Amy is interested in estimating the number of hours of sleep a typical student at her middle school gets on Saturday nights. She asks each of the other students in her science class to write down how many hours of sleep they got last Saturday on a piece of paper passed around the class.
Which of the following statements are true?
Choose all that are correct.
A.
Amy should have included students from one other science class.
B.
To get a good estimate, Amy must have all the students at the school answer the question.
C.
To estimate the value, Amy must first mix up the data from the science class.
D.
Amy's results cannot be used to estimate the value she wishes to estimate.
E.
The sample Amy used is not a true random sample.

The answers are, For C(x, y) = 500−5xy + 12x2y, ∂C/∂x = -5y + 24xy and ∂C/∂y = -5x + 12x².

For q = 6p₁ + 4p₂ / (p₁ + p₂),  ∂q/∂p₁ = -2(p₁ - p₂)/(p₁ + p₂)² and ∂q/∂p₂ = 2(p₁ - p₂)/(p₁ + p₂)².

A function is a mathematical object that accepts one or more inputs, processes those inputs according to a predetermined procedure, and then generates an output.

The domain and range of a function are its inputs and outputs, respectively.

An equation, a graph, or a table can all be used to depict a function.

To find ∂C/∂x and ∂C/∂y for C(x, y) = 500 − 5xy + 12x²y, we differentiate C with respect to x and y, respectively, while treating the other variable as a constant:

∂C/∂x = -5y + 24xy

∂C/∂y = -5x + 12x²

To find ∂q/∂p₁ and ∂q/∂p₂ for q = 6p₁ + 4p₂ / (p₁ + p₂), we differentiate q with respect to p₁ and p₂, respectively, while treating the other variable as a constant:

∂q/∂p₁ = (4p₂ - 2p₁ - 4p₂) / (p₁ + p₂)² = -2(p₁ - p₂)/(p₁ + p₂)²

∂q/∂p₂ = (6 - 2p₁/(p₁ + p₂)) / (p₁ + p₂) - (6p₁ + 4p₂)/(p₁ + p₂)²

= 2(p₁ - p₂)/(p₁ + p₂)²

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Answer:

Step-by-step explanation:

You want to know the names of a 4-sided figure with opposite sides congruent and adjacent sides perpendicular.

A 4-sided figure is a quadrilateral.

When opposite sides are the same length, the quadrilateral is a parallelogram.

When corners of a parallelogram are right angles, it is a rectangle.

__

Additional comment

A rhombus also has congruent adjacent sides, as does a square. We are not told that is the case here. A trapezoid is not a parallelogram.

Hence, in answering the stated questiοn, we may say that As a result, we  equatiοn must add (2x - 1)2 + 5 tο 6x² + 9x - 8 tο get 4x² - 8x + 6.

A algebraic equatiοn is a strategy fοr linking twο prοpοsitiοns and expressing equivalence using the equals symbοl (=). A mathematical sentence that shοws the equivalency οf twο fοrmulas is knοwn as an equatiοn in algebra. In the calculatiοn 3x + 5 = 14, fοr example, the equal sign puts a space between the values 3x + 5 and 14. Tο describe the relatiοnship between the twο sentences printed alοng either side οf a letter, a mathematical fοrmula can be utilised. Usually, the insignia and the prοgramme are the same. 2x - 4 = 2, fοr example.

Tο identify what shοuld be added tο 6x² + 9x - 8 tο create 4x² - 8x + 6, we need tο undertake a methοd called "cοmpleting the square".

We can cοnclude frοm cοmparing the twο fοrmulas that a = 4, b = -8, and c = 6.

Sο we must "finish the square" by adding and remοving a term equal tο (b/2a)2. In this instance, we have:

(b/2a)² = (-8/2(4))

a² = 1

4x² - 8x + 6 + 1 - 1

(4x² - 8x + 1) + (6 - 1) (6 - 1)

(4x² - 8x + 1) is a perfect square trinοmial, which may be factοred as (2x - 1)².

