A logarithmic function is defined by f(x) = [tex]log_a[/tex]x(r) y = [tex]log_a[/tex]x, where a > 0 and y = [tex]log_a[/tex]x. It is the inverse of the exponential function [tex]a^{y}[/tex] = x.
During the 16th century, Scottish mathematician, scientist, and astronomer John Napier discovered logarithms. The technique is widely used in astronomical and scientific calculations involving huge numbers. As an inverse of exponential functions, logarithmic functions are closely related to exponential functions. By transforming [tex]a^{x}[/tex] = N into [tex]log_a[/tex] N = x, the exponential function is transformed into a logarithmic function.
Let's say that y=[tex]10^{\log x}[/tex]
see this, 100=[tex]10^2[/tex],
then [tex]log _{10}[/tex] 100 = 2
therefore, [tex]log _{10}[/tex] y=[tex]\log _{10}[/tex] xy = x
[tex]10^{\log x}[/tex] = x
Hence, proved.
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what is the initial value and rate of change in y=3x-5
PLESE HELP
Answer:
the rate of change is 3x(slope)
John deposits $ 8,000 in a certificate of deposit that pays .8% interest, compounded semi-annually. How much interest does the account earn in the first six months? What is the balance after a year.
The required interest earned in the 6 months is $320 and the balance after a year is $8,652.8.
Given that,
John deposits $ 8,000 in a certificate of deposit that pays .8% interest, compounded semi-annually.
Investment is defined as when an individual is spend money on something that returns him or her higher money than the money they or invest.
Here,
Interest earned in the 6 months,
= 8000 [0.08/2]
= $320
Balance after a year,
Amount = principal [1 + rate/n]ⁿ
= 8000[1 + 0.08/2]²
= $8652.8
Thus, the required interest earned in the 6 months is $320 and the balance after a year is $8,652.8.
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Please help me Limited time I’ll give brainliest
Answer: C - I agree
D - Square root 50 lies between integers 7 and 8
E - Find the closest integer to 40
Step-by-step explanation: C - 7/9 will be 0.77777778 which you can simplify to 0.777
D - The square root of 50 is 7.07106781187 so it is between the integers 7 and
E - The square root of 40 is 6.32455532034 which so find the clossest integer to 40
United Parcel Service has contracted you to design an open box with a square base that has a volume of 5000 cubic inches. Express the surface area S of the box as a function of x.
The surface area of the box as a function of x will be f(x) = x² + 20000/x² where x is the length of the square base's edge.
Here it is given that the box has a square base.
This implies that length = breadth
Now, the volume of a box = lbh = 5000 cu in
where l is the length of the box. b is the breadth of the box, and h is the height of the box.
or, x²h = 5000
or, h = 5000/x²
Let the surface area function be f(x) where x is the length of the edge of the square base.
Since the box is open, the surface area will be
lb + 2bh + 2lh
= x² + 10000/x² + 10000/x
= x² + 20000/x²
Hence the surface area as a function of x will be
f(x) = x² + 20000/x²
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find the distance between the two points, round to the nearest tenth (if necessary).
(−2,−5) and (−7,−7)
Leg 1:
Leg 2:
Distance:
The distance between the points A ( -2 , -5 ) and B ( -7 , -7 ) is 5.4 units
What is the distance between two points?
Let the two points be A ( x₁ , y₁ ) and B ( x₂ , y₂ )
The distance from A to B is the same as the distance from B to A
Distance between two points is the length of the line segment that connects the two points in a plane.
The formula to find the distance between the two points is usually given by D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)
This formula is used to find the distance between any two points on a coordinate plane or x-y plane
Given data ,
Let the first point be A ( x₁ , y₁ )
The value of A ( x₁ , y₁ ) = A ( -2 , -5 )
Let the second point be B ( x₂ , y₂ )
The value of B ( x₂ , y₂ ) = B ( -7 , -7 )
Now , the distance between the two points is given by the formula
D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)
where D is the distance
Substituting the values in the equation , we get
Distance D = √ [ ( -7 - (-2) )² + ( ( -7 - (-5) )² ]
On simplifying the equation , we get
Distance D = √ (-7 + 2 )² + ( -7 + 5 )²
Distance D = √ ( -5 )² + ( -2 )²
So , the value of D is
Distance D = √ ( 25 + 4 )
Distance D = √29 units
So , the approximate value of distance D = 5.39 units
Therefore , the value of Distance D = 5.4 units
Hence ,
The distance between the points A ( -2 , -5 ) and B ( -7 , -7 ) is 5.4 units
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what is the value of p
The value of p is 18, it can be find out by using concepts of line and slope of a line.
