Evaluate the expression using De Moivre’s Theorem: √2+3i

Give your answer in a+bi form.

Answer: 5.08333 repeating three

The value of x and y after solving the equation -5x - 10y = 30 and - 3x + 3y = 27 by elimination method is -6 and 3 respectively.

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Given:

-5x - 10y = 30 and - 3x + 3y = 27

Solve by using the elimination method,

Divide the equation - 3x + 3y = 27 by 3 and equation -5x - 10y = 30 by 5 on both sides,

(- 3x + 3y) / 3 = 27 / 3  and (-5x - 10y) / 5 = 30 / 5

-x + y = 9  and -x - 2y = 6

Subtract equation

-x + y = 9 - (-x - 2y = 6)

-x + y - 9 = x - 2y - 6

y = 3

and - x + 3 = 9, x = -6

Therefore, the value of x and y after solving the equation -5x - 10y = 30 and - 3x + 3y = 27 by elimination method is -6 and 3 respectively.

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Answer:

4

Step-by-step explanation:

Solve for x over the real numbers:

x^3 = 64

Take cube roots of both sides:

Answer: x = 4

4^2 = 16

4^3 = 64

Answer:

  3x +3

Step-by-step explanation:

You want to simplify 2x+ (9+x) -6.

Like terms have the same constellation of variables. Here, there are terms containing x, and terms not containing x.

  2x+ (9+x) -6 = (2 +1)x +(9 -6) = 3x +3

The simplified expression is 3x +3.

Answer:3x+3

Step-by-step explanation:

First we remove the parenthesis because they are not needed in an addition problem to make it 2x+9+x-6

Then we sort and combine like terms, [2x+x]+[9-6]

After that, you add the coefficients of the the first term, which makes 3x and subtract 6 from 9 to get 3

This then leads you to 3x+3

The Cost make up of procedure 1 is $280000.

Cost make up of procedure 2 is 140000

The cost makeup will be calculated thus:

Cost make up of procedure 1

Labour (40%) 112000

Materials (45%) 126000

Overhead (15%) 42000

Total =[280000

Cost make up of procedure 2

Labour ( 60%) 84000

Materials (30%) 42000

Over head (10%) 14000

Total 140000

Working note:

Sales $600000

Less: Gross profit (sale *30%) $ 180000

COGS $420000

Procedure 1 ( COGS *2/3) $ 280000

Procedure 2 (COGS * 1/3) $ 140000

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Complete question

Blue Skies Inc. is a retail gardening company that is piloting a new strategic initiative aimed at increasing gross profit. Currently, the company’s gross profit is 25% of sales, and its target gross profit percentage is 30%. The company’s current monthly sales revenue is $600,000. The new initiative being piloted is to produce goods in-house instead of buying them from wholesale suppliers. Its in-house production process has two procedures. The makeup of the costs of production for Procedure 1 is 40% direct labor, 45% direct materials, and 15% overhead. The makeup of the costs of production for Procedure 2 is 60% direct labor, 30% direct materials, and 10% overhead. Assume that Procedure 1 costs twice as much as Procedure 2.

Determine what the cost of labor, materials, and overhead for both Procedures 1 and 2 would need to be for the company to meet its target gross profit.

Answer:

x = 1, y = -5.

Step-by-step explanation:

X-3y = 16         Equation (1)

4x- y = 9          Equation (2)

We can solve this by the Method of Elimination.

One way is to multiply the second equation by -3, as follows:

-3(4x - y = 9)

= -12x + 3y = -27     Call this equation (3)

Now if we add equation (3) to equation (1) we eliminate the y terms:

    x - 3y  =  16  

-12x + 3y = -27       Adding:

-11x  + 0    = -11

-11x = -11

x = -11/-11 = 1

Finally, we find the value of y by substituting x = 1 into equation (2):

4(1) - y = 9

-y = 9 - 4

-y = 5

y = -5.

So, the answer is x = 1, y = -5.

or we can write it as an ordered pair (1, -5).

Hope this helps.

Answer:

x=1 and

y= -5

there are about millions of multinational and national companies which are working for the better Gross National Product(GNP).

