(a) Simplify $\[\dfrac{\dbinom{n}{k}}{\dbinom{n} {k - 1}}.\]$
(b) For some positive integer $n,$ the expansion of $(1 + x)^n$ has three consecutive coefficients $a,$ $b,$ $c$ that satisfy $a:b:c = 1:7:35.$ What must $n$ be?

Answer: d. 39 cmin the diagram, the approximate length of the minor arc de is 39 centimetres.step-by-step explanation: the formula for the length of an arc in a circle is as displayed below.let the length of the minor arc de = xx = 2( pi )r × angle of sector / 360°from this, we will substitute the values given from the problem into the formula to obtain the length of the minor arc de.x = 2( pi )r × angle of sector / 360°r = radius = 25cmpi as an approximate value = 3.14angle of sector = 120°x = 2( 3.14 )( 25 ) × 120° / 360°x = 157 × 1 / 4x = 39.25x = 39 ( rounded to the nearest whole number as an approximate value )

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