Question 1: Write down the square numbers from the list below
91 101 1024
81 200

From the properties of a complex number, it was found that the value for  [tex]i^{21}[/tex] is i.

A complex number is represented by the following form: a+bi, where a and b are real numbers.  The variables: a is the real part and bi imaginary part. See an example: 6 + 13i , then: 6 represents the real part and   14i represents the imaginary part.

Regarding operations math, the same properties used for real numbers can be applied to complex numbers. And for solving the operations math with these numbers, it is important to know that i²= -1. Thus, 6i² = 6*(-1)= -6.

The question gives [tex]i^{21}[/tex], thus.

[tex]i^{21}=i^{20}*i[/tex]

[tex]i^{21}=(i^{2})^{10}*i\\ \\ i^{21}=(-1)^{10}*i\\ \\ i^{21}=1*i=i[/tex]

Therefore, the result for the question is i.

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Answer:

5 percent

Step-by-step explanation:

100/40=2.5

2.5*2=5

The area of the shaded region is equal to half the area of the circle.

What is the area of the circle?

The approximating parallelograms arbitrarily close and approximate the area of the circle by cutting it into ever-increasing slices.

The radius of the arc BC is |AB|=2rcosθ, and ∡AOB=π−2θ.

Dashed area= Area of sector BAC+ 2(Area of sector BOA−Area of triangleBOA)

= 1/2|AB|²(2θ)+2[1/2r²(π−2θ)−1/2r²sin(π−2θ)]

On the other hand, the area of the dashed surface is 1/2πr², then

1/2|AB|²(2θ)+2[1/2r²(π−2θ)−1/2r²sin(π−2θ)] = 1/2πr²

(2rcosθ)2(θ) + r²[π−2θ−sin(π−2θ)] = 1/2πr²

4θcos2θ+π−2θ−sin2θ = 1/2πr²

2θ(2cos2θ−1) = sin2θ−1/2π

2θcos2θ = (2sin2θ−π)/2

cos2θ = (2sin2θ−π)/4θ

Hence, the area of the shaded region is equal to half the area of the circle.

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Answer:

y=5/2x-4

Step-by-step explanation:

y=mx+b

5/2 is the slope

-4 is the y intercept

The inequality is [tex]|x|\geq4[/tex].

What are the inequalities of a graph?

We can see the areas that satisfy one or more inequalities by visualizing them as inequalities on a graph. These inequalities can be represented using straight-line graphs in GCSE maths because they are frequently linear. You might need to draw lines and designate a region that fulfills the system of inequalities to find solutions to the inequalities, or you might need to use the graphs that have already been provided.

Here, in the graph given, we see that the points on and from 4 / -4 are highlighted. Since the interval has 0 in between, we write the variable as [tex]|x-0|[/tex]. Now, the graph excludes points from -4 to 4.

Therefore, we conclude that the absolute value inequality for the given graph is [tex]|x|\geq4[/tex].

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Absolute value is 7 or greater.

What is inequality?

In mathematics, an inequality is a statement that compares two values or expressions using one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). For example:

2 < 3 (2 is less than 3)

5 > 3 (5 is greater than 3)

2 ≤ 3 (2 is less than or equal to 3)

5 ≥ 3 (5 is greater than or equal to 3)

Inequalities can be used to describe a range of values that a variable can take on. For example, the inequality x > 0 describes all values of x that are greater than 0.

Inequalities can be solved by finding the values of the variable that make the inequality true. For example, the solution to the inequality x > 0 is all values of x that are greater than 0, such as 1, 2, 3, etc.

Inequalities can also be combined using the logical operators "and" (represented by the symbol ∧) and "or" (represented by the symbol ∨). For example, the inequality x > 0 ∧ x < 10 describes all values of x that are greater than 0 and less than 10, such as 1, 2, 3, etc. The inequality x > 0 ∨ x < 10 describes all values of x that are either greater than 0 or less than 10, which includes all values of x.

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Answer:

3/32

Step-by-step explanation:

When dividing fractions, we use keep change flip.

We keep the 1/4, change into multiplication, and flip 2 and 2/3.

First, we want to change 2 and 2/3 into improper fraction form, which is 8/3.

Our equation is now :

1/4 divided by 8/3

Now, we apply keep change flip.

1/4 * 3/8

Multiply numerator by numerator and denominator by denominator.

3/32

3/32 is your final answer. It cannot be simplified further.

The table that represents a proportional relationship is Table A.

A proportional relationship exists between two variables when their ratios are equal or equivalent.

With a proportional relationship, there is a constant rate of change between the comparable variables.

Proportions refer to ratios of equality between two or more variables.

Where there is a proportional relationship, we can determine the constant rate of change as the same quotient.

