4.02 Lesson check ! (10)

Given:

Vince has 1/2 ton of gravel.

It is to be spread equally in 8 square yards.

To find:

How many tons of gravel will be spread in each square yard?

Solution:

Total gravel = 1/2 ton

To be spread equally in 8 square yards.

No. of tons of gravel will be spread in each square yard = (1/2) / 8 = 1/16 tons.

Therefore, 1/16 tons of gravel will be spread in each square yard.

Answer:

Given:

Vince has 1/2 ton of gravel.

It is to be spread equally in 8 square yards.

To find:

How many tons of gravel will be spread in each square yard?

Solution:

Total gravel = 1/2 ton

To be spread equally in 8 square yards.

No. of tons of gravel will be spread in each square yard = (1/2) / 8 = 1/16 tons.

Therefore, 1/16 tons of gravel will be spread in each square yard.

Step-by-step explanation:

Answer:

u multiply 3 with 8 then u get ur answer the u do the same method which is multiplication with 6 with 4 to get ur answer

The answer is no, you do not have enough time to climb all 3 walls within 7 1/2 minutes.

What is the conversion of the unit?

A conversion factor is a fraction equal to ' 1 '.  It has the same quantity in the numerator and denominator, but they're in different units.  You use it to convert a number from one unit to another unit.

There are different ways to approach this problem, but one possible method is to convert everything to a common unit, such as seconds.

First, convert 7 1/2 minutes to seconds by multiplying by 60:

7.5 minutes x 60 seconds/minute = 450 seconds

Next, multiply the time it takes to climb each wall by 3 to find the total time needed:

3 walls x 155 seconds/wall = 465 seconds

Comparing the total time needed (465 seconds) to the available time (450 seconds), we see that there is not enough time to climb all three walls.

Therefore, the answer is no, you do not have enough time to climb all 3 walls within 7 1/2 minutes.

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The mean when the time required to play a certain board game is uniformly distributed between 15 and 60 minute is 35.6.

In statistics, the mean is a measure of central tendency that is calculated by summing up a set of numerical values and dividing by the number of values in the set. The mean is also known as the arithmetic mean or the average.

For example, suppose we have the following set of numbers: 3, 5, 7, 10, and 12. To find the mean, we add up these numbers (3 + 5 + 7 + 10 + 12 = 37) and divide by the number of values in the set (5). The mean of this set of numbers is 7.4, which represents the typical or average value of the set.

The formula for the mean is:

mean = (sum of values) / (number of values)

By using the Excel formula= AVERAGE (data), sample mean will be 35.6.

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Answer:

its bar graph

Step-by-step explanation:

thanks for the question

please mark me brainless

The respοnses fοr favοurite vacatiοn spοt can be described best by a pie chart.

One sοrt οf graph that illustrates the infοrmatiοn in the circular graph is a pie chart. It is a sοrt οf graphical representatiοn οf data where the slices οf pie depict the relative sizes οf the data. A list οf numerical and categοrical variables is necessary fοr a pie chart. Pie in this cοntext refers tο the entire thing, and slices tο its cοmpοnent pοrtiοns.

If yοu asked "What is yοur favοrite vacatiοn spοt?" tο a grοup οf peοple, the mοst apprοpriate type οf graph tο represent the respοnses wοuld be a pie chart.

A pie chart is a circular chart that is divided intο slices tο represent the prοpοrtiοn οf each categοry in a dataset.

In this case, each slice οf the pie chart wοuld represent a different vacatiοn spοt, and the size οf each slice wοuld cοrrespοnd tο the prοpοrtiοn οf respοndents whο selected that vacatiοn spοt as their favοrite.

Pie charts are useful fοr displaying categοrical data, where the categοries are mutually exclusive and add up tο 100%.

They are easy tο read and understand, and can quickly shοw the distributiοn οf respοnses amοng the different categοries.

On the οther hand, a bar graph οr a line graph wοuld nοt be apprοpriate fοr this type οf data since the respοnses are nοt numerical οr cοntinuοus.

