If z = 1+ i√3, what is z^5? ​

Answer:

Here is the full list of equivalent fractions to 32.  3/2, 6/4, 96, 12/8, 15/10, 18/12, 21/14, 24/16, 27/18, 30/20, 33/22, 36/24, 39/26, 42/28, 45/30, 48/32, 51/34, 54/36, 57/38, 60/40

Step-by-step explanation:

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Step-by-step explanation:

we have 2 blocks, as the graphic shows.

the surface areas of both blocks are the sum of their 6 sides each.

the special thing about seeing them as "composite figure" is that 2 sides (one for each block) are partly or even completely blocking each other off from being seen, so these parts and whole side are not part of the combined surface area.

let's start with the large block :

it is 5cm × 6cm × 20cm.

its surface area is the sum of

top and bottom 5×6

front and back 20×5

left 20×6

visible right (20 - 12)×6 = 8×6

it is (20-12)cm long, because the short block

is 12cm high.

so, we have

2 times 5×6 =2×30 = 60 cm²

2 times 20×5 = 2×100 = 200 cm²

20×6 = 120 cm²

8×6 = 48 cm²

in total : 428 cm²

now the small block :

it is 4cm × 6cm × 12cm.

its surface area is the sum of

top and bottom 4×6

front and back 4×12

no left (completely covered by the large block)

right 6×12

so, we have

2 times 4×6 = 2×24 = 48 cm²

2 times 4×12 = 2×48 = 96 cm²

6×12 = 72 cm²

in total : 216 cm²

the complete surface area of the composite figure is

428 + 216 = 644 cm²

The values associated to the exponential function are listed below:

Herein we have the exponential function [tex]g(x) = 1\,296^{x}[/tex], which has to be evaluated, that is, replacing the variable x by constants and make use of algebra properties until result is found.

g(- 1.75) = 3.572 × 10⁻⁶

g(- 1) = 7.716 × 10⁻⁴

g(- 0.25) = 0.167

g(0) = 1

g(0.25) = 6

g(0.50) = 36

g(0.75) = 216

g(1) = 1 296

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Answer: c. a-15= 20

Step-by-step explanation:

The answer is c because a represents her age and 15 less than that would mean that you have to subtract 15 from her age which is represented by a, and then 15 less than a would equal 20, so a-15=20

Answer: B) -8

Step-by-step explanation:

We add 12 both sides

Add −18 and 12 to get −6.

Multiply both sides by 3/4 by the reciprocal of 3/4.

Express a -6 x (3/4) as a single fraction.

Multiply −6 and 4 to get −24.

Divide −24 by 3 to get −8.

Answer: Option "2" is correct. ✅

Using a quadratic regression equation, it is found that the prediction of the number of songs that Kimberly will download on Month 9 is of:

c. 16.

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, we have that the function initially decreases, then it increases , which means that it is a quadratic function. The points (x,y) to  be inserted into the calculator are given as follows:

(1,8), (2,6), (4,5), (6,7), (7,9)

Inserting these points into the calculator, the prediction of y for a value of x is given as follows:

y = 0.391x² - 2.937x + 10.455

Hence, when x = 9, the prediction is:

y = 0.391 x 9² - 2.937 x 9 + 10.455

y = 15.69

Rounded to 16, hence option c is correct.

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All subsets of the set s = {(i, 0), (0, i), (i, i)} that form a basis for r2 is

{( 0,1) (-1,1)}

{(1,0)(0,1)}

{(1,0)(-1,1)}

A fixed A is a subset of some other set B if all elements of set A are factors of set B. In other phrases, set A is contained within set B. The subset relationship is denoted as A⊂B.

Subsets are a part of one of the mathematical ideas known assets. a hard and fast is a set of items or factors, grouped within the curly braces, consisting of {a,b,c,d}. If a set A is a set of even numbers and set B includes {2, 4,6}, then B is stated to be a subset of A, denoted by B⊆A and A is the superset of B.

In mathematics, set A is a subset of a fixed B if all factors of A are also elements of B; B is then a superset of A. It's far possible for A and B to be equal; if they may be unequal, then A is a proper subset of B. The relationship of one set being a subset of every other is known as inclusion.

A set which is (is linearly independent andoil generates/ spans the space (like R) is called a baris.

