a) what additional info is needed to prove the triangles are congruent by ASA postulate, explain.

b) what additional info is needed to prove the triangles are congruent by the HL theorem, explain.

Answer:

1) -3^5 + 7x^4 - 15x^2 + 8x + 13

2) 12x^5 + 8x^3 - 2x^2 + 3

3) 9x^2 - 4x + 11

4) 8x^2 + 6x + 11

5) -32a + 12b - 3c

-3^5 + 2x^4 - 7x^2 + 8x + 9 + 5x^4 - 8x^3 + 10x^2 - 3x + 4

Combining like terms, we get:

-243 + 7x^4 - 8x^3 + 3x^2 + 5x + 13

9x^5 + 3x^2 - 6 + 2x^4 + 5x^3 - 4x^2

Combining like terms, we get:

9x^5 + 2x^4 + 5x^3 - x^2 - 6

3x^2 - 6 - 4x^2 + 7x^2 - 4x+11

Combining like terms, we get:

6x^2 - 4x + 5

-2x^2 + 10x^2 - 3x - 4x + 11

Combining like terms, we get:

8x^2 - 7x + 11

-19a + 7b - 8c + 5a - 32b + 23c - 22a + 5b - 20c

Combining like terms, we get:

-36a - 25b - 5c

The value 0.35 as a fraction is 7/20.

In mathematics, fractions are defined as part of a whole. A whole can be an object or a group of objects. In real life, if you cut a pie out of the whole pie, that piece becomes part of the pie. Fractions are words of Latin origin. "Fractus" means "broken" in Latin. In ancient times, rest was expressed in words. Later it was introduced in numerical form.

Fractions are also called parts or sections of any quantity. Represented by the symbol '/'. Bachelor/Bachelor For example, 2/4 is the numerator above and the fraction below the denominator. In this article, you will learn the definition of fractions in mathematics, types of fractions, how to convert fractions to decimals, and many solved examples and full explanations

to convert in fraction we will muliply and devide by 100.

.35*100/100 = 7/20

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The value of the expression is (X -a) (X - b) (X - c) (X - d)……(x-z) = X26 - 26C1 X25a + 26C2 X24a2 - 26C3 X23a3 + .... + (-1)25-1a25-1 + (-1)26a26.

Value of subjective concept that refers to the word of important that an individual group of people places on the something it is often associated with principal beliefs and the standard that are accepted by society when you can be seen as a matter of how important something is true person of organization it is often seen as a reflection of funds for view and can help to save decision.

To find the value of (X -a) (X - b) (X - c) (X - d)……(x-z), we can use the formula of expansion of a binomial expression, which is (x - y) n = xn -nC1 xn-1y + nC2 xn-2y2 - nC3 xn-3y3 + .... + (-1)n-1yn-1 + (-1)n yn.

In this case, n = 26 and x = X, and y = a, b, c, d, …, z. Therefore, the value of the expression is

(X -a) (X - b) (X - c) (X - d)……(x-z) = X26 - 26C1 X25a + 26C2 X24a2 - 26C3 X23a3 + .... + (-1)25-1a25-1 + (-1)26a26.

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The inverse function is:

f⁻¹(x)  = ∛(x + 3) + 2

And the graph can be seen in the image at the end.

We want to find the inverse of the function f(x) = (x - 2)³ - 3

If the inverse is f⁻¹(x), then we know that:

f⁻¹(f(x)) = x

f(f⁻¹(x)) = x

Using the second one we can write:

f(f⁻¹(x)) = (f⁻¹(x) - 2)³ - 3

And that must be equal to x, then:

(f⁻¹(x) - 2)³ - 3 = x

(f⁻¹(x) - 2)³ = x + 3

f⁻¹(x) - 2 = ∛(x + 3)

f⁻¹(x)  = ∛(x + 3) + 2

Now to graph it, we need to find some points, let's evaluate in x = -3, -2, and 5

f⁻¹(-3)  = ∛(-3 + 3) + 2 = 2

f⁻¹(-2)  = ∛(-2 + 3) + 2 = 3

f⁻¹(5)  = ∛(5 + 3) + 2 = 4

So we have the points (-3, 2), (-2, 3), (5, 4), and the graph will be the one at the end.

