Question

9 at a hardware store, 20 kilograms of sand costs \\$4.50 and 40 kilograms of the same sand costs \\$9.00.
which graph could show the relationship between the amount of sand and its cost?

10 james spins the arrow on the wheel to win a prize.
the arrow has an equal chance of landing on each section.
what is the probability that the arrow will land on the laptop?
0.125
0.200
0.375
0.380
0.600

Explanation:

Calculate the unit rate of sand

Using the Unit Rate Problems and Proportional Reasoning knowledge points

$$ \text{Unit Rate} = \frac{\$4.50}{20\text{ kg}} = \$0.225\text{ per kg} $$

$$ \text{Cost for 40 kg} = 40\text{ kg} \times \$0.225\text{/kg} = \$9.00 $$

Identify the correct graph for Question 9

Using the Proportional Reasoning knowledge point

$$
LATEXBLOCK0
$$

Looking at the three graphs:

• Graph 1: At \(x = 20\), \(y \approx 3\). At \(x = 40\), \(y \approx 6\). (Incorrect)
• Graph 2: At \(x = 20\), \(y = 4.5\). At \(x = 40\), \(y = 9\). (Correct)
• Graph 3: At \(x = 20\), \(y \approx 5.5\). At \(x = 40\), \(y \approx 11\) (off-chart). (Incorrect)

Count the total and favorable outcomes for Question 10

The wheel is divided into equal-sized sectors.
Let's count the total number of sectors:
There are 8 equal sectors in total.
Let's count the sectors containing the laptop icon:
There are 3 sectors with the laptop icon.

Calculate the probability of landing on a laptop

The probability \(P\) of landing on a laptop is the ratio of favorable outcomes to total outcomes:

$$ P(\text{laptop}) = \frac{3}{8} $$

Convert the fraction to a decimal:

$$ P(\text{laptop}) = 0.375 $$

Answer:

Question 9

• (A) First graph (passes through (20, 3) and (40, 6))
• (B) Second graph (passes through (20, 4.5) and (40, 9)) (Correct answer)
• (C) Third graph (passes through (20, 5.5))

Question 10

• (A) 0.125
• (B) 0.200
• (C) 0.375 (Correct answer)
• (D) 0.380
• (E) 0.600