The United States is super power and has multiple resources to maintain itself  and the over all economic system. As, there are about millions of multinational and national companies which are working for the better Gross National Product(GNP). As, there is agriculture, car manufacturer, and the military industry for improving and adding the value to the over all GNP of the United States.

The Oil and gas sector is the one major factor for the development of the United State's GNP(Gross National Product). As, the exports of the region is well known to be very high and generates more revenue for the over all system as well.    

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Answer:

$800

Step-by-step explanation:

Let's say that Shola's salary is x dollars. This means that Akin's salary is 0.8x dollars, because his salary is 20% less than Shola's salary.

Since Shola spent 45% of his salary on accommodation, he had 0.55x dollars left, or $550. This means that we can write the equation 0.55x = 550.

To solve for x, we can divide both sides of the equation by 0.55 to get x = 1000. This means that Shola's salary is $1000, and since Akin's salary is 20% less than Shola's, his salary is 0.8 * 1000 = $800. Therefore, Akin's salary is $800.

Kanoi and Ale'a can weed the same garden together in 22.22 minutes

Rate of work refers to amount to of work completed at a given time

Information from the question include

Kanoi can weed a garden in 40 minutes

Kanoi's rate = 1/40 per minute

Ale'a can weed the same garden in 50 minutes

Ale'a rate = 1/50 per minute

When both are working together the rate will be

1/40 per minute + 1/50 per minute

= 9/200 per minute

The time is solved

1 / 9/200

= 200/9

= 22.2222 minutes

= 22.22 minutes to the nearest hundredth

The time it will take both of them to weed is 22.22 minute

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Answer:

20

Step-by-step explanation:

20.

[tex]\frac{8}{\frac{2}{5} }[/tex]

Check the attached image below.

[tex]\frac{8}{1}* \frac{5}{2}[/tex]

[tex]\frac{8}{1}*\frac{5}{2}=\\\\ \frac{8*5}{1*2} =\\\\ \frac{40}{2}=\\ \\20[/tex]

[tex]\frac{8}{\frac{2}{5} }=20[/tex].

Answer:

Therefore, the correct solution graph for the inequality is a line with no solution. This means that there is no value of x that satisfies both inequalities at the same time.

Step-by-step explanation:

To solve this inequality, we need to consider the two separate cases of 7x+2≥30 and 2x-3≤-11 separately.For the first case, 7x+2≥30, we can rewrite the inequality as 7x≥28, which simplifies to x≥4. This means that the solution for this inequality is x≥4.For the second case, 2x-3≤-11, we can rewrite the inequality as 2x≤-8, which simplifies to x≤-4. This means that the solution for this inequality is x≤-4.To find the combined solution for both inequalities, we need to take the intersection of these two solutions. The intersection of x≥4 and x≤-4 is the empty set, which means that there is no solution that satisfies both inequalities

If m∠ 1=(3 x) degrees and m ∠2=(x+48) degrees

The equation to solve the value of x is

3x = x+48

The value of x = 33

The angle 1 = 99 degrees

The angle 2 = 81 degrees

The measure of angle 1 = 3x degrees

The measure of angle 2 = x + 48 degrees

The sum of the angles on a straight line is add up to 180 degrees. Therefore angle 1 and angle 2 are supplementary angles.

∠1 + ∠2 = 180 degrees

Substitute the values in the equation

3x + x + 48 = 180

4x + 48 = 180

4x = 180 - 48

4x = 132

x = 132/4

x = 33

Part b

Then the measure of angle 1 = 3x

= 3 × 33

= 99 degrees

The measure of angle 2 = x + 48

= 33 + 48

= 81 degrees

Therefore, the equation to solve x is 3x = x + 48 and the measure of angles 1 and 2 is 99 degrees and 81 degrees respectively

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Applying a coat of paint 0.07 cm thick to a hemispherical dome with a diameter of 40 meters will require an estimated 1759291.886 cubic centimeters of paint, using a linear approximation.

Given that,

We have to find applying a coat of paint 0.07cm thick to a hemispherical dome with a diameter of 40 meters will require an estimated volume of paint in cubic centimeters, which may be calculated using a linear approximation.

