Calculate the mean, Variance and Standard deviation of the age of 12 student 16, 17, 18, 16/0.5, 17, 18, 19, 17, 17, 13, 17/½/2 and 16​

Answer:

25

Step-by-step explanation:

let farhan's age be x and his cousin's age be y

sum of ages = x + y = 38

7 years ago (so x-7 and y-7), farhan was thrice as old as his cousin, so 3 * his cousin's past age = farhan's past age= 3 *(y-7) = x-7

subtract y from both sides in the first equation to solve for x

x = 38-y

substitute this into the second equation

3 *(y-7) = 38-y-7

3y-21 = 31-y

add y to both sides to put all y values on one side

4y  -21 = 31

add 21 to both sides to solve for y

4y = 52

y = 13

sum of ages = x + y = 38 = 13 + x so x = 25 = 38-13

Answer:

Fruit mass = 63.2 g

Biscuit mass = 94.8 g

Step-by-step explanation:

Since the ratio of fruit mass to biscuit mass is 2:3, the fraction of fruit mass to the total of fruit and biscuit mass is 2/5 and the fraction of biscuit mass to the total of fruit and biscuit mass is 3/5.

For Monkey A, the total of fruit and biscuit mass is 73 g, which means that the fraction of fruit mass is 2/5 × 73 g = 29.2 g and the fraction of biscuit mass is 3/5 × 73 g = 43.8 g. Therefore, the values for fruit mass and biscuit mass are:

Fruit mass = 29.2 g

Biscuit mass = 43.8 g

For Monkey B, the total of fruit and biscuit mass is 73 + 85 = 158 g, which means that the fraction of fruit mass is 2/5 × 158 g = 63.2 g and the fraction of biscuit mass is 3/5 × 158 g = 94.8 g. Therefore, the values for fruit mass and biscuit mass are:

Fruit mass = 63.2 g

Biscuit mass = 94.8 g

True. bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.

A confidence intervals bar chart (shown as red lines)

In graphs, error bars are used to graphically show data variability and to denote error or uncertainty in reported measurements. They provide a basic indication of a measurement's accuracy or, alternatively, how far the true (error-free) value may deviate from the reported value. The standard deviation of uncertainty, the standard error, or a specific confidence range (such a 95% interval) are frequently represented as error bars. Due to the fact that these values are not the same, the measure chosen needs to be specified clearly in the graph or supporting text.

According to the definition the statement is true.

True. bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.

Learn more about bar graph here:

https://brainly.com/question/30582994

#SPJ1

We receive the ratio as follows:

7/17.5 = 12/x

We can cross-multiply and solve for x to determine x:

7x = 17.5 × 12

7x = 210

x = 210/7

x = 30

Hence, x has a value of 30 cm.

Measuring is a method that involves comparing an object's characteristics to a reference value to ascertain its attributes. The primary metric for expressing any quantity of items, things, and occurrences is measurement.

In a number of branches of mathematics, we work with several fundamental categories of measurement variables. As follows:

The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently. Also, in that, it requires a specific number of items to complete a specific task. We frequently encounter many measurements kinds for length, weight, times, etc. in our daily lives.

Learn more about measurements at:

https://brainly.com/question/4725561

#SPJ1

The probability the card is a diamond or a face card is [tex]\frac{11}{26}[/tex].

Probability refers to the likelihood that any random occurrence will occur. This expression refers to estimating the probability that any specific event will take place. For example, when we throw a coin into the air. Possibility: P(A) = f / N, determines the likelihood that an event will occur. Although probability and ratios are linked, the former dictates the latter. The probability of an occurrence must be known before determining its probability.

When we find the probability, we obtain:

There are 52 cards in a standard deck of cards.As there are four suits, there are 12 face cards, which we identify as the Kings, Queens, and Jacks. There are 13 diamonds total, 3 of which are face cards that have previously been counted. There are thus 10 diamonds without faces.

Out of the 52 cards in the deck, 10 diamonds plus 12 face cards equal 22.

P= [tex]\frac{22}{52}[/tex]= [tex]\frac{11}{26}[/tex].

