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The number of pages in ten A4 books and their corresponding weights (in grams) are given in the table below - NSC Mathematics - Question 1 - 2024 - Paper 2
Question 1
The number of pages in ten A4 books and their corresponding weights (in grams) are given in the table below. The data is also represented in the scatter plot. Numbe... show full transcript
Worked Solution & Example Answer:The number of pages in ten A4 books and their corresponding weights (in grams) are given in the table below - NSC Mathematics - Question 1 - 2024 - Paper 2
Step 1
Determine the equation of the least squares regression line.
Answer
To find the least squares regression line, we use the formula:
y = a + bx, where 'a' is the y-intercept and 'b' is the slope.
From the marking scheme, we have:
a = -43.72,
b = 2.36.
Thus, the equation is:
y = -43.72 + 2.36x.
Step 2
Draw the least squares regression line on the scatter plot in the ANSWER BOOK.
Answer
To draw the least squares regression line:
- Identify points corresponding to the equation y = -43.72 + 2.36x.
- Choose at least two values of 'x' to plot.
- For example, if x = 85 and x = 150:
- For x = 85: y = -43.72 + 2.36(85) = 165.08
- For x = 150: y = -43.72 + 2.36(150) = 360.08
- Plot these points on the scatter plot and draw the line.
Step 3
Step 4
Calculate the percentage weight increase between a book with 110 pages and a book with 130 pages.
Answer
First, determine the weight of the book with 130 pages using the regression equation:
y = -43.72 + 2.36(130).
Calculating:
y = -43.72 + 306.8 = 263.08 grams.
Next, use the percentage increase formula:
Percentage increase = ( \frac{(New - Old)}{Old} \times 100 )
Old = 215.88 grams (weight of book with 110 pages) New = 263.08 grams (weight of book with 130 pages)
Calculating:
Percentage increase = ( \frac{(263.08 - 215.88)}{215.88} \times 100 \approx 21.86% ).
Therefore, the percentage weight increase is approximately 21.86%.