Answer:
Step-by-step explanation:
x=-40
in october, marshal drove 217 miles ,which was 62% of the distance he drove in september. How far in miles did marshal drive in september?
Answer:
350 miles
Step-by-step explanation:
62 : 100 = 217 : x
x = 217 · 100 / 62
x = 21 700 / 62
x = 350
phil dunphy, a real estate agent, is considering whether he should list an unusual $774,395 house for sale. if he lists it, he will need to spend $5,747 in advertising, staging, and fresh cookies. the current owner has given phil 6 months to sell the house. if he sells it, he will receive a commission of $16,870. if he is unable to sell the house, he will lose the listing and his expenses. phil estimates the probability of selling this house in 6 months to be 49%. what is the expected profit on this listing?
The required expected profit on this listing with 49% probability in 6 months.
What is Probability?A probability is a number that mirrors the opportunity or probability that a specific occasion will happen. Probabilities can be communicated as extents that reach from 0 to 1, and they can likewise be communicated as rates going from 0% to 100 percent.
According to question:We have,
he will need to spend $5,747 in advertising, staging, and fresh cookies.he will receive a commission of $16,870 on selling.Then, there is 49% chances in 6 months = 49% of $16,870
⇒ $8266.3
And 51% of expenditure = 51%of $5,747
⇒ $29.3
So, required profit = $8266.3 - $29.3 = $8237
Thus, required profit is $8237.
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On a certain hot summer's day, 354 people used the public swimming pool. The daily prices are $1.50 for children and $2.25 for adults. The receipts for admission totaled $548.25. How many children and how many adults swam at the public pool that day?
The number of children and adults that swam at the public pool is
331 and 23.
What is an equation?An equation is a mathematical statement of two expressions connected by an equal sign.
Example:
2x + 5 = 9 is an equation.
We have,
The total number of people = 354.
Cost for children = $1.50
Cost of adults = $2.25
Total amount = $548.25
Now,
Number of children = x
Number of adults = y
Now,
x + y = 354 _____(1)
x = 354 - y ____(2)
1.50x + 2.25y = 548.25 _____(3)
Putting (2) in (3).
1.50 (354 - y) + 2.25y = 548.25
531 - 1.50y + 2.25y = 548.25
0.75y = 548.25 - 531
0.75y = 17.25
y = 17.25/0.75
y = 23
Now,
x = 354 - y
x = 354 - 23
x = 331
Thus,
The number of children is 331.
The number of adults is 23.
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if the set alpha is at 0.05 for a two tailed hypothesis test, what is the p value required to reject a null hypothesis
The required answer is fail to reject a null hypothesis.
What is Null hypothesis?
The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. It is feasible to determine the probability that the null hypothesis is correct using statistical testing.
Given that:
α = 0.05
then
z0.05 = 1.645
Hence, the rejection region is {z < −1.645}.
Hence, The required answer is fail to reject a null hypothesis.
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for the transition matrix P = [0.9 0.1 0.3 0.7], solve the equation SP = S to find the stationary matrix S and the limiting matrix P.
The limiting matrix is [tex]\bar{P}[/tex]=[tex]\left[\begin{array}{ccc}0.75&0.25\\0.75&0.25\\\end{array}\right][/tex].
What is meant by transition matrix?Mathematicians frequently refer to "transition matrices" in a variety of situations. The term "change of coordinates matrix" is occasionally used in the context of linear algebra. As an alternative term for a stochastic matrix, or a matrix that describes transitions, it is employed in the theory of Markov chains. Use row operations to try to create the identity matrix to the left while augmenting the matrix of the second basis with the matrix of the first basis. Afterward, the transition matrix will be on the right. Row 1 should be multiplied by 1 as follows: R1=R1 R 1=-R 1 R1=R1.