To know more about probability visit:

https://brainly.com/question/30034780

#SPJ1

Answer: To simplify the expression, we can start by rewriting it as the product of the first fraction and the reciprocal of the second fraction. Then, we can factor the denominators of each fraction and simplify as much as possible.

x + 1 / (x^2 + x - 6) ÷ (x^2 + 5x + 4) / (x - 2)

= (x + 1 / (x + 3)(x - 2)) ÷ ((x + 4)(x + 1) / (x + 4)(x - 1))

= (x + 1 / (x + 3)(x - 2)) * ((x + 4)(x - 1) / (x + 4)(x + 1)) (reciprocal of second fraction)

= (x + 1 / (x + 3)(x - 2)) * (x - 1 / (x + 1)) (cancel out (x + 4) and simplify)

= (x + 1) * (x - 1) / (x + 3)(x - 2)(x + 1) (multiply the numerators and simplify)

= (x - 1) / (x + 3)(x - 2) (cancel out (x + 1) in the numerator and denominator)

Therefore, the simplified form of the expression is 1 / ((x + 3)(x - 2) / (x - 1)). This can be further simplified to:

1 / ((x + 3)(x - 2) / (x - 1)) = (x - 1) / ((x + 3)(x - 2)) * (x - 1) / 1 = (x - 1)^2 / ((x + 3)(x - 2))

So the answer is: 1 over the quantity (x + 3) times the quantity (x - 2), all multiplied by the quantity (x - 1) squared.

Step-by-step explanation:

The simplified form of the given expression is 1 over the quantity x plus 3 times the quantity x plus 4.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one maths operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

The given expression is:

[tex]\frac{x+1}{x^2+x-6} / \frac{x^2+5x+4}{x-2}[/tex]

When a fraction is in the denominator, we take the reciprocal of the fraction and multiply it with the numerator.

So the expression becomes,

[tex]\frac{x+1}{x^2+x-6} * \frac{x-2}{x^2+5x+4}[/tex]

We can factorize the expression x² + x - 6

x² + 3x - 2x - 6

= x(x+3) -2 ( x+3)

= (x-2) (x+3)

We can also factorize the expression x² +5 x +4

x² + 4x + x +4

= x(x+4) +1 ( x+4)

= (x+1) (x+4)

Substituting these values, the expression becomes as follows:

[tex]\frac{x+1}{(x-2)*(x+3)} * \frac{x-2}{(x+1)(x+4)} = \frac{1}{(x+3)(x+4)}[/tex]

Therefore the simplified form of the given expression is 1 over the quantity x plus 3 times the quantity x plus 4.

To learn more about expressions, follow the link.

brainly.com/question/1859113

#SPJ1

The distance between the man and the monument is 1060.16 feet.

Here we have the angle of elevation to be 18°

and the angle of depression to be 3°

Let the distance between the man and the monument be x feet

Now for any angle a, tana = opposite angle / adjacent angle

Hence we can sum up the building's height to be

x tan18 + x tan3 = 400

or, x(tan18 + tan3) = 400

or, x(0.3249 + 0.0524) = 400

or, 0.3773x = 400

or, x = 400/0.3773

or, x = 1060.16

Hence the distance between the man and the monument is 1060.16 feet.

To learn more about Heights and Distances visit

https://brainly.com/question/16716174

#SPJ4

On solving the provided question we can say that Variable, semi-variable, fixed, and variable is the right answer, hence it is (D).

A variable is something that may be changed in the setting of a math concept or experiment. Variables are often represented by a single symbol. The characters x, y, and z are often used generic symbols for variables. Variables are characteristics that can be examined and have a large range of values.

A semi-variable cost (Mixed)

Cost A's overall cost rises as manufacturing volume grows, but the per-unit cost stays the same. This implies that there are two types of costs: fixed and variable.

B: Variable Cost

The manufacturing volume directly correlates with the overall cost of Cost B. This suggests that the price is purely arbitrary.

Price C: Fixed

Regardless of the volume of output, the overall cost of Cost C is constant. This suggests that the price is set in its entirety.

D: Variable Cost

The manufacturing volume directly correlates with the overall cost of Cost D. This suggests that the price is purely arbitrary.

Variable, semivariable, fixed, and variable is the right answer, hence it is (D).

To know more about variable visit:

https://brainly.com/question/2466865

#SPJ1

The equation of the lines with the points (-8, 3) and (-6, 0) is y = -3x/2 + 9.

