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3 years ago

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:

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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

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Zcritical at 99% confidence level = 2.58

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

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0.994 ± 0.00774

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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

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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

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y inverse is

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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

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

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