(sqrt3-sqrt3i)^4
(-1+sqrt3i)^12
(sqrt 3-i)^6
(sqrt2-sqrt2i)^8
(sqrt2-i)^6Simplify the complex numbers and arrange them in increasing order of their absolute value (modulus).

Answer:

61 + 142 + 44 = 247˚

Step-by-step explanation:

Just add haha

the person above is right

Volume is a three-dimensional scalar quantity. The number of boxes that can fit in the cargo hold of the truck is 54.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of the box = Volume of the cube = a³ = (2.50)³ = 15.625 ft³

The volume of cargo hold = 7.50 × 7.50 × 15 = 843.75 ft³

Now, the number of boxes that can fit in the cargo hold of the truck will be,

Number of boxes = (Volume of truck container)/(Volume of box)

                              = 843.75/15.625

                              = 54

Hence, the number of boxes that can fit in the cargo hold of the truck is 54.

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What is volume of the box in diagram (in cubic ft.)

Volume of cube = a³

putting the value of a

Volume = (2.5ft.)³

Volume = 15.625 ft³

To find how many such boxes can be fit into the truck , we need to first find the volume of cargo hold of the truck and then divide it by the volume of 1 box

Volume of Cargo hold of truck =

= 15ft. × 7.5ft. × 7.5ft

= 843.75 ft³

No. of boxes that can be fit into the truck =

Volume of truck/ Volume of one box

= 843.75ft.3³/15.625ft.³

= 54 boxes

Answer:

x=√15 or x = -5 or x=3

Step-by-step explanation:

Possibility one:

x=x^2+x-15

x-x^2=x^2+x-15-x^2 (subtract x^2 from both sides)

-x^2+x=x-15

-x^2+x-x=x-15-x (subtract x from both sides)

-x^2=-15

-x^2/-1=-15/-1 (divide both sides by -1)

x^2=15

square root both sides

x=√15 or x=-√15

Possibility two:

x=(-x^2+x-15)

x=-x^2-x+15 (simplify)

x-(-x^2-x+15)=-x^2-x+15-(-x^2-x+15) (subtract both sides by -x^2-x+15)

x^2+2x-15=0

(x-3)(x+5)=0 (factor left side of equation)

x-3=0 or x+5=0 (set factors equal to 0)

x=3 or x=-5

Answer:

? ≈ 6.5 yd

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here A = 13.3 and h = 4.1 , then

[tex]\frac{1}{2}[/tex] × 4.1b = 13.3 ( multiply both sides by 2 to clear the fraction )

4.1b = 26.6 ( divide both sides by 4.1 )

b = ? ≈ 6.5 yd ( to the nearest tenth )

Answer:

the probability is 1.01

Answer:

Step-by-step explanation:

Remark

If the figures are similar then this is a proportion question. A proportion is 2 equation ratios. The ratios can have at most 1 unknown.

Givens

DC = 7

ML = 4.9

AB = 4

JK = x

Equation

DC/ML = AB/x                  Substitute values into equation and solve

Solution

7/4.9 = 4/x                        Cross Multiply

7x = 4 * 4.9                       Combine the right.

7x = 19.6                           Divide by 7

7x/7 = 19.6/7

x = 2.8

Answer

x = 2.8

Answer:

cos 90°

Step-by-step explanation:

(cos 60°)(cos 30°) − (sin 60°)(sin 30°)

= cos ( 60° + 30°)

= cos 90°

The expression (cos 60°) (cos 30°) − (sin 60°) (sin 30°) is cos 30°.

There are three commonly used trigonometric identities.

Sin x = Perpendicular / Hypotenuse

Cosec = Hypotenuse / Perpendicular

Cos x = Base / Hypotenuse

Sec x = Hypotenuse / Base

Tan x = Perpendicular / Base

Cot x = Base / Perpendicular

We have,

(cos 60°)(cos 30°) − (sin 60°)(sin 30°)

We can use the trigonometric identity for the difference of angles between cosines.

cos(x - y) = cos(x)cos(y) - sin(x)sin(y)

By setting x = 60° and y = 30°.

