Given D(5, 7) and E(3, -3), find the midpoint of DE.

Mathematics

1 answer:

just olya [345]3 years ago

4 0

Answer:

$(4,2 )$

Step-by-step explanation:

Midpoint Formula: $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )$

Simply plug in your 2 coordinates into the midpoint formula to find midpoint:

$(\frac{5+3}{2},\frac{7-3}{2} )$

$(\frac{8}{2},\frac{4}{2} )$

$(4,2 )$

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Step-by-step explanation:

Let X be the height of a woman randomly choosen. We know tha X have a mean of 63.6 inches and a standard deviation of 2.5 inches. For an x value, the related z-score is given by z = (x-63.6)/2.5. We are looking for a value $x_{0}$ such that $P(X < x_{0}) = 0.76$ , but, $0.76 = P(X < x_{0}) = P((X-63.6)/2.5 < (x_{0}-63.6)/2.5) = P(Z < (x_{0}-63.6)/2.5)$ , i.e., $(x_{0}-63.6)/2.5$ is the 76th percentile of the standard normal distribution. So, $(x_{0}-63.6)/2.5 = 0.7063$ , $x_{0} =63.6+(2.5)(0.7063) = 65.3658$ . Therefore, the height of a woman who is at the 76th percentile is 65.3658 inches.