A line plοt wοuld alsο nοt be apprοpriate since it is used tο display a series οf data pοints, and in this case, there is οnly οne data pοint per categοry.

Therefοre, a pie chart is the best chοice.

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After addressing the issue at hand, we can state that As a result, the equation value of x is roughly 10.57 units (rounded to two decimal places).

An equation is a mathematical proclamation that proves the equality of two expressions capable of connecting through an equal sign '='. For instance, 2x - 5 = 13. Explanations include 2x-5 and 13. The '=' symbol links up the two expressions. A mathematical formula containing two formulas on either side of a =) (=) is known as an equation. It depicts the equivalence relationship between left and right methodologies. L.H.S. = R.H.S. (left edge = top half) in any formula.

Using the information provided, we can construct the following equation based on the concept of similar triangles:

x/(9+18) = 10/(BC) (BC)

9 + 18 = 27 = AB = AP + PB

Because triangle ABC is a right triangle (angle B is 90 degrees), we can apply the Pythagorean theorem to calculate the length of segment BC:

BC2 = AB2 - AC2 BC2 = 272 - 102 BC2 = 649 BC = sqrt (649)

When we plug this value into our original equation, we get:

x/(9+18) = 10/sqrt (649)

When we simplify, we get:

x/27 = 10/sqrt (649)

When we multiply both sides by 27, we get:

x = 270/sqrt (649)

As a result, the value of x is roughly 10.57 units (rounded to two decimal places).

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Simplified form of the algebraic expression (x^2 - x - 12) / (x^2 - 4) = (x + 3) / (x - 2)

To simplify the given algebraic expression (x^2 - x - 12) / (x^2 - 4), we first need to factor both the numerator and denominator as much as possible.

We can factor the numerator using the product-sum method or the quadratic formula, which yields:

x^2 - x - 12 = (x - 4)(x + 3)

Similarly, we can factor the denominator as a difference of squares, which gives:

x^2 - 4 = (x - 2)(x + 2)

Now, we can substitute these factorizations into the original expression:

(x^2 - x - 12) / (x^2 - 4) = [(x - 4)(x + 3)] / [(x - 2)(x + 2)]

At this point, we can simplify the expression by canceling out the factors that appear in both the numerator and denominator. Specifically, we can see that (x - 4) and (x + 2) appear in both the numerator and denominator, so they cancel out:

[(x - 4)(x + 3)] / [(x - 2)(x + 2)] = (x + 3) / (x - 2)

So the simplified expression is (x + 3) / (x - 2).

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if () is not defined for non-integer values of d, then f (3.5) would not make sense.

In mathematics, an inequality is a statement that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠). The values being compared can be numbers, variables, or expressions.

by the question.

a. At the beginning of the epidemic, the number of days since the epidemic began is 0. Therefore, substituting d = 0 in the equation f(d) = 50- () gives f (0) = 50 - 0 = 50. So, there were 50 people with the flu at the beginning of the epidemic.

b. The rate at which the flu is spreading can be determined by examining the coefficient of d in the equation f(d) = 50- (). Specifically, if the coefficient is positive, then the flu is spreading at an increasing rate, and if the coefficient is negative, then the flu is spreading at a decreasing rate. Additionally, the magnitude of the coefficient gives an indication of how quickly the flu is spreading. However, since the expression in the parentheses is not given in the question, it is not possible to determine the rate at which the flu is spreading.

c. f(1) represents the number of people with the flu after one day since the epidemic began. Substituting d = 1 in the equation f(d) = 50- (), we get f(1) = 50 - (). Therefore, f (1) depends on the value of ().

d. It is not possible to determine whether f(3.5) makes sense in this situation without knowing the value of (). If () is defined for non-integer values of d, then f(3.5) would make sense and represent the number of people with the flu after 3.5 days since the epidemic began.

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The domain can be written as 3 <x < 81.75, which includes all x values that are feasible and fit within the constraints of the issue.

