3 of 8 The area of a circle is 16.71cm2. Find the length of the radius rounded to 2 DP.
1 answer:
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Answer:
x = x = 9 ± or x ≈ 12.61 or x ≈ 5.39
Step-by-step explanation:
x² - 18x + 68 Solve by completing the square.
x² - 18x = - 68
Now complete the square and add that number to both sides of the equation.
1/2 (of the coefficient of the x term)² = (1/2 · -18)² = 81 .
x² - 18x + 81 = -68 + 81
(x - 9) (x - 9) = 13 Now find the square root of both sides
=
Solve
x - 9 = ± Solve for x
x = 9 ±
x = 9 + or x = 9 -
x ≈ 12.61 or x ≈ x 5.39
In order to factor, we must pull out factors common to each term. In this case, each term has factors of 2 and y:
4ay = 2 * 2 * a * y
2y = 2 * y
So, we'll pull out the 2y:
To check, distribute the 2y back through the terms in parentheses to ensure you end up with the original expression 4ay - 2y.
4ay = 2 * 2 * a * y
2y = 2 * y
So, we'll pull out the 2y:
To check, distribute the 2y back through the terms in parentheses to ensure you end up with the original expression 4ay - 2y.
Answer:
0.9699 = 96.99% probability of a bulb lasting for at most 637 hours.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Find the probability of a bulb lasting for at most 637 hours.
This is the pvalue of Z when X = 637. So
has a pvalue of 0.9699
0.9699 = 96.99% probability of a bulb lasting for at most 637 hours.