The probability that a randomly selected Atlantic cod has a length of 39.08 cm or more is 0.9981. The probability that a randomly selected Atlantic cod has a length of 59.08 cm or less is 0.9935. The probability that a randomly selected Atlantic cod has a length between 39.08 and 59.08 cm is 0.9914. The probability of a randomly selected Atlantic cod having a length that is at least 62.99 cm is 0.0002. 48% of all Atlantic cod have a length of more than 50.25 cm.
a) The random variable is the length of a sample of Atlantic cod, denoted by X.
b) The probability that a randomly selected Atlantic cod has a length of 39.08 cm or more can be found using the standard normal distribution table or a calculator. We first standardize the value of 39.08 using the formula
z = (x - μ) / σ, where μ is the mean length and σ is the standard deviation.
Therefore, z = [tex](\frac{39.08- 49.9}{ 3.74 } )[/tex]= -2.89.
From the standard normal distribution table, the probability of a z-score less than or equal to -2.89 is 0.0021.
Thus, the probability of a randomly selected Atlantic cod having a length of 39.08 cm or more is 1 - 0.0021 = 0.9981.
c) The probability that a randomly selected Atlantic cod has a length of 59.08 cm or less can be found using the same method as in part (b).
Standardizing the value of 59.08, we get z = [tex](\frac{59.08- 49.9}{ 3.74 } )[/tex]= 2.45.
Using the standard normal distribution table, the probability of a z-score less than or equal to 2.45 is 0.9935. Thus, the probability of a randomly selected Atlantic cod having a length of 59.08 cm or less is 0.9935.
d) The probability that a randomly selected Atlantic cod has a length between 39.08 and 59.08 cm can be found by subtracting the probability in part (b) from the probability in part (c).
Thus, P(39.08 < X < 59.08) = P(X ≤ 59.08) - P(X ≤ 39.08) = 0.9935 - 0.0021 = 0.9914.
e) The probability that a randomly selected Atlantic cod has a length that is at least 62.99 cm can be found using the same method as in parts (b) and (c).
Standardizing the value of 62.99, we get z = [tex](\frac{62.99- 49.9}{ 3.74 } )[/tex] = 3.49.
Using the standard normal distribution table, the probability of a z-score less than or equal to 3.49 is 0.9998.
Thus, the probability of a randomly selected Atlantic cod having a length that is at least 62.99 cm is 1 - 0.9998 = 0.0002.
f) Yes, a length of 62.99 cm is unusually high for a randomly selected Atlantic cod because the probability of having a value of length at least that high is less than or equal to 0.05.
g) To find the length that 48% of all Atlantic cod have more than, we need to find the z-score that corresponds to a cumulative probability of 0.52 (1 - 0.48).
Using the standard normal distribution table, we find that the z-score is approximately 0.10.
Then, we use the formula z = (x - μ) / σ to solve for x, where μ = 49.9 and σ = 3.74.
Thus, x = μ + σz = 49.9 + 3.74(0.10) = 50.25 cm.
Therefore, 48% of all Atlantic cod have a length of more than 50.25 cm. The units for length are in centimeters.
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what is the value of the expression
2/-3 x -1/5
Sophia, Malcolm, and Oren are playing a money game. Their bank
balances are shown in the table. Complete the table by writing the
absolute value of each bank balance to show how much each
player owes. Who owes the greatest amount?
Bank Balance Amount Owed
-$150
- $325
- $275
Answer:
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Bank Balance | Amount Owed
---------------------|-------------
-$150 | $150
-$325 | $325
-$275 | $275
To find the amount owed, we simply take the absolute value of each bank balance. The player who owes the greatest amount is the one with the largest absolute value bank balance. In this case, that would be Malcolm, who owes $325.
Step-by-step explanation:
If the slope of a line is 5/8 and the run of a triangle connecting two points on the line is 16, what is the rise?
The rise of the line that has a slope of 5/8 and a run of 16 is calculated as: 10.
What is the Slope of a Line?The slope of a line is defined as the ratio of the rise of the line to the run of the line. This can also be defined as change in y over the change in x of a line.
Given the following:
Slope of a line (m) = 5/8
Run of the triangle = 16
Rise = x
Using the slope formula, we have:
Slope of a line (m) = rise/run
5/8 = x/16
Solve for x:
x = (5 * 16) / 8
x = 80/8
x = 10
Therefore, we can conclude that the rise is 10.
