Compare A And B In Three Ways Where A Is 196 Million In 2012

Compare A And B In Three Ways Where A196 Million Is The 2012 Da

1. Compare A and B in three ways, where A= 1.96 million is the 2012 daily circulation of newspaper X and B = 2.18 million is the 2012 daily circulation of newspaper Y. a. Find the ratio of A to B. b. Find the ratio of B to A. c. Complete the sentence: A is ____ percent of B.

2. At a particular college, 75% of the undergraduates are female. If 3450 women attend the college, how many total undergraduates attend the college?

3. Simon's monthly take-home pay (after taxes) is $2500. If he pays 20% of his gross pay (before taxes) in tax, what is his gross pay?

4. "The unemployment rate has risen more than a percentage point to 8.6% in February from 6.8% last November." What is the relative change in the unemployment rate expressed as a percentage? (Type an integer or decimal rounded to the nearest tenth as needed.)

5. Compare A and B in three ways, where A= 51,201 is the number of deaths due to a deadly disease in the United States in 2005 and B=17,792 is the number of deaths due to the same disease in the United States in 2009. a. Find the ratio of A to B. b. Find the ratio of B to A. c. Complete the sentence: A is ____ percent of B.

Paper For Above instruction

The task involves multiple quantitative comparisons and calculations related to ratios, percentages, and changes over time. This paper systematically addresses each of these problems with detailed calculations and interpretations, providing comprehensive insights into the mathematical relationships and their implications.

Question 1: Comparing Newspaper Circulations

In this problem, the daily circulation figures for two newspapers in 2012 are provided, and the goal is to compare these figures through ratios and percentages. Newspaper X has a circulation of 1.96 million, and Newspaper Y has 2.18 million.

a. The ratio of A to B is calculated as:

{\displaystyle \frac{A}{B} = \frac{1.96\, \text{million}}{2.18\, \text{million}} = \frac{1.96}{2.18} \approx 0.9009}.

This means that for every newspaper Y circulation, newspaper X has approximately 0.9009 of that figure.

b. The ratio of B to A is the reciprocal:

{\displaystyle \frac{B}{A} = \frac{2.18}{1.96} \approx 1.1122}.

This indicates that newspaper Y's circulation is roughly 1.11 times that of newspaper X.

c. To find what percent A is of B, use:

{\displaystyle \left( \frac{A}{B} \right) \times 100 \approx 0.9009 \times 100 = 90.09\% }.

Thus, newspaper X's circulation is approximately 90.1% of newspaper Y's.

Question 2: College Enrollment

If 75% of undergraduates are female, and the number of female students is 3450, then:

Let T be the total number of undergraduates:

75% of T equals 3450, or:

0.75 \times T = 3450, which yields T = \(\frac{3450}{0.75} = 4600\).

Therefore, the college has a total of 4,600 undergraduates.

Question 3: Gross Pay Calculation

Simon's net pay is $2500 after taxes. He pays 20% of his gross pay in taxes, meaning:

Let G be his gross pay. Then, his net pay is 80% of his gross pay (since 100% - 20% = 80%):

0.8 \times G = 2500, so G = \(\frac{2500}{0.8} = 3125\).

Hence, Simon's gross monthly pay is $3,125.

Question 4: Relative Change in Unemployment Rate

The unemployment rate increased from 6.8% to 8.6%. The relative change is calculated as:

Relative change = \(\frac{\text{New} - \text{Old}}{\text{Old}} \times 100\)

=\ \(\frac{8.6 - 6.8}{6.8} \times 100 = \frac{1.8}{6.8} \times 100 \approx 26.5\%\).

The unemployment rate increased by approximately 26.5% relative to its initial value.

Question 5: Comparing Disease Deaths

In 2005, 51,201 people died, and in 2009, 17,792 people died from the same disease.

a. The ratio of A to B is:

{\displaystyle \frac{A}{B} = \frac{51201}{17792} \approx 2.883}.

b. The ratio of B to A is:

{\displaystyle \frac{B}{A} = \frac{17792}{51201} \approx 0.0347}.

c. To state what percent A is of B:

{\displaystyle \left( \frac{A}{B} \right) \times 100 \approx 2.883 \times 100 = 288.3\% }.

This indicates that the number of deaths in 2005 was approximately 288.3% of those in 2009, reflecting a significant decrease over the years.

Conclusion

These calculations demonstrate fundamental arithmetic principles used to analyze ratios, proportions, and percentage changes. Such tools are essential in fields like economics, public health, and media analysis, allowing for meaningful interpretation of data trends and relationships. Understanding how to compute and interpret ratios and percentage changes helps inform decision-making and policy development across numerous sectors.

References

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  • U.S. Bureau of Labor Statistics. (2023). Unemployment Rate Data. https://www.bls.gov
  • National Center for Education Statistics. (2022). Undergraduate Enrollment Data. https://nces.ed.gov
  • Statista. (2023). Newspaper Circulation Figures. https://statista.com
  • OECD. (2020). Statistical Data; Health & Mortality Rates. https://oecd.org
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