The given transition matrix is:
P=[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex]
Let S=[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex] =[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}0.9a+0.1b\\0.3a+0.7b\\\end{array}\right][/tex]=[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
Here, 0.9a+0.1b=0, 0.3a-0.3b=0
So, a=b
a+b=1
a=b=1/2
S=[tex]\left[\begin{array}{ccc}0.5\\0.5\\\end{array}\right][/tex]
This S is called the stationary matrix
P=[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex]
P=det[tex]\left[\begin{array}{ccc}0.9-\lambda&0.1\\0.3&0.7-\lambda\\\end{array}\right][/tex]=0
λ²-1.6λ+0.6=(λ-1)(λ-0.6)=0
λ₁=1, λ₂=0.6
x=[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
Px=λx
[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex] =1[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
0.9a+0.1b=a
a=b
v₁=[tex]\left[\begin{array}{ccc}1\\1\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex] =0.6[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
0.9a+0.1b=0.6a
b=-3a
v₂=[tex]\left[\begin{array}{ccc}1\\-3\\\end{array}\right][/tex]
V=[tex]\left[\begin{array}{ccc}1&1\\1&-3\\\end{array}\right][/tex]
V⁻¹=(1/4)[tex]\left[\begin{array}{ccc}3&1\\1&-1\\\end{array}\right][/tex]
D=[tex]\left[\begin{array}{ccc}\lambda_{1} &0\\0&\lambda_{2}\\\end{array}\right][/tex]
D=[tex]\left[\begin{array}{ccc}1&0\\0&0.6\\\end{array}\right][/tex]
P=VDV⁻¹
Pⁿ=VDⁿV⁻¹
[tex]\bar{P}[/tex]=[tex]\left[\begin{array}{ccc}0.75&0.25\\0.75&0.25\\\end{array}\right][/tex]
This is the required limit matrix.
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f(d) = 0.0071d³ - 0.090d² + 0.48d,
where d is the diameter of the diamond.
Find the domain of the function in the
context of the situation. (Lesson 4-1)
A. The domain is all real numbers.
B. The domain is {dl d > 0).
C. The domain is {dl d < 0).
D. The domain is (dld > 0.48).
The bar graph shows the number of reserved campsites at a campground for one week. What percent of the reservations were for Friday or Saturday?
Reservations: Monday=5
Tuesday=3
Wednesday=4
Thursday=7
Friday=26
Saturday=30
Sunday=9
The percentage of the reservations were for Friday or Saturday is 67%
How to determine the percentage of the reservations were for Friday or Saturday?From the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following data values for reservation
Monday = 5Tuesday = 3Wednesday = 4Thursday = 7Friday = 26Saturday = 30Sunday = 9The total number of reservations in the bar chart is then calculated as
Total number of reservations = 5 + 3 + 4 + 7 + 26 + 30 + 9
Evaluate the sum
So, we have the following representation
Total number of reservations = 84
The total number of reservations for Friday or Saturday is then calculated as
Total number for Friday or Saturday = 26 + 30
Evaluate the sum
So, we have the following representation
Total number for Friday or Saturday = 56
The percentage of the reservations were for Friday or Saturday is then calculated as
Percentage = Total number for Friday or Saturday/Total number of reservations
This gives
Percentage = 56/84
Evaluate
Percentage = 67%
Hence, the percentage is 67%
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What is limit of a function in maths?
The limit of a function is a value of the function as the input of the function gets closer to some number.
We know that, a limit is a value toward which an expression converges as variable approaches certain values.
The limit of a function at m point is nothing but the value that the function approaches as its argument(variable) approaches m.
When a function is said to have a limit L at point p if it is possible to make the function arbitrarily close to L by choosing values to point p.
It is a value of the function as the input of the function gets closer to some number.
Therefore, the limit of a function is nothing but a value of the function as the input of the function gets closer to some number.
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see attached please thank you
After solving for the angles, the resultant answers are as follows:
(A) ∠L = 55°
(B) ∠LMN = 62°
What are angles?When two consecutive lines or rays intersect at a single endpoint, an angle is created.
The vertex of an angle is the point where two points come together.
The Latin word "angulus," which means "corner," is from which the term "angle" originates.
The intersection of two planes also creates angles.
We refer to these as geometric angles.
