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1 answer:
the length of a spool of ribbon with a z-score of 0.7 is 92.3 cm
<u>Step-by-step explanation:</u>
Here we have , The lengths of spools of ribbon are normally distributed with a mean of 91.4 centimeters and a standard deviation of 1.3 centimeters. What is the length of a spool of ribbon with a z-score of 0.7 . Let's find out:
According to Question we have following parameters as :
X = the length of a spool of ribbon
Mean(x) = 91.4 cm
standard deviation(y) = 1.3 cm
Z = 0.7
We know that Z score is given by :
⇒
⇒
⇒
⇒
Therefore , the length of a spool of ribbon with a z-score of 0.7 is 92.3 cm
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Answer:
20 units²
Step-by-step explanation:
The x-intercepts are symmetrically located around the x-coordinate of the vertex, so are at
1.5 ± 5/2 = {-1, 4}
Using one of these we can find the unknown parameter "a" in the parabola's equation (in vertex form) ...
0 = a(4 -1.5)² +12.5
0 = 6.25a +12.5 . . . . . simplify
0 = a +2 . . . . . . . . . . . divide by 6.25
-2 = a
Then the standard-form equation of the parabola is ...
y = -2(x -1.5)² +12.5 = -2(x² -3x +2.25) +12.5
y = -2x² +6x +8
This tells us the y-intercept is 8. Then the relevant triangle has a base of 5 units and a height of 8. Its area is given by the formula ...
A = (1/2)bh = (1/2)(5)(8) = 20 . . . . units²