The equation of the lines with the points (5, 4.5) and (5, -1) is y = 4.5.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data point (-8, 3), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 3 = (0 - 3)/(-6 + 8)(x + 8)

y - 3 = -3x/2 - 12

y = -3x/2 + 9

For points (5, 4.5) and (5, -1), we have:

At data point (5, 4.5), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 4.5 = (-1 - 4.5)/(-5 - 5)(x - 5)

y - 4.5 = 0

y = 4.5

Read more on slope here: brainly.com/question/23086745

#SPJ1

The value of x in the triangle, given the angle measures of the other angles, is D. 100 degrees

To find the value of x, you first need to find the value of the last interior angle in the triangle.

The sum of the interior angles of a triangle would add up to 180 degrees which means that the angle inside would be :

= 180 - 65 - 35

= 180 - 100

= 80 degrees

Angles on a straight line add up to 180 degrees so the value of x, which is on a straight line with 80 degrees, is :

= 180 - 80

= 100 degrees

Find out more on triangles at https://brainly.com/question/29591996

#SPJ1

The maximum total deduction that can be claimed is OE. $17,100.

What is deduction ?

Deduction refers to the process of subtracting or taking away something. In the context of taxes, a deduction is a specific amount of money that a taxpayer is allowed to subtract from their income before calculating their tax liability. Deductions are one way to reduce the amount of taxes owed and can help to lower a person's overall tax burden.

There are two main types of deductions in the U.S. tax system: standard deductions and itemized deductions. The standard deduction is a fixed amount that varies depending on the taxpayer's filing status, while itemized deductions are specific expenses that a taxpayer can deduct from their taxable income. Some common examples of itemized deductions include mortgage interest, charitable contributions, medical expenses, and state and local taxes.

It's important to note that not all deductions are available to all taxpayers, and there are specific rules and limits that apply to each type of deduction. It's also important to keep accurate records and documentation to support any deductions that are claimed on a tax return.

The maximum total deduction that can be claimed is OE. $17,100, because that is the sum of the deductible expenses and the standard deduction.

The question is asking for the maximum total deduction that can be claimed, given certain deductible expenses and a standard deduction.

The standard deduction for the tax year is $6,100, and the deductible expenses are $6,000 in mortgage interest and $5,000 in charitable contributions.

Since the deductible expenses ($6,000 + $5,000 = $11,000) are less than the standard deduction of $6,100, it makes sense to use the standard deduction instead of itemizing deductions.

Therefore, the maximum total deduction would be the sum of the deductible expenses and the standard deduction:

$11,000 + $6,100 = $17,100

So, the maximum total deduction that can be claimed is OE. $17,100.

To know more about deduction visit :

https://brainly.com/question/29307306

#SPJ1

The sine, cosine and tangent are obtained applying the trigonometric ratios presented in this problem.

The three trigonometric ratios are defined as follows:

The hypotenuse is the slanted segment connecting the horizontal and the vertical segment.

For the desired angle, you must identify the adjacent side(between the angle and the angle of 90º) and the opposite side.

The problem is incomplete, hence the concepts needed to obtain the sine, cosine and tangent were presented.

More can be learned about trigonometric ratios at brainly.com/question/24349828

#SPJ1

cos(0) and sin(0) both have a value of 0, so they would be selected.

cos(pi)/2 is equal to -0.5, and sin(3(pi)/2) is equal to -1, so they would not be selected.

Answer:

1 | 3 | 5

Step-by-step explanation:

sin 0 sin 3pi/2 and tan pi

cos pi/2 is -.5

cos 0 is 1

Answer:

A commonly used fraction that helps you understand a different size or amount is called a ratio.

Step-by-step explanation:

A ratio is a comparison of two or more quantities or measurements, expressed as a fraction or a colon. Ratios are commonly used to express the relationship between different amounts or sizes, and they can be used to help solve problems involving proportions, rates, and percentages. For example, if you are making a recipe that calls for two cups of flour and one cup of sugar, the ratio of flour to sugar is 2:1, or 2/1. Ratios can also be expressed in decimal or percentage form!

The units for the amount of time that the plane descends are minutes, and the units for the plane's altitude are feet. Let's define a variable t for the amount of time that the plane descends. Then we can write an expression for the plane's altitude in terms of t as:

Altitude = 34,000 - (1,000 * t)

This expression represents the plane's initial altitude of 34,000 feet, minus the rate of descent (1,000 feet per minute) times the amount of time that the plane descends.