As a result, the ultimate sοlutiοn is:

6x² + 9x - 8 + 1 - 1 + (2x - 1) (2x - 1)

a² + 5

As a result, we must add (2x - 1)² + 5 tο 6x² + 9x - 8 tο get 4x² - 8x + 6.

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Answer:

i think it will decrease

Step-by-step explanation:

Therefore, Equations 1 and 2 are: Equation 1: g = 360h

Equation 2: w = 2,000 + 360h.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). The expressions on both sides of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal in solving an equation is to find the value of the variable that makes the equation true. Equations are used extensively in mathematics and science to model real-world phenomena and solve problems.

by the question.

We know that the hose puts water into the pool at a rate of 360 gallons per hour. Therefore, after h hours, the hose has put g gallons of water into the pool. We can express this relationship using the following equation:

Equation 1: g = 360h

We also know that the pool already had 2,000 gallons of water in it before Johnathan started filling it with the hose. Therefore, the total number of gallons of water in the pool after h hours is given by:

w = 2,000 + g

We can substitute the expression for g from Equation 1 into this equation to obtain an equation that relates g and w:

Equation 2: w = 2,000 + 360h

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The rule broken in the first argument is of undistributed middle.

The rule broken in the second argument is of exclusive middle.

What is Converse?

In logic and mathematics,  converse of statement is formed by switching  hypothesis and conclusion of original statement. For example,  converse of the statement "If it rains, the streets get wet" is "If the streets get wet, it is raining."

The first argument violates the rule of the undistributed middle. The argument appears to be the fallacy of the converse of the inverse. This is a form of invalid reasoning where the contrapositive of a true statement is used as evidence for the original statement. The argument could be stated in syllogistic form as:

Premise 1: All P are Q.

Premise 2: No Q are S.

Conclusion: Some P are not S.

This argument is invalid because it violates the rule of the undistributed middle. The middle term Q is not distributed in either premise, which means that we cannot logically conclude anything about the relationship between P and S.

The second argument violates the rule of the exclusive middle. The argument appears to be the fallacy of the illicit conversion. This is a form of invalid reasoning where the subject and predicate terms of a statement are switched without changing the truth value of the statement. The argument could be stated in syllogistic form as:

Premise 1: All A are B.

Premise 2: All B are C.

Conclusion: All C are A.

This argument is invalid because it violates the rule of the exclusive middle. The argument assumes that there are only three categories of things: A, B, and C. However, this assumption is not justified, and there may be other categories that are not included in the argument.

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Answer:see answer

Step-by-step explanation:see answer

Answer:

y=96                                          

     




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

The height corresponding to the given side is 18cm

Some of the properties of a parallelogram are given below as;

The formula for calculating the area of a parallelogram is expressed as;

Area = bh

Given that;

b is the base side of the parallelogram and h is the height

Substitute the values

540 = 30h

Divide by the coefficient of h

h = 18 cm

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The probability that the sample mean weight change is greater than 10 pounds is p(M > 10) = 0.9088.

To find the probability that the sample mean will be greater than M = 10 pounds, we need to standardize the sample mean using the formula for z-score:

z = (M - µ) / (σ / √n)

Substituting the given values, we get:

z = (10 - 15) / (6 / √4)

z = -1.33

Using a standard normal distribution table or calculator, we can find the probability that z is greater than -1.33, which is approximately 0.9088.

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Part A:

We are given that the height of a tree in a scale drawing is 3.75 inches. The scale of the drawing is 1 inch: 50 feet.

To find the height of the actual tree, we can use the ratio of the drawing scale to the real-life scale. For every 1 inch on the drawing, there are 50 feet in real life.