S= (1,0), (0,1), (-1))}

option-1

As, dimension of R²=2, so, Ary set

conists of three vectors cannot be baris for R²

so, option-1 is wrong.

option-2

As, dimention of R2-2.

{(10), (-11)} is a linearly independent

subset of S. so And as, this subset

has 2 vectors so it will as also

span R se, it will be a baris

of IR?

So, option-6 is correct

{(0,1)} is linearly independent subset

option-7

As (LO) has one vector. So, it cannot

Span/generate R so, it also cannot be balis

for R2

of S.

But it cannot span R²

So ut cannot

be a baris of R2

se, option-2 is wrong.

Option-3

AS, {(0,1), (-1,1)} is linearly independent

So, option -7, is wrong.

Answer

[as fox amy KER, (-1,1) K (0,1)] subset of s

And also as dim {(0,1), (-11)}=2

which is same as the dimention of IR2

so {(0,1), (-11)} forms a baris of R2

{(1,0), (0,1), (-11)}

{(1,0)}

So, option-3 is

Connect

option-4

{(1,0), (3, 1)} is standard balis of R2

which is subset of S.

10

[{(1,0), (0,1)}]

So, option-4 is correct.

option-5

{(-11)}

consists of one vertex,

so, ut cannot span R², so, ut cannot

be a baris of R²

9090

LO {(1,0), (-1,1)}]

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Complexes with a coordination number 4 mostly adopt tetrahedral and squar planar geometries.

Complexes with a coordination number 4 mostly adopt tetrahedral and squar planar geometries.

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Answer: D 1881

Step-by-step explanation: 6889 and 1961 don't read the same forwards and backward. 1991 upside down is 1661. So, only 1881 works

If the data is symmetrical, then the mean is the best measure of central tendency to use, and the standard deviation is the best spread to use.

If the data is asymmetrical, the median is the best measure of central tendency to use, and the inter-quarterly range is the best spread to use.

A histogram for symmetrical data will give a symmetrical shape, and the mean, median and mode will all be the same value. Therefore, the best measure of the central tendency to use is the mean. The standard deviation shows how far away the values in a given data set are from the mean, and since the mean is used as the measure of central tendency in this case, the standard deviation should be used as the spread.

A histogram for a an asymmetric data set will give an asymmetric shape, and the mean is not always equal to the median. Therefore, the best measure of central tendency to use is the median. The inter-quarterly range shows the range of the middle 50% of a certain data, which is considered from the median value. Since the median is used as the measure of central tendency in this case, it is wise to use the inter-quarterly range as the measure of spread.

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Answer:

x:12×2−6(a2+b2)x+3a2b2=0

Step-by-step explanation:

equation

Answer:

x - intercept: (3, 0)

y - intercept: (0, 9)

Step-by-step explanation:

This equation is written in standard form,

To find the intercepts it would be easier to put the equation in

slope-intercept form y = mx + b

9x + 3y = 27

subtract 9x from both sides

(9x - 9x) + 3y = 27 - 9x

3y = 27 - 9x

Divided both sides by 3

3y / 3 = 27 - 9x / 3

y = 27 / 3 - 9x / 3

y = - 3x + 9

Now we can plug in x = 0, to find y - intercept:

y = - 3(0) + 9

y = 0 + 9

y = 9

Now we can plug in y = 0, to find x - intercept:

0 = - 3x + 9

0 - 9 = - 3x + 9 - 9

-9/3 = -3x/3

-3 = -x

3 = x

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The Volume of the Cylinder B is gotten as; 720 cm³

We are given 2 similar cylinders with;

ratio of heights = a : b

Thus;

ratio of areas = a² : b²

We are given that;

Height of A is 5cm.

Height of B is 10cm.

Thus;

Ratio of heights = 5 : 10 = 1 : 2

Therefore;

ratio of areas = 1² : 2² = 1 : 4

The cross sectional area of B is 4 times the cross sectional area of A. Thus;

Cross sectional area of B = 4 × 18 = 72 cm²

Volume of cylinder = cross section area × height

Volume of cylinder B = 72 × 10 = 720 cm³

The complete question is;

A and B are two cylinders that are mathematically similar.

The area of the cross-section of cylinder A is 18cm².

Height of A is 5cm.

Height of B is 10cm.

Work out the volume of cylinder B

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The option c is correct. Linear model suits best to this graphical representation out of the exponential and quadratic model.

According to the statement

We have given that a model in the graphical representation and we have to tell that which type of model used in this representation.