To find when the plane will be at an altitude of 3,000 feet, we can set the expression equal to 3,000 and solve for t:

3,000 = 34,000 - (1,000 * t)
31,000 = 1,000 * t
t = 31

So the plane will be at an altitude of 3,000 feet after 31 minutes of descent.

To find how long before the plane touches down on the runway, we can set the expression equal to 0 and solve for t:

0 = 34,000 - (1,000 * t)
34,000 = 1,000 * t
t = 34

So the plane will touch down on the runway after 34 minutes of descent.

Here is the completed worksheet:

Quantity Name | Time | Altitude
--- | --- | ---
Unit | minutes | feet
Given Value 1 | 10 | 34,000
Given Value 2 | | 24,000
Slope | | -1,000
Intercept | | 34,000
Expression | t | 34,000 - (1,000 * t)
Question 1 | 31 | 3,000
Question 2 | 34 | 0

https://brainly.com/question/29739212

#SPJ1

Answer:

b

Step-by-step explanation:

because u can tell

At the closing of her home purchase, Michelle should expect to pay prepaid interest of $6,934.50. This amount represents the interest accrued from April 8th to the end of the month.

The monthly payment for Michelle's mortgage is calculated as follows:

Principal and interest payment = (95,000 - 15,000) x 0.0495 / 12

This equals a monthly payment of $420.63.

Michelle's total interest over the life of the loan is $119,750. This amount is the sum of her prepaid interest and the total interest she pays over the life of the loan.

The coordinates of point l are (8,9).

Numbers used to identify the position of a point in a plane or in space. It is mostly used in mathematics, science, and engineering. Coordinates are used to define locations on maps, to plot graphs, and to identify points on a two-dimensional plane. By knowing the coordinates of two points, one can calculate the distance between them.


To find this point, we must first calculate the midpoint between j and k. The midpoint can be found by taking the average of the x-coordinates and y-coordinates. The midpoint between j and k is (8,10). Since the ratio of jl:kl is 5:1, we can determine that l is 5 units away from j and 1 unit away from k. This means that l must be 5 units up and 1 unit to the right from the midpoint. Thus, the coordinates of l are (8,9).

To know more about coordinates click-
https://brainly.com/question/27481419
#SPJ1

The triangle XYZ has a scale factor of 2.53 and hence side length XY is

7.6 units.

The scale factor defines a variable in a ratio of two different measurements.

Sometimes drawings of large models are represented in a scale factor of a smaller unit.

Given, The side WV, of the triangle UVX is 6 and the corresponding side XZ  of triangle 15.2.

So, The scale factor is 15.2/6 = 2.53.

Therefore, The side length XY = 3×2.53 = 7.6.

learn more about scale factors here :

https://brainly.com/question/30215119

#SPJ1

It is cheaper to drive the old truck, which costs $11.58 to drive 60 miles, compared to the diesel truck, which costs $15.44 to drive the same distance, given the current fuel prices.

An algebraic expression is a mathematical phrase that consists of variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. It is a combination of constants, variables, and operators that represent a value or a relationship between values.

For example, "3x + 5" is an algebraic expression where "3" and "5" are constants, "x" is a variable, and "+" is an operator. The expression can be evaluated by substituting a value for "x" and performing the necessary operations.

Algebraic expressions can also be simplified by combining like terms and using the rules of arithmetic to simplify the expression. For instance, the expression "2x + 3x" can be simplified to "5x" by adding the coefficients of the like terms "x".

Algebraic expressions are used extensively in algebra to represent equations and relationships between variables. They are also used in a wide range of mathematical and scientific applications, including physics, engineering, and finance.

To compare the cost of driving the old truck to the diesel truck, we need to know the fuel efficiency of the old truck. Let's assume that the old truck uses gasoline and has a fuel efficiency of 20 miles per gallon.

To drive 60 miles, the old truck will use 60/20 = 3 gallons of gasoline.

At $3.86 per gallon, the cost of 3 gallons of gasoline is 3 * $3.86 = $11.58.

The diesel truck uses 4 gallons of diesel to drive 60 miles. The cost of diesel is not given in the problem, so we'll assume it's the same as the cost of gasoline, $3.86 per gallon.

At $3.86 per gallon, the cost of 4 gallons of diesel is 4 * $3.86 = $15.44.

Therefore, it is cheaper to drive the old truck, which costs $11.58 to drive 60 miles, compared to the diesel truck, which costs $15.44 to drive the same distance, given the current fuel prices.

To know more about efficiency visit:

https://brainly.com/question/13646957

#SPJ1

We require x = 170 televisions to minimize total cost

The minimum of a function is the lowest value of that function.

Given that a television manufacturer produces x sets per week so the total cost of production is given by relation C(x) = x² - 195x² + 66000x + 15000.

To find the minimum value, we differentiate C(x) with respect to x and equate to zero.

So,  C(x) = x² - 195x² + 66000x + 15000

dC(x)/dx = d(x² - 195x² + 66000x + 15000)/dx

= dx²/dx - d195x²/dx + d66000x/dx + d15000/dx

= 2x - 195(2)x + 66000 + 0

= 2x - 390x + 66000

= -388x + 66000

Equating to zero, we have

dC(x)/dx = 0

-388x + 66000 = 0

-388x = -66000

x = -66000/-388

x = 170.1

x ≅ 170

So, we require x = 170 televisions to minimize total cost

Learn more about minimum cost here:

https://brainly.com/question/27060649

#SPJ1

The vertical function of the ball can be modelled using the equation h(t) = 16t^2 + 75t + 4, where h(t) is the height of the ball at time t, 16 is the acceleration due to gravity, 75 is the initial velocity of the ball, and 4 is the initial height of the ball.

Acceleration due to gravity is the rate of change of velocity (speed) of an object in free fall due to the force of gravity. It is denoted by g and is equal to 9.80665 m/s2 at sea level. It is the force of gravity that causes objects to fall to the ground and accelerates them as they approach the ground. When an object is in free fall, it accelerates at a rate of 9.8 m/s2. This means that after one second, the object will be travelling at 9.8 m/s, after two seconds it will be travelling at 19.6 m/s, and so on. Without the force of gravity, objects would not accelerate in free fall.

The equation h(t) = 16t^2 + 75t + 4 models the vertical function of the ball by combining the effects of acceleration due to gravity (16), initial velocity (75), and initial height (4). The term 16t^2 represents the acceleration due to gravity, which causes the ball to accelerate in the vertical direction at a rate of 16 meters per second squared. The term 75t represents the initial velocity of the ball, which causes the ball to move in the vertical direction at a rate of 75 meters per second. Finally, the term 4 represents the initial height of the ball, which is 4 meters. By combining these three effects, the equation h(t) = 16t^2 + 75t + 4 accurately models the vertical function of the ball.

To know more about Acceleration due to gravity, visit:

https://brainly.com/question/88039

#SPJ1

Answer:

[tex]\sf{The\;Marginal\;Revenue\;} $MR(8) = \boxed{288} \;dollars per unit$}[/tex]

Step-by-step explanation:

What is Marginal Revenue?
Marginal Revenue is the revenue that is gained from the sale of an additional unit. It is the revenue that a company can generate for each additional unit sold

Given the equation for revenue function
[tex]R(q) = -7q^2+400q[/tex]

the Marginal Revenue [tex]MR(q)[/tex] is the first derivative of this function wrt [tex]q[/tex]

[tex]MR(q) = \dfrac{d}{dq}\left(R(q)\right)\\= \dfrac{d}{dq}(-7q^2 + 400q)\\\\= \dfrac{d}{dq}(-7q^2) + \dfrac{d}{dq}(400q)\\\\= -14q + 400\\\\[/tex]

For [tex]q = 8,[/tex] this works out to:

[tex]MR(8) = -14(8) + 400\\\\= -112 + 400\\\\= 288[/tex]

And that is the answer

Step-by-step explanation:

is given above in the pdf

Answer:

Step-by-step explanation

The bottle had 20 ounces that before and 8 ounces after

8+x=20

20-x=8

20-8=x

20-8=12

The mean of the sampling distribution is 200, and the standard deviation of the sampling distribution is 4.

The sampling distribution is a theoretical distribution that represents the behavior of sample means from all possible samples of a given size that can be drawn from a population.

However, the standard deviation of the sampling distribution is not the same as the standard deviation of the population.

Mathematically, we can represent the mean of the sampling distribution as follows:

μ(x) = μ = 200

Where μ(x) represents the mean of the sampling distribution and μ represents the mean of the population.

