Rates & Ratios — Quiz 5

Questions in this quiz (5)

1. A box contains apples that are either red or yellow. The ratio of red apples to yellow apples in the box is $$5:4$$. When $$6$$ red apples and $$6$$ yellow apples are removed, the ratio becomes $$4:3$$. How many yellow apples were originally in the box?

   • $$6$$
   • $$24$$
   • $$16$$
   • $$4$$

2. The time $$T$$ a pendulum takes to complete one full oscillation is directly proportional to the square root of its length $$L$$ and inversely proportional to the square root of the acceleration due to gravity $$g$$. If $$k$$ represents the constant of proportionality, which of the following expressions represents the time $$T$$ for a pendulum of length $$L$$ when the acceleration due to gravity is $$g$$?

   • $$\frac{k}{Lg}$$
   • $$\frac{kL^2}{g^2}$$
   • $$k\frac{\sqrt{L}}{\sqrt{g}}$$
   • $$\frac{k}{Lg}$$

3. Lucas is designing a decorative hanging ornament composed of 3 circular metal plates of different sizes. The smallest circle has a diameter of 10 inches, and the diameters of the three circles are in the ratio $$1:3:5$$. To stabilize the ornament, Lucas will attach a straight metal rod from the center of the smallest circle, through the center of the middle circle, to the center of the largest circle. What is the total length, in inches, of the metal rod?

   • $$60$$
   • $$100$$
   • $$50$$
   • $$45$$

4. A factory hires workers to assemble and pack smartphones. Each worker assigned to assembly can produce $$20$$ smartphones per hour. Each worker assigned to packaging can pack $$4$$ smartphones every $$10$$ minutes. The factory currently has $$10$$ workers, all assigned to assembly. How many additional workers should be hired and assigned to packaging so that the number of smartphones assembled and packaged are equal per hour?

   • $$8$$
   • $$9$$
   • $$7$$
   • $$10$$

5. Lena deposits $$800$$ into a savings account that earns $$4\%$$ interest compounded quarterly. After $$1.5$$ years, she withdraws $$250$$. How much money does she have after $$2$$ years?

   • 599.22
   • 849.22
   • 749.50
   • 611.26