1. 25 km; cm
2. 3mi; ft
3. 60 min; s

The additive inverse of a complex number is the opposite of the complex number. The complex conjugate of a complex number is which is the real part plus the opposite of the imaginary part of the complex number.

The additive inverse of a number is its opposite number. If a number is added to its additive inverse, the sum of both numbers becomes zero.

When the sum of two real numbers is zero, then each real number is said to be the additive inverse of the other. So, we have R + (-R) = 0, where R is a real number.

A complex conjugate of a complex number is another complex number whose real part is the same as the original complex number and the magnitude of the imaginary part is the same with the opposite sign.

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The length of the yard as calculated from the given data is found out to be as 5 yards long.

let the length of the yard be , 27 - 9x

and the width of the yard is x.

Given , the are of the yard = 360.

Therefore, we can say that

=>x(27 - 9x) = 360

=>27x - 9x² = 360

=> 3x - x²  = 40

=> x²  - 3x + 40 = 0

=>x²  + 5x - 8x + 40 = 0

=> x ( x - 5) -8 ( x - 5 )

Therefore, the value of x will be 5 or 8.

On putting these values in the equation we get that , the length being 5 is the correct answer.

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The value on simplifying the fraction expression 5/6 - 7/12 is obtained as 1/4.

What is a fraction?

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

The fraction expression is given as 5/6 - 7/12.

5/6 - 7/12

First take the LCM of the denominator -

LCM = 12

Now, multiply 2 by 5 in first fraction numerator, as 6 multiplied by 2 is 12 (LCM) -

10/12 - 7/12

Now, use the arithmetic operation of subtraction -

(10 - 7)/12

3/12

Divide numerator and denominator by 3 -

1/4

Therefore, the final value as a fraction is obtained as 1/4.

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A system of two linear equations in two variables has no solution if their graphs c. do not intersect at any point.\

When a system of two linear equations in two variables has no solution, it means that there is no point of intersection between the two lines represented by the equations. This means that the lines are parallel, and do not intersect at any point. This is also known as an inconsistent system. On the other hand, if the two lines intersect at exactly one point, it is a consistent system and has a unique solution. If the two lines are coincident, it will have infinitely many solutions.

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The length of each leg, just divide the hypotenuse, 12 , by the square root of 2. Then to remove the radical from the denominator, multiply both numerator and denominator by square root of 2.

Find the length of each leg?

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To find the distance between two places, we can apply the distance formula d=((x2 - x1)² + (y2 - y1)²).

The distance of an object is its overall motion, regardless of direction.

Distance is the amount of space that an object has covered, regardless of where it began or concluded.

By understanding how far an object is from us, we may calculate its actual size.

It is possible to calculate the area that an object takes up in the sky.

The actual size of an object can then be determined by taking into account its distance.

The further away something is, the smaller it appears.

The distance between two locations on a plane is the length of the line segment connecting them.

The formula d=((x2 - x1)² + (y2 - y1)²) is frequently used to calculate the separation between two points.

Therefore, to find the distance between two places, we can apply the distance formula d=((x2 - x1)² + (y2 - y1)²).

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The total distance cover by Sagar is, 15 km 385 m.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

To reach the Powai lake picnic spot from star apartments,

Sagar went 13 km 665m by bus ,1 km220 m by autorickshaw and 500 m by foot.

Now, Total distance cover by Sagar is,

⇒ 13 km 665 m + 1 km 220 m + 500 m

We know that;

1 km = 1000m

Hence, We get;

⇒ 13665 m + 1220 m + 500 m

⇒ 15,385 m

⇒ 15 km 385 m

Thus, The total distance cover by Sagar = 15 km 385 m.

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The solution to the system of equation 4y + x = 15 and x = 8y + 3 is (11, 1)

An equation shows the relationship between numbers and variables in an expression.

The standard form of a linear equation is:

Ax + By = C

Where A, B and C are constants

Given that:

4y + x = 15

multiply by 2:

8y + 2x = 30    (1)

Also:

x = 8y + 3

8y - x = -3     (2)

Subtract equation 2 from 1 to solve using elimination method:

3x = 33

x = 11

put x = 11 in equation 2:

8y - 11 = -3

y = 1

The solution is (11, 1)

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The introduction of harmful chemicals into the air is known as air pollution.