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The hire purchase plan, regular price $4 049, Warranty $599, interest rate 54% with36 monthly instalments​ is $216.45.

Suppose we're given that:

P_v = Present value of the loan amount

r = rate of interest (compound interest) per period of time

n = number of period of time in which loan is to be paid off

P = A fixed period payment needed to be done for paying off the loan in n number of periods.

Then, we get:

[tex]P = \dfrac{r\times P_v}{1 - (1 + r)^{-n}}[/tex]

We are given that;

Price = $4049

Warranty= $599

Interest rate=54%

Number of installments= 36

Now,

Assuming no down payment, the total cost of the purchase with the warranty is $4,049 + $599 = $4,648.

The interest rate is 54% per annum, which translates to a monthly interest rate of 54%/12 = 4.5%.

Using the formula for the monthly payment in a hire purchase plan:

Monthly payment = Total cost / Number of months / (1 - 1 / (1 + monthly interest rate)^number of months)

Plugging in the values, we get:

Monthly payment = $4,648 / 36 / (1 - 1 / (1 + 4.5%)^36)

= $4,648 / 36 / (1 - 1 / 2.7223)

= $4,648 / 36 / 0.6322

= $216.45

Therefore, the monthly payment in this hire purchase plan will be $216.45.

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The complement of the given event, that all 100 engines are free of defects, is that at least one engine among the 100 shipped has a defect.

The complement of the given event, which is that all 100 engines shipped are free of defects, is the event that at least one engine among the 100 shipped has a defect. The complement represents the event that is the opposite of the given event. In this case, it is the event that at least one engine among the 100 has a defect, which could be described as the event of "failure" or "non-conformance". This is important in probability theory as it allows us to calculate the probability of the complement event and use it to determine the probability of the original event, among other applications.

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Complete question:

When 100 engines are shipped, all of them are free of defects. Select a written description the complement of the given event

A) At most one of the engines is defective.

B) All of the engines are defective.

C) At least one of the engines is defe

D) None of the engines are defective

Answer:

C

...................

A man claims to be capable of extrasensory perception. A fair coin is flipped 25 times as just a test, and the man is asked to predict the outcome ahead of time. He gets 17 of the 25 questions right.

What is the likelihood that he could have performed at least as well if he didn't have ESP?

Let X = the number of correct responses he receives without using ESP (25, 0.5)

p(X = 17) = 1 - p(X = 16)

With n = 25 and p = 0.5, p(X = 16) = 0.9461.

As a result, p(X = 17) = 1 - 0.9461 = 0.0539.

If you don't have Binomial tables, a normal approximation to the Binomial can be used.

X is roughly equal to N(np, npq) = N. (12.5, 6.25)

p(X = 17) = 1 - p(X < 16.5) with a continuity correction = 1 - p(Z (16.5 - 12.5) / v6.25) = 1 - F(1.6) = 1 - 0.9452 = 0.0548

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A number placed in front of a chemical symbol or formula in order to balance the equation is called a coefficient.

In a chemical equation, the coefficients are used to balance the number of atoms on both sides of the equation. The coefficients are placed in front of the chemical formulas or symbols to indicate the number of molecules or atoms involved in the reaction. For example, in the chemical equation for the reaction between hydrogen gas and oxygen gas to form water:

2H2 + O2 → 2H2O

The coefficient "2" in front of the H2O formula indicates that two water molecules are formed in the reaction. The coefficients are adjusted in order to ensure that the number of atoms of each element is equal on both sides of the equation, and that the law of conservation of mass is satisfied.

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Answer:

Step-by-step explanation:

yes

The equation that shows how the total number of science quizzes, y, depends on the number of months that have passed, x is y = 4x.

An equation is a mathematical statement that shows the relationship between two or more values.

In this case, Leon has already had 4 science quizzes this semester and expects to have 4 quizzes per month going forward.

We can use an equation to show how the total number of science quizzes, y, depends on the number of months that have passed, x.