The most appropriate domain for this situation is (c) 3 < x < 81.75.

The reason for this is that the taxi charges $3 for the first mile, so x must be greater than 1. After that, the taxi charges $2.25 for every mile after the first, so the domain must exclude x = 0. Additionally, the problem states that the farthest the taxi will travel is 35 miles, so the domain must also include x < 35.

Therefore, the domain can be expressed as 3 < x < 81.75, which allows for all possible values of x that fall within the given parameters of the problem.

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a) The probability is equal to the proportion of the range that lies below 17 minutes.P(X< 17) = (17 - 16) / (23 - 16) = 1/7

b) The probability is equal to the proportion of the range that lies above 22 minutes.P(X > 22) = (23 - 22) / (23 - 16) = 1/7

c)  The probability is equal to the proportion of the range that lies between 18 and 20 minutes.P(18 ≤ X ≤ 20) = (20 - 18) / (23 - 16) = 2/7

d) The mean and standard deviation of the download times are 19.5 and 1.4 minutes, respectively.

The probability that the download time will be less than 17 minutes.The probability is equal to the proportion of the range that lies below 17 minutes.P(X< 17) = (17 - 16) / (23 - 16) = 1/7

The probability that the download time will be more than 22 minutes.The probability is equal to the proportion of the range that lies above 22 minutes.P(X > 22) = (23 - 22) / (23 - 16) = 1/7

The probability that the download time will be between 18 and 20 minutes.The probability is equal to the proportion of the range that lies between 18 and 20 minutes.P(18 ≤ X ≤ 20) = (20 - 18) / (23 - 16) = 2/7

The mean and standard deviation of the download times.Using the formula for the mean and standard deviation for a uniform distribution with a range of [a, b],μ = (a + b) / 2 = (16 + 23) / 2 = 19.5σ = (b - a) / sqrt(12) = (23 - 16) / sqrt(12) ≈ 1.4 Therefore, the mean and standard deviation of the download times are 19.5 and 1.4 minutes, respectively.

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Answer:

4

Step-by-step explanation:

The volume of small pyramid with base length 2, base width 2, and height 2. Its volume was 8/3π. We then scaled it by a factor of 2 and verified the formula V' = V × k3 holds true.

To create the smallest pyramid possible, we will use a tool such as a ruler or protractor to measure and construct the pyramid. Let's assume that we are using a ruler and that the smallest pyramid we can construct has a base length of 2 units, a base width of 2 units, and a height of 2 units.

To calculate the volume of the pyramid, we use the formula:

V = (1/3) × base area × height

The base area of the pyramid is:

A = base length × base width = 2 × 2 = 4 square units

Therefore, the volume of the pyramid is:

V = (1/3) × 4 × 2 = 8/3 cubic units (in terms of π, this is 8/3π cubic units)

Now, let's scale the original pyramid by a factor of k = 2. To find the new dimensions of the scaled pyramid, we multiply each dimension of the original pyramid by the scale factor k:

Base length = 2 × 2 = 4 units

Base width = 2 × 2 = 4 units

Height = 2 × 2 = 4 units

The base area of the scaled pyramid is:

A' = base length × base width = 4 × 4 = 16 square units

The volume of the scaled pyramid is:

V' = (1/3) × A' × height = (1/3) × 16 × 4 = 64/3 cubic units (in terms of π, this is 64/3π cubic units)

Now, we can verify that the formula V' = V × k3 holds true for the scaled pyramid:

V' = 64/3 cubic units

V = 8/3 cubic units

k = 2

V' = V × k3

64/3 = (8/3) × 23

64/3 = 8/3 × 8

64/3 = 64/3

Therefore, the formula V' = V × k3 holds true for a pyramid, and we have successfully verified it using the scaled pyramid.

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The dimensions of the ramp are approximately 1.73 feet in height, 5.19 feet in width, and 22.96 feet in length.

First we can use the formula for the volume of a rectangular prism:

volume = length × width × height

Substituting the expressions we found for the length, width, and height in terms of h, we get:

150 cubic feet = (10h + 5 feet) × (3h feet) × (h feet)

Multiplying out the terms on the right-hand side, we get:

150 cubic feet = 30h^3 + 15h^2 cubic feet

Subtracting 150 cubic feet from both sides, we get:

0 = 30h^3 + 15h^2 - 150 cubic feet

Dividing both sides by 15 cubic feet, we get:

0 = 2h^3 + h^2 - 10

This is a cubic equation that we can solve using various methods as factoring. One solution is:

h ≈ 1.73 feet

Substituting this value back into the expressions we found for the width and length, we get:

The width is 3h ≈ 5.19 feet.

The length is 10h + 5 ≈ 22.96 feet.

Therefore, the dimensions of the ramp are approximately 1.73 feet in height, 5.19 feet in width, and 22.96 feet in length.

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Aproximate speed of the Earth's rotation around the Sun is 18.5 miles per second (30 km per second). 110,000 kilometers per hour is equal to 30 kilometers per second.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

Hence, Aproximate speed of the Earth's rotation around the Sun is 18.5 miles per second (30 km per second). 110,000 kilometers per hour is equal to 30 kilometers per second.

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Answer:

3% of 600 is (3/100) x 600 = 18.

So, a number that is 3% larger than 600 would be:

600 + 18 = 618.

Therefore, the number that is 3% larger than 600 is 618

Answer:

618

Step-by-step explanation:

Let us first see what is 3% of the 600

3/100 x 600 = 18

a number that is 3% larger than 600 is 600+18 = 618.

Mode: The mode of this data is 8 hours. This is because 8 hours was the most frequently reported amount of time that the students watched TV during a school week.

Amount is a quantitative expression of magnitude, size, or degree of a particular quantity. It is typically used to describe an object, person, or an event. Amount is used to quantify something, to describe its size, duration, or extent. It can be used to measure a wide range of physical and abstract entities, such as money, time, energy, resources, and emotions. For example, you might say “there was a large amount of people at the event” or “I have a certain amount of money saved up.”

Range: The range of this data is 8 hours. This is because the difference between the highest amount of time reported (16 hours) and the lowest amount of time reported (8 hours) is 8 hours.

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Probability that the thread length of a randomly selected bolt is within 1.5 SDs of its mean value is 0.8664, is farther than 2.5 SDs from its mean value is 0.0124 and between 1 and 2 SDs from its mean value is 0.2728.

Probability that the thread length of a randomly selected bolt is within 1.5 SDs of its mean value P (μ - 1.5σ < X < μ + 1.5σ)= P(Z < 1.5) - P(Z < -1.5)Here, Z is the standard normal variable P(Z < 1.5) = 0.9332 (from standard normal table)P(Z < -1.5) = 0.0668 (from standard normal table) So, P (μ - 1.5σ < X < μ + 1.5σ) = 0.9332 - 0.0668= 0.8664

Thus, probability that the thread length of a randomly selected bolt is within 1.5 SDs of its mean value is 0.8664. Probability that the thread length of a randomly selected bolt is farther than 2.5 SDs from its mean value P (X < μ - 2.5σ) + P (X > μ + 2.5σ) = P (Z < -2.5) + P (Z > 2.5)P (Z < -2.5) = 0.0062 (from standard normal table)P (Z > 2.5) = 0.0062 (from standard normal table)

So, P (X < μ - 2.5σ) + P (X > μ + 2.5σ) = 0.0062 + 0.0062 = 0.0124  Probability that the thread length of a randomly selected bolt is between 1 and 2 SDs from its mean value P (μ - 2σ < X < μ - 1σ) = P (Z < -1) - P (Z < -2) + P (Z < 1) - P (Z < 2)P (Z < -1) = 0.1587 (from standard normal table)

P (Z < -2) = 0.0228 (from standard normal table)P (Z < 1) = 0.8413 (from standard normal table)P (Z < 2) = 0.9772 (from standard normal table) So, P (μ - 2σ < X < μ - 1σ) = 0.1587 - 0.0228 + 0.9772 - 0.8413= 0.2728

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Answer: The asnwer is 8

Step-by-step explanation:

The radius is half that distance.r = 1/2(d) where d = distance between the endpoints of the diameter.

