The bar graph below shows the marks scored by some pupils in Mock Examinations. Use it to answer the question…

Question

The bar graph below shows the marks scored by some pupils in Mock Examinations. Use it to answer the question that follows.

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the questions.

6. Find their range.

Identify the highest and lowest marks from the bar graph.
The lowest mark interval shown is 30.
The highest mark interval shown is 80.
Calculate the range using the formula
Range = Highest mark - Lowest mark.
$\text{Range} = 80 - 30$ $\text{Range} = 50$
The range is $\boxed{\text{50}}$ .

7. Given that $a = \frac{1}{16}$ , $b = 8$ . Find the value of $(ab)^2$ .
Calculate the product $ab$ .
$ab = \frac{1}{16} \times 8$ $ab = \frac{8}{16}$ $ab = \frac{1}{2}$
Calculate $(ab)^2$ .
$(ab)^2 = \left(\frac{1}{2}\right)^2$ $(ab)^2 = \frac{1^2}{2^2}$ $(ab)^2 = \frac{1}{4}$
The value of $(ab)^2$ is $\boxed{\frac{1}{4}}$ .

8. Find the length of the arc BD (Use $\pi = \frac{22}{7}$ ).
Identify the radius of the quarter circle.
From the diagram, the side BC is 14 cm. Since the arc BD is part of a quarter circle centered at C, the radius $r$ is equal to BC.
$r = 14 \text{ cm}$
Use the formula for the length of a quarter circle arc.
The length of a full circle's circumference is $C = 2\pi r$ .
The length of a quarter circle arc is $\frac{1}{4}$ of the circumference.
$\text{Length of arc BD} = \frac{1}{4} \times 2\pi r$ $\text{Length of arc BD} = \frac{1}{2}\pi r$
Substitute the values of $r$ and $\pi$ into the formula and calculate.
$\text{Length of arc BD} = \frac{1}{2} \times \frac{22}{7} \times 14$ $\text{Length of arc BD} = \frac{1}{2} \times 22 \times \frac{14}{7}$ $\text{Length of arc BD} = \frac{1}{2} \times 22 \times 2$ $\text{Length of arc BD} = 22 \text{ cm}$
The length of the arc BD is $\boxed{\text{22 cm}}$ .

Rounding off 39.986 to the nearest tenths.
Identify the tenths digit and the digit immediately to its right (the hundredths digit).
In 39.986, the tenths digit is 9. The hundredths digit is 8.
Apply the rounding rule.
Since the hundredths digit (8) is 5 or greater, round up the tenths digit.
Rounding 9 up means it becomes 10. This carries over to the units place.
So, 39.9 becomes 40.0.

39.986 rounded to the nearest tenths is $\boxed{\text{40.0}}$ .

3 zimekamilika, zimebaki 2 leo. Unapiga hatua.

The bar graph below shows the marks scored by some pupils in Mock Examinations. Use it to answer the question that follows.

Step-by-step solution

Identify the highest and lowest marks from the bar graph.

Calculate the range using the formula

Calculate the product $ab$ .

Calculate $(ab)^2$ .

Identify the radius of the quarter circle.

Use the formula for the length of a quarter circle arc.

Substitute the values of $r$ and $\pi$ into the formula and calculate.

Identify the tenths digit and the digit immediately to its right (the hundredths digit).

Apply the rounding rule.

Still stuck on this one?

More Mathematics Questions

The bar graph below shows the marks scored by some pupils in Mock Examinations. Use it to answer the question that follows.

Step-by-step solution

Identify the highest and lowest marks from the bar graph.

Calculate the range using the formula

Calculate the product ababab.

Calculate (ab)2(ab)^2(ab)2.

Identify the radius of the quarter circle.

Use the formula for the length of a quarter circle arc.

Substitute the values of rrr and π\piπ into the formula and calculate.

Identify the tenths digit and the digit immediately to its right (the hundredths digit).

Apply the rounding rule.

Still stuck on this one?

More Mathematics Questions

Calculate the product $ab$ .

Calculate $(ab)^2$ .

Substitute the values of $r$ and $\pi$ into the formula and calculate.