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The functions f(x)=−34x+214 and g(x)=(12)x+1 are shown in the graph. What are the solutions to −34x+214=(12)x+1? Select each correct answer.
The graphs cross at x=-1 and x=1. Those are the solutions to to the equation
How to explain the graphWe know that, If two functions are equal then there solution is the intersection point of the curves.
When we determine the graph the intersection points are (0,2) and (1,1.25).
The values of x of the intersection points are the solutions of the system
Using a graphing tool, there are two intersection points and therefore the solutions are x = -1 and x [ 1.
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frankie has a new cell phone plan. he will pay a one-time activation fee of 30$, and 45$ each month. which equation can be used to determine the total amount, t, Frankie will have spent after m months on his cell phone plan
The equation which can be used to determine the total amount, t, Frankie will have spent after m months on his cell phone plan is t = 30 + 45m.
Given that,
Frankie has a new cell phone plan.
He will pay a one-time activation fee of 30$, and 45$ each month.
One time activation fee = $30
Amount each month = $45
Amount for m months = 45m
Total amount for the plan = 30 + 45m
If t represents the total amount for the cell phone activation plan, the required equation can be written as,
t = 30 + 45m
Hence the required equation for the cell phone plan is t = 30 + 45m.
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Researchers studying osteoporosis (bone loss) suspected that women over the age of 50 in the United
States are diagnosed with the disease more often than women over 50 in Mexico. They took a random
sample of 200 women over the age of 50 from each country. Here are the results:
Diagnosed with osteoporosis? US. Mexico
Yes. 40. 20
No 160 180
Total 200. 200
The researchers want to use these results to test He: pus - PM = 0 versus H₂: Pus-PM > 0.
Assume that all conditions have been met.
What is the P-value associated with these sample results?
a. P-value is greater than or equal to
0.20
b. 0.05 is less than or equal to the P-
value < 0.10
c. 0.10 is less than or equal to the P-
value < 0.20
d. P-value < 0.01
e. 0.01 is less than or equal to the P-
value < 0.05
Answer:
A P-value < 0.01
Step-by-step explanation:
An amount is increased by 20% 40% of the new amount is 288 Work out the original amount.
What is the coefficient of x^3 term in the power series expansion (or Taylor's expansion) of f(x) = e^(x) sin(x)
The coefficient of x³ term in the power series expansion of f(x) = [tex]e^x[/tex] sin(x) is 1/15.
To find the coefficient of x³ term in the power series expansion of f(x) = [tex]e^x[/tex] sin(x), we need to write the Taylor series for [tex]e^x[/tex] and sin(x) and then multiply them to get the Taylor series for f(x). The Taylor series for e^x is:
[tex]e^x[/tex] = 1 + x + (x²/2!) + (x³/3!) + ...
The Taylor series for sin(x) is:
sin(x) = x - (x³/3!) + (x⁵/5!) - ...
Multiplying these two series, we get:
f(x) = [tex]e^x[/tex] sin(x) = (1 + x + (x²/2!) + (x³/3!) + ...) × (x - (x³/3!) + (x⁵/5!) - ...)
Expanding this out and collecting the terms with x³, we get:
f(x) = x - (x³/3!) + (7x³/5!) + ...
Therefore, the coefficient of x³ term in the power series expansion of f(x) = [tex]e^x[/tex] sin(x) is -1/6 + 7/120 = 1/15.
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suppose you are interested in using regression analysis to estimate an nba player's salary using the following independent variables: the player was traded in the last 5 years, player's age, player's height, career free throw percentage, average points per game, and the team had greater than 45 wins in the previous season. which of the following independent variables are indicator (dummy) variables? select all that apply.
Based on the information provided, only one of the independent variables can be an indicator (dummy) variable, which is:
- The player was traded in the last 5 years
Based on the information provided, only one of the independent variables can be an indicator (dummy) variable, which is:
- The player was traded in the last 5 years
This variable can take on a value of 0 or 1, where 0 represents that the player was not traded in the last 5 years, and 1 represents that the player was traded in the last 5 years. The other independent variables are continuous variables (e.g., player's age, player's height, career free throw percentage, average points per game) or categorical variables that do not need to be represented as dummy variables (e.g., the team had greater than 45 wins in the previous season).
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Suppose a bag contains 4 white chips and 6 black chips. What is the probability of randomly choosing a black chip, not replacing it, and then randomly choosing another black chip?