1. Writing the equation of the circle in standard formWe know that the endpoints of a diameter are (2,4) and (-14,-8) respectively, and that the midpoint of the diameter is the center of the circle. Therefore, let's begin by calculating the midpoint of the diameter using the midpoint formula:x = (x1 + x2)/2y = (y1 + y2)/2x = (2 + (-14))/2 = -6y = (4 + (-8))/2 = -2So, the midpoint is (-6,-2) which is the center of the circle. Now, we can use the distance formula to calculate the radius. Recall that the diameter is the distance between the two endpoints of the diameter, so the radius is half that distance.r = 1/2(d) where d = distance between the endpoints of the diameter.So, d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]d = sqrt[(-14 - 2)^2 + (-8 - 4)^2]d = sqrt[(-16)^2 + (-12)^2]d = sqrt[256 + 144]d = sqrt[400] = 20So, r = 20/2 = 10. Now that we have the center and radius, we can use the standard form equation of a circle which is:(x - h)^2 + (y - k)^2 = r^2where (h,k) is the center and r is the radius.Substituting our values into the equation, we have:(x + 6)^2 + (y + 2)^2 = 100Expanding and simplifying, we can write the equation of the circle in standard form as:x^2 + 12x + y^2 + 4y + 20 = 0This is the equation in standard form.2. Graphing the circleTo graph the circle, we need to plot the center which is (-6,-2) and then draw the circle with radius 10 units. The circle will be a curve that is equidistant from all points on it to the center. Here's a sketch of the circle.
3. An equation of the circle in standard form is x² + 12x + y² + 4y + 20 = 0.

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Answer:

The square root of 45 is approximately 6.708203932.

Answer:

Step-by-step explanation:

Answer: 8

Step-by-step explanation:

Using SOHCAHTOA, we need TOA as we have the opposite (1) and the adjacent (7)

θ = [tex]tan^{-1}(\frac{1}{7} )[/tex] = 8.13 = 8

Answer:

d = negative 5 cosine (StartFraction pi Over 2 EndFraction t)  [y=-5*cos(π/2)]

Step-by-step explanation:

See the attached graph for the explanation.  Desmos graphing software was used to plot the 4 equation options (using x in place of t and y in place of d).

The given points were added to see which of the graphed lines they best match.  We can see that the third option, y=-5*cos(π/2), intersects all four points.

Two of the options (1st and 3rd) lie too close to y=0 to see their difference on the scale of the graph, so we can eliminate them.  (Options 1 and 3)

Option 2 has an amplitude higher than the given points, so it can also be eliminated.

y=-5*cos(π/2) best represents the given points.

First vector v = [- 2 - 2 2] is in W and the second vector v = [6 - 1 - 3] is not in W.

W be the set of all vectors [x y x + y] with x and y real. To find: Whether each of the following vectors is in W. Let's check each vector whether it is in W or not: v = [- 2 - 2 2] To check the given vector is in W or not, we need to find the values of x and y such that the third component equals 2.So, x + y = 2 ⇒ y = 2 - x

The given vector can be written as v = [x y x + y]= [x, 2 - x, 2] Thus, given vector v is in W. v = [6 - 1 - 3]. To check the given vector is in W or not, we need to find the values of x and y such that the third component equals -3. So, x + y = -3 ⇒ y = -3 - x The given vector can be written as v = [x y x + y]= [x, -3 - x, -3]Thus, given vector v is not in W.

Moreover, Vectors, in Maths, are objects which have both, magnitude and direction. Magnitude defines the size of the vector. It is represented by a line with an arrow, where the length of the line is the magnitude of the vector and the arrow shows the direction.

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At the 1% level of significance, both the number of security guards (g) and the unemployment rate (u) have a significant effect on the dollar loss from theft each week (t). This is indicated by the p-values for both variables, which are both less than 0.01 (0.0012 for g and 0.0096 for u).

This means that there is less than a 1% chance that the observed relationship between these variables and the dependent variable (t) is due to chance. Therefore, we can reject the null hypothesis that there is no relationship between these variables and the dependent variable, and conclude that they have a significant effect on the dollar loss from theft each week.

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Answer:

First, let's simplify both sums by combining like terms:

3x + 5y - 2 + 2x - 3y + 1 = 5x + 2y - 1

4x - 8y + 3 - 5x + 6y + 7 = -x - 2y + 10

Now we can subtract the second sum from the first:

(5x + 2y - 1) - (-x - 2y + 10) = 5x + 2y - 1 + x + 2y - 10

Simplifying this expression, we get: 6x + 4y - 11

167.7 feet is the length of the zipline.

The angle of inclination is the angle formed between a horizontal line and a line or surface that is sloping or inclined. It is a measure of the steepness or slope of the line or surface and is typically expressed in degrees or as a trigonometric ratio.

We have a zipline that drops 30 feet from one treetop to a second treetop.

If the angle of inclination from the shorter tree to the taller tree is 10 degrees.

Let AB be the distance between two trees and BC be the drop in height from A to C. Then,

We have BC/AB = tan(θ)

Where θ = 10 degrees

We know BC = 30 feet.

So,

AB = BC/tan(θ) = 30/tan(10°) = 167.7 feet (rounded to one decimal place)

Therefore, the length of the zipline is 167.7 feet.

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For the second order differential equation, we find that Height = 1333.33 meters, Velocity = 240 meters/second.

The acceleration of a rocket fired vertically upwards t seconds after launch is given by a = 20 + 4t m/s². The second order differential equation for the height of the rocket is given by ℎ′′ = a.

The initial conditions for the rocket are:

ℎ(0) = 0 (the rocket starts from the ground) and ℎ′(0) = 0 (the rocket is not moving initially). For the differential equation, we integrate the acceleration once to obtain the velocity, and then integrate the velocity to obtain the height.

Integrating a = 20 + 4t gives v = 20t + 2t² + C1, where C1 is a constant of integration. Using the initial condition v(0) = 0, we get C1 = 0. Integrating v = 20t + 2t² gives ℎ = 10t² + 2/3 t³ + C2, where C2 is another constant of integration.  Using the initial condition ℎ(0) = 0, we getC2 = 0.

Therefore, the general solution for the height of the rocket is ℎ = 10t² + 2/3 t³.The velocity of the rocket is given by v = ℎ′.

At t = 10 s, the height of the rocket is ℎ(10) = 10 × 100 + 2/3 × 1000 = 1333.33 m. The velocity of the rocket at t = 10 s is v(10) = ℎ′(10) = 20 × 10 + 2 × 10² = 240 m/s.

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The required expression can express h in terms of A and b as [tex]$ h = \frac{2A - a}{b} $$[/tex]

Mathematical expressions consist of at least two numbers or variables, at least one math procedure, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical procedure. An expression's form is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

First, we can start by isolating the term that contains h on one side of the equation. To do this, we will first distribute the 0.5 term to get:

A = 0.5a + 0.5bh

Then, we can subtract 0.5a from both sides to get:

A - 0.5a = 0.5bh

Next, we can divide both sides by 0.5b to isolate h:

[tex]$ \frac{A - 0.5a}{0.5b} = h $$[/tex]

Simplifying the expression further, we can see that:

[tex]$$ \boxed{h = \frac{2A - a}{b}} $$[/tex]

Therefore, we can express h in terms of A and b as:

[tex]$ h = \frac{2A - a}{b} $$[/tex]

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