The reciprocal of h.C.F and lcm of two number are 1/12 and 1/312 respectively. If one of the number is 24. Find the other number?

The dimensions of the region which enclose the maximal area will be  40.5 feet in length by width 27 feet.

Given that the farmer has 162 feet of fencing, we will have:

2L + 3W = 162 feet

2L = 162 - 3W

L = 162 - 3W\2

L = 81 -3/2W  Eqn 1

Given that the area of a rectangle is A = L × W we will call this equation 2

Now we substitute the first equation in the second one to give

A = (81 -3/2W) × W

A = 81W -3/2W²

When we take the derivative W will equal

81/3 = 27

Now we substitute in the second equation, we will have:

= 81 - 3/2(27)

= 81 - 40.5

= 40.5.

So the length will be 40.5 feet while the width will be 27 feet.

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If Jared uses two theorems together to make a conjecture about the sum of the interior angles of pentagons, Jared is using deductive reasoning. Correct option is B.

Deductive reasoning is a logical process in which a conclusion is reached by applying general principles or known information to specific situations. In this case, Jared is using two theorems, which are general principles that have been proven to be true, to make a conclusion about a specific situation, the sum of interior angles of pentagons.

The conclusion that Jared makes is a conjecture, which is a hypothesis or a tentative conclusion that is based on limited evidence or observation.

In contrast, inductive reasoning is a logical process in which a conclusion is reached based on a series of observations or specific instances. Inductive reasoning involves making generalizations based on specific observations, which can lead to a hypothesis or a theory.

Therefore, Jared's use of two theorems to make a conclusion is an example of deductive reasoning. Correct option is B.

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Answer: D

Step-by-step explanation: formal proofs deeply uses tables or a list of steps where informal proofs are proven in paragraphs.

I: TRUE - A limit is a value that a function, pattern, or sum of a series approaches as the number of terms or input value increases.

II: TRUE - A limit can also be a value that a function approximates for a specific input value, especially when dealing with continuity or differentiability.

III: FALSE - Although a limit might seem like a value that is never quite achieved, it can be reached or even exceeded, depending on the function and its behavior.

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The remainder that is found when dividing 2x^2+7x-4 by x-3 is 35

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

Dividing 2x^2+7x-4 by x-3

This means that

Dividend = 2x^2 + 7x - 4

Divisor = x - 3

Set the divisor to 0

So, we have

x - 3 = 0

Evaluate

x = 3

Substitute 3 for x in the dividend equation, so, we have the following representation

Remainder = 2(3)^2 + 7(3) - 4

Evaluate

Remainder = 35

Hence, teh remainder is 35

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The correct equation for the following sentence is 24 = 31.4n + (–8.4) . Option C

Algebraic expressions are simply described as those expressions that are made up of factors, coefficients, constants, terms and variables.

Additionally, algebraic expressions are made up of arithmetic or mathematical operations, such as;

From the information given, we have that;

24 is the constant

Let the number be represented as n

Then, the expression is given as;

24 = 31.4(n) - 8.4

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Answer:

31

Step-by-step explanation:

the next number is 31 in this series

The equation of the line representing Main Street is option C. y = -2x + 11

The slope of the parallel lines is ½. The Main Street is perpendicular to Oak and Maple. So, the slope of Main Street is -2.

[The product of slopes of perpendicular Lines is -1.)

y - 1 = -2 (x -5)

y - 1 = -2x +10

y = -2x + 10 + 1

y = -2x + 11

Therefore, the best choice is option C. y = -2x + 11

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Since Main Street is perpendicular to Oak and Maple, its slope will be the negative reciprocal of the slope of Oak and Maple. Let's first find the equation of Oak Street.

We don't have enough information to determine the equation of Oak Street, so we need to make an assumption about its equation. Let's assume that Oak Street passes through the point (0,3) and has a slope of 2 (since the options suggest that Oak Street has a positive slope).

Using the point-slope form of a line, we have:

y - 3 = 2(x - 0)

y - 3 = 2x

y = 2x + 3

Now we can find the slope of Maple Street by noticing that it is parallel to Oak Street. Since parallel lines have the same slope, Maple Street also has a slope of 2.

To find the equation of Main Street, we need to use the fact that it passes through the point (5,1). Using the point-slope form of a line, we have:

y - 1 = -1/2(x - 5)

y - 1 = -1/2x + 5/2

y = -1/2x + 7/2

Therefore, the equation of the line representing Main Street is y = -1/2x + 7/2. The answer is (D).

Answer:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] {a}^{2} = {c}^{2} - {b}^{2} [/tex]

[tex]a = \sqrt{ {c}^{2} - {b}^{2} } [/tex]

The correct answer is D.

The maximum possible product of two numbers that have a sum of -8 is 16.

Let us name the two numbers "x" and "y".

We are aware of the following: x + y = -8

We're looking for the greatest possible product of x and y.

The number we're looking  that are as near together as feasible and have a sum of -8.

-4 and -4 are the two numbers that are as near together as possible and have a sum of -8. As a result, x = -4 and y = -4.

The sum of these two figures is:

x * y = (-4) * (-4) = 16

So, the maximum possible product of two numbers that have a sum of -8 is 16.

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A. The expression that represents the total amount of canned food they have collected so far is: 4x² + 2xy + 3

B. Number of canned food still remaining to be collected is: 2x² - 4xy + 5

A polynomial expression is a mathematical expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication of non-negative integer exponents.

Part A: To find the expression that represents the total amount of canned food they have collected so far, add the expression for each person given together.

3x² - 2 + x² + 2xy + 5

Combine like terms:

4x² + 2xy + 3

Part B: Number of canned food still remaining to be collected is calculated below.

(6x² - 2xy + 8) - (4x² + 2xy + 3)

Open bracket:

6x² - 2xy + 8 - 4x² - 2xy - 3

Combine like terms:

2x² - 4xy + 5

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If you look at the six numbers (101, 203, 407, 512, 98, 642) you can see they range from 98 all the way to 642. the best interval to use for this group be 100.

The right interval to utilize for this set of numbers depends on the aim of the analysis.

If we want to look on the single values and small differences between them, then using interval of 10 would be more better. This would give u room to see small changes that exist between adjacent numbers.

So,  in the event that we need to look on the full range and distribution of the numbers, an interval of 100 would be more better. This would permit us to see how the numbers are shared over a larger area of values.

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See full question below

If you look at these six numbers, you can see they range from 98 all the way to 642. Would the best interval to use for this group be 10 or 100?

101, 203, 407, 512, 98, 642

Company B needs approximately 55 applicants to apply in order to meet their hiring target of 30 new employees, taking into account the percentages of applicants who do not meet the requirements or pass the various stages of the hiring process.

Let's start with the total number of applicants needed to meet the hiring target of 30 new employees. We can call this number "x". We'll work backwards from there to find the number of applicants that need to apply in order to get 30 new employees.

We know that 5% of the remaining applicants fail the background investigation, which means that 95% pass. We also know that 23% of the remaining applicants do not show up for the interview, which means that 77% do show up.

Similarly, 12% of the remaining applicants do not pass the pre-screening assessment, which means that 88% do pass. Finally, 10% of all applicants do not meet the basic business requirements for the job, which means that 90% do meet the requirements.

Putting all of this information into the following equation;

0.9x × 0.88 × 0.77 × 0.95 = 30

Simplifying and solving for x, we get;

x = 30 / (0.9 × 0.88 × 0.77 × 0.95)

x ≈ 55.24

Therefore, Company B needs approximately 55 applicants.

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Answer:

the answer for this question is x=8

The value of 6+4 3/4 +(-2.5) is 3 3/10

PEDMAS is an acronym that shows the correct order of operations in mathematical problems. The full meaning of PEDMAS is ;

Parentheses

Exponents

Division

Multiplication

Addition

Subtraction

This order is followed when solving mathematical problems.

Solving 6+4 3/4 +(-2.5)

= 6+ 19/4 - 5/2

= ( 24+19-10)/4

= 33/10

= 3 3/10

Therefore the value of 6+4 3/4 +(-2.5) is 3 3/10

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Answer:10-x

Step-by-step explanation:5 containers 2 cups in each. 5 x 2= 10. we don't know how many cups of rice he uses for a recipe so we call it x. Then we subtract it from the 10 cups of rice.

Answer:

Step-by-step explanation:

The answer is A. 16.25cm.

Explanation:-

We know,

The Volume of Prism  =height*width*length;

Here, In the question Height and length is given.

So We have to do a simple calculation to find,width=

=> 5890.625/(14.5*25)

=>16.25 cm .

We don't need to worry about dimensions because all are in the same cm dimensions.

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Answer:

A. 16.25 cm

Step-by-step explanation:

To solve for the volume of a rectangular prism, we would use the formula V = l·w·h, where:

"l" is the base length

"w" is the base width

"h" is the height of the prism

In this problem, we are given the volume, height, and length of the rectangular prism. That means we need to find the value of w, the base width. To do this, we plug our known values into the equation and solve for w.

