Explain the meaning of the following percentiles in parts (a) and (b). (a) the 5th percentile of the weight of males 36 months of age in a certain city is 11.0 kg. (b) the 90th percentile of the length of newborn females in a certain city is 53.3 cm. (a) choose the correct answer below. a. 5% of 36-month-old males weigh 11.0 kg or less, and 95% of 36-month-old males weigh more than 11.0 kg. b. 5% of males weigh 11.0 kg or more, and 95% of 36-month-old males weigh less than 11.0 kg. c. 5% of males weigh 11.0 kg or less, and 95% of 36-month-old males weigh more than 11.0 kg. d. 5% of 36-month-old males weigh 11.0 kg or more, and 95% of 36-month-old males weigh less than 11.0 kg.

5% of 36-month-old males weigh 11.0 kg or less and 95% of 36-month-old males weigh more than 11.0 kg

Step-by-step explanation:

A value V is in the Pth percentile if P% of the measures are SMALLER or EQUAL then P. So

(a) The 5th percentile of the weight of males 36 months of age in a certain city is 11.0 kg.

The correct answer is

5% of 36-month-old males weigh 11.0 kg or less and 95% of 36-month-old males weigh more than 11.0 kg

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.