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#30880

statistics

data analysis

inequalities

hard

90 sec

A company conducted a market research study on 750 potential customers. The first 400 customers surveyed indicated their interest in a new product, with 75 choosing "very interested." Among the remaining 350 customers, $k$ chose "very interested." If the proportion of all customers who chose "very interested" was greater than $\frac{1}{6}$ , which of the following inequalities best describes the possible values of $k$ ?

A.

$k + 75 ＞ \frac{1}{6} (750)$ , where $k \leq 350$

B.

$k + 75 ＞ \frac{1}{6} (750)$ , where $0 \leq k \leq 350$

C.

$k ＞ \frac{1}{6} (750 - 75)$ , where $0 \leq k \leq 350$

D.

$k ＞ \frac{1}{6} (750)$ , where $k \leq 350$