Answer:
= 16+49 = 65
Step-by-step explanation:
The error is at the end of the first line. (-7i)(7i) = -49i² ≠ +49i².
The correct work is ...
(4-7i)(4+7i)=16+28i-28i-49i^2
= 16+49
= 65
Answer:
a) BOC and AOD
b) BOA and AOE
c) BOE and EOD
d) BOA and AOD
e) AOE and EOD
Step-by-step explanation:
An obtuse angle is an angle that has more than 90° and vertically opposite angles are angle formed by two lines crossed. So, Obtuse vertically opposite angles are BOC and AOD
Adjacent angles are angles in which one angle is beside the other and complementary angles are angles whose sum is equal to 90°, so, a pair of adjacent complementary angles are BOA and AOE.
Supplementary angles are angles whose sum is equal to 180°, so BOE and EOD are equal suplementary angles and BOA and AOD are unequal supplementary angles
Finally, AOE and EOD are adjacent angles that don’t form a linear pair.
Annual Social Security benefit = 0.42 x $37,991 = $15,956.22
Annual bills = $1,755 x 12 = $21,060
Outstanding annual bill to be settled after using the Social Security benefit = $21,060 - $15,956.22 = $5,103.78
Monthly supplementary money needed = $5,103.78/12 = $425.32
Answer:
5/3
Step-by-step explanation:
using the "rise over run" method you can find out that the slope is 5/3.
Answer:
n=601
Step-by-step explanation:
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
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 population proportion have the following distribution
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by and . And the critical value would be given by:
The confidence interval for the mean is given by the following formula:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
Since we don't have a prior estimation for the proportion we can use 0.5 as estimation. And replacing into equation (b) the values from part a we got:
And rounded up we have that n=601