So,

cos(60° - 30°) = (cos 60°)(cos 30°) − (sin 60°)(sin 30°)

cos 30° = (cos 60°) (cos 30°) − (sin 60°) (sin 30°)

Thus,

(cos 60°) (cos 30°) − (sin 60°) (sin 30°) is cos 30°.

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Answer:

7.53

3.5 + 0.02 = 3.52

11 + 0.05 = 11.05

11.05 - 3.52 = 7.53

A,D and E are not polynomials.

Step-by-step explanation:

Well you see my friend, that's how things work.

A polynomial does not have the variable in the denominator.

The area of the shaded region is 75.5cm^2.

The radius of the inner circle=10cm

The radius of the outer circle=14cm

angle made by sector is 90 degrees.

[tex]A=\frac{\theta}{360}\times \pi r^2[/tex]

For an outer sector

[tex]Area of the sector=\frac{90}{360} \times \frac{22}{7} \times 14^2[/tex]

area of the sector=154cm^2

Now we have to find the area of the sector for the inner circle.

[tex]Area of the sector=\frac{90}{360} \times \frac{22}{7} \times 10^2[/tex]

Area of sector=78.5cm^2

Area of the shaded region =area outer sector - area of inner sector

Area of the shaded region=154-78.5.

Area of the shaded region75.5cm^2.

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Answer:

B.) As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞.

Step-by-step explanation:

[tex]\lim_{x\rightarrow -\infty } f\left( x\right) =\lim_{x\rightarrow -\infty } -4\sqrt[3]{x} = (-4)\times(-\infty) = +\infty[/tex]

[tex]\lim_{x\rightarrow \infty } f\left( x\right) =\lim_{x\rightarrow \infty } -4\sqrt[3]{x} = (-4)\times(+\infty) = -\infty[/tex]

A. True. We see this by taking the highest order term in each factor:

[tex]f(x) = -3x(x-5)^3(x+2)^2 = -3x (x^3 + \cdots) (x^2 + \cdots) = -3x^{\boxed{6}} + \cdots[/tex]

B. True. Again we look at the leading term's degree and coefficient. f(x) behaves like -3x⁶ when x gets large. The degree is even, so as x goes to either ± ∞, x⁶ will make it positive, but multiplying by -3 will make it negative. So on both sides f(x) approaches -∞.

C. False. f(x) = 0 only for x=0, x = 5, and x = -2.

D. False. Part of this we know from the end behavior discussed in part B. On any closed interval, every polynomial is bounded, so that for any x in [-2, 5], f(x) cannot attain every positive real number.

E. True. x = 0 is a root, so f(0) = 0 and the graph of f(x) passes through (0, 0).

F. False. (0, 2) corresponds to x = 0 and f(x) = 2. But f(0) = 0 ≠ 2.

Using scientific notation, it is found that the number in standard notation is represented by:

[tex]74.94 \times 10^3 = 74940[/tex]

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

In this problem, the number is given by:

[tex]74.94 \times 10^3[/tex]

Hence, applying the multiplication, we have that:

[tex]74.94 \times 10^3 = 74.94 \times 1000 = 74940[/tex]

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Answer:

C . The sun

plants absorb light which make carbohydrates which makes a part of bodies of animals and plants . When they die this compound in their bodies which later became coal

Answer: the slope is y=-1/2

Step-by-step explanation:

because the line is moving from left to right, it is a negative slope

Answer:

  y = 15x

Step-by-step explanation:

The equation for direct variation is ...

  y = kx

where k is the constant of proportionality.

__

We can find k by dividing by x:

  y/x = k

Using the given values, we find it to be ...

  75/5 = k = 15

Using this value of k in the equation, we find the equation of direct variation is ...

  y = 15x

Answer:

[tex]\huge \orange{b = \boxed{ 6} \sqrt{ \boxed{3}} }[/tex]

Step-by-step explanation:

[tex]a = 12 \sin 30 \degree \\ \\ \implies \: a = 12 \times \frac{1}{2} \\ \\ \implies \: \huge \red{ a = 6} \\ \\ b = 12 \cos 30 \degree \\ \\ \implies \: b = 12 \times \frac{ \sqrt{3} }{2} \\ \\ \implies \: b = 6 \times \sqrt{3} \\ \\ \implies \: \huge \orange{b = \boxed{ 6} \sqrt{ \boxed{3}} }[/tex]

Answer:

$1,923.08.