The equation for this would be y = 4x, where x is the number of months that have passed and y is the total number of science quizzes.

This equation shows that for each month that passes, the total number of science quizzes increases by 4

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The surface area of the NBA basketball in terms of π is 87.96π square inches.

What is surface area ?

Surface area is the measure of the total area that the surface of an object occupies. It is a two-dimensional measure of the exposed area of an object, and is typically expressed in square units, such as square inches, square feet, or square meters.

The surface area of an object can be calculated by adding up the areas of all of its individual faces and sides. The exact method for calculating surface area depends on the shape and dimensions of the object in question. For example, the surface area of a cube can be found by multiplying the area of one face of the cube by six, while the surface area of a sphere can be calculated using the formula 4πr².

Surface area is an important concept in mathematics, and has many practical applications in fields such as architecture, engineering, and physics. For example, in architecture, surface area is used to calculate the amount of materials needed to construct a building, while in physics, surface area plays a role in determining heat transfer and other physical properties of objects.

The surface area of a sphere can be calculated using the formula:

Surface Area = 4πr²

where r is the radius of the sphere.

In this case, the radius of the NBA basketball is 4.7 inches. So, we can substitute r = 4.7 into the formula to get:

Surface Area = 4π(4.7)²

Surface Area = 4π(22.09)

Surface Area = 87.96π

Therefore, the surface area of the NBA basketball in terms of π is 87.96π square inches.

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the ball will be traveling downward at a velocity of 24 feet per second after approximately 2.75 seconds.

What is velocity ?

Velocity can be defined as ratio of displacement and time taken.

To find the time when the ball will be traveling downward at a velocity of feet per second, we need to find the time when the velocity is equal to that value, which means the velocity is negative.

The velocity of the ball at any time t can be found by taking the derivative of the height function with respect to time:

v(t) = -32t + 64

We need to find the time t when v(t) = -24 feet per second. So we can set up the equation:

-32t + 64 = -24

Solving for t:

-32t = -88

t = 2.75 seconds (rounded to three decimal places)

Therefore, the ball will be traveling downward at a velocity of 24 feet per second after approximately 2.75 seconds.

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The solution for each parts is shown below.

Where two lines intersect, there are two vertical angles.

Given:

1. Two adjacent angles

<1 + <2 = 135

2x + 2x+ 7 = 135

4x + 7 = 135

4x = 128

x= 32

2. If one of the angles has a measure of 39° then other angle is

= 90 - 39

= 51 degree.

3. The angles are complementary.

2x + 3 + 2x = 90

4. Two complementary angles are expressed as 2x and 3x.

2x + 3x= 90

5x = 90

x = 18

So, 2x = 36 and 3x = 54 degree.

5. Angles j and k are supplementary angles.

<j + <k = 180

<j + 117 = 180

<j = 63

6. Two supplementary angles are ∠ABC=105° and ∠CBD=(3x−24)°.

105 + 3x -24 = 180

3x + 81 = 180

7. Two angles are supplementary. ∠ACB=4x° and ∠BCD=6x+50°.

<ACB + <BCD = 180

4x + 6x + 50 = 180

10x = 130

x= 13

So, <ACB = 4x = 4(13)= 52.

8. For two vertical angles where ∠1=2x+26° and ∠3=3x−32°

<1 = < 3

2x + 26 = 3x -32

2x - 3x = -32 - 26

-x =-58

x= 58

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You can estimate the value of a dependent variable (Y) from a given independent variable (X) using this straightforward linear regression calculator, which uses the least squares method to find the line of best fit for a set of paired data.

You must enter paired data in the two text boxes below, with your independent variable going in the X Values box and your dependent variable going in the Y Values box (either one value per line or as a comma-delimited list).

As an illustration, if you wanted to determine the line of best fit for the relationship between height and shoe size so that you could predict shoe size based on a person's height, height would be your independent variable and shoe size your dependent variable.

This calculator is capable of estimating the value of a dependent variable (Y) given any given independent variable (X) value. Simply enter the X values for which you want to generate an estimate into the Estimate box below (either as one value per line or as a comma-delimited list).