We know that,

Volume of a sphere = 4/3 πr³

Volume of a hemisphere is

V= 2/3 πr³

dV = 2πr² dr

Here,

dr=0.07cm

r=(1/2)×40m=2000cm

Let plug in the formula

dV = 2×π×(2000²)×(0.07)

dV=1759291.886 cubic centimeters

Therefore, Applying a coat of paint 0.07 cm thick to a hemispherical dome with a diameter of 40 meters will require an estimated 1759291.886 cubic centimeters of paint, using a linear approximation.

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Answer: D is  the right answer .The slope of KM is 1 and the slope of NL is –1.

A rhombus is a parallelogram whose all sides are equal. Its diagonals perpendicularly bisect each other.

i.e. product of its slope should be -1.

[∵if one line is perpendicular to the other lines then product of its slope should be -1.]

Slope of  KM= 1

Slope of NL= -1

Product of slope of diagonals=1×-1=-1

∴diagonals of given parallelogram perpendicularly bisect each other.

Therefore, it is a rhombus.

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The minimum usual value, μ-2σ is 17.8 and the maximum usual value, μ+2σ is 54.04

From the information, n = 108, p = 0.24

minimum usual value μ-2σ

maximum usual value μ+2σ

Find the mean, μ:

μ = np = 108 × 0.24 = 35.92

Find the variance, n(1-p):

n(1-p) = 108 ×( 1-0.24) = 82.08

Find the standard deviation, σ:

σ  = √82.08 = 9.06

minimum usual value, μ-2σ:

μ-2σ = 35.92 - (2×9.06) = 17.8

maximum usual value, μ+2σ:

μ+2σ = 35.92 + (2×9.06) = 54.04

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X-μ Use the formula Z where is the mean, o is the standard deviation, and X is the baby kitten σ weight. a. Z= 1.98, X = b. Z-2.87, X ,,a. X = 16.786 , b. X = 8.014

To find the baby kitten weight corresponding to the given z-scores, we use the formula X = μ + Zσ, where μ is the mean, σ is the standard deviation, and Z is the z-score. For the first z-score of 1.98, we substitute the values and solve for X. X = 12.3 + (1.98)(2.2) = 16.786. For the second z-score of 2.87, we substitute the values and solve for X. X = 12.3 + (2.87)(2.2) = 8.014. Therefore, the baby kitten weights corresponding to the given z-scores are 16.786 and 8.014, respectively.

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Multiplication of matrices is not commutative by determining the product matrices ST and TS .

Given :

Consider the matrices

S = [tex]\left[\begin{array}{ccc}4&1\\-3&-2\end{array}\right][/tex]     and  T = [tex]\left[\begin{array}{ccc}0&4\\-4&3\end{array}\right][/tex]

Show that multiplication of matrices is not commutative by determining the product matrices ST and TS.

ST = [tex]\left[\begin{array}{ccc}4&1\\-3&-2\end{array}\right][/tex]  [tex]\left[\begin{array}{ccc}0&4\\-4&3\end{array}\right][/tex]

[tex]ST_{11[/tex] = 4 * 0 + 1 * -4 = -4

[tex]ST_{12[/tex] = 4 * 4 + 1 * 3 = 19

[tex]ST_{21[/tex] = -3 * 0 + -2 * -4 = 8

[tex]ST_{22[/tex] = -3 * 4 + -2 * 3 = -18

ST = [tex]\left[\begin{array}{ccc}-4&19\\8&-18\end{array}\right][/tex]

TS = [tex]\left[\begin{array}{ccc}0&4\\-4&3\end{array}\right][/tex]  [tex]\left[\begin{array}{ccc}4&1\\-3&-2\end{array}\right][/tex]

[tex]TS_{11[/tex] = 0 * 4 + 4 * -3 = -12

[tex]TS_{12[/tex] = 0 * 1 + 4 * -2 = -8

[tex]TS_{21[/tex] = -4 * 4 + 3 * -3 = -25

[tex]TS_{22[/tex] = -4 * 1 + 3 * -2 = -10

TS  = [tex]\left[\begin{array}{ccc}-12&-8\\-25&-10\end{array}\right][/tex]

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3 is the value of (fog⁻¹)(5) for functions f(x)=7-2x and g(x)=x+3.