5,890.625 = (14.5)(25)w

To get w by itself, we first divide each side of the equation by 14.5. Remember that when you divide a number by itself, they cancel out.

(5,890.625)/(14.5) = (14.5)(25)w/(14.5)

406.25 = (25)w

Next, we can divide each side of the equation by 25 to get our answer.

406.25/25 = (25)w/25

w = 16.25 cm

Answer:

28

Step-by-step explanation:

i did 7 times 4

Answer:

10. 120 Degrees 12. 60 Degrees

Step-by-step explanation:

#12. Since CAD is 30, and BAD is a 90 degree angle, angle BAF is 60 degrees. Since BAF is 60 degrees and FAE and BAF are vertical angles, they have the same angle measure. 60 Degrees.

#10. Since BAF is 60, and FAE and BAF are on a line, we can do 180-60 to get the measure in degrees of that angle. FAE = 120 Degrees.

Answer:

Step-by-step explanation:

10. somewhere between 126 and 129, i feel its 128

12. between 60 and 65

The approximate standard error of the mean, assuming a 99.7% confidence level is 40.41.

Given population mean (µ) = $49,829

population standard deviation (σ) = $933

the randomly selected households (n) = 533 households

the confidence level = 99.7%

To find the standard error of the mean at a 99.7% of confidence level, we will substitute the above values in the below equation,

Standard error of the mean = σ/√n = 933/√533 ≅ 40.41

From the above analysis, we can conclude that the standard error of the mean at a 99.7% confidence level is 40.41.

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Answer:

40.41

Step-by-step explanation:

Plato/Edmentum

Answer:

47 months

Step-by-step explanation:

find 6.1% of 15k then divide that by 300

6.1% = 915

15,000 - 915 = 14085

14085 divided by 300 is 46.95 then rounded is 47

The functions f(x) = cos 2x + 1 and g(x) = sin x + 2 intersect at x = pi/6, pi/2, 5pi/6, and 3pi/2 in the interval [0, 2π).

To find the intersection points, we set f(x) equal to g(x) and solve for x.

cos 2x + 1 = sin x + 2

Rearranging, we get:

cos 2x = sin x + 1

Using the identity cos 2x = 1 - 2sin²x, we can rewrite this as:

1 - 2sin²x = sin x + 1

Simplifying and factoring, we get:

2sin²x + sin x = 0

sin x(2sin x + 1) = 0

Therefore, sin x = 0 or sin x = -1/2. Solving for x in the interval [0, 2π), we get x = pi/6, pi/2, 5pi/6, and 3pi/2. These are the values at which f(x) and g(x) intersect.

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Answer:

I am sorry this is just so new for me like what even is an "imaginary" solution, i am in 6th grade wth

The absence of the value 105.0 from the interval shows that the medication therapy significantly reduces wake time.

In statistics, mean is a measure of central tendency that represents the average value of a set of data. It is commonly referred to as the "arithmetic mean" or simply the "average." To calculate the mean, you add up all the values in the data set and divide the total by the number of values. For example, if you have the following data set: 2, 5, 8, 9, 12, the mean would be calculated as follows:(2 + 5 + 8 + 9 + 12) ÷ 5 = 7.2 . So the mean of this data set is 7.2. The mean is a useful measure of central tendency because it takes into account all the values in the data set and provides a single representative value that can be used to describe the overall characteristics of the data.

given

For a population receiving pharmacological treatments, the mean wake time was estimated with a 95% confidence interval.

where t/2 is the crucial value from the t-distribution with n-1 degrees of freedom and a confidence level of 95%, and x is the sample mean, s is the sample standard deviation, n is the sample size.

When we enter the provided values, we obtain:

s = 23.3

n = 23

t0.025,22 = 2.074

The mean wake time estimate with a 95% confidence interval for a population receiving medication is thus:

82.1 ± 2.074 * (23.3/√23)

which is equivalent to:

(71.4, 92.8)

The absence of the value 105.0 from the interval shows that the medication therapy significantly reduces wake time.

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In triangle ACE, with BD parallel to CE, using similar triangles and ratios, we get a quadratic equation with two possible solutions. Only the positive one is chosen, so AC is approximately 30.96 units long.

Since BD is parallel to CE, we can use the property of similar triangles to find the length of AC.

Triangles ABD and ACE are similar because they have the same corresponding angles. This means that the ratios of their corresponding side lengths are equal.

We know that AB = 10, AD = 16, and DE = 22.

