Find the value of each variable provide proofs

Answer: The likelihood of randomly selecting a gold coin from the box is "Likely."

When the probability of an event is 50%, it means that there is an equal chance of the event happening or not happening. In this case, the probability of randomly selecting a gold coin from the box is 50%, so it is likely to occur.

Step-by-step explanation:

The inverse function is  v⁻¹ = ( v/T)^1/3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that the formula of the volume of the sphere is,

⇒ v = 4/3 πr³

T = 4/3π

Now,

To determine the inverse function we can solve the formula for the term r as;

⇒ v = 4/3 πr³

Multiply by 3/4 we get;

⇒ 3v/4 = πr³

Divide by π both side, we get;

⇒ 3v/4π = r³

Substitute r = v⁻¹ in above equation, we get;

⇒  v⁻¹ = ( v/T)^1/3

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The simplification process of the expression 6(4y+8)−2y involves distributing '6' to '4y' and '8', and then combining like terms, yielding the simplified expression as 22y+48.

To rewrite the given expression in simplest terms, distribute the 6 to the terms inside the parentheses:

Now subtract 2y:

So, the expression 6(4y+8)−2y can be simplified to 22y + 48.

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An octant's main features are :

An octant is formed by three perpendicular axes, labeled X, Y, and Z. These axes intersect at a common point called the origin. Each octant contains both positive and negative values along the X, Y, and Z axes. The positive region is located on one side of each axis, while the negative region is on the other side.

Each of the three axes divides an octant into two quadrants. These quadrants are numbered from 1 to 8, with quadrant 1 being in the positive X, Y, and Z regions and quadrant 8 being in the negative X, Y, and Z regions.

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Answer: Rational functions are defined as the ratio of two polynomials. A rational function has the most solutions in common with the function y = 2x + 6 if their graphs intersect at the most points.

If a rational function has the same degree as the polynomial function y = 2x + 6, which is degree 1, and has a leading coefficient that is the same sign as the leading coefficient of y = 2x + 6, then their graphs will intersect at the most points.

One such rational function that has the same degree as y = 2x + 6 and has a leading coefficient that is the same sign is:

y = (2x + 6) / 1

So the rational function y = (2x + 6) / 1 has the most solutions in common with the function y = 2x + 6.

Step-by-step explanation:

The method that can be used to prove that the triangles are congruent is B. AAS.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

There are two angles in the two triangles that are shown to be equal and there is also a side of one triangle that is equal to anther side. These triangles are therefore congruent.

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The prime factorization of 51 is 3 * 17.

Answer: The original price of the lawn mower was $649

Step-by-step explanation:

If Joaquin bought the lawn mower for $519.20 after a 20% discount, it means that he paid only 80% of the original price. We can use this information to calculate the original price of the mower by setting up the following equation:

0.8x = 519.20

where x is the original price of the lawn mower. To solve for x, we can divide both sides of the equation by 0.8:

x = 519.20 / 0.8

x = $649

The population of the town after 10 years is expected to be about 12766

We can use the formula for exponential decay to find the population of the town after 10 years.

The formula is:

P = P₀ * (1 - r)^t

Substituting the given values into the formula, we get:

P = 25000 * (1 - 0.065)^10

Simplifying and evaluating using a calculator:

P = 12766

Hence, the population is expected to be about 12766 .

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Answer:

x > 6

Step-by-step explanation:

4(3x+2) < 5(3x-2)

12x+8 < 15x-10

12x-15x < -10-8

-3x < -18

3x > 18

x> 6

Answer:

efgdfhncdrt gguhd r g sixtieth sex

Answer: You sold 16 bracelets and 21 necklaces

Step-by-step explanation

X# Bracelets        x+y=37     -2(x+y=37)     -2x-2y= -74      x+21=37

Y# Necklaces      2x+3y=95     [tex]\frac{+(2x+3y=95)}{y=21}[/tex]          x=16

              You sold 16 bracelets and 21 Necklaces

To select a sample of 50 students at your school in order to learn something about how many hours per week, on average, students at your school spend engaged in a particular activity, you could use random sampling.

Random sampling involves selecting a sample of individuals from a larger population in a way that ensures each individual has an equal chance of being selected. This helps ensure that the sample is representative of the larger population and can provide accurate results.