Therefore, we can set up a proportion:

[tex]$\frac{1 \ \text{inch}}{50 \ \text{feet}} = \frac{3.75 \ \text{inches}}{x \ \text{feet}}$where $x$ is the height of the actual tree in feet.We can solve for $x$ by cross-multiplying:$1 \ \text{inch} \cdot x = 3.75 \ \text{inches} \cdot 50 \ \text{feet}$$x = \frac{3.75 \ \text{inches} \cdot 50 \ \text{feet}}{1 \ \text{inch}} = 187.5 \ \text{feet}$Therefore, the height of the tree is $\boxed{D \ 187.5 \ \text{ft}}$.[/tex]

[tex]Part B:We are now given a new scale drawing where the height of the same tree is 6 inches. We need to find the new scale.Since the tree's height in the new drawing is different, we can use a new proportion to find the new scale.Let the new scale be $1$ inch to $x$ feet. We can set up a proportion:[/tex]

[tex]$\frac{1 \ \text{inch}}{x \ \text{feet}} = \frac{6 \ \text{inches}}{187.5 \ \text{feet}}$where $187.5$ feet is the height of the tree in real life.We can solve for $x$ by cross-multiplying:$1 \ \text{inch} \cdot 187.5 \ \text{feet} = 6 \ \text{inches} \cdot x \ \text{feet}$$x = \frac{1 \ \text{inch} \cdot 187.5 \ \text{feet}}{6 \ \text{inches}} = 31.25 \ \text{ft}$Therefore, the new scale is $\boxed{1 \ \text{inch} : 31.25 \ \text{ft}}$.[/tex]

Answer:

Step-by-step explanation:

Part A:

We can use a proportion to solve for the height of the tree:

1 inch on the drawing represents 50 feet in real life.

So, 3.75 inches on the drawing would represent:

3.75 inches * (50 feet/1 inch) = 187.5 feet

Therefore, the height of the tree is 187.5 feet.

The answer is D) 187.5 ft.

Part B:

The ratio of the height of the tree on the new scale drawing to its actual height must be the same as the ratio of the height of the tree on the original scale drawing to its actual height.

Let the new scale be 1 in. : x feet.

Then, we have the proportion:

1 in. / 50 ft. = 6 in. / (x) ft.

Solving for x, we get:

x = (6 in. * 50 ft.) / 1 in.

x = 300 ft.

Therefore, the new scale is 1 in. : 300 ft.

The answer is 1 in. : 300 ft.

We may take the number of people who ordered a salad out of the total to find the number of individuals who did not order one:

12 - 4 = 8 people did not order a salad.

The expression to use to estimate the number of persons that ordered the salad would be

(1/3) x 12 = 4 people ordered a salad

Every mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Everything with a variable value is anything whose value changes over time. Typically, alphabetical letters like a, b, c, m, n, p, x, y, and z are used to denote expression variables. A combination of several variables and integers can be used to create a variety of expressions.

from the question:

We can utilize the information that 1/6 of customers ordered a shrimp po'boy and 1/2 ordered a cheeseburger to estimate how many individuals ordered the salad. Hence, the proportion of customers that choose a salad is:

1 - (1/6 + 1/2) = 1 - 2/3 = 1/3

Hence, to count how many people ordered the salad, the statement would be:

4 individuals (1/3) x 12 ordered salads.

We may take the number of people who ordered a salad out of the total to find the number of individuals who did not order one:

Those who did not order a salad were 12 - 4 = 8.

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The true inequality from the list of options is (c) -x - 6 > -3.5

To determine which inequality is true when x is -5, we need to substitute -5 for x in each inequality and simplify.

a) -x – 6 < -3.5

Substituting x = -5, we get:

-(-5) - 6 < -3.5

5 - 6 < -3.5

-1 < -3.5

This is false, so option a) is not true.

b) -x – 6 > 3.5

Substituting x = -5, we get:

-(-5) - 6 > 3.5

5 - 6 > 3.5

-1 > 3.5

This is false, so option b) is not true.

c) -x - 6 > -3.5

Substituting x = -5, we get:

-(-5) - 6 > -3.5

5 - 6 > -3.5

-1 > -3.5

This is true, so option c) is true.