The chief causes of man-made air pollution include vehicle emissions, fuel oils and natural gas used to heat houses, byproducts of manufacturing and electricity generation, notably coal-fueled power plants, and odors from chemical manufacture.Industrial emissions, automobile emissions, and any other place where fossil fuels are burnt are all sources of atmospheric pollution, or air pollution. Another major contaminant that can cause ozone depletion is methane, which is released by landfills and cattle.

Air pollution can have long-term harmful consequences, such as acid rain, which pollutes the Earth’s bodies of water and ruins infrastructure.

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Answer:

-5

Step-by-step explanation:

4-5=-1

So therefore:

-5+4=-1

If the caffeine in the body drops by 15% each hour then the equation for this problem is [tex]f(t) = 150\times (0.85)^{t}[/tex]  and the equation represents a exponential decay problem .

the amount of caffeine present in the cup of coffee (a) = 150 mg  ;

the percent drop in caffeine in body each hour (r) = 15% = 0.15  ;

Since the percent of caffeine is dropping in the body , the exponential decay function will be used to represent this situation ;

the exponential decay equation is written as : [tex]f(t) = a\times (1-r)^{t}[/tex] ;

substituting the given values of "a" and "r" in the equation ,

we get ;

⇒ [tex]f(t) = 150\times (1-0.15)^{t}[/tex]

⇒ [tex]f(t) = 150\times (0.85)^{t}[/tex]

Therefore , the exponential decay equation is [tex]f(t) = 150\times (0.85)^{t}[/tex] .

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A) The required population sets are

Population set 1 : Women whose mothers took the drug DES during pregnancy.

Population set 2 : Women whose mothers did not take the drug DES during pregnancy.

B) It is a survay not experiment.

C) The estimate of the number of women out of 1,000 who would be expected to have tissue abnormalities is 16 per 1000 people.

D) The estimate of the number of women out of 1,000 who would be expected to have not tissue abnormalities is 8 per 1000 people.

E) Yes, medical studies often use a relatively large sample to represent the population in the best possible way so that results can be more reliable and can be generalized.

The purpose of a research study is that to uncover something hidden or unknown. Because the study does not use the entire set of data, but it consider sample in an appropriate manner to represent the population as accurately as possible. We have a seven-year medical research study : Women whose mothers took the drug DES during pregnancy were twice as likely to develop tissue abnormalities that might lead to cancer as were women whose mothers did not take the drug.

A) Population is defined as the entire group that we want to draw conclusions. In this case, population seta are :

Population set 1 : Women whose mothers took the drug DES during pregnancy.

Population set 2 : Women whose mothers did not take the drug DES during pregnancy.

B) Since, there is no manipulation in the variables has been done, it is not an experiment but a survey.

C.)Consider a sample from population of women whose mothers took the drug DES during pregnancy. Sample size, n = 3980

The number of women who developed tissue abnormalities that might lead to cancer, x = 63

The sample proportion, p = x/n = 63/3980

≈0.0158

A descriptive statistic that used to estimate the number of women out of 1000. So, population who have tissue abnormalities out of 1000,

Required number = 0.0158 ×1000 ≈15.8 ≈ 16

i.e., 16 per 1000 people

D) Now, for the population of women whose mothers did not take the drug DES during pregnancy, the estimate of the number of women out of 1000

1000 who would be expected to have tissue abnormalities can be given as:

Required number ≈ 8 per 1000 people ( because those who took drug have twice the risk).

E) Yes, medical studies often use a relatively large sample to represent the population in the best possible way so that results can be more reliable and can be generalized, which is the main purpose of the medical study.

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You can determine if three variables are linear if their graph forms a straight line when plotted. Additionally, the relationship between the variables should follow a linear equation.

Linearity between three variables can be determined by examining their relationship. If the variables are linearly related, then plotting them on a graph will result in a straight line. Additionally, the relationship between the variables should follow a linear equation, which is a form of an equation where each term is either a constant or the product of a constant and a single variable. To determine if a given equation is linear, you can examine its terms to see if they are all either constants or the product of a constant and the variable. If a variable is raised to a power other than 1, the equation is not linear. In short, if the graph of the three variables forms a straight line and the equation between them is linear, then the variables are linear.

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It is been proved that c(a+b) = ab.

Prove:-

c(a+b) = ab.

it is given that ∠ ABD = ∠ XYD = ∠ CDB = 90°

So, Lines AB, XY, and CD are parallel to Each other.