So,

According to this representation,

A linear representation is a representation on a category of vector spaces or similar.

The other meaning is that when the growth increases linearly or at the constant speed.

In this graphical representation, linear representation is used because it increases or decreases linearly not suddenly.

linear representation explain this graph perfectly.

So, Linear model suits best to this graphical representation.

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its c! there isnt a decrease between x = -1 and x = 0, as when x = -1 y = 0 and when x = 0 y = 2, showing an increase of +2.

Answer:

87

Explanation:

This is an arithmetic sequence with common difference: 7 and first term: 17

Arithmetic sequence:

a + (n - 1)d                    where n is term position, d is difference, a is first term

17 + (n - 1)7

7n + 10

The eleventh term:

7n + 10

7(11) + 10

77 + 10

87

To Find :-

Solution :-

Given A.P.,

First term (a) is 17.

Common difference (d) = 24 - 17 => 7

We know that :

Here n would be 11.

>> t11 = 17 + (11 - 1) 7

>> t11 = 17 + (10) 7

>> t11 = 17 + (10) × 7

>> t11 = 17 + 70

>> t11 = 87

Therefore, eleventh term in the sequence is 87.

Considering that the two lines intersect at only one point, the system of equations described by them is consistent.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

According to the number of solutions, the system is classified as follows:

In this graph, each equation is described by a line, and they intersect once, meaning that there is one solution and the system is consistent.

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The double integral. 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d is given as

[tex]\int _D 7xcosydA =7/2(-cos49+1)[/tex]

Generally, the equation for is  mathematically given as

The area denoted by the letter D that is bordered by y=0, y=x2, and x=7

The equation for the X-axis is y=0.

y=x² ---> (y-0) = (x-0)²

Therefore, the equation of a parabola is y = x2, and the vertex of the parabola is located at the point (0,0), and the axis of the parabola is parallel to the Y axis.

The equation for a straight line that is parallel to the Y-axis and passes through the point (7,0) is x=7.

[tex]\int _D 7xcosydA\\\\\int^7_0 \int^x^2 _0 7xcosydA[/tex]

Integrating we have

[tex]7/2 \int^7_0 (2xsinx^2)dx[/tex]

If x equals zero, then we know that u equals zero as well.

When x equals seven, we know that u=72=49.

Therefore, by changing x2=u into our integral, it becomes from

 [tex]7/2 \int^7_0 (2xsinx^2)dx[/tex]

[tex]7/2 \int^49_0 sin u dx[/tex]

Hence

=7/2(-cos49+1)

In conclusion,

[tex]\int _D 7xcosydA =7/2(-cos49+1)[/tex]

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Answer:

180

Step-by-step explanation:

If she received requests for 150 tickets, and that is 120% of what they have, you would find 20% of 150. You would do this because 100% of 150 is 150, now you need to add the other 20%, so you have to find 20% of 150. Which is 30. You would then add that to 150 sine it is 120% of what they have. So, they have 180 tickets

Answer:

f = 78 , g = 32 , h = 74

Step-by-step explanation:

f and 78° are alternate angles and are congruent , then

f = 78

---------------------------

h and 74° are alternate angles and are congruent , so

h = 74

--------------------------

the sum of the 3 angles in the triangle = 180°

sum the 3 angles and equate to 180

78 + g + h = 180

78 + g + 74 = 180

152 + g = 180 ( subtract 152 from both sides )

g = 28

The board with a length of 4.8 feet would require 5 pounds of pressure to break.

An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Let p represent the pressure and l represent the length.

l ∝ 1/p

l = k/p (k is constant)

When l = 3, p = 8, hence:

3 = k/8

k = 24

For p = 5:

l = k/p = 24/5 = 4.8 feet

The board with a length of 4.8 feet would require 5 pounds of pressure to break.

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The theorem that justifies why triangles ABC and DEF are congruent is: HL.

The hypotenuse-leg congruence theorem (HL) states that if two triangles that are right triangles have a pair of congruent hypotenuse and a pair of corresponding congruent legs, then both right triangles are proven to be congruent to each other. This means both right triangles are have the same shape and size.

Given that:

angle ABC = angle DEF = 90° (congruent right angles, this means both triangles are right triangles)

AC = FD (a pair of congruent hypotenuse)

AB = DE (a pair of congruent legs)

Thus, we can conclude that since triangle ABC and triangle DEF have a pair of congruent hypotenuses and a pair of congruent legs, therefore, the two right triangles, triangle ABC and triangle DEF are congruent to each other by the HL congruent theorem.