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The lithosphere's reservoir of carbon is approximately 10^5.25 or about 177,828 times greater than the biosphere's reservoir of carbon. Rounding this to the nearest order of magnitude gives an answer of (b) 10⁶.

Carbon is one of the most important elements on Earth as it forms the building blocks for life and plays a crucial role in regulating the planet's climate. The carbon cycle is a complex process that involves the exchange of carbon between different reservoirs such as the atmosphere, oceans, biosphere, and lithosphere.

To compare the size of the carbon reservoirs in the biosphere and lithosphere, we can take the ratio of the two reservoirs:

Lithosphere/Biosphere = 100,005,500/560

Simplifying the expression on the right-hand side gives:

Lithosphere/Biosphere = 178,933.93

To convert this ratio to orders of magnitude, we can take the logarithm base 10 of the ratio:

log10(Lithosphere/Biosphere) = log10(178,933.93)

log10(Lithosphere/Biosphere) ≈ 5.25

Therefore, the lithosphere's reservoir of carbon is approximately 10^5.25 or about 177,828 times greater than the biosphere's reservoir of carbon.

Rounding this to the nearest order of magnitude gives an answer of (b) 10⁶.

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The square root of 12 is approximately 3.464. To calculate the square root of 12, you can use a calculator or manually by using long division or the Babylonian method.

The Babylonian method involves making an initial guess, dividing the number by the guess, averaging the result with the guess, and repeating the process until the desired level of accuracy is achieved. In this case, the process would look like this:

Repeat the process until the desired level of accuracy is achieved.

The square root of 12 is an irrational number, which means it cannot be expressed as a fraction and its decimal representation goes on forever without repeating.

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Step-by-step explanation:

3 is never equal to -27, no matter what we put into the blanks.

I think what you mean is

3 × blank × blank = -27

or simply

blank × blank × blank = -27 (without the 3)

there are 2 different solutions possible :

all 3 blanks are -3.

any 2 blanks are 3, and the third one is -3.

as

-3×-3×-3 = -27

and

3×3×-3 = 3×-3×3 = -3×3×3 = -27

The average of the data set is 275

The range is given as 300

The average would be a summation of the data under the electric vehicle divided by the total number of data in the table

We have 250 + 250 + 250 + 400 + 300 + 300 + 350 + 100 / 8

= 2200 / 8

= 275

The range can be described as the distance that lies between the maximum and the minimum value in a data set

= 400 - 100

= 300

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270 people enter the line for the escalator during" the time interval 0 < / < 300 and  80 people are at Mn Line at time 300. 414.285714 sec. is the first time that there are no people in line for the escalator and 33. 0133 time is the number of people in line minimum.

X(t) = 44 ( t/100)³ * (1-t/300)⁷

for 0≤t≤300

for t≥ 300

a) Total number of people = ∫³⁰⁰₀ r(t)*dt

∫³⁰⁰₀ 44(t/100)³ * (1-t/300)⁷ * dt

∫³⁰⁰₀ (11 (1-t/300)⁷ / 250000 * t³) * dt

∫³⁰⁰₀ -11 / 250000 * (t-300)⁷ * t³ * (1/300)⁷ dt

= -11 (1/300)⁷ / 250000 ∫³⁰⁰₀ (t-300)⁷ * t³ * dt

Now Integrate with respect to 't'

using substitution

Let  u = t-300

du = dt

∫ u⁷ * (u + 300)³ * du

∫ (u¹⁰ + 900 u⁹ +270000 u⁸ + 27000000 u⁷) * du

= u¹¹/11 + 90 u¹⁰ + 30000 u⁹ + 3375000 u⁸

Undo the substitution

u= (t-300)

= [ (t-300)¹¹ / 11 + 90 (t-300)¹⁰ + 30000(t-300)⁹ + 337500(t-300)⁸]³⁰⁰₀

Substitutes the limits

= [0- ((-300)¹¹/ 11 + 90 * (-300)¹⁰ + 30000 * (-300)⁹ + 3375000 * (-300)⁸]