Hence, the correct option is (c) -x - 6 > -3.5

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Complete question

Which inequality is true when the value of x is -5?

a) -x – 6 < -3.5

b) -x – 6 > 3.5

c) -x - 6 > -3.5

d) x - 6 > -3.5

Answer:

slope = [tex]\frac{11}{15}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-x_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (9, 4 ) and (x₂, y₂ ) = (- 6, - 7 )

m = [tex]\frac{-7-4}{-6-9}[/tex] = [tex]\frac{-11}{-15}[/tex] = [tex]\frac{11}{15}[/tex]

The probability of obtaining at least 1 six in 5 throws of the die is 1 - (1-p)⁵.

What is the probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen.

The probability of obtaining a six on one throw of the die is given as a fraction, say p.

We are not given the value of p, but we know that the die is biased so that the probability of obtaining a six is greater than 1/6.

The probability of not obtaining a six on one throw of the die is (1-p), since the sum of the probabilities of all possible outcomes must be 1.

To find the probability of obtaining at least 1 six in 5 throws of the die, we can use the complement rule.

This states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

So, the probability of not obtaining any sixes in 5 throws of the die is:

(1-p)⁵

The probability of obtaining at least 1 six in 5 throws of the die is therefore:

1 - (1-p)⁵

This formula gives the probability of obtaining at least one six in any 5 throws of the die, regardless of the order in which the throws occur.

Note that we cannot determine the exact value of the probability without knowing the value of p, but we can use the given information that the die is biased so that the probability of obtaining a six is greater than 1/6 to conclude that the probability of obtaining at least one six in 5 throws of the die is also greater than 1/6.

Therefore, The probability of obtaining at least 1 six in 5 throws of the die is 1 - (1-p)⁵.

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Answer: Let's denote the first term of the geometric sequence as "a", and the common ratio as "r". Then, we can use the given information to set up a system of equations:

a * r^3 = 18 (the fourth term is 18, so ar^3 is the fourth term)

a * r^6 = 16/3 (the seventh term is 16/3, so ar^6 is the seventh term)

To solve for "a" and "r", we can divide the second equation by the first equation:

(a * r^6) / (a * r^3) = (16/3) / 18

Simplifying this expression, we get:

r^3 = (16/3) / 18 = 16/54 = 8/27

Taking the cube root of both sides, we get:

r = 2/3

Substituting this value of "r" into the first equation, we can solve for "a":

a * (2/3)^3 = 18

a = 18 / (2/3)^3

a = 27

Therefore, the first term of the geometric sequence is 27, and the nth term is given by:

a * r^(n-1) = 27 * (2/3)^(n-1)

Step-by-step explanation:

By using the data in the given table, the missing coefficients should be filled as followed;

y = x + 6.128.

In this scenario, the x-values would be plotted on the x-axis (x-coordinate) of the scatter plot while the y-values would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the x-values and y-values, a linear equation for the line of best fit is given by

y = x + 6.128

In conclusion, we can reasonably infer and logically deduce that the scatter plot most likely indicates a linear relationship between the x-values and y-values.

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Answer:

The answer is B)2

Step-by-step explanation:

As you can see, the length and height of the bigger rectangle is twice the length and height of the smaller rectangle.

According the question given above the present value of the cash flows is $12,114.36.

Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants.

