Kim ran total 7.1 miles.
Further explanation:
Front end estimation is the specific technique for rounding off numbers to estimates sums and differences. The numbers to be added or subtracted are rounded off to nearest one, tenth and hundredth.
So in the given scenario, we will round off to the nearest tenth.
So,
2.76 miles will be rounded off to 2.8 as the number right to the digit 7 is greater than 5, 7 will be rounded off to the next digit.
2.34 miles will be rounded off to 2.3 as the number right to 5 is less than 5, so 3 will be as it is.
1.97 miles will be rounded off to 2.0 as the number right to 9 is greater than 5 so it will be rounded off to the next number.
So, after estimation
Keywords: Front-end estimation, decimals
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The bill after applying the coupon = 31.84*(85%) = 27.064
so each of them will pay : 27.064/3 = $9.021
F(x)= 2/(x+1) and g(x)= -x2-12 => f(-7)= ? , g(2.5)= ?, g(f(- 0.5))= ?
In the expression of the function f(x) we will replace instead of x the number in bracket (-7) => f(-7) = 2/(-7+1)= 2/-6 = - 1/3
In the expression of the function g(x) we will replace instead of x number in bracket (2.5) => g(2.5) = - (2.5)squared -12= - 6.25 -12= - 18.25
Expression f(g(x)) or g(f(x)) is multiplication (composition) of the reflecting of functions f and g. We will do this in the following way => g(f(x))= g(2/(x+1))= -(2/(x+1))2 - 12= -(4/(x+1)2) -12= -4-12(x+1)2/(x+1)2=> we will replace instead of x the number in bracket (-0.5) or (-1/2) => g(f(-1/2) = -4-12((-1/2)+1)2/ ((-1/2+ 1)2= -4-12(1/2)2/(1/2)2=-4-12*(1/4)/(1/4)= (-4-3)/(1/4)=-28
Eaisier way => f(-1/2)=2/((-1/2)+1)=2/(1/2)= 4 g(4) -(4)2-12 = -16-12= -28
