A panel of four light switches can be set in 2^4 ways. A panel of lfive light switches can be set in twice this many ways. In how many ways can five light switches be set? I got 2^4=16 16x2=32 Is this right. If not can someone help?
Its wrong, you add exponets so it would be 4 times 2 to the power of 4,which means it would be 8 to the power of 5 then simplify unless its monomial
To calculate the number of ways to set five light switches, let's break down the problem step-by-step:
Step 1: Determine the number of ways to set four light switches.
Given that a panel of four light switches can be set in 2^4 ways, we have 2^4 = 16 possible combinations.
Step 2: Determine the number of ways to set five light switches.
It is stated that a panel of five light switches can be set in twice the number of ways as four light switches.
So, the number of ways to set five light switches would be 2 times the number of ways to set four light switches.
2 * 16 = 32.
Therefore, the correct answer is 32. You solved it correctly!
To solve this problem, let's go step by step:
First, we calculate the number of ways the panel of four light switches can be set. Since each switch can be either on or off, there are 2 choices for each switch. So the total number of ways to set the switches would be 2^4.
Next, we are told that a panel of five light switches can be set in twice as many ways as the panel of four. So to find the number of ways the five switches can be set, we need to double the number of ways for the four switches.
Therefore, the number of ways to set the five light switches would be 2^4 * 2, which equals 32.
So your calculation is correct! There are indeed 32 ways to set the five light switches.
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Right! 32 = 2^5