Tο calculate the present value (PV) οf the cash flοws (CFs), we need tο discοunt each cash flοw tο its present value using the given rate οf 12%. The fοrmula tο calculate the present value οf a cash flοw is:

[tex]PV = CF / (1 + r)^n[/tex]

where:

PV = present value οf the cash flοw

CF = cash flοw amοunt

r = discοunt rate

n = number οf periοds (in this case, the number οf years)

Using this fοrmula, we can calculate the present value οf each cash flοw as fοllοws:

[tex]PV(CF0) = 0 / (1 + 0.12)^0 = 0[/tex]

[tex]PV(CF1) = 1500 / (1 + 0.12)^1 = 1339.29[/tex]

[tex]PV(CF2) = 1500 / (1 + 0.12)^2 = 1191.08[/tex]

[tex]PV(CF3) = 3000 / (1 + 0.12)^3 = 2382.16[/tex]

[tex]PV(CF4) = 4500 / (1 + 0.12)^4 = 3221.56[/tex]

[tex]PV(CF5) = 5000 / (1 + 0.12)^5 = 3080.27[/tex]

Tο find the present value οf all the cash flοws, we simply add up the present values οf each cash flοw:

PV = PV(CF0) + PV(CF1) + PV(CF2) + PV(CF3) + PV(CF4) + PV(CF5)

= 0 + 1339.29 +1191.08 + 2382.16 + 3221.56 + 3080.27

= 12114.36

Therefοre, the present value οf the cash flοws is $12,114.36.

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Answer:

-f(x+3) and -2f(x)+4

Step-by-step explanation:

it is all the ones with a negative in front of the function, so that is -f(x+3) and -2f(x)+4.

Answer:

80 percent

Step-by-step explanation:

The answer is each of the 4 friends would get 13 snowballs.

52 divided by 4 = 13

Answer: 52 divided by 4 is 13 each of them would get 13 snowballlllsssssss!!!!

Step-by-step explanation:

We cannot determine whether the method of donation is independent from the type of donor in this sample based on the information given in the question.

Statistical analysis is the process of collecting, cleaning, analyzing, and interpreting data using statistical methods and techniques. It involves summarizing and describing data, identifying patterns and relationships, testing hypotheses, and making predictions based on the data.

We cannot determine whether the method of donation (online vs. not online) is independent from the type of donor (regular vs. new) in this sample based on the information given in the question.

To determine whether two categorical variables (in this case, method of donation and type of donor) are independent, we would need to conduct a chi-square test of independence. This would involve comparing the observed frequencies of each combination of the two variables to the expected frequencies if the two variables were independent.

However, the question only provides information on the percentage of donations from online sources and the percentage of donations from regular donors that were submitted through the organization's website. It does not provide information on the percentage of donations from new donors that were submitted through the website, or the percentage of donations from regular donors that were not submitted through the website. Therefore, we cannot determine whether the method of donation is independent from the type of donor in this sample.

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The other leg measures 4 centimetres in length.

The right triangle in the illustration has a hypotenuse that is 5 cm long and a leg that is 3 cm long. The length of the other leg must be determined.

Applying the Pythagorean theorem, which asserts that the square of the hypotenuse's length is equal to the sum of the squares of the two legs of a right triangle, we may write:

[tex]a^2 + 3^2 = 5^2[/tex]

When we simplify this equation, we obtain:

[tex]a^2[/tex] + 9 = 25

By taking 9 away from both sides, we arrive at:

[tex]a^2[/tex] = 16

By multiplying both sides by their square roots and keeping in mind that a must be positive, we arrive at:

a = 4

Hence, the other leg is 4 cm long.

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There are total 56 combination of your locker contains 3 non-repeating digits from the numbers 0-9.

Combinations are mathematical operations that count all possible arrangements of a set of components when the order in which they are selected is irrelevant. Components for combos can be selected in any hierarchy.

Moreover, there are two other kinds of combinations (the specific sequence is not relevant at this time): It's acceptable to repeat phrases like "coins in your pocket" (5,5,5,10,10) In the same way, lottery numbers (2,14,15,27,30,33)

Combinations are mathematical operations that count all possible arrangements of a set of components when the order in which they are selected is irrelevant. Components for combos can be selected in any hierarchy.

Permutations and combinations are compatible.