What is the slope of a line?
Slope of line measures its steepness. Mathematically, its calculated as "rise over run".
Slope of a line : (y2 - y1)/(x2-x1)
In the given que,
given graph equation is of line ,
to find slope of graph : we need to differentiate the equation
[tex]\frac{d}{dx}[/tex](3y + 2x = 7) = 3[tex]\frac{dy}{dx}[/tex] + 2 = 0
So, [tex]\frac{dy}{dx}[/tex] = -2/3
We, if any line are perpendicular then
slope of one * slope of two = -1
So, slope of 1 = (-9-6)/(8-p)
= -15/(8-p)
slope of 2 = -2/3
Now product of both = -15/(8-p) * (-2/3 )
By simplifying all these equation,
we get p = 18.
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simplify. express your answer using positive exponents. (2c7)(9c)
The simplified form of the given expression, (2c7)(9c), is 18c⁸
Simplifying an expressionFrom the question, we are to simplify the given expression
The given expression is
(2c7)(9c)
First, we will write the expression properly
The given expression written properly is
(2c⁷)(9c)
Now, we will simplify the expression
Simplifying the expression
(2c⁷)(9c)
Multiply
2c⁷ × 9c
Collect like terms
2×9 × c⁷ × c
18 × c⁷⁺¹
18 × c⁸
18c⁸
Hence, the expression is 18c⁸
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Need a response bias question. So i have a Statistics project where I need to interview people at my school with a certain response bias question. Can anyone come up with any ideas?? also using random assignment or sample?
Answer:
Response bias would be something where answers would be skewed one way or another because of the way you asked. So maybe ask something embarrassing for someone to admit, like asking random students if they pick their nose. Some people will answer truthfully as no, and the people who do will likely also say no because they do not want to tell you that.
differences on the dependent measure between the levels of one variable within one level of another variable are known as
The differences in dependent measures between levels are the main effects
The differences in the dependent measure between the levels of one variable within one level of another variable are known as simple main effects. These effects can be tested statistically to determine if they are statistically significant, which would indicate that the difference between the levels of the first variable is meaningful within the context of the second variable.
One independent variable having a certain degree of another independent variable is the simple main effect of a factorial experiment. The levels of the other independent variable are averaged over the primary effect of one independent variable. Results for a straightforward main effect are examined as though every level of the other independent variables had its own experiment.
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How do you write 2 4/5 as a decimal?
Answer:
2.8
Step-by-step explanation:
Set aside the 2 for now.
Divide 4÷5=0.8 NOTE: Order Matters!!
Add: 2 + 0.8 = 2.8 (Just put the 2 to the Left of the decimal.)
evaluate.−|a b|2−c when a=4 , b=−1 , and c=−3
When a=4, b=1, and c=3, the value of the given expression, which is |a-b|²-c, is 28.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.
Here,
|a-b|²=(4-(-1))²
=25
25-(-3)
=28
The value of given expression that is |a-b|²-c is 28 when a=4, b=−1, and c=−3.
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A college student is buying a used car for $10,000. The student can either pay in full with cash from savings, or finance the car for 60 months at a monthly compounding interest rate of 5.25%, which results in a monthly payment of $216.57.
How much more is paid over the life of the loan versus paying in cash?
O $2,994.20
O$12,994.20
O $1,082.85
O $11,082.85
Therefore, the student would pay $2,994.20 more over the life of the loan than if they paid in cash.
What is percent?Percent is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". Percentages are commonly used to express ratios, proportions, and rates. They are used in many areas of everyday life, such as in finance, business, and statistics. Some common examples include: Interest rates on loans and credit cards, Discounts on sale items in stores, Tax rates on income or purchases, Probability of events occurring, Performance metrics in sports and other competitions. Percentages can be converted to decimals or fractions for calculations, and vice versa.
Here,
If the student pays in full with cash, the total cost of the car is $10,000.
If the student chooses to finance the car, the monthly payment is $216.57 and the number of months is 60. The total amount paid over the life of the loan is:
Total paid = Monthly payment * Number of months
= $216.57 * 60
= $12,994.20
The amount paid over the life of the loan is the difference between the total paid and the initial cost of the car:
Amount paid over life of loan = Total paid - Initial cost
= $12,994.20 - $10,000
= $2,994.20
The correct answer is option O: $2,994.20.
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In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Meena sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
53 visitors purchased no costume.
151 visitors purchased exactly one costume.
22 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase exactly one costume as a percent to the nearest whole number.
The probability that the next person will purchase exactly one costume is 67%.
How to calculate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.
53 visitors purchased no costume.
151 visitors purchased exactly one costume.
22 visitors purchased more than one costume.
Total visitor = 53 + 151 + 22
= 226
Probability that the next person will purchase exactly one costume will be:
= Those with one custome / Total visitors × 100
= 151 / 226 × 100
= 67%
The probability is 67%.
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Frames-for-All sells framed pictures to hotels and other corporations across the country. Last year, the company sold a total of 720,460 pictures. This year, they sold 972,621 pictures. What is the percent of increase in yearly sales?
Therefore the percentage of increase in yearly sales is 35% by last year.
What is percentage?
Percentage refers to a number that is "out of one hundred." As with fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When utilizing percentages, the total is regarded as being composed of 100 equally sized components. In addition to the abbreviation "pct," which is used less frequently, the symbol "%" is used to denote percentages in numbers.
Here,
the company sold a total of 720,460 pictures Last year.
This year, they sold 972,621 pictures
therefore first we have to find the difference between the last year and this year pictures sold
it comes out to be,
=>972,621-720,460=252,161
Therefore the increase in percentage this year=
=> 252,161/720460 * 100
=>0.35*100
=> 35%
Therefore the percentage of increase in yearly sales is 35% by last year.
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Question attached through files! Can anyone help?? Thank you!
Answer:
(-1.732,0) and (1.732,0)
Step-by-step explanation:
Ignore f(x). The solutions are also called x-intercepts and zeros. So the solutions would be where the parabola crosses the x axis. In my answer ignore the 0 in the coordinates. Just put in the -1.732 and 1.732.
A line intersects the points (4, 3) and (11, -4). What is the slope of the line in simplest form? m = [?]
Answer: M=1
Step-by-step explanation:
hope this help!
1. After a pay raise, Kate's monthly salary increased from $3500 to $3780. Find the percentage increase in her pay raise.
Answer:
8%
Step-by-step explanation:
1. Subtract the larger number from the smaller:
3780 - 3500 = 280
2. Divide the result from step 1 by the FIRST salary amount:
280 ÷ 3500 = 0.08 NOTE: Order Matters!!!
3. Change the decimal to a percent
An ice cream shop sells a small bowl of ice cream for $2.25 and a large bowl for $3. One day, the shop sold 63 bowls of ice cream and made $159. How many of each size bowl did the shop sell?
After using the arithmetic: They sold 40 small bowl of ice cream and 23 large bowl of ice cream.
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the standard operations on numbers—addition, subtraction, multiplication, division, operation, and extraction of roots.
Main body:
Cost of small bowl of ice cream = $2.25
Cost of large bowl of ice cream = $3
Total number of bowls sold = 63
total value = $159
let number of small bowls be x and large bowl be y.
Hence ,
x +y = 63 ---(1)
2.25 x +3 y = 159 ---(2)
from equation 1 substitute the value of x in equation 2 .
2.25 x + 3 (63- x) = 159
2.25 x + 189 - 3x = 159
taking like terms to one side ,
3x - 2.25x = 189-159
0.75x = 30
x = 40
so x = 40 then y = 23.
Hence they sold 40 small bowl of ice cream and 23 large bowl of ice cream.
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four standard six-sided dice are to be rolled. what is the probability that the product of the numbers on the top faces will be prime? express your answer as a common fraction.
The probability of the product of the numbers present on the top faces of all the four six sided dice is equal to 1/108.
As given in the question,
Number of six sided dice to be rolled = 4
Number of outcomes on one dice = 6
Total number of outcomes of 4 dice = 6⁴
= 1296
Conditions for the product of the numbers of top faces all four dice is prime:
Three dice should have 1 on the top face and fourth one should have prime number less than 6.prime number less than 6 are 2, 3, 5.Each prime number will comes on all the four dices top faces.Favourable outcomes are : ( 1, 1, 1,2), (1,1,2,1), (1,2,1,1), (2,1,1,1),
( 1, 1, 1,3), (1,1,3,1), (1,3,1,1), (3,1,1,1),( 1, 1, 1,5), (1,1,5,1), (1,5,1,1), (5,1,1,1)
Total number of favourable outcomes = 12
Required Probability = 12 / 1296
= 1 / 108
Therefore, the probability of the product of all the four numbers on the top faces of the dice is equal to 1/108.
