$\bf \begin{array}{ccll} minutes&\stackrel{juice}{cups}\\ \cline{1-2} 15&3\frac{1}{4}\\\\ x&32\frac{1}{2} \end{array}\implies \cfrac{15}{x}=\cfrac{3\frac{1}{4}}{32\frac{1}{2}}\implies \cfrac{15}{x}=\cfrac{\frac{3\cdot 4+1}{4}}{\frac{32\cdot 2+1}{2}}\implies \cfrac{15}{x}=\cfrac{\frac{13}{4}}{\frac{65}{2}}$

$\bf \cfrac{15}{x}=\cfrac{~~\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{\underset{2}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot \cfrac{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{\underset{5}{~~\begin{matrix} 65 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{15}{x}=\cfrac{1}{10}\implies 150=x\leftarrow \begin{array}{llll} \textit{150 minutes or}\\\\ \textit{2 hours and a half} \end{array}$

4 0

3 years ago

At 3:20 the hands of a clock form an acute angle that measures exactly how many degrees

Goryan [66]

Answer:

The answer is 30°.

Step-by-step explanation:

The hand of a clock rotates a full 360°, let's say 12 o'clock is 0°/360°. The hour hand for this example is at 3, it moved 90° and the minute hand marks 20 minutes meaning it's positioned on the 2. From 12 to 2 the minute hand has moved 60°. 90-60= 30. Therefore 3:20 forms a 30° angle.

7 0

3 years ago