A man standing in front of a house built on top of a rock 70m away from the rock observes that the angle of elevation of the top and foot of the house are 63degrees and60 degrees respectively.Find the height of the house

Answer:

polynomial; left 3 right 1

Step-by-step explanation:

The type of function is a polynomial.

The parent function is translated by moving -2x^3 to the left 3 and right 1.

Answer:

The function is a quadratic function.

Series of transformations:

Step-by-step explanation:

A quadratic function is a polynomial function of degree 2 (the highest exponent of the variable is 2).

Therefore, the given equation, y = -2(x + 3)² + 1, represents a quadratic function as the term (x + 3)² indicates that the highest power of the x-variable is 2.

[tex]\hrulefill[/tex]

The parent function of a quadratic function is y = x².

To translate the parent function to produce the given equation, we need to apply this series of transformations:

1. Horizontal translation

When "a" is added to the x-variable, the graph is shifted "a" units to the left. Therefore, the addition of 3 inside the parentheses shifts the graph horizontally to the left by 3 units.

2. Vertical Stretch

The coefficient in front of the squared term (x + 3)² indicates a vertical stretch or compression. In this case, since the coefficient greater than 1, it stretches the graph vertically, making it narrower compared to the parent function.

3. Reflection

As the stretch coefficient is negative, the graph is reflected across the x-axis, meaning the parabola opens downwards.

4. Vertical translation

When "a" is added to the function, the graph is shifted "a" units up. Therefore, the addition of 1 to the function shifts the graph vertically up by 1 unit.

In summary, the series of transformations that maps the parent function to the given function is:

The members of the given set in this problem are given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

The union and intersection sets of multiple sets are defined as follows:

The intersection of the sets Y and Z for this problem is given as follows:

Y ∩ Z = {0, 6, 23, 26}

(which are the elements that belong to both of the sets).

The union of the above set with the set X is given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

(elements that belong to at least one of the sets).

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The number of subsets in the given set is as follows:

128.

Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:

[tex]2^n[/tex]

The set in this problem is composed by integers between 2 and 8, hence it has these following elements:

{2, 3, 4, 5, 6, 7, 8}.

The set has four elements, meaning that n = 7, hence the number of subsets is given as follows:

[tex]2^7 = 128[/tex]

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Answer:

The least number that should be subtracted from 1456 to make a perfect square with formula is 9^2, which is equal to 81.

Step-by-step explanation:

To find the least number that should be subtracted from 1456 to make a perfect square with formula, we need to use the formula for the square of a number.

(n + a)squared = nsquared + 2nas + asquared

In our case, since we want to find the least number to be subtracted, we need to make the result of the formula 2nas + asquared negative (so the difference is a perfect square)

2nas + asquared < 0

Let's try for some values of n:

1456 - n = aperfect square

1456 - 5^2 = (1456 - 25)^2 = 1431^2

1456 - 7^2 = (1456 - 49)^2 = 1407^2

1456 - 9^2 = (1456 - 81)^2 = 1375^2

Since 1375^2 is the smallest of the squares calculated so far, we can conclude that the smallest number that should be subtracted from 1456 to make a perfect square formula with a perfect square result is 1456 - 9^2 == 1456 - 81 == 9^2 == 81

So in this case, the least number that should be subtracted from 1456 to make a perfect square with formula is 9^2, which is equal to 81.

The proportional sides/corresponding sides of the triangles are ST/XY = RT/YZ = SR/XZ.

The value of a and b are 5 and 20 respectively.

Corresponding sides refers to a pair of matching sides that are in the same spot in two different shapes.

ST/XY = RT/YZ = SR/XZ

ST/XY = 3/15

= 1/5

RT/YZ = 4 ÷ 1/5

= 4 × 5/1

YZ, b = 20

Hypotenuse² = opposite² + adjacent²

5² = 3² + 4²

25 = 9 + 16

25 = 25

Therefore,

SR = a = 5

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The number of subsets in the given set is as follows:

16.

Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:

[tex]2^n[/tex]

The set in this problem is composed by integers between 2 and 5, hence it has these following elements:

{2, 3, 4, 5}.