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Figure c is similar by
In the figure of triangles given figure C is not similar
Not similar
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
In figure C no information is given about the angles hence they are not similar.
Figure B is similar by Side - Side - Side (SSS) and shows a proportion of 2
Figure D is similar by Side - Angle - Side (SAS), the include angle here are equal by vertical angle theorem
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Which value of x makes the equation 3-0.5(2x-8)=(3X+28) true
Step-by-step explanation:
In order to solve this equation, you will need to use the following steps:
First, simplify the left side of the equation by performing the operation of multiplying 0.5 and (2x-8) to get 0.5(2x-8)=x-4.
Then, subtract 3 from both sides of the equation to get x-4=3x+28.
Next, subtract 3x from both sides of the equation to get -3x+x-4=28.
Combine the like terms on the left side of the equation to get -2x-4=28.
Add 4 to both sides of the equation to get -2x=32.
Finally, divide both sides of the equation by -2 to get x=16.
Therefore, the value of x that makes the equation 3-0.5(2x-8)=(3x+28) true is 16.
How do you simplify (−2−i)^2?
[tex](-2-i)^{2}[/tex] can be simplified by multiplying the integer by itself.
Multiply the integer by itself.
[tex](a+b)^{2} =a^{2} +2ab+b^{2}[/tex]
[tex](-2-i)^{2} =((-2)^{2}+(-i)^{2})[/tex]
Simplify
[tex](-2)^{2} +2.(-2).(-i)+(-i)^{2}[/tex]
[tex]=4+4i-1[/tex]
Make use of the property [tex]i^{2} =-1[/tex] to decrease the imaginary units.
[tex]4+2i+21i+1(-1)[/tex]
Simplify and use the a+bi formula in standard form.
[tex]3+4i[/tex]
A real number is the result of a complex number and its conjugate. This knowledge will be used to remove the complex number from the given expression's denominator.
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simplify p=sqrt5.2^3
Answer:
11.857
Hope this helps!
Answer: p≈11.86
Step-by-step explanation:
[tex]p=\sqrt{5.2^3} \\\\p=\sqrt{5.2^2(5.2)} \\\\p=5.2\sqrt{5.2}\\\\p\approx5.2(2.28)\\\\p\approx11.86[/tex]
What is the slope-intercept equation for the linear function represented by the
table?
Answer: y= 3/2x - 6
Step-by-step explanation:
The equation is y=mx + b
The y-intercept is when x = 0, so on the table y-intercept = -6
The slope is rise/run, we see that y increase by three and x increase by 2, so the slope is 3/2
to get the slope of any straight line, we simply need two points off of it, let's use those ones in the picture below.
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{3 +3}{4} \implies \cfrac{ 6 }{ 4 } \implies {\Large \begin{array}{llll} \cfrac{3 }{ 2 } \end{array}}[/tex]
now, the y-intercept occurs when x = 0, recheck the picture below.
If the area of an equilateral triangle is
[tex]64 \sqrt{3} cm {}^{2} [/tex]
find its perimeter
The perimeter of the equilateral triangle is 48 cm
How to find the perimeter of an equilateral triangle?equilateral triangle
An equilateral triangle is a type of triangle in which all three sides are equal in length and all three angles are also equal, measuring 60 degrees each.
Given that: the area of an equilateral triangle is 64√3 cm²
The formula for the area of an equilateral triangle is given by:
A = (√3)/4 × a²
Where a is the length of the side
64√3 = (√3)/4 × a²
4 × 64√3 = (√3) × a²
4 × 64 = a²
a² = 4 × 64
a² = 256
a = √256
a = 16 cm
Perimeter of the equilateral triangle = a + a + a = 3a
Perimeter of the equilateral triangle = 3 × 16 = 48 cm
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Which of the following is not a criteria for the construction of a triangle?
A
ASA
B
SAS
C
SSS
D
AAA
Answer:
D) AAA
Step-by-step explanation:
has mean 20.2 years and standard deviation 1.60 years. of all of those enrolled in the course, 54 percent are men and 46 percent are women. what is the mean age of the combined distribution of both men and women in the course?
