Final answer:
The standard deviation of the data set is 2.98, calculated by finding the mean, squaring the differences, averaging them, and taking the square root. One standard deviation below the mean is 2.52.
Explanation:
To find the standard deviation of the data set 8.2, 10.1, 2.6, 4.8, 2.4, 5.6, 7.0, 3.3, follow these steps:
Calculate the mean (average) of the data set.
Subtract the mean from each data point and square the result.
Calculate the average of these squared differences.
Take the square root of the average to find the standard deviation.
Using a calculator or computer:
The mean of the data set is 5.5
The squared differences would be (8.2-5.5)^2, (10.1-5.5)^2, etc.
The average of these squared differences is approximately 8.86.
The square root of 8.86 gives us the standard deviation of approximately 2.98.
Therefore, the standard deviation of the data set, rounded to the nearest hundredth, is 2.98.
To find the value that is one standard deviation below the mean, you subtract the standard deviation from the mean:
5.5 - 2.98 = 2.52.
Find the standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8.
Select one:
a. y = 1/32 x^2
b. y^2 = 8x
c. y^2 = 32x
d. y = 1/8 x^2
The standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8 is y = 1/32 x², as it is the only option that correctly represents a parabola opening upward with the vertex at the origin and a focus 8 units away.
To find the standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8, we begin by noting that the vertex of the parabola will be midway between the focus and directrix. Since the focus is 8 units above the x-axis and the directrix is 8 units below the x-axis, the vertex is at the origin (0, 0).
The distance between the vertex and the focus (which is also the distance between the vertex and the directrix) is 8 units; this distance is the value 'p' in the parabola's standard equation.
The parabola opens upward because the focus is above the directrix. The standard form for an upward-opening parabola centered at the origin is y = {1}/{4p}x². In our case, p = 8, so the equation becomes y = {1}/{4(8)}x² which simplifies to y = {1}/{32}x².
Based on the options available, the correct standard form of the equation of the parabola is A. y = {1}/{32}x².
A logger is spending his afternoon splitting logs for firewood. He can split 11 logs in a hour. If he already has 12 logs split, how many hours can he split 40 logs?
Answer:
If it is 40 total then:
about 3 more hours
Exact answer:
2.545454... hours
If it is 40 more:
about 4 hours
Exact answer:
3.63636363... hours
Answer:
• 3 hours
• 11 hours
• 12 hours
Step-by-step explanation:
Check with substitution in the inequality: 12 + 11h > 40
IS 90 INCHES GREATER THAN , LESS THAN , OR EQUAL TO 2 3/4 YARDS?
Answer: Less than
Step-by-step explanation:
2 3/4 yards equals 99 inches
the answer is Less than.
Zeituni's standard deduction on her federal income tax return is $5700. If she paid $4670 in state taxes and $1180 in mortgage interest last year, should she use her standard deduction?
A. Yes, because it's less than the deduction she would get from itemizing.
B. No, because it's less than the deduction she would get from itemizing.
C. No, because it's more than the deduction she would get from itemizing.
D. Yes, because it's more than the deduction she would get from itemizing.
No, she should not use her standard deduction because it is less than the deduction she will get from itemizing OPTION B is correct answer.
What is Standard deduction ?
Standard deduction is that amount of someone's income, for which tax is not to be paid, thus reducing the tax bill amount. The amount of the standard deduction is based on one's filing status, age, disability, dependency etc.
Zeituni's standard deduction on her federal income tax return is $5700.
she paid $4670 in state taxes and $1180 in mortgage interest last year, totaling to = $4670+ $1180
= $5850
So, no, she should not use her standard deduction because it is less than the deduction she will get from itemizing.
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Zeituni should itemize her deductions, as the total of her state taxes and mortgage interest ($5850) is more than her standard deduction ($5700). So the correct answer is B.
Explanation:To decide whether Zeituni should use her standard deduction or itemize her deductions, we should add up her state taxes and mortgage interest. The total of her state taxes ($4670) and mortgage interest ($1180) comes to $5850. Comparing this with her standard deduction of $5700, we can see that $5850 is more than $5700. Thus, the better option would be for Zeituni to itemize her deductions.
