Let's analyze and solve the two distinct questions step by step.
### Question 12:
Problem Statement:
Marie spends 30 minutes reading and 20 minutes playing the piano every day. We need to write an equation that shows the total number of minutes, [tex]\( m \)[/tex], she plays the piano in [tex]\( d \)[/tex] days.
Solution:
1. Identify the given values:
- Marie plays the piano for 20 minutes each day.
2. Define the variables:
- Let [tex]\( d \)[/tex] be the number of days.
- Let [tex]\( m \)[/tex] be the total number of minutes she plays the piano in [tex]\( d \)[/tex] days.
3. Establish the relationship between the minutes and the days:
- Each day, she plays 20 minutes.
- Therefore, in [tex]\( d \)[/tex] days, she plays [tex]\( 20 \times d \)[/tex] minutes.
Therefore, the equation that represents the total number of minutes [tex]\( m \)[/tex] she plays the piano in [tex]\( d \)[/tex] days is:
[tex]\[ m = 20d \][/tex]
Answer:
A. [tex]\( m = 20d \)[/tex]
### Question 13:
Problem Statement:
Determine the value of the expression:
[tex]\[ (4.8 \times 10^7) + 6,500,000 \][/tex]
Solution:
1. Convert [tex]\( 6,500,000 \)[/tex] into scientific notation:
- [tex]\( 6,500,000 = 6.5 \times 10^6 \)[/tex]
2. Add the two numbers:
- [tex]\( 4.8 \times 10^7 \)[/tex] and [tex]\( 6.5 \times 10^6 \)[/tex] can be combined by converting them into the same power of ten.
- Convert [tex]\( 6.5 \times 10^6 \)[/tex] to [tex]\( 0.65 \times 10^7 \)[/tex] (since [tex]\( 6.5 \times 10^6 = 0.65 \times 10^7 \)[/tex]).
- Now the addition becomes:
[tex]\[ (4.8 \times 10^7) + (0.65 \times 10^7) = (4.8 + 0.65) \times 10^7 = 5.45 \times 10^7 \][/tex]
Answer:
A. [tex]\( 5.45 \times 10^7 \)[/tex]
This solution matches the result obtained, providing us with a comprehensive and clear understanding of how each step leads to the final answers for both questions.
