Find the area of the shaded region. Round your answer to one decimal place, if necessary. Note: The figure is not drawn to scale.

Answer:

8

Step-by-step explanation:

The green team has 11 9-year-olds, so the red team has 2 * 11 = 22 10-year-olds.

Since each team has 15 players, the red team has 15 - 22 = -7 more 10-year-olds than the maximum number of players it can have.

Therefore, the red team must have 22 - 7 = 15 - 7 = 8 9-year-olds.

The area of the region inside the curve formed by the given complex number is  28.26 sq. units.

What are complex numbers?

A complex number in mathematics is part of a number system that includes an element with the symbol i, often known as the imaginary unit, to expand the real numbers. The formula a + bi, where a and b are real numbers, can be used to express any complex number.

Given a complex number z.

Let z = a +bi

Then,

[tex]\frac{1}{z} = \frac{1}{a+bi} =\frac{a -bi}{(a+bi)(a-bi)} = \frac{a -bi}{(a^2+b^2)}[/tex]

The real part of the above equation is a / (a²+b²)

This value is given as 1/6.

a / (a²+b²) = 1/6

 (a²+b²) = 6a

 a² - 6a + 9 - 9 + b² = 0

(a - 3)² + b² = 9

This is an equation of a circle with a centre of (3,0) and a radius of 3.

This is the curve formed.

Therefore for the given complex number the area of the region inside the circle = πr² = 3.14 * 3² = 28.26 sq. units

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Answer:

Step-by-step explanation:

If 6/2 = 3 then x/2 = 23.7

Multiply 2 to both sides

then we get x=47.4

μ = 80, σ = 10 represents the parameters of the distribution. Parameters are the characteristics used to define a dataset.

A parameter in mathematics is an element that is transferred from one equation to another. In statistics, it has a different meaning. It's a value that provides information about a population as opposed to a statistic, which provides information about a relatively tiny portion of the population. Because everyone (or everything) was surveyed to determine the parameter, it never changes. For instance, you could be curious about what the average age is in your class. Perhaps you polled everyone and discovered that the median age was 25. That qualifies as a parameter because you polled the entire class. Imagine if you were curious about the average age of the students in your grade or year.

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Answer:

Step-by-step explanation:

We can solve this problem by finding all the perfect squares with square roots that can be expressed in the form a√b, where a and b are integers, and n is greater than or equal to 10, and b is as small as possible.

The first few perfect squares with roots that can be expressed in this form are:

10^2 = 100 = 10√1

13^2 = 169 = 13√1

17^2 = 289 = 17√1

19^2 = 361 = 19√1

23^2 = 529 = 23√1

There are 5 perfect squares in the range n <= 500 with roots that can be expressed in the form a√b. So, the answer is 5.

Answer:

[tex]18x^3-33x^2+20x-4[/tex]

Step-by-step explanation:

Given

[tex](3x-2)^2(2x-1)[/tex]

Lets simplify.

Rewrite [tex](3x-2)^2[/tex] as  [tex](3x-2)(3x-2)[/tex].

[tex](3x-2)(3x-2)(2x-1)[/tex]

Expand using the FOIL method.

Apply the distributive property.

[tex]\left(3x(3x-2)-2(3x-2)\right)(2x-1)[/tex]

[tex](3x(3x)+3x*-2-2(3x-2))(2x-1)[/tex]

[tex](3x(3x)+3x*-2-2(3x)-2*-2)(2x-1)[/tex]

Rewrite using the commutative property and simplify.

[tex](3*3x*x+3x*-2-2(3x)-2*-2)(2x-1)[/tex]

[tex](3*3(x*x)+3x*-2-2(3x)-2*-2)(2x-1)[/tex]

[tex](3*3x^2+3x*-2-2(3x)-2*-2)(2x-1)[/tex]

[tex](9x^2+3x*-2-2(3x)-2*-2)(2x-1)[/tex]

[tex](9x^2-6x-2(3x)-2*-2)(2x-1)[/tex]

[tex](9x^2-6x-6x-2*-2)(2x-1)[/tex]

[tex](9x^2-6x-6x+4)(2x-1)[/tex]

[tex](9x^2-12x+4)(2x-1)[/tex]

Expand by multiplying each term in the first expression by each term in the second expression.

[tex]9x^2(2x)+9x^2*-1-12x(2x)-12x*-1+4(2x)+4*-1[/tex]

Rewrite using the commutative property and simplify.

