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Flashcards: Understanding two-part analyses

Over a seven-year period, from 2002 to 2009, the number of babies born to married couples increased despite a decrease in marriages from 17,000 marriages in 2002.

In the given expression, $\displaystyle B$ and $\displaystyle M$ represent the percent change in the babies and marriages, respectively. $\displaystyle I$ represents the number of babies per married couple in 2002. The percent change in a quantity is calculated by the formula:

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$ $\displaystyle \left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

Identify the following with the given information,

I. The expression that represents the number of babies born in 2002.

II. The expression of the number of babies born per family in 2009.

I. The expression that represents the number of babies born in 2002.

17,000I $\displaystyle 17,000I$

II. The expression of the number of babies born per married couple in 2009.

$\left( \frac{100+B}{100+M}\right)\times I$ $\displaystyle \left( \frac{100+B}{100+M}\right)\times I$

I. The expression that represents the number of babies born in 2002.

17,000I $\displaystyle 17,000I$

II. The expression of the number of babies born per married couple in 2009.

$\left( \frac{100-B}{100+M}\right)\times I$ $\displaystyle \left( \frac{100-B}{100+M}\right)\times I$

I. The expression that represents the number of babies born in 2002.

17,000I $\displaystyle 17,000I$

II. The expression of the number of babies born per married couple in 2009.

$\left( \frac{100-M}{100+B}\right)\times I$ $\displaystyle \left( \frac{100-M}{100+B}\right)\times I$

I. The expression that represents the number of babies born in 2002.

$\frac{17,000}{I}$ $\displaystyle \frac{17,000}{I}$

II. The expression of the number of babies born per married couple in 2009.

$\left( \frac{100+B}{100+M}\right)\times I$ $\displaystyle \left( \frac{100+B}{100+M}\right)\times I$

I. The expression that represents the number of babies born in 2002.

$\frac{17,000}{I}$ $\displaystyle \frac{17,000}{I}$

II. The expression of the number of babies born per married couple in 2009.

$\left( \frac{100+M}{100+B}\right)\times I$ $\displaystyle \left( \frac{100+M}{100+B}\right)\times I$

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Flashcards: Understanding two-part analyses

Over a seven-year period, from 2002 to 2009, the number of babies born to married couples increased despite a decrease in marriages from 17,000 marriages in 2002.

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$ $\displaystyle \left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

Identify the following with the given information,

I. The expression that represents the number of babies born in 2002.

II. The expression of the number of babies born per family in 2009.

I. The expression that represents the number of babies born in 2002.

17,000I $\displaystyle 17,000I$

II. The expression of the number of babies born per married couple in 2009.

$\left( \frac{100+B}{100+M}\right)\times I$ $\displaystyle \left( \frac{100+B}{100+M}\right)\times I$

I. The expression that represents the number of babies born in 2002.

17,000I $\displaystyle 17,000I$

II. The expression of the number of babies born per married couple in 2009.

$\left( \frac{100-B}{100+M}\right)\times I$ $\displaystyle \left( \frac{100-B}{100+M}\right)\times I$

I. The expression that represents the number of babies born in 2002.

17,000I $\displaystyle 17,000I$

II. The expression of the number of babies born per married couple in 2009.

$\left( \frac{100-M}{100+B}\right)\times I$ $\displaystyle \left( \frac{100-M}{100+B}\right)\times I$

I. The expression that represents the number of babies born in 2002.

$\frac{17,000}{I}$ $\displaystyle \frac{17,000}{I}$

II. The expression of the number of babies born per married couple in 2009.

$\left( \frac{100+B}{100+M}\right)\times I$ $\displaystyle \left( \frac{100+B}{100+M}\right)\times I$

I. The expression that represents the number of babies born in 2002.

$\frac{17,000}{I}$ $\displaystyle \frac{17,000}{I}$

II. The expression of the number of babies born per married couple in 2009.

$\left( \frac{100+M}{100+B}\right)\times I$ $\displaystyle \left( \frac{100+M}{100+B}\right)\times I$

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Flashcards: Understanding two-part analyses

Over a seven-year period, from 2002 to 2009, the number of babies born to married couples increased despite a decrease in marriages from 17,000 marriages in 2002.

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$ $\displaystyle \left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

Identify the following with the given information,

I. The expression that represents the number of babies born in 2002.

II. The expression of the number of babies born per family in 2009.

Your answer:

I. The expression that represents the number of babies born in 2002.

17,000I $\displaystyle 17,000I$

II. The expression of the number of babies born per married couple in 2009.

$\left( \frac{100-B}{100+M}\right)\times I$ $\displaystyle \left( \frac{100-B}{100+M}\right)\times I$

Your answer:

I. The expression that represents the number of babies born in 2002.

17,000I $\displaystyle 17,000I$

II. The expression of the number of babies born per married couple in 2009.

$\left( \frac{100-M}{100+B}\right)\times I$ $\displaystyle \left( \frac{100-M}{100+B}\right)\times I$

Your answer:

I. The expression that represents the number of babies born in 2002.

$\frac{17,000}{I}$ $\displaystyle \frac{17,000}{I}$

II. The expression of the number of babies born per married couple in 2009.

$\left( \frac{100+B}{100+M}\right)\times I$ $\displaystyle \left( \frac{100+B}{100+M}\right)\times I$

Your answer:

I. The expression that represents the number of babies born in 2002.

$\frac{17,000}{I}$ $\displaystyle \frac{17,000}{I}$

II. The expression of the number of babies born per married couple in 2009.

$\left( \frac{100+M}{100+B}\right)\times I$ $\displaystyle \left( \frac{100+M}{100+B}\right)\times I$

Correct answer:

I. The expression that represents the number of babies born in 2002.

17,000I $\displaystyle 17,000I$

II. The expression of the number of babies born per married couple in 2009.

$\left( \frac{100+B}{100+M}\right)\times I$ $\displaystyle \left( \frac{100+B}{100+M}\right)\times I$

Explanation:

To identify,

I. The expression that represents the number of babies born in 2002.

Recall the given information in this particular question.