The probability of choosing a black chip and then another black chip is,
⇒ 1/3
Since, There are 4 + 6 = 10 chips in the bag.
And, 6 of them are black .
Hence, The probability that the first chip chosen will be black is,
⇒ 6/10
⇒ 3/5.
After that, there is one black chip less in the bag, so there are 9 chips in the bag, 5 of them are black.
Hence, The probability that the second chip chosen will be black is,
⇒ 5/9
Now, Multiply the probabilities to find the probability that the first chip will be black and the second chip will be black:
⇒ 3/5 × 5/9
⇒ 1/3
Thus, The probability of choosing a black chip and then another black chip is,
⇒ 1/3
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Suppose that it is known that on any given day in the month ofmarch there is a 0.3 probability of rain. Find the standarddeviation of rainy days in March.
The standard deviation of rainy days in March is approximately 2.55 days.
To find the standard deviation of rainy days in March, we first need to determine the expected value or the mean number of rainy days in March.
The expected value of a binomial distribution can be found using the formula: E(X) = np, where X is the random variable representing the number of rainy days in March, n is the number of trials (days in March), and p is the probability of success (rain) on a given day.
In this case, n = 31 (number of days in March) and p = 0.3 (probability of rain on any given day in March). Therefore, the expected value of rainy days in March is
E(X) = np = 31 × 0.3 = 9.3
Next, we need to find the variance of the binomial distribution, which is given by the formula: Var(X) = np(1 - p).
Var(X) = 31 × 0.3 × (1 - 0.3) = 6.51
Finally, the standard deviation of rainy days in March is the square root of the variance:
SD(X) = √Var(X) = √6.51 ≈ 2.55
Therefore, the standard deviation of rainy days in March is approximately 2.55 days.
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Sales associates at an electronics store earn different commission
percentages based on the items they sell. The table shows the total
sales and commission earnings for four sales associates at the
electronics store last month.
GIFTING EXTRA POINTS
The required model is c = 0.03d+1.81.
Given are 4 entries, but we just need 2 to plot the relation lets pick the first two, we would be using the equation of a line in the two-point form,
c - c₁ / d - d₁ = c₂ - c₁ / d₂ - d₁
We, put in the points, (673,22) and (3277,101), we get,
c - 22 / d-673 = 0.03
c-22 = 0.03 (d-673)
c-22 = 0.03d-20.19
c-22 / d-673 = 101-22 / 3277-673 = 79 / 2604 = 0.03
c = 0.03d+1.81
Hence, the required model is c = 0.03d+1.81.
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3(n + 5) is equivalent to (n + p)3.
Answer:
[tex]3(n + 5) = (n + 5)3[/tex]
So p = 5.
The point A is shown below.
Reflect A across the x-axis.
Then reflect the result across the y-axis.
Plot the final point.
Important: Only plot the final point in your answer.
8-1
X
5
The coordinate of final point of A after transformation is,
A'' = (0, - 7)
We have to given that;
Coordinate of A = (0, 7)
We know that;
Rule for the across the x - axis is,
(x, y) = (x , - y)
Hence, We get;
Point after transformation is,
A' = (0, - 7)
And, Rule for the across the y - axis is,
(x, y) = (-x , y)
Hence, Point after transformation is,
A'' = (0, - 7)
Thus, The coordinate of final point of A after transformation is,
A'' = (0, - 7)
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Classifiy the triangle by using its side lengths
Answer: Where is the triangle?
Step-by-step explanation: Brainliest pls:)
"needed in 20 mins i will rateyour answerQuestion 1 dy Find for the following functions, simp dx 9 (i) y = 2x5 – 4x3 + 9/4x^(3)
The derivative of the given function is:
y' = 10x^4 - 12x^2 + (27/4)x^2
To find the derivative of the given function, y = 2x^5 - 4x^3 + (9/4)x^3, we can use the power rule and the sum rule of differentiation.
The power rule states that the derivative of x^n is nx^(n-1), where n is any real number.
Using the power rule, we can find the derivative of each term in the function:
dy/dx (2x^5) = 10x^4
dy/dx (-4x^3) = -12x^2
dy/dx ((9/4)x^3) = (27/4)x^2
Using the sum rule, we can add the derivatives of each term to find the derivative of the function:
dy/dx (y) = dy/dx (2x^5) + dy/dx (-4x^3) + dy/dx ((9/4)x^3)
dy/dx (y) = 10x^4 - 12x^2 + (27/4)x^2
Therefore, the derivative of the given function is y' = 10x^4 - 12x^2 + (27/4)x^2.