As the first digit is fixed i.e. 9,

So, there are 2 non-repeating digits left,

Using permutations,

we are left with 8 × 7 = 56 ways.

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The angle of elevation represented by θ is equal to 1.13186 in radian approximately to 5 decimal place.

The angle of elevation is the angle θ between the horizontal line given as 2000 feet and the line of sight which is above the horizontal line.

The angle θ in degree is calculated, and then converted to radian as follows:

since the camera and the rocket is 4255 feet apart, then;

θ = tan⁻¹(4255/2000)

θ = 64.82482°

To convert 64.82482° to radian, we multiply by π/180

θ' = 64.82482° × π/180

θ' = 1.13186 approximately to 5 decimal place.

Therefore, the angle of elevation represented by θ is equal to 1.13186 in radian approximately to 5 decimal place.

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Answer : 14

Explanation : Divide The Circumference By π, Or 3.14 For The Answer.

Answer: 14

Step-by-step explanation:

To find the diameter, divide your circumference by pi "3.14".

43.9/3.14 = 13.9808917197

Rounded to the nearest whole number is: 14

Have a good day!

Answer:

Step-by-step explanation:

If 1-2i is a zero of the polynomial, then its conjugate 1+2i is also a zero. This is because complex zeros of a polynomial with real coefficients always occur in conjugate pairs.

Let's use synthetic division to factor out the polynomial with the given zeros:

1-2i | 4 0 17 14 65

| 4 -8i -9+2i -12

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

4 4 -8i -9+2i 53

So we have factored the polynomial as:

f(x) = (x - 1 + 2i)(x - 1 - 2i)(4x^2 + 4x - 53)

Now we need to find the zeros of the quadratic factor:

4x^2 + 4x - 53 = 0

Using the quadratic formula, we get:

x = (-4 ± sqrt(16 + 4453)) / 8

x = (-4 ± sqrt(848)) / 8

x = (-4 ± 4sqrt(53)) / 8

x = (-1 ± sqrt(53)) / 2

So the remaining zeros are (-1 + sqrt(53))/2 and (-1 - sqrt(53))/2.

Therefore, the probability that the average weight of the sample of 39 Goliath Grouper is within 14 pounds of the average weight of all Goliath Grouper caught on the Treasure Coast is approximately 0.2342 or 23.42%.

In mathematics and statistics, the mean is a measure of central tendency of a set of numerical data. It is also known as the arithmetic mean or average, and is calculated by summing up all the values in the dataset and then dividing by the number of values. The mean provides a useful summary of the data as it gives an idea of the typical or average value in the dataset. It is commonly used in various fields, including finance, science, and social sciences, to analyze and interpret data. However, the mean can be sensitive to extreme values or outliers in the dataset, so it is important to consider other measures of central tendency, such as the median and mode, in addition to the mean.

Here,

We can approach this problem using the central limit theorem, which states that the distribution of sample means will be approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Let's first calculate the standard error of the mean:

standard error of the mean = standard deviation / sqrt(sample size)

= 74 / √(39)

≈ 11.83

Next, we need to find the z-score corresponding to a sample mean within 14 pounds of the population mean:

z = (sample mean - population mean) / standard error of the mean

= (418 - 14 - 418) / 11.83

= -1.19

Using a standard normal distribution table or calculator, we can find that the probability of a z-score less than -1.19 is about 0.1171. Since we're interested in the probability that the sample mean is within 14 pounds of the population mean, we can multiply this probability by 2 to account for the area under the curve in both tails:

P(sample mean within 14 pounds of population mean) ≈ 2 * 0.1171 ≈ 0.2342

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Answer:

Let the two numbers be x and y. We know that:

xy = 23

We also know that:

1/x + 1/y = 2

Multiplying both sides of the second equation by xy, we get:

y + x = 2xy

Substituting the value of xy from the first equation, we get:

y + x = 2(23)

y + x = 46

Therefore, the sum of the two numbers is 46.

Step-by-step explanation: