Answer:

Step-by-step explanation:
For this case we have a sample size of n = 250 units and in this sample they found that 24 units failed one or more of the tests.
We are interested in the proportion of units that fail to meet the company's specifications, and we can estimate this with:

The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The confidence interval for a proportion is given by this formula
For the 98% confidence interval the value of
and
, with that value we can find the quantile required for the interval in the normal standard distribution.
And the margin of error would be:

<span>After the two cuts, 1 3/4 ft of the board is left.</span><span> </span>
Probability of getting a red marble: 3/10
probability of getting a blue marble (after removing a red marble): 2/9
multiply the two fractions together:
6/90
simplify (divide by 6): 1/15 or .06666 repeating
The lengths of the three line segments after dilation is
,
and 
Explanation:
Given that the length of three line segments are PQ = 2 cm, AB = 1.5 cm and MN = 3 cm
Also, given that the dilation with a scale factor of 2 is applied to the three line segments.
We need to determine the length of line segments P'Q', A'B' and M'N'
Dilation means the transformation of the same shape with different size.
Since, it is given that the dilation with a scale factor of 2, we shall multiply each of the line segments with 2.
Thus, we have,



Thus, the lengths of the three line segments after dilation is
,
and 
Answer:
(4b-9) (4b+9)
Step-by-step explanation:
16b^2 – 81
This is the difference of squares
(a^2 -c^2) = (a-c) (a+c)
a^2 = 16b^2 so a= 4b
c^2 = 81 so c = 9
(16b^2 – 81) = (4b-9) (4b+9)