The set has four elements, meaning that n = 4, hence the number of subsets is given as follows:

[tex]2^4 = 16[/tex]

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Answer: The first one ⊄

Step-by-step explanation: A is not a subset of E.

However, E is a subset of A

The average speed in miles per minute during the interval of 30 and 40 is -1.5 miles per minute

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

The graph

During the interval of 30 and 40, we have

Distances = 15 and 0

So, we have

Average speed = (15 - 0)/(30 - 40)

Evaluate

Average speed = -1.5

Hence, the average speed in miles per minute is -1.5

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When 'x' is 5, the Algebraic  expression 3x - 4 evaluates to 11.

To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.

First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.

Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.

In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.

To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:

3(5) - 4

This simplifies to:

15 - 4 = 11

So, when 'x' is 5, the expression 3x - 4 evaluates to 11.

In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.

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Note the complete question:

Algebraic expression for 4 less than the product of 3 and some number

What is the algebraic expression for "4 less than the product of 3 and some number?

Please help me understand the meaning of how to calculate.

We can express the number 98 in exponential form as 10 raised to the power of 2. This means that by multiplying the base, which is 10, by itself twice, we obtain the value of 98.

To express 98 in exponential form, we need to determine the base and exponent that can represent the number 98.

Exponential form represents a number as a base raised to an exponent. Let's find the base and exponent for 98:

We can express 98 as 10 raised to a certain power since the base 10 is commonly used in exponential notation.

To find the exponent, we need to determine how many times we can divide 98 by 10 until we reach 1. This will give us the power to which 10 needs to be raised.

98 ÷ 10 = 9.8

Since 9.8 is still greater than 1, we need to continue dividing by 10.

9.8 ÷ 10 = 0.98

Now, we have reached a value less than 1, so we stop dividing.

From these calculations, we can see that 98 can be expressed as 10 raised to the power of 1 plus the number of times we divided by 10:

98 =[tex]10^1[/tex] + 2

Therefore, we can write 98 in exponential form as:

98 = [tex]10^3[/tex]

In summary, 98 can be expressed in exponential form as 10^2. The base is 10, and the exponent is 2, indicating that we multiply 10 by itself two times to obtain 98.

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Answer:

16 deliveries

Step-by-step explanation:

238 ≤ 10d + 78

160 ≤ 10d

16 ≤ d

Thus, he needs to make at least 16 deliveries to make at least $238 in one day.  Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.

Answer:

Hey, math brainiac, check this  out. If our hybrid electric car gets 36 miles per charge and goes through 6 gallons of gas, that means she'll cover another 210 miles. Total trip length? Some sweet 246 miles, bro. That's enough juice to cruise cross-country without ever needin' to stop at a gas station. Talk about efficiency.

The distance traveled by the car by 6 gallons is 246 miles.

Given data:

To determine the distance the car can travel using 6 gallons of gasoline, substitute the value of g = 6 into the formula D = 36 + 35g and evaluate it.

Formula: D = 36 + 35g

Gasoline amount: g = 6

Substituting g = 6 into the formula, we have:

D = 36 + 35(6)

On simplifying the equation:

D = 36 + 210

D = 246

Therefore, the value of D = 246 miles

Hence, the car can travel a distance of 246 miles using 6 gallons of gasoline.

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The Brady & Matthew Camera Company has recently introduced its latest high-quality digital camera designed for professional use.

1. The Brady & Matthew Camera Company: The company known as Brady & Matthew Camera is the manufacturer of the newly released digital camera.

2. Newest professional quality digital camera: The recently launched camera by Brady & Matthew Camera Company is their latest product in their lineup of professional-grade digital cameras.

3. Features: The new camera is equipped with advanced features that cater to the needs of professional photographers, such as high-resolution image sensors, a wide range of ISO sensitivity, and customizable shooting modes.

4. Image Quality: The camera is designed to deliver exceptional image quality with sharp details, accurate colors, and low noise, ensuring professional-grade results.

5. Durability: The camera is built to withstand the rigors of professional use, featuring a robust body construction and weather sealing to protect against dust and moisture.