The mean age of the combined distribution of both men and women in the course is 20.47 years
What is average/mean ?
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.
Mean age of men , M = 20.7 years
Mean age of Women , W = 20.2 years
Percentage of Men = 54%
Percentage of Women = 46%
Recall, :
Mean, μ = np
The mean age of men in the distribution = (20.7 × 54%) = 11.178 years
The mean age of women in the distribution = (20.2 × 46%) = 9.292 years
The mean age of the combined distribution is :
11.178 + 9.292 = 20.47 years
Therefore, the mean age of the combined distribution is 20.47 years
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find the common ratio.
1\text{,}2\text{,}4\text{,}8\text{,}16\text{,}..1,2,4,8,16,...
48\text{,}12\text{,}4\text{, }2\text{,}..48,12,4, 2,...
The common ratios of the sequence are 4 and 1/4
How to calculate the common ratioFrom the question, we have the following parameters that can be used in our computation:
Sequence 1
1, 2, 4, 8, 16,...
The common ratio is the quotient of a term and the previous term
Using the first term and the second term, we have
Common ratio = Second term/First term
Substitute the known values in the above equation, so, we have the following representation
Common ratio = 2/1
Evaluate
Common ratio = 2
Sequence 2
Here, we have
48, 12, 4, 2,...
The common ratio is the quotient of a term and the previous term
Using the first term and the second term, we have
Common ratio = Second term/First term
Substitute the known values in the above equation, so, we have the following representation
Common ratio = 12/48
Evaluate
Common ratio = 1/4
Hence, the common ratio is 1/4
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. A study was conducted to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction. With a substrate concentration of 1.5 moles per liter, the reaction was run 15 times, with an average velocity of 7.5 micromoles per 30 minutes and a standard deviation of 1.5. With s substrate concentration of 2.0 moles per liter, 12 runs were made, yielding an average velocity of 8.8 micromoles per 30 minutes and a sample standard deviation of 1.2. Is there any reason to believe that this increase in substrate concentration causes an increase in the mean velocity of the reaction of more than 0.5 micromole per 30 minutes? Use a 0.01 level of significance and assume the populations to be approximately normally distributed with equal variances.
At the significance level, 0.01
p-Value=0.973 > 0.01 which implies fail to reject null hypothesis and no evidence to support the claim.
So, there is no reason to believe that this increase in substrate concentration causes an increase in the mean velocity of the reaction of more than 0.5 micromole per 30 minutes.
We have given that,
A study conducted to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction.
x₁-bar = 8.8 micromoles
Standaard deviations, s₁= 1.2
x₂-bar = 7.5 ; s₂ = 1.5
n₁ = 12 ; n₂ = 15
significance level = 0.01
Consider the Null hypothesis and alternative hypothesis othesis
H₀ : μ = 0.5
Hₐ : μ > 0.5
Consider,
Pooled Standard Deviation = √(((n₁ - 1)s₁² + (n₂- 1)s₂²)/(n₁ + n₂-2))
plugging all known values
= sqrt(((12-1)(1.2²) + (15 -1)(1.5²))/(12+15-2))
Sp = 1.3761
Now , test statistic :
t =((x₁-bar - x₂-bar) - 0.5) / (Sp×√(1/n₁+ 1/n₂))
substitute all known values we get,
= ((8.8 - 7.5) - 0.5) / (1.3761× sqrt(1/12 + 1/15))
=> t = 1.5
Degree of freedom = n₁+ n₂ - 2
= 12 + 15 - 2
= 25
Now the p-value corresponding to t = 1.5 & df = 25 is 0.073
Here p-value > 0.01 (significance level) thus, we fail to reject null hypothesis.
So there is no enough evidence to support the claim.
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the odds of a particular event occurring is 0.66. determine the probability as a decimal rounded to the nearest hundredth.
The probability of odds as a decimal rounded to the nearest hundredth is 0.398.
The probability of odds is given by the formula -
Probability of odds = probability odds ÷ probability (1 + odds)
Probability odds = 0.66
Probability (1 + odds) = 1 + 0.66
Performing addition on Right Hand Side of the equation
Probability (1 + odds) = 1.66
Keep the values in formula to find the probability of odds
Probability of odds = 0.66/1.66
Performing division on Right Hand Side of the equation
Probability of odds = 0.398
Hence, the probability of odds is 0.398.
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