[tex]9*2x^2x+9x^2*-1-12x(2x)-12x*-1+4(2x)+4*-1[/tex]

[tex]9*2(x*x^2)+9x^2*-1-12x(2x)-12x*-1+4(2x)+4*-1[/tex]

[tex]9*2x^3+9x^2*-1-12x(2x)-12x*-1+4(2x)+4*-1[/tex]

[tex]18x^3+9x^2*-1-12x(2x)-12x*-1+4(2x)+4*-1[/tex]

[tex]18x^3-9x^2-12x(2x)-12x*-1+4(2x)+4*-1[/tex]

Rewrite using the commutative property and simplify.

[tex]18x^3-9x^2-12*2x*x-12x*-1+4(2x)+4*-1[/tex]

[tex]18x^3-9x^2-12*2x^2-12x*-1+4(2x)+4*-1[/tex]

[tex]18x^3-9x^2-24x^2-12x*-1+4(2x)+4*-1[/tex]

[tex]18x^3-9x^2-24x^2+12x+4(2x)+4*-1[/tex]

[tex]18x^3-9x^2-24x^2+12x+8x+4*-1[/tex]

[tex]18x^3-9x^2-24x^2+12x+8x-4[/tex]

Simplify by adding terms.

[tex]18x^3-33x^2+12x+8x-4[/tex]

[tex]18x^3-33x^2+20x-4[/tex]

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They must invest the money in order to purchase the new equipment in 3.5 years.

Simple interest is the calculation of interest for savings or loans that is made only once, namely at the end of the period. Before maturity, no interest is calculated or paid. Simple interest can be used to calculate savings, time deposits and short term loans, i.e. 1 month to 12 months.

For periods longer than 12 months such as 15 and 18 months, simple interest is used very rarely. For long term periods (more than 1 year) such as in the stock market, we use compound interest. So, for simplicity's sake, simple interest is used for the money market or short term.

I = P.r.t

The main equation used for compound interest is SI = P.r.t, which means simple interest or simple interest (I) is the product of P (principal value), r (interest rate), and t (time).

According to the question:

This problem boils down to the time it takes for the original $15,000 to become $2,500 at a 4.75% annual rate. 

We use this formula:

I= p r t

$2,500 = $15,000 (0.0475) t

Find out value of t (the number of years):

t = $2,500 / [$15,000*0.0475]

t=$2,500/ [712.5]

t=3.5 years

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tan(-20°) ≅ -0.364

Trigonometric functions are the functions which relates an angle of right-angled triangle to ratios of two sides of the triangle. It is a real function.

tan(-20°) = - tan(20°)

tan 20° = 0.363970234

tan 20°≅ 0.364

tan (-20°) = -tan 20° ≅ 0.364

Hence, tan(-20°)≅0.364.

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Answer: Y-axis

Step-by-step explanation:

It is reflected across the y-axis , which cam be seem as it goes up

Answer: It's the Y-Axis

Step-by-step explanation:

the green triangle and the orange triangle are flipped from left and right, that means its on the y axis. if it was up and down it would be x axis.

Answer:

OptionB. Graph O

Step-by-step explanation:

Graph O shows She knits one scarf every 4 days which means it is the correct Graph and option B will be the correct answer

The option c yields the greatest balance after 8 years.

The formula for compounding Interest

n times a year :

[tex]A=P(1+\frac{r}{100n})^{nt}\\[/tex]

(a)

Investing $20,000 implies P=20000 and t=8,

interest is compounded daily, which means that n=365 r is given as 6%.

Substitute these values in the formula to get find balance after 8 years,

[tex]20000(1+\frac{6}{100*365})^{365*8}=$ $ 32320.21[/tex]

(b)

$ 30,000 after eight years, is the final balance. Because there is no time left to invest it,

(c)

We get $8000, which we can invest for 8 years,

and we will get $20,000 after 4 years which we can invest for 4 years.

final balance on the $ 8000 invested for 8 years can be found using the formula substitute p=8000, t=8 and r=6%, n=365.

[tex]8000(1+\frac{6}{100*365})^{365*8}=12928.09$[/tex]

final balance on the $ 20,000 invested for 4 years can be found using the formula P=20,000, t=4, and r=6, and n=365.

= 25424.58.

