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patriot [66]
3 years ago
12

In the top row of an chessboard, Tom writes the values 1, 2, 4, 8, 16, 32, 64, 128. In the leftmost column, Tom writes the value

s 1, 3, 9, 27, 81, 243, 729, 2187. In every other square that doesn't have a number yet, Tom writes the product of the leftmost number in that square's row and the topmost number in that square's column. What is the sum of all the numbers on the chessboard?
Mathematics
1 answer:
solmaris [256]3 years ago
7 0
sum\ of\ the\ values\ in\ the\ top\ row:\\\\S=1+2+4+8+16+32+64+128= \frac{1-2^8}{1-2} =2^8-1=255\\\\ the\ sum\ of\ all\ the\ numbers\ on\ the\ chessboard:\\\\S\cdot1+S\cdot3+S\cdot9+S\cdot27+S\cdot81+S\cdot243+S\cdot729+S\cdot2187=\\\\=S\cdot(1+3+9+27+81+243+729+2187)=255\cdot \frac{1-3^8}{1-3} =\\\\=255\cdot \frac{-6560}{-2} =255\cdot3280=836,400\\\\Ans.\ the\ sum\ of\ all\ the\ numbers\ on\ the\ chessboard\ is\ 836,400
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Answer:

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Step-by-step explanation:

Let's recall that the Domain of a relationship is the set of values in the starting set for which there is a correspondent value in the final set.

In this case, we have a set of numbers on the x axis, which are connected with values in the y axis as indicated by the plotting of the points on the (x,y) plane.

The Domain will consist of all those x-values for which we see in the given plot connected to a corresponding y-value.

So, we see that:

the x-value -3 is connected to the y-value -4

the x-value -2 is connected to the y-value -3

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and the x-value 2 is connected to two y-values:  4 and 5

Therefore all those x-values are part of the Domain of this relationship. That is, the set: {-3, -2, -1, 0, 1, 2}

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Answer:

<u>The two statements that apply are A and B.</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

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Gray envelopes Hadley has = 1/3 of a box

When full, each box of envelopes has the same number of envelopes

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B. Hadley's answer is incorrect, because 3/6 plus 1/3 equals 5/6.   This is correct.

C. Hadley's answer is incorrect, because 3/6 plus 1/3 equals 2/6.  This is wrong

D. Hadley's answer is correct, because 3 and 1 is 4, and 6 and 3 is 9. This is wrong.

<u>The two statements that apply are A and B.</u>

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