→ AB || XY || CD

Now In ΔABD, we have,

→ AB || XY

So,

→ DY/BD = c/a

→ DY = (c/a)*BD ----------------------- Equation (1)

In Δ BDC we have

→ CD || XY

So,

→ BY/BD = c/b

→ BY = (c/b)*BD ----------------------- Equation (2)

______________________

Adding Equation(1) and Equation(2) now, we get

→ DY + BY = (c/a)*BD + (c/b)*BD

taking (c * BD) common From LHS, we get,

→ BD = c * BD(1/a + 1/b)

BD will be canceled from both sides,

→ 1/c = 1/a + 1/b

→ 1/c = (a+b)/ab

→ c(a+b) = ab

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The Question is incomplete although I've found a similar question of it.

: Picture attached:

The function that could be used to define and continue this function is f(n) = 1.25n -3

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

Thus, the nth term of arithmetic sequence is given by:

Tₙ  = a + (n-1)d         (for all positive integer values of n)

where a is the first term, n is the number of term and d is common difference

d is the constant difference between each subsequent terms. That is:

d = -0.5 - (-1.75) = 1.25

Tₙ  = -1.75 + (n - 1)1.25

Tₙ  = -1.75 + 1.25n - 1.25

Tₙ  = 1.25n - 3

If we take Tₙ = f(n) , then the function that gives the nth term is:

is f(n) = 1.25n + 3

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Answer:

4x²+4x+3

Step-by-step explanation:

g(f(x))= (2x+1)²+2

= 4x²+4x+1+2

=4x²+4x+3

The area of triangle OPQ is 44 square units.

How to find the area of tringle?

There are different ways to find the area of a triangle, depending on the information given. Here are a few common methods:

There are different methods to find the area of a triangle, but one common method is to use the coordinates of its vertices and the distance formula. The distance formula is

d = √((x2-x1)^2 + (y2-y1)^2)

We can use the distance formula to find the lengths of the sides of the triangle OPQ, which are:

OP = √((8-3)^2 + (3-4)^2) = √((5)^2 + (-1)^2) = √(25+1) = √26

OQ = √((4-3)^2 + (8-4)^2) = √((1)^2 + (4)^2) = √(1+16) = √17

PQ = √((4-8)^2 + (8-3)^2) = √((-4)^2 + (5)^2) = √(16+25) = √41

Once we have the lengths of the sides of the triangle, we can use the Heron's formula to find its area:

s = (OP + OQ + PQ)/2

Area = √(s(s-OP)(s-OQ)(s-PQ))

s = (√26 + √17 + √41)/2 = (√44)/2 = 4√11

Area = √(4√11(4√11-√26)(4√11-√17)(4√11-√41))

Area = √(4√11 * √(44-26) * √(44-17) * √(44-41))

Area = √(4√11 * √18 * √27 * √3)

Area = √(4√11 * 3√2 * 3√3 * √3)

Area = 4*11 = 44 square units

Hence, the area of triangle OPQ is 44 square units.

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Note that the box and whisker plot is attached accordingly and the measure are given as follows:

A box plot is a figure that depicts the distribution of data by showing where the majority of values reside and those values that deviate significantly from the norm, known as outliers. Box plots are sometimes known as box and whisker plots or box and whisker diagrams.

The bottom of the box indicates the first quartile, while the upper side represents the third quartile. As a result, the inter-quartile deviation is represented by the vertical width of the middlebox.

The median is the horizontal line inside the box. The vertical lines projecting from the box extend to the data set's minimum and highest values, as long as these values are not outliers. Two shorter horizontal lines represent the ends of the whiskers.

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The rule of the functions for the ordered pairs will be f(x) = (2/3)².

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values written in parentheses in a specific order. In order to understand a point visually, it can be helpful to locate it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers.

Given that the ordered pairs are (1,2/3), (2,4/9),(3,8/27),(4,16/81) (5,32/243).

x          y

1        2/3        = (2/3)^1

2        4/9        = (2/3)^2

3        8/27      = (2/3)^3

4        16/81    = (2/3)^4

5        32/243  = (2/3)^5

Function rule is f(x) = (2/3)²

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Answer:

1/2x-10

Step-by-step explanation:

[tex]\frac{1}{5} x+\frac{1}{2} (\frac{3}{5}) +\frac{1}{2}(-20)\\\frac{1}{5} x+\frac{3}{10} x-10\\\frac{1}{2} x-10\\[/tex]

Hope this helped! :)

Hey there!