A relation is a function if it has only One y-value for each x-value.

Given that the functions are f(x)=7-2x and g(x)=x+3.

We need to find the value of  (fog⁻¹)(5)

g⁻¹(x)=x-3.

By composite functions

f(g⁻¹)(x)=7-2(x-3)

f(g⁻¹)(x)=7-2x+6

Now plug in the value of x as 5

f(g⁻¹)(5)=7-2(5)+6

=7-10+6

=-3+6

=3

Hence, the value of  (fog⁻¹)(5) is 3.

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Answer:

The inequality form is 0≤x≤9 0 ≤ x ≤ 9 .

To get the equation which combines with the graphed equation to create a system of equations whose solution set is comprised of the points (−1,−5) and (3,3) we need to plug the points into each equation choice.

Therefore , this is the first step to solve this equation.

The equations of degree 1 are known as linear equations.

These are the equations which are defined for a straight line in a coordinate system.

A linear equation is one that describes a straight line. The general form of a linear equation is  y= mx + b, where m denotes the slope and b its y-intercept.

Note:

The complete question is ,

A linear equation is graphed to the left. Which of the following equations combines with the graphed equation to create a system of equations whose solution set is comprised of the points (−1,−5) and (3,3)?

WHAT IS THE FIRST STEP IN SOLVING THIS PROBLEM?

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the dimensions of a rectangle with area 64000 m2 whose perimeter is as small as possible. (give your answers in increasing order, to the nearest meter.)Length: 200 m and Width: 320 m

The area of a rectangle is given by the formula A = lw, where l is the length and w is the width. To find the dimensions of a rectangle with an area of 64000 m2 and a perimeter that is as small as possible, we can use the formula P = 2l + 2w. We can use this to create an equation with the area and solve for l and w: 64000 = lw, and 2l + 2w = P (min). Solving for l and w, we get l = 200 m and w = 320 m. Thus, the dimensions of the rectangle with an area of 64000 m2 and a perimeter that is as small as possible are 200 m by 320 m.

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Answer:

So the payoff balance of the car loan after 4 years will be approximately $22,169.73.

Step-by-step explanation:

payoff balance after 4 years can be calculated using the following formula:

Payoff balance = Principal * (1 + APR/n)^(nt) - [(Principal * (1 + APR/n)^(nt) * (APR/n)) / (1 + APR/n - 1)]
Where:
Principal is the loan amount, which is $28,550 in this case.
APR is the annual percentage rate, which is 8% in this case.n is the number of times per year that interest is compounded, which is usually 12 for monthly compounding.t is the number of years for which the loan is taken, which is 4 years in this case.
Plugging in the values, we get:
Payoff balance = $28,550 * (1 + 0.08/12)^(124) - [($28,550 * (1 + 0.08/12)^(124) * (0.08/12)) / (1 + 0.08/12 - 1)]
Payoff balance = $28,550 * 1.006669^48 - [$28,550 * 1.006669^48 * 0.006669] / 0.006669Payoff balance = $22,169.73

The ratio of p:r is 6/5

A ratio can be described as the comparison of two or more numbers which indicates their sizes in relation to one another.

From the information given, we have that;

t: w = 7:2

We have that;

Now, substitute the values into the formula

p = 4t + w

p = 4(7) + 2

expand the bracket

p = 28 + 2

Add the values

p = 30

r = t + 9w

r = 7 + 9(2)

expand the bracket

r = 25

The ratio, p:r

p:r = 30/25

p: r = 6/5

Hence, the value is 6/5

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There is actually enough evidence for the manufacturer to believe that the mean number of hours and mobs will last has actually changed.

We are supposed to use Israel and

significance level  α=.05  to perform hypothesis test on the statement of the manufacturer.

So Let's move into our worksheet, our population is 700, our sample size is 48.

