Find an equation of the largest sphere with center (4, 3, 6) that is contained in the first octant.

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• In Sara's class, 2/5 of the students ride a bus, and 1/3 ride a car to school, while the rest walk. To find the fraction of students who walk to school, you must determine the total fraction that ride either a bus or a car and subtract this from the whole. To find the fraction of students who use a bus or car to get to school, add the fractions of students who ride a bus (2/5) and those who ride a car (1/3). To add these fractions, you need a common denominator, which, in this case, could be 15. Converting to the common denominator, we get: Students who ride the bus: \( \frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15} \) Students who ride a car: \( \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} \) Now, add the fractions: \( \frac{6}{15} + \frac{5}{15} = \frac{11}{15} \) This means that 11/15 of the students ride a bus or a car to school. To find the fraction of students who walk to school, subtract the fraction that rides a bus or car from 1, since the total class represents one whole: \( 1 - \frac{11}{15} = \frac{15}{15} - \frac{11}{15} = \frac{4}{15} \) So, 4/15 of the students walk to school. For visualization, you can draw a diagram of a circle (representing the whole class) divided into 15 equal parts. Shade 6 parts for bus riders and an additional 5 parts for car riders. The remaining 4 unshaded parts represent the students who walk to school. To summarize: - The fraction of students who ride a bus or car is 11/15. - The fraction of students who walk to school is 4/15.
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