= 270 people

b) Constant rate of 0.7 people per second

This is the rate of exit

at t = 0.20 people in line

People in a line at t = 300 is = 20+ ∫³⁰⁰₀ ((r(t) - 0.7 ) * dt

= 20 + ∫³⁰⁰₀ 44(t/100)³ * (1-t/300)⁷- 0.7 dt

= 20 + 270 - 0.7 * 300

= 80 people

c) t = 300 sec

people = 80

when t>300 , r(t) = 0

rate of exit remains the same

= 80 + ∫ ( 0-0.7) * dx

= 80 + [-0.7x] = 0

= 80 - [0.7x] = 0

= 80 - 0.7 t + 0.7 * 300 = 0

= 80 - 0.7t + 210 = 0

= - 0.7 t = -290

t = 414.285714 sec.

d) f(t) = 20 + ∫⁶₀ (r(x) - 0.7) * dx

f(t) = r(t) - 0.7

f(t) = 0       (for critical point)

r(x) = 44 (t/100)³ * (1-t/300)⁷

r(t) = 0

we get t= 33.0133 sec.

t = 166.575 sec.

Now check for the value

when t=0

f(t) 20

when t= 33.0133

f(t) = 3.803 ≈ 4

when t = 166.575

f(t) = 158.07 ≈ 158

when t= 300

f(t) = 80

so the minimum number of people is 4 at the time t= 33. 0133

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A 90° rotation around the origin characterised the transition.

A logical principle that specifies the circumstances in which one assertion can be legitimately inferred from one or more other statements, particularly in codified languages.

(x, y)(x, y) is the formula for a reflection over the x-axis.

Triangle ABC was changed utilizing the (x, y) rule (–y, x). The triangles' vertices are displayed. A (–1, 1) B (1, 1) C (1, 4) (1, 4) A' (–1, –1) (–1, –1) B' (–1, 1) C' (–4, 1) (–4, 1) Which phrase best sums up the change? A 90° rotation around the origin characterised the transition. A 180° rotation of the origin occurred during the transformation.  The transformation was a 270° rotation about the origin. The transformation was a 360° rotation about the origin.

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Answer: A reflection over the y-axis justifies ∆ABC ≅ ∆A'B'C'.

Step-by-step explanation: Took the test, no thanks neeeded :)

There are 20 many ways can three items be selected from a group of six items.

Here we consider simple random sampling which can be further of two types that are:

With replacement,  when the samples used in previous round of choosing are put back in the population for the upcoming rounds.

When the data are sampled with replacement the number of samples are [tex]N^{n}[/tex], where N is population and n is sample number.

Without replacement, when the samples used in previous round are not returned back in the population for the upcoming rounds of sampling.

When the data are sampled without replacement  there are n P r  or n C r number of items as sample in given set.

The number of ways to select three items from a group of six items can be found using the combination formula:

C(6, 3) = 6! / (3! * (6 - 3)!) = 20

So there are 20 different combinations of three items that can be selected from the group of six items. Here they are listed as three-letter combinations:

ABC, ABD, ABE, ABF, ACD, ACE, ACF, ADE, ADF, AEF, BCD, BCE, BCF, BDE, BDF, BEF, CDE, CDF, CEF, DEF

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The correlation coefficient is a number that measures the strength of the linear association between two numerical variables.

The correlation coefficient is a statistical measure used to determine the strength and direction of the linear relationship between two numerical variables. It ranges from -1 to 1, where values closer to -1 or 1 indicate a stronger correlation, and values closer to 0 indicate a weaker correlation. A negative correlation means that as one variable increases, the other decreases, while a positive correlation means that both variables increase or decrease together. The correlation coefficient is an important tool in many fields, such as finance, economics, and healthcare, where it can help identify patterns and predict future outcomes based on past data.

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The sum of fractions [tex]\frac{1}{4}[/tex] and [tex]\frac{6}{8}[/tex] is equal to one.

Fraction addition teaches us how to combine two or more fractions with the same or different denominators. The addition of fractions is determined by two major factors:
1.Identical denominators
2.Various denominators
If the denominators of two fractions are the same (such fractions are said to be like fractions), they can be added directly. If the denominators are different (such fractions are known as unlike fractions), we must change the denominators and then add the fractions.