So the answer is B. No, because it's less than the deduction she would get from itemizing.
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What is the range of the function represented by these ordered pairs? {(–2, 1), (0, 0), (3, –1), (–1, 7), (5, 7)}
1,0,-1,7,7.
The range always be the Y values
Help me find the area of the triangle... ****picture attached
Answer:
60 cm^2
Step-by-step explanation:
The formula for the area of a triangle is ...
A = (1/2)bh
where b is the length of the base, and h is the height. Your triangle shows a base length of 12 cm + 3 cm = 15 cm, and a height of 8 cm. Using these values in the formula, we have ...
A = (1/2)(15 cm)(8 cm) = 60 cm^2
A cell-phone company has noticed that the probability of a customer experiencing a dropped call decreases as the customer approaches a cell-site base station. A company representative approached a cell site at a constant speed and calculated the probability of a dropped call at regular intervals, and the probabilities formed the geometric sequence 0.8, 0.4, 0.2, 0.1, 0.05. If the company representative continues calculating the probability of a dropped call, what will be the next term in the sequence?
Answer:
the answer is 0.00221184
Step-by-step explanation:
as we can see 3rd term is product of first two terms
4th term is product of third and second term
5th term is the product of fourth and third term
the next term in the sequence which is the sixth term will be the product of fifth and fourth term
Answer:
The next term of geometric sequence is 0.025 which is the probability of dropped call.
Step-by-step explanation:
We are given the following information in the question:
The probability of a customer experiencing a dropped call decreases formed the geometric sequence.
The geometric sequence is:
0.8, 0.4, 0.2, 0.1, 0.05
First term = a = 0.8
Common difference = r =[tex]\frac{a_{n}}{a_{n-1}} = \frac{0.4}{0.8} = \frac{1}{2}[/tex]
We have to find the next term of the geometric series to find the next probability.
Next term of sequence =
[tex]a_n = a_{n-1}\times r\\= 0.05\times \displaystyle\frac{1}{2}\\\\= 0.025[/tex]
Hence, the next term of geometric sequence is 0.025 which is the probability of dropped call.
Will give BRAINLIEST
How much cash did Vera receive
Answer:
1040.70 is the answer
Step-by-step explanation:
that is the total
Answer:
$80.00
Step-by-step explanation:
The deposit slip shows the value Vera received. If you look closely at the right side of the ticket has a one table, next to the table, has the denomination of each field of the table. The penultimate denomination is called "Less cash received" that represents the amount Vera wants to receive directly from that check. That is, vera received 80.00 dollars.
50 points, Based on the table, write a function rule that represents the relationship between x and y.
Answer:
y = (1/2)|x -8| -3
Step-by-step explanation:
The first five points fall on a straight line with a slope of ...
∆y/∆x = -0.5/1 = -0.5
The last point is not on that line.
So, several options are available:
write a piecewise function with f(10) having a special definition: y={1-x/2, x≠10; -2, x=10}write a piecewise function with any definition for x > 5 such that f(10) = -2: y={1-x/2, x≤6; -2, x>6}use a function, such as absolute value, that changes slope in a way that makes f(10) = -2. Such a function is shown in the first attached graphsimply list the points. Such a list is a "function rule". (x, y) ∈ {(1, 0.5), (2, 0), (3, -0.5), (4, -1), (5, -1.5), (10, -2)}.25pts awarded and brainliest awarded, plz help asap!!!!!!
Here is a table of values for y = f(x).
x -2 -1 0 1 2 3 4 5 6
f(x) 5 6 7 8 9 10 11 12 13
Mark the statements that are true
Answer:
B. f(-1)=6
C. The domain of f(x) is the set {-2.-1,0,1,2,3,4,5,6}
Step-by-step explanation:
To find f(5) from the table means, the y-value that corresponds to x=5.
This value is 12.
This implies that:
f(5)=12
Also the y-value that corresponds to -1 is 6.
Hence f(-1)=6
The domain of f(x) are the set of all the x-values.
The domain is : {-2.-1,0,1,2,3,4,5,6}
The range for f(x) is the set of all the corresponding y-values.