We can also calculate the standard error of the mean using the following formula:

σ(x) = σ / √(n)

Where σ(x) represents the standard deviation of the sampling distribution, σ represents the standard deviation of the population, and sqrt(n) represents the square root of the sample size.

Plugging in the values given in the problem, we get:

σ(x) = 20 / √(25) = 4

To know more about standard deviation here.

https://brainly.com/question/16555520

#SPJ4

Answer:

they are

Step-by-step explanation:

divide 12*4=3

9*3=3

same ratio

Answer:

Step-by-step explanation:

ITS GOING LEFT AND RIGHT HOPE THIS HELPS IF NOT TEXT ME PLSS .

a. Thor works more hours each week, the quantity of donations the organization raises each week declines, but the link is not very strong.

When two variables are correlated negatively, the other variable's value falls as the value of the first variable rises.

The correlation coefficent, which expresses correlation on a scale from +1 to -1, is used. Numbers less than 0 indicate a negative connection. An increase in one variable confidently foretells a drop in the other when there is a perfect negative correlation, with a coefficient of -1. Non-zero coefficients between +1 and -1 are used to show lower degrees of connection. 0 means there is no propensity for the variables to change simultaneously, either positively or negatively.

a. A weak negative linear relationship between hours worked and donations collected in this context means that as Thor works more hours each week, the quantity of donations the organization raises each week declines, but the link is not very strong.

b. When we say there is a weak correlation between two variables, we are referring to their level of relationship. The negative correlation in this instance indicates that there is a propensity for the amount of donations collected to decline as the time spent working increases, but the relationship is not very strong, indicating that there is a lot of variability in the data and making firm predictions or conclusions based on this correlation alone is challenging.

c. Tom's boss's claim is wrong as the negative correlation or the decline in donation is a mere coincidence and does not have a relation to Thor's work.

Learn more about correlation here:

https://brainly.com/question/30116167

#SPJ1

The library is 20 miles from the community pool as calculated after performing mathematical operations.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, In Hillsdale, the library is due south of the courthouse and due west of the community swimming pool.

Also given,

The distance between the library and the courthouse is 15 miles.

The distance between the courthouse and the city pool is 25 miles,

Using the Pythagorean theorem, we have:

x = 25² - 15²

x² = 625 - 225

x = 400

Taking the square root of both sides, we get:

x = 20

Therefore, the library is 20 miles from the community pool

Learn more about Mathematical operations here:

https://brainly.com/question/8959976

#SPJ9

For x = 4.1:

Slope of PQ =5.1

For x = 4.01:

Slope of PQ =6.01

For x = 3.9:

Slope of PQ =15.1

For x = 3.99:

Slope of PQ =105.99

From the results above, we can guess that the slope of the tangent line to the curve at P is approximately 6.

To find the slope of the secant line PQ, we need to first find the coordinates of point Q in terms of x:

Q = (x, x² + x + 8)

Then, the slope of the secant line PQ is given by:

(yQ - yP) / (xQ - xP)

where yP = 28 and xP = 4, and yQ and xQ depend on the value of x.

For x = 4.1:

Q = (4.1, 4.1² + 4.1 + 8) = (4.1, 28.51)

Slope of PQ = (28.51 - 28) / (4.1 - 4)

= 0.51 / 0.1

= 5.1

For x = 4.01:

Q = (4.01, 4.01² + 4.01 + 8) = (4.01, 28.0601)

Slope of PQ = (28.0601 - 28) / (4.01 - 4)

= 0.0601 / 0.01

= 6.01

For x = 3.9:

Q = (3.9, 3.9² + 3.9 + 8) = (3.9, 26.49)

Slope of PQ = (26.49 - 28) / (3.9 - 4)

= -1.51 / -0.1

= 15.1

For x = 3.99:

Q = (3.99, 3.99² + 3.99 + 8) = (3.99, 26.9401)

Slope of PQ = (26.9401 - 28) / (3.99 - 4)

= -1.0599 / -0.01

= 105.99

As x approaches 4 from both sides, the x-coordinate of Q approaches 4, and the slope of PQ approaches the slope of the tangent line to the curve at P(4,28). From the results above, we can guess that the slope of the tangent line to the curve at P is approximately 6.

Learn more on calculating slopes of tangent here https://brainly.com/question/6353432

#SPJ1