6. Ergonomics: Brady & Matthew Camera Company has paid attention to ergonomic design, ensuring that the camera is comfortable to hold and operate for extended periods.

7. Connectivity: The camera is equipped with various connectivity options, including Wi-Fi and Bluetooth, allowing photographers to transfer images wirelessly and control the camera remotely.

8. Accessories: Brady & Matthew Camera Company offers a range of compatible accessories for their new camera, including lenses, external flashes, and battery grips, expanding the capabilities of the camera system.

9. Market Availability: The new professional-quality digital camera by Brady & Matthew Camera Company is now available for purchase from authorized retailers and their official website.

10. Customer Support: The company provides reliable customer support services, including warranty coverage, technical assistance, and firmware updates to ensure a satisfying user experience.

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The measure of line segment x in the game board is approximately 13.6.

The secant-tangent power theorem states that "if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.

It is expressed as:

( tangent segment )² = External part of the secant segment × Secant segment.

From the given figure:

Let;

Tangent segment = 12

Secant segment = 7 + x

External part of the secant segment = 7

Plug these values into the above formula and solve for x.

( tangent segment )² = External part of the secant segment × Secant segment.

12² = 7( 7 + x)

144 = 49 + 7x

7x = 144 - 49

7x = 95

x = 95/7

x = 13.6

Therefore, the value of x is approximately 13.6.

Option C) 13.6 is the correct answer.

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The instantaneous rate of change of f(x)=4-2 [tex]x^{2}[/tex] at x=0.5 is −2. This means that at that specific point, the function is changing at a rate of -2 units per unit change in x.

The instantaneous rate of change of a function at a specific point can be found by taking the derivative of the function and evaluating it at that point. In this case, we have the function f(x)=4-2 [tex]x^{2}[/tex] and we want to find the instantaneous rate of change at x=0.5.

To find the derivative of f(x), we apply the power rule for differentiation. Taking the derivative of each term, the derivative of 4 is 0, and the derivative of −2[tex]x^{2}[/tex] is −4x. Therefore, the derivative of f(x) is  (x)=−4x.

Now, to find the instantaneous rate of change at x=0.5, we substitute

x=0.5 into the derivative function. f′(0.5)=−4(0.5)=−2.

This means that the function is changing at a rate of -2 units per unit change in x.

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The transformation of g(x) to f(x) is g(x) is shifted up 15 units and shifted left by 16 units

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

The functions f(x) and g(x)

Where, we have

f(x) = 1/(x + 16) + 15

g(x) = 1/x

From the above, we have

Horizontal difference = 16 - 0 = 16

Vertical difference = 15 - 0 = 15

This means that the transformation of g(x) to f(x) is g(x) is shifted up 15 units and shifted left by 16 units

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Answer:

The 3.907 is approximate.

====================================

Explanation:

x = number of hours that elapse

y = f(x) = number of tokens

If we use a graphing tool like a TI84 or GeoGebra, then the approximate solution to -3(2)^(x+1) + 90 = 0 is roughly x = 3.907

At around 3.907 hours is when the number of tokens is y = 0. Therefore, this is the approximate upper limit for the domain. The lower limit is x = 0.

The domain spans from x = 0 to roughly x = 3.907, and we shorten that down to 0 ≤ x ≤ 3.907

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

Plug in x = 0 to find y = 84. This is the largest value in the range.

The smallest value is y = 0.

The range spans from y = 0 to y = 84, so we get 0 ≤ y ≤ 84

Keep in mind y is the number of tokens. A fractional amount of tokens does not make sense, so we must have y be a whole number 1,2,3,...,83,84.

The x value can be fractional because 3.907 hours for instance is valid.

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

Extra info:

Answer:

y= -x²-4x+2

Step-by-step explanation:

write in vertex form

a(x-h)²+k

in our case h = -2 and k= 6

y=a(x+2)²+6

now we just need to solve for a. we know that when x= 1 y = -3. plug these values in and solve for a

-3= a(1+2)²+6

-9=9a

a= -1

thus the formula is -(x+2)²+6

generally, teachers want things in standard form, so expand the exponent and simplify.