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 6%/100 = 0.06 per year.

Solving our equation:

P = 2500 / ( 1 + (0.06 × 5)) = 1923.0769230769

P = $1,923.08

The principal investment required to get a total amount, principal plus interest, of $2,500.00 from simple interest at a rate of 6% per year for 5 years is $1,923.08.

a. The cost of the stock is $19

b.  Tanya Elliot paid total amount of $ 7629.95.

The cost of preferred stock to a company is effectively the price it pays in return for the income it gets from issuing and selling the stock.

a. It is given that , each share= $19.00

Total number of shares = 400

Price for 400 shares be,

= 400 x $19.00

= $7600.00

Cost of the stock= [tex]\frac{ 7600}{400}[/tex]

                            = $19

b. Total paid by Tanya = $7600.00 +$29.95

                                      = $7629.95

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Answer:

Step-by-step explanation:

Solve each equation and compare the solutions

1.

2.

Both a and b have same value

Answer:

Yes, a and b have the same value in the given equations.

Step-by-step explanation:

Equation 1

      [tex]2(a-1.1)=5.8[/tex]

[tex]\implies 2a-2.2=5.8[/tex]

[tex]\implies 2a-2.2+2.2=5.8+2.2[/tex]

[tex]\implies 2a=8[/tex]

[tex]\implies \dfrac{2a}{2}=\dfrac{8}{2}[/tex]

[tex]\implies a=4[/tex]

Equation 2

    [tex]\dfrac{5}{2}b-2\frac{3}{4}=7 \frac{1}{4}[/tex]

[tex]\implies \dfrac{5}{2}b-\dfrac{2 \times 4+3}{4}=\dfrac{7 \times 4+1}{4}[/tex]

[tex]\implies \dfrac{5}{2}b-\dfrac{11}{4}=\dfrac{29}{4}[/tex]

[tex]\implies \dfrac{5}{2}b-\dfrac{11}{4}+\dfrac{11}{4}=\dfrac{29}{4}+\dfrac{11}{4}[/tex]

[tex]\implies \dfrac{5}{2}b=\dfrac{40}{4}[/tex]

[tex]\implies \dfrac{5}{2}b=10[/tex]

[tex]\implies 2 \cdot \dfrac{5}{2}b=2 \cdot 10[/tex]

[tex]\implies 5b=20[/tex]

[tex]\implies \dfrac{5b}{5}=\dfrac{20}{5}[/tex]

[tex]\implies b=4[/tex]

Conclusion

As  a = 4  and  b = 4, the two variables have the same value in the given equations.

Answer:

5√6

Step-by-step explanation:

√25 x 6

√25 x√6

5√6

Volume is a three-dimensional scalar quantity. The height of the cuboid is 7 cm.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Given the volume of the cuboid is 385cm³, the length of the cuboid is 10cm, while the width of the cuboid is 5.5 cm, therefore, the height of the cuboid is,

385cm³ = 10cm × 5.5cm × H

H = 385cm³/(10cm×5.5cm)

H = 7cm

Hence, the height of the cuboid is 7 cm.

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Reason:

The standard error of the mean has the formula [tex]\frac{\sigma}{\sqrt{n}}[/tex] where [tex]\sigma[/tex] (greek letter sigma) is the standard deviation and n is the sample size.

As n gets bigger, the standard error [tex]\frac{\sigma}{\sqrt{n}}[/tex] gets smaller, and vice versa. This assumes sigma is fixed. A larger sample indicates the error goes down to narrow in better on the population mean.

Based on what I mentioned, this tells us that sample A has the larger standard error since n = 350 is smaller than n = 500 for sample B.

Answer:  [tex]\frac{219}{100}[/tex]

======================================================

Explanation:

Think of [tex]2.19[/tex] as [tex]\frac{2.19}{1}[/tex] or [tex]\frac{2.19}{1.00}[/tex]

This works because dividing anything over 1 does not change the original number.

Then we can move the decimal point two spots to the right for each number

Therefore, [tex]2.19 = \frac{219}{100}[/tex]