The sample mean is 675

Sample standard deviation is 77.

So the first step is to state the null and alternative hypothesis and we have that our hate notes is based on the fact that μ is a cost of 700.

This is what the manufacturer wants, but she thinks that it might have changed probably lesser than or greater than Saddam is our alternative hypotheses, his meal is not equals to 700. So she is not sure whether it does, it's either decrease or increase but it has actually changed.

So after stating our null and alternative protesters, the next needs to state the decision rule that we will be using to either reject or accept the no like protesters.

So will be making a use of the PVA limited to make the decision. It is your roost is that if our evil is better than alpha we are supposed to accept, protesters and if our pivot is lesser than alpha, We are supposed to reject the null hypothesis is that our alpha is equals deserve .05.

So that being said it's time for us to move to draw our test statistics. Now for our test statistic is going to be AT. Test. Yes, our sample size is greater than 30. There's no issue with that. But we actually don't know the value of the population standard deviation. We are making use of the samples and activation which is 27. So that means it would be better if we use our T. Test as our test statistics. So our test statistic is a teacher has given towards us. T is a cost to extra minus meal divided by S divided by the square root of n. Our expert in this case is 6 75 minus. We have 700 divided by our s is 77 divided by the square root of 48. So let's do the math. 6 75 minus 700. We have a -25 divided by so we have 77 divided by the spirit of 48. We have this to be 11.11399. So uh -25 divided by 11.11399. We have our answer to be -2.249. So they simply implies that our test statistics is manners two points 249. So the next step is for us to get the p value attached to this test statistic scenes, we are using the p value method uh to make our decision. So we need a P value. We already have the level of significance. So to get the P value, we can decide to make itself. It it it's a distribution table but that will only give us a range of values in which the p value is located. It won't give us the actual P value. So most times we decide to use calculator to get the p value the exact p value. So our test is actually a two tailed tests were testing for a T score.

Our degree of freedom is the sample size minus one.

48-1=47

And our T score uh is minus two points 249.

So that we have a miners 2.249. And as you can see our p value here is 0.02 0.0294. T. Value is 0.029 so far. Alright, so there's our p value. So the next thing is to make our decision. So we have that as you can see their .0-9 Too far is actually lesser than 0.05 hands.

We make a decision by saying, we are going to reject the null hypothesis. So the decision is that we're going to be rejected the null hypothesis.

As a result, the manufacturer has sufficient reason to think that the average number of hours and mob duration have altered.

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By using distance formula, it can be calculated that-

Distance between  (-4, -5) and (4, 2) is [tex]\sqrt{113}[/tex] units

What is distance formula?

Distance formula is used to find the distance between two coordinates.

If the points are [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex], then distance is calculated by the formula

d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

The points are (-4, -5) and (4, 2)

Distance between  (-4, -5) and (4, 2) = [tex]\sqrt{(-4-4)^2+(-5-2)^2}[/tex]

                                                            = [tex]\sqrt{64 + 49}\\\sqrt{113}[/tex]units

Distance between  (-4, -5) and (4, 2) is [tex]\sqrt{113}[/tex] units

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Answer:

C) inconsistent

Step-by-step explanation:

3x+y=−5

3y+15=−9x

3x + y = -5

9x + 3y = 15

3x + y = -5

3x + y = 5

The system graphs as two parallel lines.

Answer: C) inconsistent

 2 sin A sin B with two angles A and B, 2 sin A sin B = cos (A-B) - cos (A + B). The 2sinasinb formula is equivalent to the difference between the angle sum and the angle difference of the cosine functions. The formula for two sins is two sins A and two sins B: cos (A-B) - cos (A + B).

What is 2SinASinB Identity?

2SinASinB identity is a trigonometric formula and it is used for the simplification of trigonometric expressions. It is also used for evaluating integrals involving trigonometric functions for easy calculation. We can derive the formula for 2SinASinB using the angle sum and angle difference formulas of the cosine function. Using the 2SinASinB formula, we can derive another trigonometric formula for SinA SinB given by, sinA sinB = (1/2)[cos(A - B) - cos(A + B)].

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