Under the option c, the final balance is 12928.09+25424.58=38352.57

(d)

under this option, we get $ 9000, which we can invest for 8 years.

we will again get 9000 after 4 years, which we can invest for four year,

we will again get

9000 after 8 years, for which we have not invested.

final balance on the 8000 invested for 8 years can be found using above formula p=9000, t=8 and r=6

=14544.1$

final balance of 9000 invest for four years is = 11441.02

total final balance = 34985.12$

Option c yields the greatest balance after 8 years.

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The linear function graphed is defined as follows:

y = 3x/2 - 3.

(third option).

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:

b = -3.

When x increases by 2, y increases by 3, hence the slope m is given as follows:

m = 3/2.

Then the function is defined as follows:

y = 3x/2 - 3.

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The equations of each line are listed below:

Case 5: y = - (1 / 2) · x + 5

Case 6: y = 7

Case 7: y = (1 / 3) · x

Case 8: y = (1 / 3) · x + 2 / 3

Case 9: y = - (5 / 2) · x - 1

Case 10: y = 6 · x - 2

Case 11: x = - 4

Case 12: y = - (3 / 8) · x

In this problem we find eight cases of equations of the line, whose form is described below:

y = m · x + b

Where:

We need to determine the slope and intercept of each line to write the resulting line. Slope of the line is determine by secant line formula:

m = Δy / Δx

Now each line equation is determined below:

Case 5

Slope

m = (0 - 9) / [10 - (- 8)]

m = - 9 / 18

m = - 1 / 2

Intercept

b = y - m · x

b = 5

Equation of the line

y = - (1 / 2) · x + 5

Case 6

Slope

m = 0 (Horizontal line)

Intercept

b = y - m · x

b = 7 - 0 · 0

b = 7

Equation of the line

y = 7

Case 7

Slope

m = [3 - (- 2)] / [9 - (- 6)]

m = 5 / 15

m = 1 / 3

Intercept

b = y - m · x

b = 0 - (1 / 3) · 0

b = 0

Equation of the line

y = (1 / 3) · x

Case 8

Slope

m = (1 - 0) / [1 - (- 2)]

m = 1 / 3

Intercept

b = y - m · x

b = 0 - (1 / 3) · (- 2)

b = 2 / 3

Equation of the line

y = (1 / 3) · x + 2 / 3

Case 9

Slope

m = (- 1 - 9) / [0 - (- 4)]

m = - 10 / 4

m = - 5 / 2

Intercept

b = y - m · x

b = - 1 - (- 5 / 2) · 0

b = - 1

Equation of the line

y = - (5 / 2) · x - 1

Case 10

Slope

m = [- 2 - (- 8)] / [0 - (- 1)]

m = 6

Intercept

b = y - m · x

b = - 2 - 6 · 0

b = - 2

Equation of the line

y = 6 · x - 2

Case 11

x = - 4 (Vertical line)

Case 12

Slope

m = (- 3 - 0) / (8 - 0)

m = - 3 / 8

Intercept

b = y - m · x

b = 0 - (- 3 / 8) · 0

b = 0

Equation of the line

y = - (3 / 8) · x

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Based on the given data:

If the company hire 5 workers in the US to do the same work with the same productivity, the total cost would be $12,175 (fixed cost and labor cost).

From the case, we know that:

Number of worker = 5

Indonesia minimum wage = $2.5 per day per worker

Working hour = 10 hours per day, 6 days per week

Number of shirt produced = 500 per week

Fixed cost = $10,000 per week

Shirt price = $40 per piece

Total labor cost = Number of worker x Minimum wage x working days per week

Total labor cost = 5 x $2.5 x 6

Total labor cost = $75

Labor cost per shirt = Total labor cost : number of shirt produced

Labor cost per shirt = $75 : 500

Labor cost per shirt = $0.15

Total revenue = Number of shirt produced x shirt price

Total revenue = 500 x $40

Total revenue = $20,000

Fixed cost = $10,000

Total profit = Total revenue - Total cost

Total profit = Total revenue - (Total labor cost + Fixed cost)

Total profit = $20,000 - ($75 + $10,000)

Total profit = $9,925

Profit per shirt = Total profit : Number of shirt produced

Profit per shirt = $9,925 : 500

Profit per shirt = $19.85

If the company hires 5 workers in the US to do the same work with the same production capacity and fixed cost, the total cost would be:

Total cost = Total labor cost + Fixed cost

Total cost = (Number of workers x US minimum wage x working hours per day x working days per week) + Fixed cost

Total cost = (5 x $7.25 x 10 x 6) + $10,000

Total cost = $2,175 + $10,000

Total cost = $12,175

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The weighted average of the data is 37.