For instance, when the number of pages per book is divided by the reading time, a constant rate of change is established if the reading speed is the same for all three books.

Pages Lucas Read 208  156  234  

Time (hours)             8      6     9

Reading speed       26    26   26 (234/9)

Pages Britney Read 168  120  348  

Time (hours)               6     4       12

Reading speed        28    30    29 (348/12)

Thus, the constant rate of change or proportional relationship can be found in Table A and not in Table B.

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Pages Lucas Read 208  156  234  

Time (hours)             8      6     9

Pages Britney Read 168  120  348  

Time (hours)               6     4      12

The solutions for the given questions are given below:

Earnings from employment, investments, or company operations. Sam, for instance, had a weekly income of $770 after receiving $30 in bank interest, $700 from his employment, and an additional $40 from buying and selling veggies.

Wages is the amount of money obtained through employment; income is the entire amount of money obtained, which includes earnings, benefits, pensions, and other types of payments.

1.a 500000 shares have been authorized.

1/(210000) = 210000 shares issued Number of shares issued [Common stock account balance / par value of each share]

1-c) The number of shares outstanding is 210000 - 3100, or 206900 shares.

2) The APC Account Balance is $4620000, which is calculated as 210000 * (23 - 1).

3) Net income divided by the number of outstanding shares equals 165520 divided by 206900, or 0.8 per share.

4) The dividend per common share was paid at 53794/206900, or 0.26 per share.

5) 3100 * 21 = $65,100 should be stated for Treasury Stock in the Stockholders' Equity part of the Balance Sheet.

6) Following the stock split, the par value of each share is equal to 1 / 2 ($0.50 per share).

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Answer:

D

Step-by-step explanation:

The taxi charges $2.00 for any distance less than or up to 1 mile.

Then for every mile after the taxi will charge you a fee of $1.60 dependent upon how many miles you go.

This can be modeled as:

y = 2.00 +1.60(x)

where x is the number of miles after the first mile.

Answer:

No solution

Step-by-step explanation:

The square root of a negative number is not a real number

Answer:

y=2(x-4)^2+9

Step-by-step explanation:

Vertex form: y=a(x-h)^2+k

The vertex represents the h and k variables.

Answer:

15 1/3 miles in 23 minutes

(2/3)x in x minutes

Step-by-step explanation:

1 1/2=1.5

2 1/4=2.25

Convert to unit ratio

[tex]1.5/2.25=(2/3)/1[/tex]

2/3*23=46/3

Simplify

15 1/3 miles in 23 minutes

(2/3)x in x minutes

The total time worked by Vernon in decimal hours is 19.50 hours.

Last week, Vernon worked the following days and times:

Therefore, the total time Vernon worked in decimal hours can be calculated as follows:

We have to sum the whole time Vernon worked in the 4 days.

Therefore, we have to convert all the minutes to hours.

total time worked = 5.25 + 6.5 + 3.75 + 4

total time worked = 19.50 hours

Therefore,

total time worked by Vernon = 19.50 hours

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On solving the linear equations we get the result  as

x1   + x2   − 2x3 + 3x4 + 2x5 = 6

3x1 + 3x2 − x3   + x4   + x5   = 12

2x1 + 2x2 − x3   + x4   − 2x5 = 5

4x1 + 4x2 + x3    +0x4 − 3x5 = 16

8x1 + 5x2 − 2x3 − x4   + 2x5 = 29

where ,

x1 =  5,x2 = -1, x3 =  3 ,x4 =  2 , x5 =  1

Finding the value of an equation's unknown variable can be done by solving the equation. If an equation contains a "equal to" sign, it is considered to be balanced. This equation so shows that the two quantities on both sides of it are equal. Left hand side and right hand side are the two sides of the equation (Right hand side).

One equation is x - 4 = 5, for instance. It illustrates that x - 4 (LHS) = 5. (RHS). Here, x is an unknowable quality or variable. Therefore, in order to determine the value of x, we must solve this equation.

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Answer: normal formula define the cup full of is Q -2+ you and me 32,000 you’re welcome

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

the answer is 8

Answer:

8

Step-by-step explanation:

total students=20

boys=2/5×20

=8

Answer: 192 cups

Step-by-step explanation: there's 16 cups in 1 gallon so you would do 2×16=32 to get 32 cups. Then you would do 10×16=160 to get 160 cups. Now add 32+160=192 cups.

Answer: 51.85

Step-by-step explanation: you use the formula given and plug is 25 for t because it is the number of years. So you get 200*e^(-0.054*25) = 51.85

Answer:

A) 2 14/25

Step-by-step explanation:

This is a question of order of operations, which PEMDAS helps describe.

P- parentheses

E - exponents

M, D - multiplication, division

A, S - addition, subtraction

In your problem, you'd start with P, what's in the parentheses.

