ANSWER
See explanation
EXPLANATION
The standard form of a quadratic equation is:
[tex]y = a {x}^{2} + bx + c[/tex]
To convert this function to standard form, you follow the steps below:
Factor 'a' from the variable termsAdd and subtract the square of half the coefficient of x.Factor the perfect squaresSimplify the constant terms to get the vertex form as [tex]y = a {(x - h)}^{2} + k[/tex]For example:
Given the standard form:
[tex]y = 2 {x}^{2} + 12x + 10[/tex]
Factor 2 from the variable terms
[tex]y = 2 {(x}^{2} + 6x) + 10[/tex]
Add and subtract the square of 3.
[tex]y = 2 {(x}^{2} + 6x + 9 - 9) + 10[/tex]
[tex]y = 2 {(x}^{2} + 6x + 9) + 2( - 9) + 10[/tex]
Factor the perfect square an simplify
[tex]y = 2 ({x + 3)}^{2} - 8[/tex]
This is the vertex form
yes, one can rewrite an equation in standard form to vertex form.
Below are the steps to convert the equation in standard form to vertex form.
What do the mathematical term standard form mean?
There are various ways to represent a parabola's equation, including standard form, vertex form, and intercept form.
A parabola's typical form is standard form i.e y = ax2 + bx + c.
Here, variables x and y represent points on the parabola, and real numbers (constants) a, b, and c are real numbers (constants) where a 0.
By completing the square, change y = a (x - h)2 + k from standard form to vertex form (y = a (x - h)2 + k).
The vertex form is y = a (x - h)2 + k in this case.
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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
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.
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)}.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:
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.
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
The exam had 60 questions. Phelix got 85 •/• (percent) correct. How many questions did he answer correctly?
felix got 51 questions correct
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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Kim and her two brothers each use one and a half cups of milk for breakfast. How many fluid ounces of milk do they use in four days
Answer: 48 fl oz ( fluid ounces )
Explanation:
1 c = 8 fl oz
1 1/2 c = 12 fl oz
12 fl oz of milk × 4 Days =
48 fl oz in four days
7. John's seafood restaurant is trying to estimate its profits. John has found that on average, each meal served costs the restaurant $14.56 and takes in $17.12. John has also found that on average, each beverage served costs the restaurant $1.20 and takes in $5.40. If c customers order a meal, and half of those customers order a beverage, which of the following functions models the restaurant's total profit?
f(c) =17.12c -14.56c + 5.40(.5c) - 1.20(.5c)
f(c) = 17.12c - 14.56c + 5.4c - 1.20c
f(c)=14.56c - 17.12c + 1.20c - 5.40c14.56c - 17.12c + 12(.5c) - 5.40(.5c)
Answer:
f(c) =17.12c -14.56c + 5.40(.5c) - 1.20(.5c)
Step-by-step explanation:
Profit is the difference between revenue (17.12c +5.40(.5c)) and cost(14.56c+1.20(0.5c)). That difference is expressed by the function shown above.
Answer:
f(c) =17.12c -14.56c + 5.40(.5c) - 1.20(.5c)
Step-by-step explanation:
Let's build the f(c) function by steps.
There are c customers.
John has found that on average, each meal served costs the restaurant $14.56 and takes in $17.12.
So, the costs for the restaurant are negative, and what takes positive.
f(c) =17.12c -14.56c
Now the final part
John has also found that on average, each beverage served costs the restaurant $1.20 and takes in $5.40.
Half of these customers order a beverage, and this is why we multiply by 0.5.
So
f(c) =17.12c -14.56c + 5.40(.5c) - 1.20(.5c)
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.
HELP PLEASE I WILL GIVE 99 POINTS IM DESPERATE!
Ivan bought a box of macadamia nuts to bring home from his trip.What volume of nuts could the container hold?
18 x 15 x 3 is 810. The volume is 810. (Also you cant give 99 points but I’ll take a brainlist answer?)
Answer:
[tex]810\text{ cm}^3[/tex].
Step-by-step explanation:
We have been given an image of a container. We are asked to find the volume of nuts could the container hold.
We can see that our given container is in form of cuboid, so we will use volume of cuboid formula to solve our given problem.
[tex]\text{Volume of cuboid}=\text{Length*Width*Breadth}[/tex]
Upon substituting our given values in above formula, we will get:
[tex]\text{Volume of container}=18\text{ cm}\times 15\text{ cm}\times 3\text{ cm}[/tex]
[tex]\text{Volume of container}=810\text{ cm}^3[/tex]
Therefore, the container can hold 810 cubic cm of macadamia nuts.
Please please help me out
12x18.2/2=109.2 is the area of the big triangle and also the same area could be found 20 x h=109.2 so
h= 109.2/20=5.46 m
100 POINTS AND BRAINLIEST
please answer #4 and #5
4. His percentage is 79% so making each shot is 79%
Multiply the percent for each shot for each shot:
Making two shots = 0.79 x 0.79 = 0.624 = 62.4% Round the answer to 62% if needed.
