 8}{360 \div 8} = \frac{13}{45} \]
Thus, the probability that the spinner does not land on sectors Q or R is: \[ \boxed{\frac{13}{45}} \]