Answer:
Step-by-step explanation:
If in doubt, multiply them out.
(-i)^4 = i^4 = 1 . . . . . results for ±i
(-1)^4 = 1^4 = 1 . . . . . results for ±1
An even power of a negative number is equivalent to the same power of the opposite (positive) number. The even number of minus signs cancel in the final product.
_____
In trig form, unity is 1∠(n·360°) . . . . . for n = any integer
Then the 4th root is ...
1^(1/4) ∠(n·360°/4) = 1 ∠(n·90°) . . . . for n = 0...3 (angles repeat after that)
That is, the roots are ...
- 1∠0° = 1
- 1∠90° = i
- 1∠180° = -1
- 1∠270° = -i
Of these, all but the first are listed among your answer choices. The appropriate selection is <em>all of the above</em>. (recognizing that not all of the appropriate choices are "above" that answer selection).
Answer:
The sum of the first two terms of a geometric series is 90. The third term is 24. A. Show That there are two possible series and find the term and the common ration in each case
Step-by-step explanation:
The sum of the first two terms of a geometric series is 90. The third term is 24. A. Show That there are two possible series and find the term and the common ration in each case
Answer:
homeostasis
Step-by-step explanation:
Homeostasis refers to the body's ability to maintain a stable internal environment (regulating hormones, body temp., water balance, etc.).
Answer:
![DE=18.38](https://tex.z-dn.net/?f=DE%3D18.38)
Step-by-step explanation:
It is given that the length of triangle base is 26 that is BC=26.
A line, which is parallel to the base divides the triangle into two equal area parts.
Therefore, from the given information,
.
Now, since it is given that A line, which is parallel to the base divides the triangle into two equal area parts, thus
![\frac{ar ADE}{arABC}=\frac{1}{2}=\frac{(DE)^{2}}{(BC)^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7Bar%20ADE%7D%7BarABC%7D%3D%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B%28DE%29%5E%7B2%7D%7D%7B%28BC%29%5E%7B2%7D%7D)
⇒![\frac{(DE)^{2}}{(BC)^{2}}=\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%28DE%29%5E%7B2%7D%7D%7B%28BC%29%5E%7B2%7D%7D%3D%5Cfrac%7B1%7D%7B2%7D)
⇒![\frac{(DE)^{2}}{(26)^{2}}=\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%28DE%29%5E%7B2%7D%7D%7B%2826%29%5E%7B2%7D%7D%3D%5Cfrac%7B1%7D%7B2%7D)
⇒![(DE)^{2}=13{\times}26=338](https://tex.z-dn.net/?f=%28DE%29%5E%7B2%7D%3D13%7B%5Ctimes%7D26%3D338)
⇒![DE=18.38](https://tex.z-dn.net/?f=DE%3D18.38)
Answer:
The sampling distribution of the sample average score for this random sample of 64 students is approximately normal, with mean 19.6 and standard deviation 0.625.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 19.6 and a standard deviation of 5.0.
This means that ![\mu = 19.6, \sigma = 5](https://tex.z-dn.net/?f=%5Cmu%20%3D%2019.6%2C%20%5Csigma%20%3D%205)
What is the sampling distribution of the sample average score for this random sample of 64 students?
By the Central Limit Thoerem, the sampling distribution of the sample average score for this random sample of 64 students is approximately normal, with mean 19.6 and standard deviation ![s = \frac{5}{\sqrt{64}} = \frac{5}{8} = 0.625](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7B5%7D%7B%5Csqrt%7B64%7D%7D%20%3D%20%5Cfrac%7B5%7D%7B8%7D%20%3D%200.625)