-(x²+4x+4)+6

y= -x²-4x+2

Answer:

[tex]y = -x^2 - 4x + 2[/tex]

Step-by-step explanation:

The equation of a parabola in vertex form is:

[tex]y = a(x - h)^2 + k[/tex]

where (h, k) is the vertex of the parabola.

In this case, the vertex is (-2, 6), so h = -2 and k = 6.

We also know that the parabola passes through the point (1, -3).

Plugging these values into the equation, we get:

[tex]-3 = a(1 - (-2))^2 + 6[/tex]

[tex]-3 = a(3)^2 + 6[/tex]

-9 = 9a

a = -1

Substituting a = -1 into the equation for a parabola in vertex form, we get the equation of the parabola:

[tex]y = -1(x + 2)^2 + 6[/tex]

This equation can also be written as:

[tex]y = -x^2 - 4x -4+6\\y=x^2-4x+2[/tex]

The 9th arrangement will have 36 dots, the 10th arrangement will have 45 dots, and when adding the number of dots in any two consecutive arrangements, the result will be the number of dots in the next arrangement.

To determine the number of dots in the 9th and 10th arrangements, we need to understand the pattern in the given sequence: 1, 3, 6, 10, 15, ...

To find the pattern, we can observe the differences between consecutive terms: 2, 3, 4, 5, ...

We notice that these differences increase by 1 each time. This indicates that the sequence is formed by adding consecutive positive integers to the previous term.

Using this pattern, we can determine the 9th and 10th arrangements as follows:

9th arrangement:

Starting with the 1st arrangement, we add the positive integers consecutively: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36.

Therefore, the 9th arrangement will have 36 dots.

10th arrangement:

Starting with the 1st arrangement, we add the positive integers consecutively: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45.

Therefore, the 10th arrangement will have 45 dots.

Now, let's address the observation when we take any two consecutive arrangements and add the number of dots.

If we take the nth arrangement and the (n+1)th arrangement, we can observe that the number of dots in the (n+1)th arrangement will be the sum of the number of dots in the nth arrangement and the number of dots added in the (n+1)th step.

For example, let's consider the 2nd and 3rd arrangements:

2nd arrangement: 3 dots

3rd arrangement: 3 + 3 (adding 2, the next positive integer) = 6 dots

This pattern holds true for any two consecutive arrangements in the sequence.

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The height of the upper end of the handrail above the floor is approximately 3.467726 meters.

To calculate the height of the upper end of the handrail above the floor, we can use trigonometry and the given information about the length of the handrail and the angle of inclination.

Let's break down the problem into two right triangles:

The first right triangle is formed by the handrail, the floor, and a vertical line connecting the lower end of the handrail to the floor. The vertical line represents the height of the lower end above the floor, which is given as 0.7m.

The second right triangle is formed by the handrail, the floor, and a horizontal line parallel to the floor, connecting the upper end of the handrail to the floor. This horizontal line represents the height we need to calculate.

Now, let's apply trigonometric ratios to find the height of the upper end of the handrail above the floor.

In the first right triangle:

Opposite side = height of the lower end = 0.7m

Hypotenuse = length of the handrail = 5.4m

Using the sine function:

sin(angle) = Opposite / Hypotenuse

sin(40°) = 0.7 / 5.4

Now, let's solve for the sin(40°):

sin(40°) ≈ 0.64279

Multiplying both sides of the equation by 5.4:

0.64279 * 5.4 ≈ 3.467726

So, the length of the vertical line in the second right triangle (representing the height of the upper end of the handrail above the floor) is approximately 3.467726 meters.

Therefore, the height of the upper end of the handrail above the floor is approximately 3.467726 meters.

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Answer: x=2, y=4

Step-by-step explanation:

Since the lines are parallel, we can say that the larger triangle and the smaller triangle are similar. Thus. x+3/(2y-1) = (3/2x+2)/(3y-5). Also, note that there are hash lines, telling us that 2y-1 and 3y-5 are equal. Thus 2y-1=3y-5, and y=4. Plugging y=4 into the first equation yields: (x+3)/(7)=(3/2x+2)/(7), or x+3=3/2x+2. Then 1/2x=1, x=2.