5. They have 4 different flavors and 6 different toppings.
a. Picking vanilla is 1 out of 4 = 1/4 and picking chocolate chips is 1 out of 6 = 1/6.
The probability of picking both is 1/4 x 1/6 = 1/24
b. There are a total of 10 different things to pick.
Picking chocolate ice cream is 1 out of 10 = 1/10, picking marshmallow topping is 1 out of 10 = 1/10
Picking one or the other would be 2 out of 10 = 2/10 which reduces to 1/5
Answer:
4. 79%
5. 1/24 and 1/5 for part a and b
Drag the tiles to the boxes to form correct pairs. Match each mixed number to its equivalent decimal number.
20 4/5 , 20 1/5 , 20.75 . 20.875 , 20.8 , 20 3/4 , 20 7/8 , 20.2 .
Answer:
20 3/4 is to 20.75
20 1/5 is to 20.2
20 7/8 is to 20.875
and 20 4/5 is to 20.8
The matching of each mixed number to its equivalent decimal number is given below -
What is the matching of each mixed number to its equivalent decimal number ?The mixed number is represented as a b/c where a, b, c are three positive non zero integers .
Mathematically -
a b/c = {(a*c) + b}/ c
Thus, the matching of each mixed number to its equivalent decimal number is -
20 3/4 is to 20.7520 1/5 is to 20.220 7/8 is to 20.87520 4/5 is to 20.8To learn more about mixed number, refer -
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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!!
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 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]
Select the statement that is NOT equivalent to-- "It is not true that England and Africa are both countries."
a. If England is a country, then Africa is not a country.
b. England is not a country and Africa is not a country.
c. England is not a country or Africa is not a country.
d. If Africa is a country, then England is not a country
The original statement is true only if:
England is a country and Africa isn'tAfrica is a country and England isn'tNeither of them are countriesOptions a and d are equivalent:
[tex]P\implies Q \iff \lnot Q \implies \not P[/tex]
and they both are true in the same cases as above.
Option c is also fine, because it is false only if both England and Africa are both countries, just like the original statement.
Option b, instead, is true only if neither of the two options are countries, so it doesn't cover the cases where only one of the two is a country.
Answer:
Both are cities smh ♂️
Step-by-step explanation:
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
The diameter of the base of the cone measures 8 units.
The height measures 6 units.
What is the volume of the cone?
A)240 cubic units
B)321 cubic units
C)48X cubic units
D)647 cubic units
Answer: [tex]32\pi[/tex] cubic units.
Step-by-step explanation:
You can use this formula for calculate the volume of a cone:
[tex]V_{cone}=\frac{1}{3}\pi r^2h[/tex]
Where "r" is the radius and "h" is the height.
You know that the diameter of the base of the cone measures 8 units, then, the radius can be found by dividing the diameter by 2:
[tex]r=\frac{8units}{2}\\\\r=4units[/tex]
Since you already know that height and the radius, you can substitute them into the formula. Then, the volume of this cone is:
[tex]V_{cone}=\frac{1}{3}\pi (4units)^2(6units)[/tex]
[tex]V_{cone}=32\pi \ units^3[/tex]
Answer:
b. 32
Step-by-step explanation:
e2020 says so
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]
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.
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.
Please please help me
The area of a parallelogram is given by
[tex]A=bh[/tex]
Now, if we consider the 9.9 inches side as the base, then the height is the one labeled with 5.5 inches.
If instead we choose the 11 inches side as the base, the height is h.
So, we can express the area in this two equivalent ways:
[tex]A = 9.9\cdot 5.5 = 11\cdot h[/tex]
Solving for h, we have
[tex]h = \dfrac{9.9\cdot 5.5}{11} = 4.95[/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]
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.
how many revolutions does each tire make while traveling 500 feet? Include the calculations and provide appropriate units (sorry that the picture isn’t great)
Answer:
tire A=39 revolutions
tire B=38 revolutions
tire C= 37 revolutions
Step-by-step explanation:
The question is on circumference
Tire A diameter = 15 +4.60+4.60=24.20 inches
Tire B diameter= 16+4.43+4.43=24.86 inches
Tire C diameter=17+4.33+4.33=25.66 inches
Finding the circumference/single revolution
Tire A = 2×3.14×24.20=151.98 inches
Tire B= 2×3.14×24.86=156.12 inches
Tire C=2×3.14×25.66=161.15 inches
Number of revolutions made
Track length=500 feet.............change feet to inches
500×12=6000inches
Revolutions for tire A= 6000/151.98 =39.47⇒39 revolutions
Revolutions for tire B=6000/156.12 =38.43⇒38 revolutions
Revolutions for tire C= 6000/161.15 =37.23⇒37 revolutions
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.
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.