It is known that in 2002 there are 17,000 marriages and $\displaystyle I$ represents $\frac{\text{Babies}}{\text{Marriage}}$ $\displaystyle \frac{\text{Babies}}{\text{Marriage}}$ .

Using this information to create a mathematical expression is as follows.

$17,000 \text{ marriages}\times \frac{\text{babies}}{\text{marriage}}\Rightarrow17,000 \text{ marriages}\times I=17,000I$ $\displaystyle 17,000 \text{ marriages}\times \frac{\text{babies}}{\text{marriage}}\Rightarrow17,000 \text{ marriages}\times I=17,000I$

Now to identify,

II. The expression of the number of babies born per married couple in 2009.

Use the formula given

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$ $\displaystyle \left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

This part of the problem is asking for a ratio, but the variables that are given are percents.

Therefore, the 100’s are there because M and B are percent quantities. They are both added because M is a negative number.

So the number in the numerator is the percentage of babies that exist in 2009 compared to 2002 (a number that will be less than 100). The denominator is the percentage of the 2002 marriages that exists in 2009 (a number greater than 100).

Thus the solution is,

$\left( \frac{100+B}{100+M}\right)\times I$ $\displaystyle \left( \frac{100+B}{100+M}\right)\times I$

Flashcards: Understanding two-part analyses

A high-school music department is putting together a two-day music festival to highlight the students' talents. The schedule for the two days will adhere to the following rules:

1. Five musical performances are scheduled for each day.

2. The majority of the performances on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, or bassoons)

3. The other day will primarily feature solo performances.

Currently, 8 of the performances (4 each day) have been scheduled. The music department must add one additional performance on each day:

Day 1

Smooth Jazz Group (10th Grade, Saxophone Trio)

Rock Your Socks Off (12th Grade, Vocal Group)

Dustin & Karen (11th Grade, Flute Duo)

James (11th Grade, Trumpet Solo)

Day 2

Adam (10th Grade, Vocal Solo)

John (11th Grade, Clarinet Solo)

Rachel (12th Grade, Brass Solo)

4 Blind Mice (9th Grade, Woodwind Quartet)

The music department must add one additional performance on each day.

Based on the rules above, identify a performance that following:

I. A performance that can be scheduled on either day.

II. A performance that cannot be scheduled on either day.

I. Susan (12th Grade, Flute Solo)

II. Henry (12th Grade, Violin Solo)

I. Jenny & Molly (12th Grade, Flute Solo)

II. James & Jimmy (10th Grade, Vocal Duo)

I. Susan (12th Grade, Flute Solo)

II. Kimmy (10th Grade, Trumpet Solo)

I. Susan & Tina (12th Grade, Flute and Clarinet Duo)

II. James & Jimmy (10th Grade, Vocal Duo)

I. Susan (12th Grade, Flute Solo)

II. James & Jimmy (10th Grade, Vocal Duo)

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Flashcards: Understanding two-part analyses

A high-school music department is putting together a two-day music festival to highlight the students' talents. The schedule for the two days will adhere to the following rules:

1. Five musical performances are scheduled for each day.

2. The majority of the performances on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, or bassoons)

3. The other day will primarily feature solo performances.

Currently, 8 of the performances (4 each day) have been scheduled. The music department must add one additional performance on each day:

Day 1

Smooth Jazz Group (10th Grade, Saxophone Trio)

Rock Your Socks Off (12th Grade, Vocal Group)

Dustin & Karen (11th Grade, Flute Duo)

James (11th Grade, Trumpet Solo)

Day 2

Adam (10th Grade, Vocal Solo)

John (11th Grade, Clarinet Solo)

Rachel (12th Grade, Brass Solo)

4 Blind Mice (9th Grade, Woodwind Quartet)

The music department must add one additional performance on each day.

Based on the rules above, identify a performance that following:

I. A performance that can be scheduled on either day.

II. A performance that cannot be scheduled on either day.

Your answer:

I. Susan (12th Grade, Flute Solo)

II. Henry (12th Grade, Violin Solo)

Your answer:

I. Jenny & Molly (12th Grade, Flute Solo)

II. James & Jimmy (10th Grade, Vocal Duo)

Your answer:

I. Susan (12th Grade, Flute Solo)

II. Kimmy (10th Grade, Trumpet Solo)

Your answer:

I. Susan & Tina (12th Grade, Flute and Clarinet Duo)

II. James & Jimmy (10th Grade, Vocal Duo)

Correct answer:

I. Susan (12th Grade, Flute Solo)

II. James & Jimmy (10th Grade, Vocal Duo)

Explanation:

Recall the criteria for this particular problem.

Five musicians are scheduled to play each day. To feature the departments strengths, the majority of the musicians on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, bassoons) and the other day will be primarily solo musicians.

Looking at day one it is clear that represents the woodwind day and day two represents the solo day.

Therefore, for someone to be able to play either day that student must play a woodwind instrument and be doing a solo. For a musician(s) to play neither day it must be a group that is composed of instruments other than woodwind.

Also recall that violins are string instruments, trumpets are brass instruments, and vocal is ones voice.

Keeping all of this in mind, the correct answer is,

I. Susan (12th Grade, Flute Solo)

II. James & Jimmy (10th Grade, Vocal Duo)

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