Q: Column A: $$37\%$$ of $$240$$Column B: $$90$$.

Compute Column A. $$37\%\text{ of }240=0.37\cdot240$$ $$=88.8$$ Compare. $$88.8$$<$$90$$ So, Column B is greater. Final answer: $$\text{Column B is greater}$$

Q: A taxi charges $$1.20$$ dollars for the first $$\frac{1}{2}$$ mile and $$0.40$$ dollars for every additional $$\frac{1}{2}$$ mile. The total cost of a trip was $$13.20$$ dollars. Compare Column A and Column B.Column A: the trip's distance in milesColumn B: $$15$$.

Subtract the first charge. $$13.20-1.20=12.00$$ Each additional $$\frac{1}{2}$$ mile costs $$0.40$$ Number of additional half-miles: $$\frac{12.00}{0.40}=30$$ Total half-miles: $$30+1=31$$ Total miles: $$31\cdot\frac{1}{2}=15.5$$ Compare. $$15.5$$>$$15$$ Final answer: $$\text{Column A is greater}$$

Question 1

The number $$18{,}000$$ has how many positive divisors?

Accepted Answer

Prime factorize $$18{,}000$$. $$18{,}000=18\cdot1000$$ $$18{,}000=(2\cdot3^2)(2^3\cdot5^3)$$ $$18{,}000=2^4\cdot3^2\cdot5^3$$ Use the divisor formula. $$(4+1)(2+1)(3+1)$$ $$=5\cdot3\cdot4$$ $$=60$$ Final answer: $$60$$

Question 2

If $$x$$ and $$y$$ are integers, and $$w=x^2y+2x+5y$$, which of the following statements must be true?A. If $$w$$ is even, then $$x$$ must be even.B. If $$x$$ is odd, then $$w$$ must be odd.C. If $$y$$ is even, then $$w$$ must be even.D. If $$w$$ is odd, then $$y$$ must be odd.

Accepted Answer

Rewrite $$w$$ modulo $$2$$. $$x^2\equiv x\pmod2$$ $$2x\equiv0\pmod2$$ $$5y\equiv y\pmod2$$ So $$w\equiv x^2y+y\pmod2$$ $$w\equiv xy+y\pmod2$$ Factor. $$w\equiv y(x+1)\pmod2$$ Check each statement. If $$w$$ is even, $$x$$ need not be even. Take $$x=1,\ y=1$$. Then $$w$$ is even. So statement $$A$$ is false. If $$x$$ is odd, then $$x+1$$ is even. So $$y(x+1)$$ is even. Thus $$w$$ is even, not necessarily odd. So, statement $$B$$ is false. If $$y$$ is even, then $$y(x+1)$$ is even. So $$w$$ is even. Statement $$C$$ is true. If $$w$$ is odd, then $$y(x+1)$$ is odd. So $$y$$ must be odd. Statement $$D$$ is true. Final answer: $$	ext{C and D}$$

Question 3

Column A: $$37\%$$ of $$240$$Column B: $$90$$.

Accepted Answer

Compute Column A. $$37\%	ext{ of }240=0.37\cdot240$$ $$=88.8$$ Compare. $$88.8$$<$$90$$ So, Column B is greater. Final answer: $$	ext{Column B is greater}$$

Question 4

A taxi charges $$1.20$$ dollars for the first $$\frac{1}{2}$$ mile and $$0.40$$ dollars for every additional $$\frac{1}{2}$$ mile. The total cost of a trip was $$13.20$$ dollars. Compare Column A and Column B.Column A: the trip's distance in milesColumn B: $$15$$.

Accepted Answer

Subtract the first charge. $$13.20-1.20=12.00$$ Each additional $$\frac{1}{2}$$ mile costs $$0.40$$ Number of additional half-miles: $$\frac{12.00}{0.40}=30$$ Total half-miles: $$30+1=31$$ Total miles: $$31\cdot\frac{1}{2}=15.5$$ Compare. $$15.5$$>$$15$$ Final answer: $$	ext{Column A is greater}$$

Question 5

The average of $$x$$, $$y$$, and $$21$$ is $$12$$. Compare Column A and Column B.Column A: Average of $$x$$and $$y$$Column B: $$9$$

Accepted Answer

Use the given average. $$\frac{x+y+21}{3}=12$$ Multiply by $$3$$. $$x+y+21=36$$ $$x+y=15$$ Average of $$x$$ and $$y$$: $$\frac{x+y}{2}=\frac{15}{2}=7.5$$ Compare. $$7.5$$<$$9$$ Final answer: $$	ext{Column B is greater}$$

Quiz 2

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