1/5x + 1/2(3/5x - 20)

DISTRIBUTE 1/2 within the PARENTHESES:
= 1/5x + 1/2(3/5x) + 1/2(-20)

= 1/5x + 3/10x - 10

COMBINE the TERMS

= (1/5x + 3/10x) - (10)

= 1/5x + 3/10x - 10

= 1/2x - 10

Therefore, your should be:

1/2x - 10

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

If the factor distributes 5% of its profits as dividends among its 500 shareholders with an equal number of shares, the dividend per shareholder is Rs. 1,200.

Dividends refer to the profits declared for sharing among partners or more specifically among shareholders.

Dividends are a means for repaying shareholders for their shareholding interest in the company.

Companies declare dividends when sufficient profits are generated.

The profit per month = Rs 1,000,000

The total profit for the year = Rs 12,000,000 (Rs. 1,000,000 x 12)

Dividends payout = 5%

Dividends declared = Rs. 600,000 (Rs. 12,000,000 x 5%)

The number of shareholders with equal shares = 500

Dividends per shareholder = Rs. 1,200 (Rs. 600,000/500)

Thus, the dividends per shareholder is the quotient of the total dividends and the number of shareholders.

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The solution for the system of equations is x = -6 and y = 8.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given the equations,

-2x + 5y = 52

x + 4y = 26

solving by elimination method,

multiply by 2 in equation x + 4y = 26

= 2x + 8y = 52

now add both equations,

-2x + 5y + 2x + 8y = 52 + 52

13y = 104

y = 104/13

y = 8

substitute the value of y in equation x + 4y = 26

x + 4(8) = 26

x = 26 - 32

x = -6

Hence the solution of an equation is at x = -6 and y = 8.

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For f(-7), it's 20. For determining x, it's 8.

For f(-7), plug-in -7 to x, and you get -3(-7), which is 21, and minus 1 is 20.

For determining x, plug in 8, you get -3(8), which is -24, minus 1 is -25.

Answer: Probability that she attended class regularly given that she receives A grade is 0.9286.

Step-by-step explanation: i looked it up man ‍♀️

Answer:

Step-by-step explanation:

a

Answer: 20 - 5

Step-by-step explanation:

The given points (3,2) and (2,3) do not represent the same point on the cartesian plane.

A Cartesian plane is defined by two perpendicular number lines: the x-axis, which is horizontal, and the y-axis, which is vertical.

It is named after the French mathematician Rene Descartes, who formalized its application in mathematics.

Any point in the plane can be described by an ordered pair of numbers using these axes.

So, we have the points:

(3,2) and (2,3)

Point P's coordinates are 3 for the x-coordinate and 2 for the y-coordinate.

Point Q's coordinates are 2 for the x-coordinate and 3 for the y-coordinate.

The point is not the same because the coordinates of the two are different.

Therefore, the given points (3,2) and (2,3) do not represent the same point on the cartesian plane.

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Correct question:

Do points (3,2) and (2,3) represent the same point in the Cartesian plane?

The algebraic expression to represent how much time he has left to drive as function is given as f(g) = g - 21.

Given is that Greg will travel on his trip across the country to attend his cousin's wedding. The first day he travels 8 hours. The second day he travels 9 hours. The third day he had mechanical problems and only drove 4 hours.

We can write an algebraic expression to represent how much time he has left to drive as function f(g). We can write -

f(g) = g - (8 + 9 + 4)

f(g) = g - 21

Therefore, the algebraic expression to represent how much time he has left to drive as function is given as f(g) = g - 21.

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The carpenter doesn't have enough tiles to cover up the wall having an area of 40 feet.

When discussing mathematics, the terms "area" and "perimeter" are crucial. This is true regardless of the field's irregular or regular shape. The perimeter is the space surrounding the object. Your home, for instance, has a yard that is enclosed. The fence's length is its perimeter. The fence is 200 feet long if the yard is 50 feet by 50 feet.

A measurement of the volume of an object is its area. To begin a lawn in the same yard, you must have an area. Units of squared distance are used to describe the area. You need 50 x 50, or 2500 square feet, of grass for a 50 ft x 50 ft.

The area of the wall is l × b

= 8 × 5

= 40 feet

As, 40 > 35

Thus, the carpenter doesn't have enough tiles to cover up the wall having an area of 40 feet.

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4times, 2inches occur on the interval 0 < x < 20

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