What is math average?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics.

                            When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

the weighted average = ( 20 *3 + 30 *2 + 50*5 )/3+2+5

                                  = 60 + 60 + 250/10

                                 = 37

Thus, the weighted average of the data is 37.

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If the correlation between two variables is close to 1.0, we cannot conclude that the explanatory variable causes changes in the response variable when the study is observational.

The correlation coefficient, a statistical idea, helps establish a connection between anticipated and actual values discovered through statistical experimentation. How well the expected and actual values match is indicated by the estimated correlation coefficient's value.

In statistics, two variables are said to be causally related if the occurrence of one variable affects or changes the other variable. In this instance, one variable is the cause and the other is the effect.

If the values of the two variables are correlated, meaning that as the value of one changes, the value of the other one does too (although it may be in the opposite direction).

Therefore, since the study is observational, we cannot draw the conclusion that the explanatory variable influences changes in the response variable.

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The value of cosθ is -0.54.

What is a trigonometric function?

The right-angled triangle's angle and the ratio of its two side lengths are related by the trigonometric functions, which are actual functions. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here, we have

Given: If sin( θ - π/2) = 0.54. find the value of cos(- θ).

According to cofunction inequalities

sin( θ - π/2) = -cosθ

cos(- θ) = cosθ

sin( θ - π/2) = 0.54

-cosθ = 0.54

cosθ = -0.54

Hence, the value of cosθ is -0.54.

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The time at which the drone's altitude reach 500 feet is given by the equation T = 15 minutes

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the drone's height at 500 feet be represented as T

Now , the equation for drone's height is given by

h ( t ) = 450 + 50 [ sin ( t - 5 ) π/20 ]   be equation (1)

where , h ( t ) is the height of drone

when height of the drone is at 500 feet

Substituting the value of h ( t ) = 500 in the equation , we get

500 = 450 + 50 [ sin ( t - 5 ) π/20 ]

On simplifying the equation , we get

Subtracting 450 on both sides of the equation , we get

50 = 50 [ sin ( t - 5 ) π/20 ]

Divide by 50 on both sides of the equation , we get

sin ( t - 5 ) π/20 = 1

From the trigonometric relations , sin 90° = 1

So , sin ( π/2 ) = 1

Substituting the values in the equation , we get

sin ( π/2 ) = sin ( t - 5 ) π/20

On further simplification , we get

( π/2 ) = ( t - 5 ) π/20

Multiply by 20 on both sides of the equation , we get

( t - 5 ) = 10

Adding 5 on both sides , we get

t = 15 minutes

Hence , the time required is 15 minutes to reach 500 feet

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The value of x in this proposition would be the first option i.e. [tex]-13\frac{1}{4}[/tex]

4/11= -33/x+5,

to get the value of x we need to get the x to the left hand side,

4(x+5)= -33,

4x+20 = -33.

subtracting 20 from both the sides,

4x= -33-20

4x = -53.

dividing both the sides by 4,

x= -53/4

x= [tex]-13\frac{1}{4}[/tex] ,

which is option A in the given question

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If a is a set of real numbers that is bounded above and b is a set of real numbers that is bounded below, there is at most one real number that can exist in both sets.

A real number is any number that can be expressed as a decimal or fraction and exists on the number line.

If a set of real numbers, represented by a, is bounded above, it means that there exists a real number, represented by M, such that all the numbers in the set are less than or equal to M. Similarly, if a set of real numbers, represented by b, is bounded below, it means that there exists a real number, represented by m, such that all the numbers in the set are greater than or equal to m.

Now, let's consider a real number, represented by x, that exists in both sets a and b. If x exists in a, it must be less than or equal to M and if x exists in b, it must be greater than or equal to m. Hence, x must satisfy both conditions: M >= x >= m.

From these conditions, it can be deduced that M and m must be equal to x. In other words, there can only be one real number that is simultaneously the greatest value in a and the smallest value in b.

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The probabilities are;

(a) 0.5648

(b) 0.3497

(c) 0.0855

The possibility of an event in time is known as probability in mathematics. How frequently does the incidence occur over the course of a specific time period, in plain English?