Thus: x=2, and y=4

Answer:

x = 2

y = 4

Step-by-step explanation:

If a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

As the line bisects the side of the triangle with the y-variables, then the line is the midsegment of the triangle. This means that the line also bisects the side of the triangle with the x-variables.

Therefore, the two expressions with the x-variable are equal.

Similarly, the two expressions with the y-variable are equal.

Solving for x:

[tex]\boxed{\begin{aligned}\dfrac{3}{2}x+2&=x+3\\\\\dfrac{3}{2}x+2-x&=x+3-x\\\\\dfrac{1}{2}x+2&=3\\\\\dfrac{1}{2}x+2-2&=3-2\\\\\dfrac{1}{2}x&=1\\\\2 \cdot \dfrac{1}{2}x&=2 \cdot 1\\\\x&=2\end{aligned}}[/tex]

Solving for y:

[tex]\boxed{\begin{aligned}3y-5&=2y-1\\\\3y-5-2y&=2y-1-2y\\\\y-5&=-1\\\\y-5+5&=-1+5\\\\y&=4\end{aligned}}[/tex]

To calculate the ratio as a decimal, we divide the number of owners by the total population for each city.

For Indianapolis: Ratio = 6,245 / 0.9 million = 0.006938

For New York: Ratio = 911,216 / 18.6 million = 0.049019

For Cairo: Ratio = 10,598 / 19.1 million = 0.000554

For Beijing: Ratio = 959,611 / 21.2 million = 0.045270

For Tokyo: Ratio = 1,700,510 / 26.5 million = 0.064234

To calculate the owners per 100, we multiply the ratio by 100.

For Indianapolis: Owners per 100 = 0.006938 * 100 = 0.7 (rounded to one decimal place)

For New York: Owners per 100 = 0.049019 * 100 = 4.9 (rounded to one decimal place)

For Cairo: Owners per 100 = 0.000554 * 100 = 0.1 (rounded to one decimal place)

For Beijing: Owners per 100 = 0.045270 * 100 = 4.5 (rounded to one decimal place)

For Tokyo: Owners per 100 = 0.064234 * 100 = 6.4 (rounded to one decimal place)

Therefore, the ratio as a decimal and the owners per 100 for each city are as follows:

Indianapolis: Ratio = 0.006938, Owners per 100 = 0.7

New York: Ratio = 0.049019, Owners per 100 = 4.9

Cairo: Ratio = 0.000554, Owners per 100 = 0.1

Beijing: Ratio = 0.045270, Owners per 100 = 4.5

Tokyo: Ratio = 0.064234, Owners per 100 = 6.4

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x = 8.33 and the solution to the equation 12x = 100 is x = 8.33 (rounded to the nearest hundredth).

To solve the equation 12x = 100, we need to isolate the variable x. We can do this by dividing both sides of the equation by 12.

12x = 100

Dividing both sides by 12:

(12x)/12 = 100/12

Simplifying:

x = 100/12

Now, let's calculate the value of x.

x = 8.33 (rounded to the nearest hundredth)

Therefore, the solution to the equation 12x = 100 is x = 8.33 (rounded to the nearest hundredth).

Here's the step-by-step solution:

12x = 100 (given equation)

Divide both sides by 12: (12x)/12 = 100/12

Simplify: x = 8.33

Please note that the answer is rounded to the nearest hundredth as requested.

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The correct answer is a set S is T-finite if every nonempty subset X of the power set P(S) has a maximal element u, meaning there is no other element v in X such that u is a subset of v.

On the other hand, if a set S does not satisfy the condition of being T-finite, it is referred to as T-infinite.The notation "T" in this context represents Tarski, referring to the mathematician Alfred Tarski, who contributed to the study of set theory and lattice theory.In set theory, Tarski introduced the concept of T-finiteness to define a notion of finiteness for sets based on their subsets. A set S is considered T-finite if every nonempty subset X of the power set P(S) (the set of all subsets of S) has a maximal element u. This means that for any subset X, there exists an element u in X such that there is no other element v in X that properly contains u.

