A rectangular painting has an area of (2x^2 + 8x + 6) cm^2 . Its length is (2x + 2) cm. Find the width of the painting.
1 answer:
Answer:
Width = x + 3
Step-by-step explanation:
The formula for the area of a rectangle is: A = LW, where A=area, L = length and W = width. In order to get the expression for the value of the width, you first need to factor each equation given for both the area and the length. Starting with the length (2x + 2), you can factor out the 2 to get: 2(x+1). With the area: 2x² + 8x + 6, you can first factor out the 2 to get: 2(x² + 4x + 3). Next, you can factor the polynomial: 2(x + 3)(x + 1). Lastly, in order to find the width, you divide the area by the length:
Crossing out the common terms from the numerator and denominator, '2' and '(x + 1)', we get a final answer of W = x + 3.
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Answer:
0.1507 or 15.07%.
Step-by-step explanation:
We have been given that the manufacturing of a ball bearing is normally distributed with a mean diameter of 22 millimeters and a standard deviation of .016 millimeters. To be acceptable the diameter needs to be between 21.97 and 22.03 millimeters.
First of all, we will find z-scores for data points using z-score formula.
, where,
z = z-score,
x = Sample score,
= Mean,
= Standard deviation.
Let us find z-score of data point 22.03.
Using probability formula , we will get:
Therefore, the probability that a randomly selected ball bearing will be acceptable is 0.1507 or 15.07%.