5 years ago i was 5 times older then my son. in 8 years time i will be 3 times older then my son. how old am i today?

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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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:

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 total area of the figure with points A(-5,4), B(4,4), C(4,1),  D(1,1), E(4,-3) F(4,-6), G(-5, -6) has been found as  51 square units.

A graph is described as a mathematical representation of a network and it describes the relationship between lines and points.

The first step is to divide the figure is into two rectangles and a triangle.

we notice that the points B, C, E, and F will form a rectangle with base BC and height of 7 units.

We also notice that the  points A, D, and G form a rectangle with base AG and height 5 units.

we notice that  points C, D, and E form a triangle with base CE and height 4 units.

we notice that the  length of BC is 4 - 4 = 0, therefore  the area of the rectangle with base BC is 0.

The area of the rectangle with base AG is (4 - (-5)) x 5 = 45 square units. The area of the triangle with base CE is (4 - 1) x 4 / 2 = 6 square units.

In conclusion, the total area of the figure with points A(-5,4), B(4,4), C(4,1),  D(1,1), E(4,-3) F(4,-6), G(-5, -6)  is 45 + 6 = 51 square units.

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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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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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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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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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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:

120

Step-by-step explanation:

25% is equal to 1/4. If you divide 30 by 1/4 you get 120. To check this, if you multiply 120 by 1/4 you get 30.

Answer: 120

Step-by-step explanation:

In order to find the missing value, divide the provided value by the percentage as follows:

30 / 0.25 = 120

This can be double-checked by plugging the number into the statement afterwards: 25% of 120 is 30, which is true

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:

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

Given a rectangle with dimensions of:

Use area equation and find the value of x:

The second root is ignored as being negative.

The dimensions of the rectangle are:

Answer:

the answer for this question is x=8

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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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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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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Answer:

h=.34

Step-by-step explanation:

1/2(bh)=A

1/2(5.5*h)=8.9375

5.5h=1.875

h=.34

Answer:

Step-by-step explanation:

Answer:

108

You rounded to the nearest tens place.

The 0 in the tens place rounds up to 1

Step-by-step explanation: because the digit to the right in the ones place is 8.

110

When the digit to the right is 5 or greater we round away from 0.

108 was rounded up and away from zero to 110

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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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 "--

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?

As per the given variables, Victor jumped a total of 4 yards.

Total yards jumped = 6 feet high

Additional yards = 2

A yard is one linear yard. "Yd" is the yard symbol. The standard of measurement has always been derived from either a natural item or a portion of the human body, such as a foot, an arm's length, or the width of a hand.

Converting the initial jump of 6 feet to yards, as the additional distance given is also in yards.

There are 3 feet in a yard, therefore -

6 feet = 6/3  

= 2

Thus, Victor jumped 2 yards initially, and then 2 more yards as given in the problem.

Calculating, the total distance Victor jumped in yards -

= 2 + 2

= 4

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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.

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 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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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

Real-estate agent tested the effect of staging on home sale prices. Out of 10 comparable homes, 5 were staged. Staged homes sold for $15k more on average, with no skewness or outliers.

Based on the information given, the real-estate agent conducted an experiment to test the effect of selling a staged home vs. selling an empty home.

The hypothesis is that empty homes sell for lower prices than staged homes. The agent randomly assigned 5 empty homes to be staged and obtained a list of 10 comparable homes.

The mean selling price of the 5 empty homes was $150,000 with a standard deviation of $22,000. The mean selling price of the 5 staged homes was $175,000 with a standard deviation of 35,000. There was no strong skewness or outliers in the dot plots of the two samples.

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The actual consumer spending at a price of $27 per unit is $268.26.

Substitute the given price into the supply equation to get the corresponding quantity supplied:

p = q + 10

27 = q + 10

q = 17

Substitute q = 17 into the demand equation to get the corresponding price:

4q² + p² = 1405

4(17)² + p² = 1405

p² = 1405 - 1156

p² = 249

p = 15.78

The actual consumer spending can be calculated by multiplying the quantity demanded by the price:

Actual consumer spending = quantity demanded x price per unit

= 17 x 15.78

= $268.26

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The demand and supply equations for a certain product are given by space 4 q squared plus p squared equals 1405 and p equals q plus 10 where p is in dollars per unit and q is in units. For a price of $27 per unit, determine the actual consumer spending.

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