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gtnhenbr [62]
3 years ago
11

The complex number _______ lies in the shaded area of the graph. The complex number _______ does not lie in the shaded area.

Mathematics
1 answer:
Anastaziya [24]3 years ago
5 0
Think of imaginary numbers on a complex plane as coordinates - take the real part, that's the x coordinate, the imaginary part that's the y coordinate.

Therefore, for the first blank, -1+3i lies in the shaded area, because its coordinates are (-1,3).
And following on from that for the second one, -4i does not lie in the shaded area, since its coordinates are (0,-4).

Tl;dr is taking a complex number a+bi and placing it on a complex plane, it will have coordinates (a,b)
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Snezhnost [94]

Answer:

The correct answer is C

Step-by-step explanation:

8 0
3 years ago
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A bottled water distributor wants to determine whether the mean amount of water contained in 1-gallon bottles purchased from a n
mash [69]

Answer:

We fail to reject H0; Hence, we conclude that there is no significant evidence that the mean amount of water per gallon is different from 1.0 gallon

Pvalue = - 2

(0.98626 ; 1.00174)

Since, 1.0 exist within the confidence interval, then we can conclude that mean amount of water per gallon is 1.0 gallon.

Step-by-step explanation:

H0 : μ= 1

H1 : μ < 1

The test statistic :

(xbar - μ) / (s / sqrt(n))

(0.994 - 1) / (0.03/sqrt(100))

-0.006 / 0.003

= - 2

The Pvalue :

Pvalue form Test statistic :

P(Z < - 2) = 0.02275

At α = 0.01

Pvalue > 0.01 ; Hence, we fail to reject H0.

The confidence interval :

Xbar ± Margin of error

Margin of Error = Zcritical * s/sqrt(n)

Zcritical at 99% confidence level = 2.58

Margin of Error = 2.58 * 0.03/sqrt(100) = 0.00774

Confidence interval :

0.994 ± 0.00774

Lower boundary = (0.994 - 0.00774) = 0.98626

Upper boundary = (0.994 + 0.00774) = 1.00174

(0.98626 ; 1.00174)

7 0
3 years ago
Insurance companies A and B each earn an annual profit that is normally distributed with the same positive mean. The standard de
krok68 [10]

Answer:

C. 0.98

Step-by-step explanation:

Let x be the mean of Company A and B annual profit and x/2 and y are standard deviation of Company A and B annual profit.

P(B<0) = 0.9*P(A<0)

P(Z<(0-x)/y) = 0.9*P(Z<(0-x)/(x/2))

P(Z<-x/y) = 0.9*P(Z<-2)

P(Z<-x/y) = 0.0205

x/y =2.04

Or y/x = 1 /2.05

y/x =0.49

Ratio of the standard deviation of company B annual profit to the standard deviation of company A annual profit =y/(x/2)

= 2*(y/x)

= 2*0.49

= 0.98

7 0
2 years ago
What is the inverse of the given relation y = 7x² ?
beks73 [17]

Answer:

y = square root(x/7)

Step-by-step explanation:

switch x and y

x = 7y^2

solve for y

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7 0
2 years ago
Find the equation of a sphere if one of its diameters has endpoints: (-9, -12, -6) and (11, 8, 14).
baherus [9]

Answer:

Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is (x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30.

Step-by-step explanation:

There are two kew parameters for a sphere: Center (h, k, s) and Radius (r). The radius is the midpoint of the line segment between endpoints. That is:

C(x,y,z) = \left(\frac{-9+11}{2},\frac{-12+8}{2},\frac{-6+14}{2}   \right)

C(x,y,z) = (1,-2,4)

The radius can be found by halving the length of diameter, which can be determined by knowning location of endpoints and using Pythagorean Theorem:

r = \frac{1}{2}\cdot \sqrt{(-9-11)^{2}+(-12-8)^{2}+(-6-14)^{2}}

r = 10\sqrt{3}

The general formula of a sphere centered at (h, k, s) and with a radius r is:

(x-h)^{2}+(y-k)^{2}+(z-s)^{2} = r^{2}

Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is (x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30.

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3 years ago
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