Answer:
C) √5(cos(117°) +i·sin(117°))
Step-by-step explanation:
The rectangular number a+bi can be written in polar form as ...
√(a^2+b^2)×(cos(arctan(b/a)) + i·sin(arctan(b/a)))
Here, we have a=-1, b=2, so the magnitude is ...
√((-1)^2 +2^2) = √(1+4) = √5
and the angle is ...
arctan(2/(-1)) = arctan(-2) ≈ 116.565° . . . . . a 2nd-quadrant angle
Then you have ...
-1 +2i = √5(cos(117°) +i·sin(117°)) . . . . . . customary "polar form"
_____
Comment on the answer
The "polar form" is generally written as ...
(magnitude)·(cos(angle) +i·sin(angle))
You may also see it as ...
(magnitude) cis (angle) . . . . . . . where "cis" is shorthand for "cos + i·sin"
In my engineering courses, we often used the form ...
(magnitude) ∠ (angle)
The form used by my calculator is ...
(magnitude)·e^(i·angle) . . . . . where angle is usually in radians
Answer:
mean = 250.2
mean = 249.4
Step-by-step explanation:
given data
experiment = 15 times
solution
we get here mean that is express as
mean = 
............1
so mean for cart 1 is
mean = 
mean = 250.2
and
mean for cart 2
mean = 
mean = 249.4
Answer:
Mean 160
Standard deviation 2.63
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean 
and standard deviation 
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean and standard deviation 
In this problem, we have that:
Find the mean and standard deviation of the sampling distribution of sample means with sample size n = 58.
Mean 160
Standard deviation 
We need 30 glass spheres whose TOTAL volume = 3,392.92 cubic inches.
Therefore each of the 30 spheres must have a volume of 3,392.92 / 30 =
<span>
<span>
<span>
113.0973333333
</span>
</span>
</span>
cubic inches
Sphere Volume = <span> 4/3 • <span>π <span>• r³
radius^3 = </span></span></span>Sphere Volume / <span>(4/3 • <span>π)
</span></span>radius^3 = 113.0973333333 /
<span>
<span>
<span>
4.1887902048
</span>
</span>
</span>
radius^3 =
<span>
<span>
<span>
26.9999994758
</span>
</span>
</span>
radius = 3 inches
diameter = 6 inches
Total amount payable= 1000+450*36
Total amount payable=1000+16200
Total amount payable=<span>$17200</span>
