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Compare quantities: mixed set 2: original cases with explanations after your first response.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
These comparisons mix counting, coordinate relations and dimensional measurement. Look for a proof that preserves the entire allowed domain before experimenting with values.
A fair six-sided die is rolled twice independently. Quantity A: Probability the sum is 7 Quantity B: Probability the sum is 8 Compare the quantities using only the stated information.
Five distinct integers have mean 8. Quantity A: Largest integer Quantity B: 8 Compare the quantities using only the stated information.
A line has equation y=3x-5. Quantity A: Its y-intercept Quantity B: Its x-intercept Compare the quantities using only the stated information.
A cube has positive edge length s. Quantity A: Numerical value of its volume Quantity B: Numerical value of its surface area Compare the quantities using only the stated information.
k is a positive integer. Quantity A: Number of positive divisors of 2 to the power k Quantity B: k+1 Compare the quantities using only the stated information.
A data set has positive standard deviation. Each observation is increased by 7. Quantity A: New standard deviation Quantity B: Original standard deviation Compare the quantities using only the stated information.
For geometric quantities, check whether changing the size of the figure can reverse a numerical comparison between area and volume.