From the table, the range is: {5,6,7,8,9,10,11,12,13}
On the main floor of a theatre the number of seats per row increases at a constant rate. Jack counts 31 seats in row 3 and 37 seats in row 6. How many seats are there in row 20
Answer: 65 seats in row 20
Step-by-step explanation: 3 = 31, 6 = 37 the difference is 3 rows but 6 seats so its going up 2 every row therefor you need 14 rows after row 6 so 14 * 2 + 37 = 65 seats
By finding a linear equation, we will see that on the row 20 there are 65 seats.
How many seats are in row 20?
Here we have a linear relationship, that can be written as:
y = a*x + b
Where a is the slope and b the y-intecept.
We know that if a line passes through two points (x₁, y₁) and (x₂, y₂), the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
In this case, we have points of the form (row, seats), and the two points that we have are:
(3, 31) and (6, 37)
So the slope is:
[tex]a = \frac{37 - 31}{6 - 3} = 2[/tex]
So the equation is:
y = 2*x + b
To find the value of b, we replace one of the points in the equation. If we use the first one, we have x = 3 and y = 31, so:
31 = 2*3 + b
31 = 6 + b
31 - 6 = 25 = b
The equation is:
y = 2x + 25
The number of seats in row 20 is what we get if we replace x by 20, then:
y = 2*20 + 25 = 65
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Find a unit vector in the same direction as the given vector: v = −14.5i + 2.5 j.
ANSWER
[tex]- \frac{29}{866} \sqrt{866} i + \frac{5}{866} \sqrt{866} j[/tex]
EXPLANATION
The given vector is v = −14.5i + 2.5 j.
The magnitude of this vector is
[tex] |v| = \sqrt{ {( - 14.5)}^{2} + {2.5}^{2} } [/tex]
[tex]v| = \sqrt{ {( - 14.5)}^{2} + {2.5}^{2} } [/tex]
[tex]v| = \sqrt{ 216.5} = \frac{ \sqrt{866} }{2} [/tex]
The unit vector in the direction of this vector is
[tex] = \frac{v}{ |v| } [/tex]
[tex] = - \frac{14.5}{ \frac{ \sqrt{866} }{2} } i + \frac{2.5}{ \frac{ \sqrt{866} }{2} } j[/tex]
[tex] = - \frac{29}{866} \sqrt{866} i + \frac{5}{866} \sqrt{866} j[/tex]
The length of a train car is 50.6 feet this is baffling 8 feet less than six times the width what is the width
Answer:
the width is 9 23/30 feet ≈ 9.767 ft
Step-by-step explanation:
Let w represent the width of the train car. Then 6 times the width is 6w, and 8 ft less than that is (6w-8). We are told this amount is 50.6 feet, so we have ...
6w -8 = 50.6
6w = 58.6 . . . . . . . add 8; next divide by 6
58.6/6 = w = 586/60 = 293/30 = 9 23/30 . . . . feet
This is a repeating decimal: 9.766666...
The width of the train car is 9 23/30 ft, about 9.77 ft.
What is the phase shift of the function ?
Answer:
The Phase Shift is how far the function is shifted horizontally from the usual position.
Step-by-step explanation:
Sondra wants to put a fence in a triangular area of her backyard as shown in the illustration. The fence will enclose a right triangle, with two of the sides measuring 8 yards and 15 yards long. How long will the third side of the triangle be?
(the question did not contain an illustration)
17 yards. The fence that enclose Sondra's backyard is a right triangle whose sides measuring 8 yards, 15 yards and 17 yards respectively.
The key to solve this problem is using the Pythagorean Theorem that dictates; In every right triangle the square of the hypotenuse is equal to the sum of the squares of the legs and the equation hypotenuse²=leg1²+leg2².
For this problem we know the measuring of two side, which mean that we can apply Pythagorean Theorem equation as follow:
Let's say that one of the side is a = 8yards, and the other side is b = 15yards. So, we want to know how long the third side c long.