For example, consider the set S = {1, 2, 3}. The power set P(S) includes subsets such as {}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, and {1, 2, 3}. According to Tarski's T-finiteness, for any nonempty subset X from P(S), there should exist a maximal element. In this case, each nonempty subset has a maximal element because every subset has a largest element that cannot be properly contained within any other subset.

On the other hand, if a set S does not satisfy the condition of T-finiteness, it is considered T-infinite. This means that there exists a nonempty subset X of P(S) for which there is no maximal element. In other words, there are subsets within the power set that do not have a largest element.

Tarski's T-finiteness provides an alternative way to define finiteness based on the behavior of subsets within a set. It is a concept used in the study of set theory and has connections to other areas of mathematics, such as lattice theory.

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The amount of inches that the plant grows in 14 days is given as follows:

420 inches.

The proportional relationship that models the situation is given as follows:

i = 30d.

This means that the plant grows by 30 inches every day.

After 14 days, we have that d = 14, hence the size of the plant after 14 days is given as follows:

i = 30 x 14

i = 420 inches.

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Answer:

D. √3

Step-by-step explanation:

The tangent ratio is given by:

tan (θ) = opposite/adjacent, where

Thus, we plug in 8√3 for the opposite side and 8 for the adjacent side, which gives us:

tan (60) = (8√3) / 8

Thus reduces down to √3 so D. is the correct answer.

Q1- The annual depreciation for the equipment is $2,000.

Q2- The book value of the equipment at the end of Year 3 is $6,500.

Q1: What is the annual depreciation for the equipment?

To calculate the annual depreciation, we need to determine the difference between the initial value and the salvage value, and divide it by the number of years.

Initial value = $12,500

Salvage value = $2,500

Number of years = 5

Annual depreciation = (Initial value - Salvage value) / Number of years

= ($12,500 - $2,500) / 5

= $10,000 / 5

= $2,000

Therefore, the annual depreciation for the equipment is $2,000.

Q2: What is the book value of the equipment at the end of Year 3?

The book value of the equipment at the end of a specific year can be calculated by subtracting the accumulated depreciation from the initial value.

Initial value = $12,500

Annual depreciation = $2,000

Number of years = 3

Accumulated depreciation = Annual depreciation * Number of years

= $2,000 * 3

= $6,000

Book value at the end of Year 3 = Initial value - Accumulated depreciation

= $12,500 - $6,000

= $6,500

Therefore, the book value of the equipment at the end of Year 3 is $6,500.

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To factor the expression 4x^2 - 25, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).

In this case, we have 4x^2 - 25, which can be written as (2x)^2 - 5^2. Comparing it with the difference of squares formula, we can identify that a = 2x and b = 5. Therefore, the correct option is:

b. (2x)^2 - (5)^2

Using the difference of squares formula, we can factor it as follows:

(2x + 5)(2x - 5)

Hence, the correct factorization of 4x^2 - 25 is (2x + 5)(2x - 5), which is equivalent to option b.

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Answer:

(A) AA similarity

Step-by-step explanation:

In ΔABC,

∠A + ∠B + ∠C = 180

∠A + 27 + 90 = 180

∠A = 180 - 90 - 27

∠A = 63

Comparing ΔABC and ΔMNP,

∠A = ∠M = 63

∠C = ∠P = 90

Therfore, by AA property, the two triangles are similar

If the total height between two floors is 9'0 1/2" and 14 risers are to be used in a set of stairs, the height of each riser would be approximately 7.75 inches.

To find the height of each riser in a set of stairs given the total height between two floors, we need to divide the total height by the number of risers.

First, let's convert the total height to a consistent unit. The distance between two floors is given as 9'0 1/2". We can convert this to inches by multiplying the feet by 12 and adding the remaining inches:

9 feet = 9 * 12 = 108 inches

0 1/2 inch = 0.5 inch

Total height = 108 + 0.5 = 108.5 inches

Next, we divide the total height by the number of risers (14) to find the height of each riser:

Height of each riser = Total height / Number of risers

Height of each riser = 108.5 inches / 14

Using a calculator, we can compute:

Height of each riser ≈ 7.75 inches

Therefore, the height of each riser in the set of stairs would be approximately 7.75 inches.

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