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Estimate the perimeter and the area of the shaded figure.
The perimeter and area of the given polygon are:
Perimeter = 22.325 units
Area = 25 square units
How to find the area and perimeter?Using Pythagoras theorem, we can find the length of the sides of the polygon as:
a = √(1² + 3²)
a = √10
b = √(3² + 3²)
b = 2√9
c = √(3² + 3²)
c = 2√9
d = √(1² + 3²)
d = √10
e = 4
Thus:
Perimeter = 2√10 + 4√9 + 4
Perimeter = 22.325 units
Area = 2(¹/₂ * 1 * 3) + 2(¹/₂ * 3 * 3) + (4 * 3)
= 25 square units
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Algibra 1, unit 5! Help
Answer: -15
Step-by-step explanation:
x+y=10
y=-x+10
2x+3(-x+10)=45
2x-3x+30=45
-x=15
x=-15
calculate the moment of inertia when an object's mass is 12 kg and the mass is distributed 4 meters from the axis of rotation.
To calculate the moment of inertia of an object, you need to know its mass and the distance it is from the axis of rotation. In this case, the object has a mass of 12 kg and is distributed 4 meters from the axis of rotation. The formula to calculate the moment of inertia is I = mr^2, where the moment of inertia, m is the mass, and r is the distance from the axis of rotation.
Using this formula, we can calculate the moment of inertia of the object:
I = 12 kg x (4 m)^2
I = 192 kgm^2
Therefore, the moment of inertia of the object is 192 kgm^2.
To calculate the moment of inertia for an object, you can use the following formula:
Moment of Inertia (I) = Mass (m) × Distance² (r²)
Given the object's mass is 12 kg and the mass is distributed 4 meters from the axis of rotation, we can plug these values into the formula:
I = 12 kg × (4 m)²
Now, we'll square the distance:
I = 12 kg × 16 m²
Finally, multiply the mass and the squared distance:
I = 192 kg·m²
So, the moment of inertia of the object is 192 kg·m².
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Both of these groups started with 22, 6-sided dice and followed the same procedure for removing dice until they had no dice left. How could they end up with such different scatterplots? Does it make sense that one set of data could look so possibly linear while the other does not?
It is possible for one set of data to have a scatterplot that appears linear while the other does not, even if both groups started with the same number of dice and followed the same removal procedure.
This is because the way the dice were removed could have been different between the two groups, leading to different patterns of results. Additionally, other factors such as the order in which the dice were removed or the number of trials conducted could also affect the resulting scatterplot.
Ultimately, the scatterplot is a visual representation of the relationship between the variables being measured, and it can take on many different forms depending on the specific data and conditions being analyzed.
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A circular region has a population of about 175,000 people and a population density of about 1318 people per square mile. Find the radius of the region. Round your answer to the nearest tenth.
The radius of the region is 11.55 mile.
We have,
Population = 175,000
So, population density
= 175,000 / 1318
= 132.77
and, the radius using from the population density
Radius = √area / (22/7)
= √1318 x 7/22
= 11.55 mile
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Phil is a 21-year-old male. What is his life expectancy? Male Female Deaths Per 1,000 Life Expectancy (Years) Probabillity of Living to This Age Deaths Per 1,000 Life Expectancy (Years) Probabillity of Living to This Age Age 19 1.0 58.2 0.9907 0.5 62.2 0.9940 20 1.0 57.2 0.9897 0.5 61.3 0.9935 21 1.0 56.3 0.9888 0.5 60.3 0.9930 22 1.0 55.3 0.9878 0.5 59.3 0.9925A. 56.3 years B. 77.3 years C. 77.2 years D. 55.3 years
Phil's life expectancy is 56.3 years.
Based on the provided data, the life expectancy for Phil, a 21-year-old male, is 56.3 years. Therefore, the correct answer is 56.3 years.
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Express in the form of a rational number: 0.1212….
Answer:
[tex]0.1212...=\dfrac{4}{33}[/tex]
Step-by-step explanation:
A repeating decimal is a decimal number with a digit (or group of digits) that repeats forever.