Let x be the length of AC. Then, we have

AB/AD = CE/EA (by similarity of triangles ABD and ACE)

10/16 = CE/(x-16+22) (substituting CE = EA - DE and simplifying)

5/8 = CE/(x-6)

CE = (5/8)(x-6)

We also know that

BD/DE = AB/AE (by similarity of triangles ABD and ADE)

BD/22 = 10/(x-22) (substituting BD = CE and AE = AC - CE - DE, and simplifying)

CE = (220 - 10x)/(x-22)

Since CE is equal in both expressions, we can equate them and solve for x

(5/8)(x-6) = (220 - 10x)/(x-22)

5x² - 196x + 1320 = 0

x² - 39.2x + 264 = 0

Using the quadratic formula, we get

x = 30.96 or x = 8.54

The length of AC must be positive, so we choose x = 30.96.

Therefore, the length of AC is approximately 30.96 units.

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--The given question is incomplete, the complete question is given

" In the diagram shown, points B and D lie on sides AC and AE such that BD is parallel to CE. If AB=10, AD=16, and De=22 then find the length of AC "--

The answer is $11,092.63.

This could be calculated using the proportion. If the value of the car decreases by 15% each year, that means that after each year the value of the car is 85% of the value from the first year.

After 1st year:

$25,000 : 100% = x1 : 85%

x1 = $25,000 · 85% ÷ 100%

x1 = $21,250

After 2nd year:

$21,250 : 100% = x2 : 85%

x2 = $21,250 · 85% ÷ 100%

x2 = $18,062.5

After 3rd year:

$18,062.5 : 100% = x3 : 85%

x3 = $18,062.5 · 85% ÷ 100%

x3 = $15,353.12

After 4th year:

$15,353.12 : 100% = x4 : 85%

x4 = $15,353.12 · 85% ÷ 100%

x4 = $13,050.15

After 5th year:

$13,050.15 : 100% = x5 : 85%

x5 = $13,050.15 · 85% ÷ 100%

x5 = $11,092.63

Therefore, the value of the car 5 years after it is purchased is $11,092.63.

The values of the expression are,

⇒ x₂ = - 9.4

⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)

Given that;

Expression is,

e²ˣ = - 2x - 1

Hence, Function is,

⇒ f (x) = e²ˣ + 2x + 1 = 0

⇒ f' (x) = 2e²ˣ + 2

Now, By newton's method;

⇒ x (n + 1) = x (n) - f (x (n)) / f' (x(n))

⇒ x₂ = x₁ - f (x₁) / f' (x₁)

⇒ x₂ = - 5 - (e¹⁰ + 10 + 1)/(2e¹⁰ + 2)

⇒ x₂ = - 5 - (e¹⁰ + 11)/(2e¹⁰ + 2)

⇒ x₂ = - 5 (2.6 + 11) / ( 2 x 2.6 + 2)

⇒ x₂ = - 68 / 7.2

⇒ x₂ = - 9.4

⇒ x (n + 1) = x (n) - f (x (n)) / f' (x(n))

⇒ x₃ = x₂ - f (x₂) / f' (x₂)

⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)

Thus, The values of the expression are,

⇒ x₂ = - 9.4

⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)

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The table is completed as follows:

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

From the first row, when x = 0.2, y = 2, hence the constant is given as follows:

k = y/x

k = 2/0.2

k = 10.

Hence the equation is:

y = 10x.

Then the numeric values are given as follows:

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Answer:

Step-by-step explanation:

The solution to the system of equations `x=9y` and `3y - 3x =24` can be found by substituting the value of `x` from the first equation into the second equation. This gives us `3y - 3(9y) = 24`, which simplifies to `-24y = 24`. Solving for `y`, we get `y = -1`. Substituting this value of `y` into the first equation, we get `x = 9(-1) = -9`. So the solution to the system of equations is `(x,y) = (-9,-1)`.

Is there anything else you would like to know?

The equation of the line passing through the point (-3,-4) and parallel to the x-axis is y = -4.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept

Given that; the line passing through the point (-3,-4) and parallel to the x-axis.

A line that is parallel to the x-axis has a slope of 0, because the y-coordinate of any point on the line does not change as the x-coordinate varies.

Hence;

The equation of the line passing through the point (-3,-4) and parallel to the x-axis can be written in the form y = b, where b is a constant.

To determine the value of b, we substitute the coordinates of the given point (-3,-4) into the equation y = b:

-4 = b

Note that: y = b, where b is a constant.

y = -4

Therefore, the equation of the line y = -4.

Option C) y = -4 is the correct answer.

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