Here are the steps you could follow to select a random sample of 50 students at your school:

1. Obtain a list of all the students at your school. This could be a roster or a directory.
2. Assign each student a unique number.
3. Use a random number generator to select 50 numbers from the list of student numbers.
4. Select the students whose numbers were chosen by the random number generator as your sample.

By following these steps, you can ensure that your sample is randomly selected and representative of the larger population of students at your school. This will allow you to accurately estimate how many hours per week, on average, students at your school spend engaged in a particular activity.

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Product of multiplication of (2+√-25) and (4-√-100) is 58.

Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1).

For example, 6+7i is a complex number, where 6 is a real number and 7i is an imaginary number.

Given complex numbers

(2+√-25) and (4 -√-100)

√-25 = √(5² . -1) = 5√-1

i = √-1

√-25  = 5i

√-100 = √(10² . -1)

√-100 = 10i

Multiplying both numbers

(2+√-25) . (4 -√-100)

then

= (2 + 5i) . (4 - 10i)

Using FOIL method

(a + b)(c + d) = ac + ad + bc + bd

= 8 - 20i + 20i - 50i²

= 8 - 50i²

i² = -1

= 8 + 50

= 58

Hence, 58 is the product of multiplication of (2+√-25)(4-√-100)

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The median of all possible values of x is 5.

A triangle is a three-sided polygon that consists of three edges and three vertices.

To find the median of all possible values of x, we need to find all the possible values of x first.

By the triangle inequality, we know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, we can write:

2 + 5 > x

2 + x > 5

5 + x > 2

Simplifying each inequality, we get:

7 > x

x > 3

x > -3

The smallest possible integer value for x is 4 and the largest possible integer value for x is 6.

Therefore, the possible integer values for x are 4, 5, and 6.

Since we have an odd number of values, the median is simply the middle value, which is 5.

Therefore, the median of all possible values of x is 5.

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The formula for Van 't Hoff's law, which is also known as the law of osmotic pressure, is: П = iMRT, where: Π is the osmotic pressure of the solution,

i is the van 't Hoff factor, which is a measure of the number of particles a solute molecule dissociates into in solution, M is the molar concentration of the solute, R is the gas constant, and T is the absolute temperature. Van 't Hoff is a term used to refer to a Dutch chemist named Jacobus Henricus van 't Hoff, who was known for his work on solutions, chemical equilibrium, and the laws of thermodynamics. To find Van 't Hoff, you can do any of the following: Research: You can learn about Van 't Hoff by doing research on his life and work. There are many online and offline resources available that provide information about his contributions to chemistry and his scientific achievements. Education: If you are a student of chemistry, you are likely to encounter Van 't Hoff's name in your coursework. You can learn about his theories and concepts in your chemistry classes or by consulting your textbooks. Application: You can apply Van 't Hoff's laws and principles in solving problems related to chemical equilibrium, colligative properties of solutions, and other thermodynamic concepts. This may involve using mathematical formulas and equations that are based on his work. In summary, Van 't Hoff refers to a Dutch chemist known for his work in thermodynamics, solutions, and chemical equilibrium. You can learn about his contributions to chemistry through research, education, and application of his principles in problem-solving.

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Answer:

125 children play tennis and golf

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Class 11

>>Applied Mathematics

>>Number theory

>>Complex Numbers

>>The complex number z satisfying the equa

Question



The complex number z satisfying the equations ∣z∣−4=∣z−i∣−∣z+5i∣=0, is

This question has multiple correct options

A

3−i

B

23−2i

C

−23−2i

D

0

Medium

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Updated on : 2022-09-05

Solution



Verified by Toppr

Correct options are B) and C)

We have two equation ∣z∣−4=0 and ∣z−i∣−∣z+5i∣=0

Putting z=x+iy i.e x2+y2=16    ....(1)

and ∣x+iy−i∣=∣x+iy+5i∣

⇒x2+(y−1)2=x2+(y+5)2

⇒y=−2   ...(2)

Putting y=−2 in (1), 

x2+4=16⇒x=±2

Step-by-step explanation:

Hence the complex numbers z satisfying the given equation are 

z1=23−2i and z2=−23−2i

The value of x the given parallelogram a rhombus is 18

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

The quadrilateral that is a rhombus

The diagonals of rhombus bisect each other

Using the above as a guide, we have the following:

Angle 1 = A

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

5x - 30 = 3x + 6

Evaluate

2x = 36

Divide

x = 18

Hence, the value is 18

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Answer:

32.4

Step-by-step explanation:

8% of 30 is 2.4. So, 2.4 + 30 is 32.4.