There are three ways to show a repeating decimal:
Several duplicates of the repeating digit or block of digits, followed by an ellipsis, e.g. 0.3333... or 0.123123...A dot or a line above a repeated digit, e.g. [tex]\sf 0.\.{3}[/tex] or [tex]\sf 0.\overline{3}[/tex]A line above a repeating block of multiple digits, e.g. [tex]\sf 0.\overline{123}[/tex]0.1212... is a repeating decimal as there are two duplicates of the repeating block of digits "12" followed by an ellipsis.
To express a repeating decimal as a rational number, begin by assigning the decimal to a variable:
[tex]x=0.1212...=0.\overline{12}[/tex]
Multiply both sides by 100:
[tex]\implies x \cdot 100=0.\overline{12}\cdot 100[/tex]
[tex]\implies 100x=12.\overline{12}[/tex]
Subtract the first equation from the second to eliminate the part after the decimal:
[tex]\begin{array}{crcr}& 100x & = & 12.\overline{12}\\- & x & = & 0.\overline{12}\\\cline{2-4} & 99x & = & 12\phantom{.12}\\\end{array}[/tex]
Divide both sides of the equation by 99:
[tex]\implies \dfrac{99x}{99}=\dfrac{12}{99}[/tex]
[tex]\implies x=\dfrac{12}{99}[/tex]
Reduce the fraction to is simplest form by dividing the numerator and denominator by 3:
[tex]\implies x=\dfrac{12 \div 3}{99 \div 3}=\dfrac{4}{33}[/tex]
[tex]\textsf{Therefore, $0.1212...$ expressed in the form of a rational number is\;$\dfrac{4}{33}$}.[/tex]
[1] Find the probabilities of the followings. (a) toss five coins and find three heads and two tails. (b) the face ‘6’ turns up 2 times in 3 rolls of a die as (6 + other + 6). (c) 46% of the population approve of the president’s performance. What is the probability that all four individuals in a telephone toll disapprove of his performance? (d) take five cards from a card deck and find ‘full house.’
The total number of ways to choose five cards from a deck of 52 cards is (52 choose 5) = 2,598,960. Therefore, the probability of getting a full house is 3,744/2,598,960 = 0.00144.
(a) The total number of possible outcomes when tossing five coins is 2^5 = 32. The number of ways to get three heads and two tails is the number of ways to choose three heads out of five times the number of ways to choose two tails out of five, which is (5 choose 3) x (5 choose 2) = 10 x 10 = 100. Therefore, the probability of getting three heads and two tails is 100/32 = 0.3125.
(b) The probability of getting a '6' on a single roll of a die is 1/6. The probability of not getting a '6' on a single roll of a die is 5/6. The probability of getting '6 + other + 6' in three rolls of a die is (1/6) x (5/6) x (1/6) x 3 = 5/216. Therefore, the probability of getting '6 + other + 6' two times in three rolls of a die is (5/216)^2 x (211/216)^1 x (3 choose 2) = 0.0029.
(c) The probability of an individual disapproving of the president's performance is 1 - 0.46 = 0.54. The probability that all four individuals in a telephone poll disapprove of his performance is 0.54^4 = 0.054.
(d) A full house consists of three cards of one rank and two cards of another rank. The number of ways to choose the rank for the three cards is 13, and the number of ways to choose the three cards of that rank is (4 choose 3) = 4. The number of ways to choose the rank for the two cards is 12 (since one rank has already been chosen), and the number of ways to choose the two cards of that rank is (4 choose 2) = 6. Therefore, the number of ways to get a full house is 13 x 4 x 12 x 6 = 3,744. The total number of ways to choose five cards from a deck of 52 cards is (52 choose 5) = 2,598,960. Therefore, the probability of getting a full house is 3,744/2,598,960 = 0.00144.
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The probability distribution for a game is shown in the table below.
What is the probability of getting more than 1 point if the game is played one time?
Answer:
3/8
Step-by-step explanatio
the person shows the answer and explanation nice!
in 2020, the population of a city was 1,596,000 . this was a 3.5% increase from 2019. the population is expected to continue to increase at the same rate per year. write a function, f(x) , to model the population, where x is the number of years since 2020.
To model the population of a city, we can use the formula:
f(x) = 1,596,000 * (1 + 0.035)^x
Where x is the number of years since 2020 and 0.035 represents the annual increase rate of 3.5%.
To model the population of a city, we need to take into account the initial population in 2020 and the annual increase rate of 3.5%. The annual increase rate of 3.5% means that the population is expected to grow by 3.5% every year from the previous year's population. To incorporate this growth rate into our model, we can use the formula for compound interest:
A = P * (1 + r)^t
Where A is the final amount, P is the initial amount, r is the annual interest rate, and t is the number of years. In our case, the final amount is the population after x years since 2020, the initial amount is the population in 2020 (1,596,000), the annual interest rate is 3.5%, and the number of years is x.
By substituting the values into the formula, we get:
f(x) = 1,596,000 * (1 + 0.035)^x
This formula can be used to calculate the expected population of the city for any year in the future. For example, if we want to know the population in 2025, we can substitute x = 5 into the formula:
f(5) = 1,596,000 * (1 + 0.035)^5
= 1,825,854
Therefore, we can expect the population of the city to be around 1,825,854 in 2025, assuming the same annual increase rate of 3.5%.
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Is the number of sit-ups Anna does proportional to the time she spends doing them?
No, the number of sit-ups Anna does, is not proportional to the time she spends doing them.
When Anna starts doing sit-ups for her first triathlon, she does a sit-up every 22 seconds. But we know that as she gets tired, each sit-up takes longer and longer to do. The situps may take 40 seconds or 75 seconds as she gets more tired.
As we can see that there is no constant rate at which she gets tired and take more seconds to do sit-ups. In order to be proportional, the increasing or decreasing rate should be constant. We can see that the time she spends doing them is not increasing or decreasing at a constant rate along with the number of sit-ups she is doing.
Therefore, the number of sit-ups Anna does is not proportional to the time she spends doing them.
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The complete question is "Anna does sit-ups to get ready for her first triathlon. When she starts, she does a sit-up every 22 seconds. But, as she gets tired, each sit-up takes longer and longer to do. Is the number of sit-ups Anna does proportional to the time she spends doing them? "
Which one of the following is true regarding the use of the mode, mean, and median for different levels of measurement?
The mode, mean, and median are all valid measures of central tendency for interval and ratio level data. For nominal level data, only the mode is appropriate, while for ordinal level data, both the mode and median can be used, but the mean is not recommended as it assumes equal intervals between categories.
The correct statement regarding the use of the mode, mean, and median for different levels of measurement is:
The mode can be used for nominal and ordinal levels of measurement, the median is used for ordinal, interval, and ratio levels, while the mean is used for interval and ratio levels of measurement.
Let's break it down:
1. Mode: applicable to nominal and ordinal levels as it represents the most frequently occurring value in the data.
2. Median: applicable to ordinal, interval, and ratio levels as it represents the middle value when data is arranged in order.
3. Mean: applicable to interval and ratio levels as it represents the average value by summing all data points and dividing by the number of data points.
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x-3y= -9 slope intercept form
Answer:
[tex]\textsf{y=\frac{1}{3}x+3}[/tex][tex]y = \frac{1}{3} x+3[/tex]
Step-by-step explanation
[tex]\textsf{*slope intercept form: y = mx +b}[/tex]
---------------------------------------------
[tex]\textsf{x - 3y = -9}[/tex]
Subtract x from both sides:
[tex]\textsf{-3y = -x - 9}[/tex]
Divide both sides by -3:
-3y/-3 = -x/-3 - 9/-3
[tex]\textsf{y = 1/3x +3}[/tex]
[tex]-jurii[/tex]
how can i prove 1/xy = 1/x * 1/y
To prove that 1/xy = 1/x * 1/y, we can start by multiplying both sides of the equation by xy.
Multiplying both sides of the equation by xy gives us:
1 = xy * 1/x * 1/y
Next, we can simplify the right-hand side by canceling out the x and y terms that appear in both the numerator and denominator:
1 = y/x + x/y
To further simplify this expression, we can multiply both sides by xy:
xy = y^2 + x^2
This equation can be rearranged to get:
x^2 + y^2 = xy
Finally, we can use the formula for the sum of squares:
x^2 + y^2 = (x+y)^2 - 2xy
Substituting this into the previous equation, we get:
(x+y)^2 - 2xy = xy
Simplifying, we get:
(x+y)^2 = 3xy
Taking the square root of both sides, we get:
x+y = sqrt(3xy)
Dividing both sides by xy, we get:
1/xy = 1/x * 1/y
Therefore, we have proven that 1/xy = 1/x * 1/y.
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