Explanation: I got this answer from multiplying each equation and listing them above. Then I sorted them least to greatest by the smallest number, to the biggest number.
I'll start by expanding everything, and 10^(x) means we move the decimal x places to the right. If we move the decimal to the right but there's no number there, that number is 0. The populations are as follows (in the order in the graph) - 127,180,000 200,000,000 80,619,000 63,708,000 173,615,000 152,510,000
The first difference is the number of digits. The more, the better. The two that stand out at the bottom are Germany and the UK. Next, we look at the leftmost number. Since 6<8, Germany's population > UK's population. All other countries are greater than Germany. Next, we look at the next smallest amount of digits, which is every other country. We look at the first number, which gives us Japan, Nigeria and Bangladesh. Next, we look at the second number, and since 2<5<7, Japan is smaller than Bangladesh and Nigeria is bigger than Bangladesh. Our current list is as follows: United Kingdom (UK), Germany, Japan, Bangladesh, Nigeria. Since Brazil has been proven to be greater than the rest (as it has more digits and 2>1), our list is now United Kingdom (UK), Germany, Japan, Bangladesh, Nigeria, Brazil
We can divide the amount of favourable cases by the total amount of cases.
The total amount of cases is the total amount of ways to put 8 rooks on a chessboard. Since a chessboard has 64 squares, this number is the combinatorialnumber of 64 with 8,
For a favourable case, you need one rook on each column, and for each column the correspondent rook should be in a diferent row than the rest of the rooks. A favourable case can be represented by a bijectivefunction with A = {1,2,3,4,5,6,7,8}. f(i) = j represents that the rook located in the column i is located in the row j.
Thus, the total of favourable cases is equal to the total amount of bijective functions between a set of 8 elements. This amount is 8!, because we have 8 possibilities for the first column, 7 for the second one, 6 on the third one, and so on.
We can conclude that the probability for 8 rooks not being able to capture themselves is
Answer:using the graph of a function you can find the value of f (x), all you need to do is locate on the x axis, the value, in this case 3, and we will find f (3), locate the number (3 ) on the x-axis and see what is the value of y that the function takes at that point, that will be the value f (3)
Step-by-step explanation:it’s a
b. The function f(x)=g(x)/h(x) will have a horizontal asymptote only if the degree of g is less than or equal to the degree of h.