Question

using the fundamental counting principle - item 30328
you are making a battery for a science project. you have copper wire for your first electrode. you need to choose a conductor, a second electrode, and a device to plug into your battery.
you have already chosen a lemon conductor. complete each statement below about the options that include a lemon conductor.
the number of battery options with a lemon conductor and a magnesium electrode is
the number of battery options with a lemon conductor and a zinc electrode is
the total number of battery options with a lemon conductor is

Explanation:

Step1: Determine options for each part when conductor is fixed

• When conductor is fixed (lemon), for the first two statements (electrode is fixed as magnesium or zinc), we only consider the number of device options.
• For the third statement (conductor is fixed as lemon), we consider the number of electrode options and device options.
• Number of device options: \(3\) (Light, Buzzer, Clock)
• Number of electrode options: \(2\) (Zinc, Magnesium)

Step2: Calculate the number of battery options for each case

• Case 1: Lemon conductor and Magnesium electrode

Since conductor (lemon) and electrode (magnesium) are fixed, the number of options is equal to the number of device options. So the number of options \(= 3\)

• Case 2: Lemon conductor and Zinc electrode

Since conductor (lemon) and electrode (zinc) are fixed, the number of options is equal to the number of device options. So the number of options \(=3\)

• Case 3: Lemon conductor

Using the fundamental counting principle \(N=\text{Number of electrode options}\times\text{Number of device options}\). So \(N = 2\times3=6\)

Answer:

The number of battery options with a lemon conductor and a magnesium electrode is \(3\).
The number of battery options with a lemon conductor and a zinc electrode is \(3\).
The total number of battery options with a lemon conductor is \(6\).