Question

the central angle of sector g is 54°. the central angle of sector h is 27°. what is the probability that the spinner does not land on either sector g or sector h? write your answer as a fraction or decimal. do not round.

Explanation:

Step1: Calculate the sum of central angles of \(G\) and \(H\)

The central angle of \(G\) is \(54^{\circ}\), and the central angle of \(H\) is \(27^{\circ}\). So the sum is \(54 + 27=81^{\circ}\).

Step2: Calculate the total central angle of the circle

The total central angle of a circle is \(360^{\circ}\).

Step3: Calculate the central angle of non - \(G\) and non - \(H\) regions

Subtract the sum of \(G\) and \(H\) from the total central angle: \(360 - 81 = 279^{\circ}\).

Step4: Calculate the probability

Probability \(P=\frac{\text{Central angle of non - }G\text{ and non - }H}{\text{Total central angle}}\). So \(P=\frac{279}{360}=\frac{31}{40}=0.775\).

Answer:

\(0.775\) (or \(\frac{31}{40}\))