The coordinates of the triangle after the dilation of k = 2 is given by

A' ( 4 , 8 ) , B' ( 6 , 14 ) and C' ( 14 , 8 )

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

Given data ,

Let the triangle be represented as ABC

Now , let the dilated triangle be represented as A'B'C'

And , the coordinates of the triangle ABC are

The coordinate of A = A ( 2 , 4 )

The coordinate of B = B ( 3 , 7 )

The coordinate of C = C ( 7 , 4 )

And , the dilation factor k = 2

So , the new coordinates of the dilated triangle are

The coordinate of A' = A' ( 4 , 8 )

The coordinate of B' = B' ( 6 , 14 )

The coordinate of C' = C' ( 14 , 8 )

Hence , the triangle is dilated by a scale factor of 2

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The probability of rolling a 5 and then 6 is 1/36

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

Number cube rolled twice

The sample space of each number cube is

Sample space = {1. 2. 3. 4. 5. 6}

From the above entries, we have

P(5) =1/6

P(6) = 1/6

Using the above as a guide, we have the following:

P = 1/6 * 1/6

Evaluate

P = 1/36

Hence, the probability is 1/36

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Answer:

3x - y - 2 = 0

Step-by-step explanation:

The line-3x - 9y - 12 is given in the general form of the equation of a line, Ax + By + C = 0, where A = -3, B = -9, and C = -12.

To find the equation of the line that passes through the point (2, -8) and is perpendicular to the line-3x - 9y - 12, we need to find the slope of the perpendicular line. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.

The slope of the line-3x - 9y - 12 can be found using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Rearranging the general form equation:

-3x - 9y - 12 = 0

9y = 3x + 12

y = (3/9)x + 4

The slope of the line is m = 3/9. To find the slope of the perpendicular line, we find the negative reciprocal:

m_perpendicular = -1 / (3/9) = -9 / 3

We have the slope of the perpendicular line, now we need to find its equation. To do this, we use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where (x1, y1) is the point through which the line passes and m is the slope of the line. Plugging in the values for the point (2, -8) and the slope -9/3:

y - (-8) = -9/3 (x - 2)

y + 8 = -3x + 6

3x - y - 2 = 0

Leo needs to pay back a total of $215 in two weeks.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Leo takes out a payday loan for $200 to cover some of his rent and will pay it back when he gets his paycheck and the lender charges $15 for every $100.

Now, (15/100)×100% = 15%.

Therefore, He has to pay back,

[(100 + 15)/100]×200.

= (115/100)×200.

= 1.15×200.

= $230.

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The equation most closely approximates C is C(x) = 22p+ 18.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that function, C calculates the number of calories recommended per day for a dog based on the dog's weight in pounds.

The equation can be written as:-

C(x) = 22p+ 18.

Here the dependent variable is C(x) and the dependent variable is p. So the value of C(x) will always depend upon the variable p.

Therefore, the correct equation will be C(x) = 22p+ 18.

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Step-by-step explanation:

n=5+3p

when p=26,

n=5+3×26=83

The value of the exponential equation is A = 5/3

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = [ 2²⁰¹⁴ + 2²⁰¹² ] / [ 2²⁰¹⁴ - 2²⁰¹² ]   be equation (1)

On simplifying the equation , we get

Taking the common factor as 2²⁰¹² , we get

A = 2²⁰¹² [ 2² + 1 ] / 2²⁰¹² [ 2² - 1 ]

On further simplification , we get

A = ( 2² + 1 ) / ( 2² - 1 )

A = ( 4 + 1 ) / ( 4 - 1 )

A = 5/3

Therefore , the value of A is 5/3

Hence , the equation is A = 5/3

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The quotient of the division is 3x - 11 with a remainder of 37x + 21

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

Divide 3x³ - 2x² + 4x - 3 by x² + 3x + 3.

Using the long division method of quotient, we have

x² + 3x + 3 | 3x³ - 2x² + 4x - 3

The division steps are as follows

                    3x - 11

x² + 3x + 3 | 3x³ - 2x² + 4x - 3

                    3x³ + 9x² + 9

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

                               -11x² + 4x - 12

                               -11x² - 33x - 33

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

                                           37x + 21

Hence, the quotient is 3x - 11

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