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Sagot :
Sure! Let's address each part of the question in detail.
### Part (a): Total Mass of the Books and Folders in the Bag
First, we need to find the total mass of the books and the total mass of the folders separately.
1. Total Mass of the Books:
We are given that there are 9 books, and each book has a mass of [tex]\(\frac{2}{9} \, \text{kg}\)[/tex].
[tex]\[ \text{Total mass of books} = \text{Number of books} \times \text{Mass per book} \][/tex]
Substitute the values:
[tex]\[ \text{Total mass of books} = 9 \times \frac{2}{9} \, \text{kg} \][/tex]
Simplifying this, we get:
[tex]\[ \text{Total mass of books} = 2 \, \text{kg} \][/tex]
2. Total Mass of the Folders:
We are given that there are 5 folders, and each folder has a mass of [tex]\(\frac{7}{25} \, \text{kg}\)[/tex].
[tex]\[ \text{Total mass of folders} = \text{Number of folders} \times \text{Mass per folder} \][/tex]
Substitute the values:
[tex]\[ \text{Total mass of folders} = 5 \times \frac{7}{25} \, \text{kg} \][/tex]
Simplifying this, we get:
[tex]\[ \text{Total mass of folders} = 1.4 \, \text{kg} \][/tex]
3. Total Mass in the Bag:
Now, we sum up the total mass of the books and the total mass of the folders:
[tex]\[ \text{Total mass in the bag} = \text{Total mass of books} + \text{Total mass of folders} \][/tex]
Substitute the values:
[tex]\[ \text{Total mass in the bag} = 2 \, \text{kg} + 1.4 \, \text{kg} \][/tex]
Simplifying, we get:
[tex]\[ \text{Total mass in the bag} = 3.4 \, \text{kg} \][/tex]
Therefore, the total mass of the books and folders in the bag is [tex]\(3.4 \, \text{kg}\)[/tex].
### Part (b): Fraction of the Total Mass that is Books
To find the fraction of the total mass that is books, we use the total mass of the books and the total mass in the bag.
1. Fraction of Mass that is Books:
[tex]\[ \text{Fraction of mass that is books} = \frac{\text{Total mass of books}}{\text{Total mass in the bag}} \][/tex]
Substitute the values:
[tex]\[ \text{Fraction of mass that is books} = \frac{2 \, \text{kg}}{3.4 \, \text{kg}} \][/tex]
Simplifying this, we get:
[tex]\[ \text{Fraction of mass that is books} \approx 0.588 \][/tex]
Therefore, the fraction of the total mass that is attributed to the books is approximately [tex]\(0.588\)[/tex] or [tex]\(58.82\%\)[/tex].
### Summary of Answers:
- (a) The total mass of the books and folders in the bag is [tex]\(3.4 \, \text{kg}\)[/tex].
- (b) The fraction of the total mass that is books is approximately [tex]\(0.588\)[/tex].
### Part (a): Total Mass of the Books and Folders in the Bag
First, we need to find the total mass of the books and the total mass of the folders separately.
1. Total Mass of the Books:
We are given that there are 9 books, and each book has a mass of [tex]\(\frac{2}{9} \, \text{kg}\)[/tex].
[tex]\[ \text{Total mass of books} = \text{Number of books} \times \text{Mass per book} \][/tex]
Substitute the values:
[tex]\[ \text{Total mass of books} = 9 \times \frac{2}{9} \, \text{kg} \][/tex]
Simplifying this, we get:
[tex]\[ \text{Total mass of books} = 2 \, \text{kg} \][/tex]
2. Total Mass of the Folders:
We are given that there are 5 folders, and each folder has a mass of [tex]\(\frac{7}{25} \, \text{kg}\)[/tex].
[tex]\[ \text{Total mass of folders} = \text{Number of folders} \times \text{Mass per folder} \][/tex]
Substitute the values:
[tex]\[ \text{Total mass of folders} = 5 \times \frac{7}{25} \, \text{kg} \][/tex]
Simplifying this, we get:
[tex]\[ \text{Total mass of folders} = 1.4 \, \text{kg} \][/tex]
3. Total Mass in the Bag:
Now, we sum up the total mass of the books and the total mass of the folders:
[tex]\[ \text{Total mass in the bag} = \text{Total mass of books} + \text{Total mass of folders} \][/tex]
Substitute the values:
[tex]\[ \text{Total mass in the bag} = 2 \, \text{kg} + 1.4 \, \text{kg} \][/tex]
Simplifying, we get:
[tex]\[ \text{Total mass in the bag} = 3.4 \, \text{kg} \][/tex]
Therefore, the total mass of the books and folders in the bag is [tex]\(3.4 \, \text{kg}\)[/tex].
### Part (b): Fraction of the Total Mass that is Books
To find the fraction of the total mass that is books, we use the total mass of the books and the total mass in the bag.
1. Fraction of Mass that is Books:
[tex]\[ \text{Fraction of mass that is books} = \frac{\text{Total mass of books}}{\text{Total mass in the bag}} \][/tex]
Substitute the values:
[tex]\[ \text{Fraction of mass that is books} = \frac{2 \, \text{kg}}{3.4 \, \text{kg}} \][/tex]
Simplifying this, we get:
[tex]\[ \text{Fraction of mass that is books} \approx 0.588 \][/tex]
Therefore, the fraction of the total mass that is attributed to the books is approximately [tex]\(0.588\)[/tex] or [tex]\(58.82\%\)[/tex].
### Summary of Answers:
- (a) The total mass of the books and folders in the bag is [tex]\(3.4 \, \text{kg}\)[/tex].
- (b) The fraction of the total mass that is books is approximately [tex]\(0.588\)[/tex].
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