Question

the average reading score of 17 - year - olds on certain tests is given by ( y = 0.192x+244.26 ) points, where ( x ) is the number of years after 1950. assuming that this model was valid, write and solve an inequality that describes when the average 17 - year - olds reading score on this test was between but not including 247 and 250.
which of the following inequalities describes the situation correctly?
a. ( 247>0.192x + 244.26>250 )
b. ( 247leq0.192x + 244.26leq250 )
c. ( 247leq0.192x + 244.26leq250 )
d. ( 247<0.192x + 244.26<250 )
between the years (square) and (square), the average 17 - year - olds reading score was between but did not include 247 and 250.

Explanation:

Step1: Define the score variable

Let $y = 0.192x + 244.26$, where $y$ is the reading score.

Step2: Translate "between but not including"

The score $y$ is greater than 247 and less than 250, so substitute $y$:
$247 < 0.192x + 244.26 < 250$

Answer:

D. $247 < 0.192x + 244.26 < 250$

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To find the years, solve the inequality:

Step1: Subtract 244.26 from all parts

$247 - 244.26 < 0.192x < 250 - 244.26$
$2.74 < 0.192x < 5.74$

Step2: Divide by 0.192

$\frac{2.74}{0.192} < x < \frac{5.74}{0.192}$
$14.27 < x < 29.89$

Step3: Convert to calendar years

$x$ is years after 1950, so $1950+14=1964$, $1950+30=1980$.
Between the years $\boldsymbol{1964}$ and $\boldsymbol{1980}$, the average 17-year-old's reading score was between but did not include 247 and 250.