Answer:
1) The graph represents a proportional relationship as it is a straight line that passes through the origin (0, 0).
2) Constant of proportionality = 2
3) $30
4) 14.7 cups
Step-by-step explanation:
Question 1
A graph that shows a proportional relationship between two variables is a straight line that passes through the origin (0,0).
Therefore, the provided graph does represent a proportional relationship as it is a straight line that passes through the origin (0, 0).
[tex]\hrulefill[/tex]
Question 2
The equation for a graph representing a proportional relationship is y = kx, where k is the constant of proportionality.
To find the constant of proportionally from the provided table of values, we can substitute an (x, y) point into the equation and solve for k.
In the given table, the independent value (x) is the number of toys, and the dependent value (y) is the price. Let's substitute point (4, 8) into the equation:
[tex]\begin{aligned}y&=kx\\\\(4,8) \implies 8&=k \cdot 4\\\\\dfrac{8}{4}&=\dfrac{k \cdot 4}{4}\\\\2&=k\end{aligned}[/tex]
Therefore, the constant of proportionality is 2.
[tex]\hrulefill[/tex]
Question 3
To find the simple interest we can use the simple interest formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Simple Interest Formula}}\\\\I = Prt\\\\\textsf{where:}\\\\ \phantom{ww}\bullet\;\textsf{$I$ is the interest earned.}\\ \phantom{ww}\bullet\;\textsf{$P$ is the principal amount.}\\\phantom{ww}\bullet\;\textsf{$r$ is the interest rate (in decimal form).}\\\phantom{ww}\bullet\;\textsf{$t$ is the time (in years).}\\ \end{array}}[/tex]
In this case:
- P = $1,000
- r = 6% = 0.06
- t = 0.5 (6 months = half a year)
Substitute the values into the formula and solve for I:
[tex]I=\$1000 \cdot 0.06 \cdot 0.5[/tex]
[tex]I=\$60 \cdot 0.5[/tex]
[tex]I=\$30[/tex]
Therefore, the simple interest for $1,000 deposited in a bank for 6 months with an interest rate of 6% per annum is $30.
[tex]\hrulefill[/tex]
Question 4
To convert liters to cups, given that 4.2 cups = 1 liter, we can simply multiply the number of liters (3.5) by the rate (4.2 cups per liter):
[tex]\begin{aligned}\sf 3.5\;L&=\sf 3.5\;L\times 4.2\;cups\;per\;L\\\\&=\sf 3.5\;L\times \dfrac{4.2\;cups}{\sf L}\\\\&=\sf 14.7\;cups\end{aligned}[/tex]
Therefore, 3.5 liters is equivalent to 14.7 cups.
