A truck is being filled with cube-shaped packages that have side lengths of \frac{1}{4} 4
1
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foot. The part of the truck that is being filled is in the shape of a rectangular prism with dimensions of 8\ \mathrm{ft}\times 6\frac{1}{4}\ \mathrm{ft}\times 7\frac{1}{2}\ \mathrm{ft}8 ft×6
4
1
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ft×7
2
1
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ft.

Find the smallest number by which the given number should be divided to make a perfect cube(with steps or the answer will get reported) a.108 b.2187

The table below represents the displacement of a fish from its reef as a function of time: time (hours) x displacement from reef (feet) y 0 4 1 64 2 124 3 184 4 244 part a: what is the y-intercept of the function, and what does this tell you about the fish? (4 points) part b: calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents. (4 points) part c: what would be the domain of the function if the fish continued to swim at this rate until it traveled 724 feet from the reef? (2 points)

(c) the diagram shows the first three shapes of a matchsticks arrangement.first shape = 3second shape = 5third shape = 7given m represents the number of matchstick used to arrange the n'th shape.(i) write a formula to represent the relation between m and n. express m as the subjectof the formula.(ii) 19 matchsticks are used to make the p'th shape. find the value of p.