Given:

A table shows the smoking habits of college students.

a) If a student is chosen at random, the probability of getting someone who is a woman or a heavy smoker is,

= P(woman) + P(heavy smoker) - P(a woman and a heavy smoker)

= 213/386 + 10/386 - 5/386

= 0.5648 to 4 decimal places.

b) If two students are chosen at random without replacement, the probability of getting both who are non-smokers and a man is,

= P(non smoker and man)

= 135/386

= 0.34974093264

= 0.3497

c) If a student is chosen at random, the probability of getting someone who is a regular smoker given the person is a woman is,

= P( regular smoker and a woman)

= 33/386

= 0.08549222797

= 0.0855

Therefore, 0.0855 is the probability.

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The value of x from the given kite is 254.

In Euclidean geometry, a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.

Given that, m∠N=53°, ∠T=67° and m∠F=(1/2 x-8)°

In kite the two angles are equal where the unequal sides meet.

So, m∠W=m∠F=(1/2 x-8)°

Now, m∠N+m∠T+m∠W+m∠F=360°

53°+67°+(1/2 x-8)°+(1/2 x-8)°=360°

120+x-16=360

x=360-104

x=254

Therefore, the value of x is 254.

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Diana is most likely to experience hot flashes, night sweats, and irregular periods as symptoms of menopause.

Menopause is the time in a woman's life when her period stops, usually occurring naturally after age 45. A gap of 12 months without a menstrual period diagnoses menopause. Common symptoms include hot flashes, night sweats, and irregular periods.

Diana is most likely to experience hot flashes, night sweats, and vaginal dryness. These are the most common symptoms of menopause and can start before a woman reaches her 50s. Other symptoms may include mood swings, difficulty sleeping, and changes in libido.

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For the given triangle the value of z = 1, y = 6, and x = 4.75.

One of the earliest areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

The value of x,y, and z will be calculated by the property states that the ratio of the median line passing from the centroid of the triangle is divided into the ratio of 1: 2.

The value of x,

( 2x - 6 ) / 7 = 1 / 2

2 ( 2x - 6 ) = 7

4x - 12 = 7

4x = 19

x = 19 / 4

The value of y,

3 / y = 1 / 2

y = 3 x 2

y = 6

The value of z,

2z / 4 = 1 / 2

4z = 4

z = 1

Therefore, the values are z = 1, y = 6, and x = 4.75.

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The volume when the pressure is 400 mm Hg is  1600  cubic centimeters

From the information given, we have that The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P

This is represented as;

V ∝ 1/P

Find the constant value

V/P = K

Substitute the values

800/200 = k

K = 400

when the pressure is 400 mm Hg, the volume would be; substitute the values, we get;

V/400= 400

cross multiply the values

V = 400(400)

Multiply

V = 1600  cubic centimeters

Hence, the value is  1600  cubic centimeters

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The complete statement is given below.

Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route.

Given:

The graph for Airplane A shows the speed at which it travels as a function of time.

The graph for Airplane B shows the distance it travels as a function of time.

Part A:

From the graph,

the speed for each airplane from 0 to t₁:

Airplane A travels at a speed that is increasing.

Airplane B travels at a speed that is increasing.

Part B:

From the graph,

the speed for each airplane from t₁ to t₂:

Airplane A travels at a speed that is constant.

Airplane B travels at a speed that is constant.

Hence, the solutions are given above.

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The range of values for the width w of the garden is 15 ≤ w ≤ 19

Given the following parameters:

Length of garden = 14 feets

Perimeter must be atleast 58 but no more than 66

The range of value for the width ;

Perimeter = 2 length + 2 width

Perimeter = 2(14) + 2w

If perimeter = 58

58 = 28 + 2w

58 - 28 = 2w

30 /2 = w

w = 15

If perimeter = 66

66 = 28 + 2w

66 - 28 = 2w

38 = 2w

w = 38 / 2

w = 19

Range of the width should be at least 15 and not more Than 19

Hence, the range of the garden is 15 ≤ w ≤ 19

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The restriction on the variable for the given equation is x ≠ 0

A restricted variable is a variable whose values are confined to some only of those of which it is capable.

Given is an equation, -3/x + 8 = 3/4,

In the given equation, -3/x + 8 = 3/4

We see that, x is in denominator, therefore, x ≠ 0,

Therefore, the restriction is x ≠ 0

Finding the value of x,

-3/x + 8 = 3/4

-3/x = 3/4 - 8

-3/x = -29/4

3/x = 29/4

x/3 = 4/29

x = 12/29

Hence, the restriction on the variable for the given equation is x ≠ 0

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