Applying the Pythagorean Theorem:
[tex]c^{2} =a^{2}+b^{2} \\c=\sqrt{a^{2}+b^{2}}[/tex]
Substituting the values of the sides a and b:
[tex]c=\sqrt{(8yards)^{2}+(15yards)^{2}}\\c=\sqrt{64yards^{2}+225yards^{2}}\\c=\sqrt{289yards^{2}}\\c=17yards[/tex]
Answer:
17 yds
Step-by-step explanation:
Lacking further info about this situation, I will assume that 8 yards and 15 yards represent the two legs of this right triangle, and not the hypotenuse. If that's the case, then the hypotenuse is found by applying the Pythagorean Theorem:
(8 yd)² + (15 yd)² = hyp², or
64 yd² + 225 yd² = 289 yd²
Taking the square root of this result yields 17 yds.
The third side will be 17 yds long.
Nancy was laid off and applied for unemployment benefits in July. In her state, the weekly unemployment benefit is 55% of the 26-week average of the two highest salaried quarters of the year leading to her application. In April, May, and June, Nancy earned a total of 13,500. In January, Febuary, and March her total income was 12,775. What will Nancy weekly benfits be?
Answer:
$277.91
Step-by-step explanation:
"The 26-week average of the two highest salaried quarters of the year leading to her application" would be the average of $13,500 and $12,775, or
$13,500 + $12,775
---------------------------- = $13137.50
2
Dividing this by 26 weeks (equivalent to 6 months), we get $505.29.
Nancy's weekly employment benefit would be 55% of that, or $277.91.
Answer: $555.82
Step-by-step explanation:
Simplify the expression below (X^3)^2
X^(3•2) =X^ 6
Think of an example such as :
(2^3)^2=8^2=64 is the same with
2^(3•2) = 2^6 = 64
Answer= x^6
When two exponents are multiplied together the two exponents multiply.
The largest prime number is a factor of 42 is multiplied by the smallest prime number tht is a factor of 28
Answer:
14
Step-by-step explanation:
largest prime number which is a factor of 42=7
smallest prime number which is a factor of 28=2
7x2=14
Answer:
14
Step-by-step explanation:
largest prime number which is a factor of 42=7
smallest prime number which is a factor of 28=2
7x2=14
Write an equation of the line that is parallel to 2x + 4y = 6 and passes through the point (6, 4).
A) y = 2x + 4
B) y = 2x - 8
C) y = -2x + 16
D) y = -12x + 7
Answer:
The answer is D my friends. Good luck.
Step-by-step explanation:
The equation of the line parallel to 2x + 4y = 6 and passing through the point (6, 4) is y = -0.5x + 7.
Explanation:To find an equation of a line parallel to a given line, we need to find a line with the same slope.
First, we need to rewrite the original equation 2x + 4y = 6 in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
By rearranging the equation, we get y = -0.5x + 1.5.
Since the new line is parallel to the original line, it will have the same slope.
Therefore, the equation of the line parallel to 2x + 4y = 6 and passing through the point (6, 4) is y = -0.5x + 7.
A conical perfume bottle has a radius of 3.7 centimeters and a height of 5.4 centimeters. Using 3.14 for , approximately how much perfume can the bottle hold? A. 338.78 cubic centimeters B. 112.93 cubic centimeters C. 232.13 cubic centimeters D. 77.38 cubic centimeters
The volume of the conical perfume bottle is 77.38 cubic centimeters of perfume, answer D.
To calculate the volume of a conical perfume bottle, we use the formula for the volume of a cone, which is V = (1/3)
3.14r²h, where r is the radius and h is the height of the cone. Given the radius of 3.7 centimeters and a height of 5.4 centimeters, we calculate:
V = (1/3)
3.14 * (3.7 cm)² * 5.4 cm
= (1/3) * 3.14 * 13.69 cm2 * 5.4 cm
= (1/3) * 3.14 * 73.926 cm3
= 3.14 * 24.642 cm3
= 77.38 cubic centimeters
Therefore, the perfume bottle can hold approximately 77.38 cubic centimeters of perfume, which corresponds to answer choice D.
In triangle ABC, D is a point on line AB and E is a point on line AC such that DE is parallel to BC. If BC = 20 centimeters, and the area of the trapezoid (trapezium) DBCE is one-fourth the area of triangle ABC, find DE.
Step-by-step Answer:
If trapezium DBCE is one-fourth of the area of the triangle ABC, that means that the area of triange ADE is (1 - 1/4) = three-fourth of ABC.
Since DE is parallel to BC, we can prove that triangles ADE and ABC are similar.
Similar triangles have corresponding sides proportional, and area is proportional to the square of the linear proportions.
From this we can conclude that
(DE/BC)^2 = 3/4
DE/BC = sqrt(3/4) = sqrt(3)/2
DE = sqrt(3)/2 * 20 = 10 sqrt(3) = 17.320508 cm (to 6 decimal places).
On the subject of similar figures/volumes, if we know the ratio of linear dimensions (such as the side of a cube) as k, then the ratio of AREA of similar squares would be k^2.
Example: A square would have a side of 8 (area=8^2=64), and a (similar) square has a side of 10 (area = 10^2= 100). The
ratio of areas = 64/100 = (8^2/10^2) = (8/10)^2
Here 8/10 is the ratio of linear dimensions = k, and the ratio of areas is k^2 = (8/10)^2 = 64/100.
The same works for cubes (or similar volumes) where the volumes would be proportional to k^3.
The dot plot represents an order of varying shirt sizes. Which histogram represents the same data?
Answer: the answer is C
The histogram and dot plot that represent the order of varying shirt sizes are illustrations of charts
How to determine the histogram?The dataset on the dot plot can be represented using the following frequency table
Shirt size Frequency
8 0
10 1
12 3
14 3
16 5
18 4
20 2
22 1
24 1
26 0
Since the options are not given, the next step is to plot and upload the histogram using a graphing tool
See attachment for the histogram that represents the dot plot
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Three friends are starting a food truck and are contributing a total of $140,000 to begin operations. Their investments are in the ratio of 3:4:7. What is the difference in investment between the smallest investor an largest investor?
Answer:
The difference in investment between the smallest investor an largest investor is $40,000
Step-by-step explanation:
Let
x ---> the contribution of the smallest investor
y ---> the contribution of the middle investor
z ---> the contribution of the largest investor
we know that
x+y+z=140,000 -----> equation A
x/y=3/4 -----> y=(4/3)x ----> equation B
x/z=3/7 ----> z=(7/3)x ----> equation C
substitute equation B and equation C in equation A and solve for x
x+(4/3)x+(7/3)x=140,000
(14/3)x=140,000
x=140,000*3/14
x=$30,000
Find the value of y
y=(4/3)x ----> y=(4/3)(30,000)=$40,000
Find the value of z
z=(7/3)x ----> z=(7/3)(30,000)=$70,000
Find the difference in investment between the smallest investor an largest investor
z-x=$70,000-$30,000=$40,000
The exam had 60 questions. Phelix got 85 •/• (percent) correct. How many questions did he answer correctly?
felix got 51 questions correct
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
What is the remainder when you divide 4x^3 - 5x^2 + 3x - 1 by x - 2?
Answer:
f(a) is the remainder of f(x)/x_a
so hence the remainder of 4×3- 5x2+3x-1/x-2 is (4.(2)^2) - (5.(2)^2) + (3.2) - 1 = 17
Answer: D) 17
Step-by-step explanation:
You can use long division or synthetic division. I will use synthetic division because it is the simplest and quickest method:
x - 2 = 0 --> x = 2
2 | 4 -5 3 -1
| ↓ 8 6 18
4 3 9 17 ← REMAINDER
Represent 372.3 in expanded notation two different ways.
Answer:
Expanded Notation Form:
300 + 70 + 2 + 0.3= 372.3
Expanded Factors Form:
3 x 100 + 7 x 10 + 2 x 1 + 3 x 0.1 = 372.3
Hope this helps!!
Find cos \theta θ if \sin\theta=-\frac{7}{15} sin θ = − 7 15 and falls in quadrant 4
let's recall that on the IV Quadrant the x/cosine is positive and the y/sine is negative, and of course the hypotenuse is just a radius unit and therefore never negative.
