Answer :
Sure! Let's break down and answer each part of the question step-by-step.
### Part (6)
Convert [tex]\(5\%\)[/tex] to a proper fraction:
To convert a percentage to a fraction, follow these steps:
1. Write the percentage as a fraction with a denominator of 100.
2. Simplify the fraction if possible.
For [tex]\(5\%\)[/tex]:
[tex]\[
\frac{5}{100} = \frac{1}{20}
\][/tex]
So, the proper fraction representation of [tex]\(5\%\)[/tex] is [tex]\(\frac{1}{20}\)[/tex].
### Part (7)
Type of fraction for [tex]\(1 \frac{1}{2} + 3 \frac{1}{2}\)[/tex]:
Let's add [tex]\(1 \frac{1}{2}\)[/tex] and [tex]\(3 \frac{1}{2}\)[/tex]:
1. Convert the mixed numbers to improper fractions.
[tex]\[
1 \frac{1}{2} = \frac{3}{2} \quad \text{and} \quad 3 \frac{1}{2} = \frac{7}{2}
\][/tex]
2. Add the improper fractions:
[tex]\[
\frac{3}{2} + \frac{7}{2} = \frac{3 + 7}{2} = \frac{10}{2} = 5
\][/tex]
The result, 5, is a whole number, not a mixed number, common fraction, or complex number.
### Part (8)
Simplify [tex]\(\frac{24}{30}\)[/tex]:
To simplify the fraction [tex]\(\frac{24}{30}\)[/tex], we find the greatest common divisor (GCD) of the numerator and the denominator.
1. The GCD of 24 and 30 is 6.
2. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{24 \div 6}{30 \div 6} = \frac{4}{5}
\][/tex]
So, [tex]\(\frac{24}{30}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].
### Combined and Final Answer for All Parts:
1. Convert [tex]\(5\%\)[/tex] to a proper fraction: [tex]\(\frac{1}{20}\)[/tex]
2. Type of fraction for [tex]\(1 \frac{1}{2} + 3 \frac{1}{2}\)[/tex]: Whole Number
3. Simplify [tex]\(\frac{24}{30}\)[/tex]: [tex]\(\frac{4}{5}\)[/tex]
### Additional Calculation Results:
Following the detailed solution for a separate part involving probability and z-scores:
1. Z-score for the lower bound: [tex]\( -2.13 \)[/tex]
2. Z-score for the upper bound: [tex]\( 0.71 \)[/tex]
3. Probability between these bounds: [tex]\( 0.7442 \)[/tex]
These calculations are based on standard statistical methods and results.
Let me know if you have more questions or need any further assistance!
### Part (6)
Convert [tex]\(5\%\)[/tex] to a proper fraction:
To convert a percentage to a fraction, follow these steps:
1. Write the percentage as a fraction with a denominator of 100.
2. Simplify the fraction if possible.
For [tex]\(5\%\)[/tex]:
[tex]\[
\frac{5}{100} = \frac{1}{20}
\][/tex]
So, the proper fraction representation of [tex]\(5\%\)[/tex] is [tex]\(\frac{1}{20}\)[/tex].
### Part (7)
Type of fraction for [tex]\(1 \frac{1}{2} + 3 \frac{1}{2}\)[/tex]:
Let's add [tex]\(1 \frac{1}{2}\)[/tex] and [tex]\(3 \frac{1}{2}\)[/tex]:
1. Convert the mixed numbers to improper fractions.
[tex]\[
1 \frac{1}{2} = \frac{3}{2} \quad \text{and} \quad 3 \frac{1}{2} = \frac{7}{2}
\][/tex]
2. Add the improper fractions:
[tex]\[
\frac{3}{2} + \frac{7}{2} = \frac{3 + 7}{2} = \frac{10}{2} = 5
\][/tex]
The result, 5, is a whole number, not a mixed number, common fraction, or complex number.
### Part (8)
Simplify [tex]\(\frac{24}{30}\)[/tex]:
To simplify the fraction [tex]\(\frac{24}{30}\)[/tex], we find the greatest common divisor (GCD) of the numerator and the denominator.
1. The GCD of 24 and 30 is 6.
2. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{24 \div 6}{30 \div 6} = \frac{4}{5}
\][/tex]
So, [tex]\(\frac{24}{30}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].
### Combined and Final Answer for All Parts:
1. Convert [tex]\(5\%\)[/tex] to a proper fraction: [tex]\(\frac{1}{20}\)[/tex]
2. Type of fraction for [tex]\(1 \frac{1}{2} + 3 \frac{1}{2}\)[/tex]: Whole Number
3. Simplify [tex]\(\frac{24}{30}\)[/tex]: [tex]\(\frac{4}{5}\)[/tex]
### Additional Calculation Results:
Following the detailed solution for a separate part involving probability and z-scores:
1. Z-score for the lower bound: [tex]\( -2.13 \)[/tex]
2. Z-score for the upper bound: [tex]\( 0.71 \)[/tex]
3. Probability between these bounds: [tex]\( 0.7442 \)[/tex]
These calculations are based on standard statistical methods and results.
Let me know if you have more questions or need any further assistance!