16 ÷ (2 1/2)²

Then do the exponent, E. It might help to convert 2 1/2 to 5/2.

16 ÷ 25/4

Then divide, D. When dividing fractions, you can flip the numerator and denominator and multiply.

16 x 4/25

= 64/25

Then simplify. 25 goes into 64 two times, and there is 14 left over.

= 2 14/25

Answer:

A

Step-by-step explanation:

Evaluate the sum in the brackets first to give 2.5 and square that to give 6.25

Divide 16 by 6.25 to get A

A parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

The value of x is 5.2.

A parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

UH and FH are the two sides of the diagonal.

UH and FH are equal.

UH = FH

19 = 5x - 7

19 + 7 = 5x

5x = 26

x = 5.2

Thus,

The value of x is 5.2.

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Part a: the rate at which the shadow's tip moves away from the pole while the subject is 25 feet distant is 48/13 ft/sec.

Part b: the speed of the shadow from the speed of the man is 22/13 ft/sec.

A 5 feet 6 inch tall individual is going away from a 12 foot tall pole with a light on top at a 2 foot per second pace.

A) the speed at which the shadow's tip moves away from the pole while the subject is 25 feet distant;

Similar triangles allow us to say:

12/L = 55/(L - x)

Simpllifying,

12(l - x) = 5.5l

12l - 12x = 5.5l

6.5l = 12x

x = (6.5/12)l

Differentiate with respect to time;

dx/dt = (6.5/12)dl/dt or

dl/dt = (12/6.5)(dx/dt)

As, dx/dt = 2

dl/dt = (12/6.5)(2)

dl/dt = 24/6.5

dl/dt = 48/13 ft/sec

B: When a person is 25 feet from a pole, the point of the shadow travelling away from them at:

Subtract the speed of the shadow from the speed of the man.

Therefore,

48/13 - 2 = 22/13 ft/sec.

Thus, the speed of shadow from the speed of the man is 22/13 ft/sec.

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Answer:

Step-by-step explanation:

You want to write exponential functions through the given points.

The exponential function ...

  f(x) = a·b^x

will have the values ...

Using these relations we can write the function from the table values:

  f(x) = 10400·(2600/10400)^x

  f(x) = 10400·(1/4)^x

Then your table is ...

  [tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7}\vphantom{\dfrac{b}{g}}x&-1&0&1&3&4&6\\\cline{1-7}\vphantom{\dfrac{b}{g}}f(x)&41600&10400&2600&162.5&40.625&2.5390625\\\cline{1-7}\end{array}[/tex]

Using the given points in the exponential function form, we have ...

   4.32 = a·b^1

   59.71968 = a·b^4

Dividing the second equation by the first, we find ...

  59.71968/4.32 = b^3   ⇒   b = 2.4

Using this in the first equation, we get ...

  4.32 = a·2.4   ⇒   a = 1.8

The equation of the function is ...

  g(x) = 1.8·2.4^x

The exponential function ...

  y = a·b^x . . . . . . a > 0, b > 0

will be increasing when the growth factor (b) is greater than 1. When 'b' is less than 1, the function will be decreasing.

Sarah's belief is incorrect.

Answer:

[tex]\textsf{1.} \quad f(x)=10400(0.25)^x[/tex]

     (-1, 41600)  and  (3, 162.5)

[tex]\textsf{2.} \quad g(x)=1.8(2.4)^x[/tex]

3.   Sarah is incorrect.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$f(x)=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

The y-intercept is when x = 0.  

Therefore, from inspection of the given table, the y-intercept is 10400:

[tex]\implies a=10400[/tex]

Substitute point (1, 2600) and a = 10400 into the exponential function and solve for b:

[tex]\implies 2600=10400b^1[/tex]

[tex]\implies 2600=10400b[/tex]

[tex]\implies b=\dfrac{2600}{10400}[/tex]

[tex]\implies b=0.25[/tex]

Therefore, the equation of the function is:

[tex]\boxed{f(x)=10400(0.25)^x}[/tex]

Find the value of x when f(x) = 41600:

[tex]\begin{aligned} f(x)&=41600\\\implies 10400(0.25)^x&=41600\\(0.25)^x &=\dfrac{41600}{10400}\\(0.25)^x &=4\\\ln (0.25)^x &=\ln 4\\x \ln (0.25)&=\ln 4\\x&=\dfrac{\ln 4}{\ln (0.25)}\\x&=-1\end{aligned}[/tex]

Find the value of f(x) when x = 3:

[tex]\begin{aligned}x=3 \implies f(3) & =10400(0.25)^3\\& =10400(0.015625)\\& = 162.5\end{aligned}[/tex]

Therefore, the completed table is:

[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} \vphantom{\dfrac12}x & -1 & 0 & 1 & 3 & 4 & 6\\\cline{1-7} \vphantom{\dfrac12}f(x) &41600 &10400 &2600 &162.5 &40.625 & 2.5390625\\\cline{1-7} \end{array}[/tex]

Given points:

Substitute the given points into the exponential formula g(x) = abˣ

[tex]\implies ab=4.32[/tex]

[tex]\implies ab^4=59.71968[/tex]

To find b, divide the equations:

[tex]\implies \dfrac{ab^4}{ab}=\dfrac{59.71968}{4.32}[/tex]

[tex]\implies b^3=13.824[/tex]

[tex]\implies b=\sqrt[3]{13.824}[/tex]

[tex]\implies b=2.4[/tex]

Substitute one of the points and the found value of b into the equation and solve for a:

[tex]\implies 2.4a=4.32[/tex]

[tex]\implies a=\dfrac{4.32}{2.4}[/tex]

[tex]\implies a=1.8[/tex]

Therefore, the equation of the function is:

[tex]\boxed{g(x)=1.8(2.4)^x}[/tex]

Sarah is incorrect.  For an exponential function in the form a · bˣ:

The distance left after x minutes is modeled by the linear equation:

f(x)= 10 - (1/4)*x

The correct option is the last one.

We know that the total distance of the race is 10 kilometers, and the student runs 1 kilometer every 4 minutes, so the student's speed is:

S = 1km/4min = 0.25 km/min

The distance to the finish line is modeled by an equation of the form:

f(x) = total distance - speed*time

Here we know that:

Then the equation is:

f(x)= 10 - (0.25)*x

We can rewrite the decimal as a fraction:

f(x)= 10 - (1/4)*x

The correct option is the last one.

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Answer:

12:52

Step-by-step explanation:

almost every card game has 52 cards, you have a 23% chance to draw a face card of any kind.

There are a king, queen, and jack for each of the four different suits: hearts, spades, clubs, and diamonds. The four suits have 13 cards each, for a total of 52 cards. Therefore, your chance of drawing a face card out of a deck of cards upon choosing the card at random is 12 out of 52, or about 23%.

The speed of the car will be 25.41 m/h

Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector quantity, whereas speed is a scalar quantity

According to the given information

d = [tex]\frac{s^{2} }{10}[/tex] + s

We are given that

distance is 90 feet

So, the expression becomes

90 = [tex]\frac{s^{2} }{10}[/tex] + s

[tex]s^{2}[/tex] + 10s - 900 = 0

which is quadratic in s

So applying the discriminant formula

[tex]$$[/tex]s [tex]=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}[/tex]

[tex]$$[/tex]and then we input the values:

s [tex]=\frac{-10 \pm \sqrt{(10)^2-4(1)(900)}}{2(1)}$$[/tex]

and solve:

s [tex]=\frac{-10 \pm \sqrt{3700}}{2}$$[/tex]

It will have two answers

s = -35.41 m/h

s = 25.41m/h

Speed cannot be negative

So

The speed of the car will be 25.41 m/h

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The volume of the picture is given as 24000 ft square

The surface area of the shape is 5360 ft square

We would have to solve for the volume of a cuboid + the volume of a triangular prism

We are aware that the prism's volume is equal to its base area divided by its length. As a result, the formula Volume of triangular prism = (1/2) bh L is used to get the volume of the prism in this instance.

Such that we would have:  (1/2) bh L

where b = 30

h = 8

L = 50

when we put the values we would have

1 / 2 x 30 x 8 x 50

= 6000

The volume of a cuboid is l x b x h

= 30 x 50 x 12

= 18000

18000 + 6000 = 24000 cubic square

B. The surface area = 2(1/2 x 8 x 30) + 2(17 x 50) + 2(50 x 12) + 2(30 x12) + 950 x 30)

= 5360ft square

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The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

The name of the point located at (4, 3) is X.

Option D is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The coordinates of a point = (4, 3)

Point (4, 3) is located on the graph at point X.

(4, 3) means 4 is on the x-axis and 3 is on the y-axis.

The meeting point is point X.

Thus,

The name of the point located at (4, 3) is X.

Option D is the correct answer.

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The area of the shelf A is 30 square feet

From the question, we have the following parameters that can be used in our computation:

Dimensions = 3 ft and 2 ft

The above parameters mean that

Length = 3 ft

Width = 2 ft

Number of shelves = 5

The area of the shelf A is then calculated as

Area = Number of shelves  * Length * Width

Substitute the known values in the above equation, so, we have the following representation

Area = 5 * 3 * 2

Evaluate the products

So, we have

Area = 5 * 6

Evaluate the products

So, we have

Area = 30

Hence, the area is 30 square feet

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