Thus, the theorem that justifies why both triangles are congruent is: HL.

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Number of ants = 6

Number of flies = 12

Number of buck = 1

Number of fawn = 1

Number of doe = 1

Number of squirrels = 3

Number of rabbit = 6

What is the number system?

A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.

A system for representing numbers is called a number system. It also defines a set of numbers to represent a quantity and is referred to as the system of numeration.

Given,

Total number of animals Cory saw = 27

Number of insects = [tex]27 \times \frac{2}{3}[/tex]

                               [tex]= 18[/tex]

Remaining number of animals = [tex]27-18[/tex]

                                                   = [tex]9[/tex]

From the insects-

Number of ants = [tex]18 \times \frac{1}{3}[/tex]

                          [tex]=6[/tex]

Number of flies = [tex]18-6[/tex]

                          = [tex]12[/tex]

Number of buck  = 1

Number of fawn = 1

Number of doe = 1

Let the number of squirrels be [tex]x[/tex]

Then, the number of rabbits = [tex]2x[/tex]

Remaining animals = [tex]2x+x[/tex]

⇒ [tex]9=3x[/tex]

⇒ [tex]x= 3[/tex]

Therefore,

Number of squirrels = 3

Number of rabbits = [tex]2x[/tex]

                               = 6

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Answer:

3600

Step-by-step explanation:

Reason is because you put the answer in your question.

Answer:

Rs.10800

Step-by-step explanation:

loss of article(L%)=10%

s.p=?

c.p of an article (c.p)=c.p

Now,

s.p=100-L%×c.p

_____

100

= 100-10 ×c.p

_____

100

=90 ×c.p

___

100

=0.9 × c.p

if article sold with Rs. 540 more

Article profit =5%

s.p =c.p + 540 =100+p%×c.p

______

100

or, c.p +540=105×c.p

______

100

or, c.p +540=1.05×c.p

or,c.p +540=1.05c.p

or, 540=1.05c.p-c.p

or,540=0.05c.p

or, 540=c.p

____

0.05

Therefore, c.p =Rs. 10800

The answers are :

y = 3ˣ ⇒ b

y = 3⁻ˣ ⇒ a

y = -3ˣ ⇒ c

For y = 3ˣ, we will get a graph that will increase exponentially in the direction of positive y-axis.

For y = 3⁻ˣ, we will get a graph that will decrease exponentially in the direction of positive x-axis.

For y = -3ˣ, we will get a graph that will decrease exponentially in the direction of negative y-axis.

Two different integers are the same numbers, which have different signs.

An integer is a number that includes negative and positive numbers, including zero. It does not include any decimal or fractional part. A few examples of integers are: -5, 0, 1, 5, 8, 97.

Given that,

x, y, and z are three integers. They follow the one condition: x-y-z = 0.

Any number in the number system that has only two signs, either + or -, So we consider that the third integer is 0 because 0 is a whole number that has neither a positive nor a negative sign.

The remaining two integers are the same numbers, but they have different signs to follow the given condition.

x-y-z = 0

x = y+z

Let y,z are the same numbers, They have different signs and x = 0.

Note: The value of x is always negative and y's value is always positive.

Example:

x = 0,  y = +6,  z = -6

x-y-z = 0

x = y+z

0 = +6-6

0 = 0

Hence, two different integers are the same numbers, which have different signs.

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The domain of the function is:

h > 0, only integers.

Then the correct option is the first one.

For a function f(x), we define the domain as the set of the possible values of x that we can use as inputs in the given function.

Here the function is:

f(h) = 6*h + 12

Where h is the number of packages that you buy.

Then h can be only integers larger than zero (as you can't buy half a package or something like that).

Then we conclude that the correct option is the first option.

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Answer:

$7.14

Step-by-step explanation:

Given:

Isabel , Nancy = 2 humans

Bill = $12.42

Tip = 15%

To Find:

How much will each girl pay if they equally divide the total amount?

Solve:

$12.42 × 15% = 1.863

1.863 ≈ 1.86

$12.42 + 1.86 = 14.28

14.28 ÷ 2 = 7.14

Therefore each girl pays $7.14 .

~Kavinsky