[tex]\bf sin(\theta )=\cfrac{\stackrel{opposite}{-7}}{\stackrel{hypotenuse}{15}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]
[tex]\bf \pm\sqrt{15^2-(-7)^2}=a\implies \pm\sqrt{176}=a\implies \stackrel{\textit{IV Quadrant}}{+\sqrt{176}=a} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill cos(\theta )=\cfrac{\stackrel{adjacent}{\sqrt{176}}}{\stackrel{hypotenuse}{15}}~\hfill[/tex]
The heights of a group of trees is normally distributed with a mean of 14.3 feet. If the z score for a 20-foot y’all tree is 1.9, what is the standard deviation?
Answer:
The standard deviation of the heights of the group of trees is 3 feet
Step-by-step explanation:
For a normal distribution, the z-score corresponding to a particular observed value is calculated as;
z-score = (observed value - mean) / (standard deviation)
The mean is given as 14.3
The z-score is 1.9
The observed value is 20 (the given height)
We can make the standard deviation to be the subject of the formula in the above equation;
standard deviation = (observed value - mean) / ( z-score)
We then substitute the given values into this equation;
standard deviation = [tex]\frac{20-14.3}{1.9}=3[/tex]
Please help! ASAP!!!
Answer:
Final answer is [tex]-112\cdot\sqrt{2}a^5[/tex].
Step-by-step explanation:
Given expression is [tex](a-\sqrt{2})^8[/tex].
Now we need to find the fourth term of the given expression [tex](a-\sqrt{2})^8[/tex]. So apply the nth term formula using binomial expansion.
exponent n=8
4th term means we use r=4-1=3
x=2, [tex]y=-\sqrt{2}[/tex]
rth term in expansion of [tex](x+y)^n[/tex] is given by formula:
[tex]\frac{n!}{\left(n-r\right)!\cdot r!}x^{\left(n-r\right)}\cdot y^r[/tex]
[tex]=\frac{8!}{\left(8-3\right)!\cdot3!}\cdot a^{\left(8-3\right)}\cdot\left(-\sqrt{2}\right)^3[/tex]
[tex]=\frac{8!}{5!\cdot3!}\cdot a^5\cdot\left(-2\sqrt{2}\right)[/tex]
[tex]=\frac{40320}{120\cdot6}\cdot a^5\cdot\left(-2\sqrt{2}\right)[/tex]
[tex]=56\cdot a^5\cdot\left(-2\sqrt{2}\right)[/tex]
[tex]=-112a^5\cdot\sqrt{2}[/tex]
[tex]=-112\cdot\sqrt{2}a^5[/tex]
Hence final answer is [tex]-112\cdot\sqrt{2}a^5[/tex].
The Eiffel Tower is 984 feet. A model of the tower is 24 inches tall. What is the ratio of the height of the model to the height of the actual Eiffel Tower?
Answer:
The ratio is [tex]\frac{1}{492}[/tex]
Step-by-step explanation:
Remember that
1 ft=12 in
The Eiffel Tower is 984 feet
Convert to inches
984 ft=984*12=11,808 in
Find the ratio of the height of the model to the height of the actual Eiffel Tower
The height of the model is 24 in
The height of the actual Eiffel Tower is 11,808 in
the ratio is equal to
[tex]\frac{24}{11,808}=\frac{1}{492}[/tex]
That means----> The height of the actual Eiffel Tower is 492 times greater than the height of the model
To find the ratio of the height of the model to the actual Eiffel Tower, convert the model's height to feet (24 inches = 2 feet) and then divide by the tower's height (2 feet / 984 feet) to get the simplified ratio of 1:492.
Explanation:To calculate the ratio of the height of the model Eiffel Tower to the actual Eiffel Tower, we need to ensure both measurements are in the same unit. Since the actual Eiffel Tower's height is given in feet and the model's height is in inches, we will convert one of these measurements so they can be directly compared.
First, we convert the model's height from inches to feet. We know that 1 foot equals 12 inches, so:
24 inches × (1 foot / 12 inches) = 2 feet.
Now we have the model's height in feet, and we can form the ratio:
Height of model / Height of actual Eiffel Tower = 2 feet / 984 feet.
By simplifying this fraction, we get:
1 / 492.
So, the ratio of the height of the model to the height of the actual Eiffel Tower is 1:492.