If the denominators of two or more fractions are the same, we can simply add the numerators while keeping the denominator constant.
To add fractions with the same denominators, follow the steps below:
1. Add the numerators while keeping the denominator constant.
2.Summarize the fraction.

When two or more fractions with different denominators are added together, we cannot directly calculate the numerators.
To add fractions with different denominators, follow the steps below:
1. Examine the fractions' denominators.
2.Make the fraction denominators the same by finding the LCM of the denominators and rationalising them.
3. Add the fraction numerators while keeping the denominator constant.
4.Simplify the fraction to obtain the final total.

As we have fractions with different denominator first of all we take LCM which is equal to 8.

[tex]\frac{1}{4} + \frac{6}{8} = \frac{2+6}{8} = \frac{8}{8} = 1.[/tex]

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Answer:

Therefore, the product of (5v + 2)(2v - 4) is 10v^2 - 16v - 8.

Step-by-step explanation:

To find the product of (5v + 2)(2v - 4), we can use the FOIL method, which stands for First, Outer, Inner, Last. This method involves multiplying the first terms, then the outer terms, then the inner terms, and finally the last terms, and then adding the resulting terms.

Using the FOIL method, we get:

(5v + 2)(2v - 4) = (5v)(2v) + (5v)(-4) + (2)(2v) + (2)(-4)

Simplifying, we get:

10v^2 - 20v + 4v - 8

Combining like terms, we get:

10v^2 - 16v - 8

Therefore, the product of (5v + 2)(2v - 4) is 10v^2 - 16v - 8.

The volume of each soup can is approximately 785.4 cubic centimeters.

The volume of a cylinder can be calculated using the formula:

Volume =[tex]\pi[/tex] ×[tex]radius^2[/tex]× height

where π (pi) is a mathematical constant approximately equal to 3.14159, the radius is the distance from the center of the circular base of the cylinder to its edge, and height is the vertical distance between the circular bases.

In other words, the volume of a cylinder is the amount of space occupied by the cylinder, and it depends on the size of the circular base and the height of the cylinder.

In this case, the radius of the can is given as centimeters and the height is also given as centimeters. So, we can substitute these values in the formula and calculate the volume:

Volume = π × [tex]radius^2[/tex] × height

Volume = π ×[tex]5^2[/tex] × 10

Substituting radius = 5 cm and height = 10 cm

Volume = 250π cubic centimeters

Volume ≈ 785.4 cubic centimeters (rounded to one decimal place)

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Let a and b be two independent events, if p (a) = 0. 4 and p (a ∪ b) = 0. 64 then the value of the p(b) = 0.4

In this question, we will utilise the notion of independent events and the probability addition rule to determine the probability of event B. The product of the individual probabilities will represent the intersection of independent events.

p(a) = 0.4

p(a∪b) = 0.64

p (a ∩ b) = p(a) x p(b)

p (a ∪ b) = p(a) + p(b) - p(a) x p(b)

0.64 = 0.4 + p(b) - 0.4 x p(b)

p(b) = 0.4

Therefore, the value of the p(b) = 0.4

Independent occurrences are ones whose occurrence is unrelated to any other event. For example, suppose we flip a coin in the air and receive the result Head, then we flip the coin again and obtain the result Tail. The occurrences occur independently of one another in both circumstances. It is one of the several kinds of occurrences in probability.

Let us now look at the whole description of independent events, including a Venn diagram, examples, and how they vary from mutually exclusive events.

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The conversion of 70°F is equal to 21.1°C.

A temperature unit developed from the SI (International System of Units) is Celsius (symbol: °C).

Prior to the adoption of the metric system, Fahrenheit (symbol: °F) was a commonly used measurement of temperature.

To convert 70°F (degrees Fahrenheit) to Celsius (°C), you can use the following formula:

°C = (°F - 32) / 1.8

Substituting 70°F for °F in the formula, we get:

°C = (70 - 32) / 1.8

Simplifying the calculation, we get:

°C = 38 / 1.8

°C ≈ 21.1

Therefore, the conversion of 70°F is nearly equal to 21.1°C.

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