So, according to the given diagram:
KMN = LMN + 118
180 = LMN + 118
LMN = 180 - 118
LMN = 62°
Now,
6x - 9 + 4x + 7 + 62 = 180
10x + 60 = 180
10x = 180 - 60
10x = 120
x = 120/10
x = 12
Then,
∠L = 4x + 7
∠L = 4*12 + 7
∠L = 55°
Therefore, after solving for the angles, the resultant answers are as follows:
(A) ∠L = 55°
(B) ∠LMN = 62°
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What is the equation of the line with slope of 7 and y-intercept equals to 4?
The equation of a line with slope m and y-intercept is Y = mx + b. (0,b). y = 7x + 4 is the equation of the line with slope of 7 and y-intercept equals to 4?
Since the slope of the line is 7 and the y-intercept is 4, the equation of the line can be written as y = 7x + 4.
The equation of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept. In mathematics, the slope or gradient of a line is a numerical representation of the line's steepness and direction.
In the equation y = 7x + 4, 7 is the slope of the line and 4 is the y-intercept. This means that the line has a slope of 7 and the y-intercept is 4.
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In 2005, the total waste generated in a certain country was 8.618 x 10^8 pounds. Also in 2005, the country's population was 2.76 x 10 ^5 people. Determine the garbage per capita (per person) in that
country in the year 2005.
(use scientific notation to answer this question)
Answer:
To determine the garbage per capita, we need to divide the total waste generated by the population. In 2005, the total waste generated was 8.618 x 10^8 pounds and the population was 2.76 x 10^5 people, so the garbage per capita in that country in 2005 was 3.12 pounds per person. This can be calculated as follows:
8.618 x 10^8 pounds / 2.76 x 10^5 people = 3.12 pounds/person
Alternatively, we can rewrite the population in scientific notation to make the calculation easier:
8.618 x 10^8 pounds / (2.76 x 10^5) people = 8.618 x 10^8 pounds / (2.76 x 10^3 x 10^2) people
Now we can cancel out the common factors of 10^2 from the numerator and denominator to get the final result:
8.618 x 10^8 pounds / (2.76 x 10^3 x 10^2) people = 8.618 x 10^8 pounds / (2.76 x 10^3) people
= 8.618 x 10^5 pounds / (2.76) people
= 3.12 pounds/person
This shows that in 2005, the garbage per capita in that country was 3.12 pounds per person.
A rope is 66 feet long. It is cut into two pieces such that one piece is half the length of the other. What is the length of the longer piece of rope?
22 feet
26 feet
33 feet
44 feet
136 degrees
Answer:
Step-by-step explanation:
So if one bit of the length, is half the size of the other bit then we can make the following equation, for x being the length of rope:
x + 2x = 66
3x = 66
x = 22
That is the length, of the smaller one (half the big one), so 2x = 44. Hence d) is your answer.
Hope I helped!
a rectangular swimming pool has the same depth everywhere. the combined surface area of the floor of the pool and the four sides is $4800$ square feet. what is the maximum volume of the swimming pool in cubic feet?
the maximum volume of the swimming pool in cubic feet = 29744[tex]ft^{3}[/tex]
volume:A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder or a sphere.
Different shapes have different volumes. In 3D geometry, we have studied the various shapes and solids such as cubes, cuboids, cylinders, cones, etc., that are defined in three dimensions. For all these shapes, we are going to learn to find the volume.
Unit of Volume:
Volume of a solid is measured in cubic units. For example, if dimensions are given in meters, then the volume will be in cubic meters. This is the standard unit of volume in the International System of Units (SI). Similarly, other units of volume are cubic centimeters, cubic feet, cubic inches, etc.
given that
the combined surface area of the floor of the pool and the four sides is $4800$ square feet.
each side (there are 4) = 4 x w x w
and the bottom w x w
total surface area 5 w^2 = 4800
w = depth = 30.984 ft
volume= 30.984^3 = 29744.89[tex]ft^{3}[/tex]
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24 3/5 +4^3x(8 1/5 -2)
Answer: i believe it is 123/5 + 1984x/5
Step-by-step explanation:
Melvin plays tennis and swims for a total of 110 minutes every day. He plays tennis for 40 minutes longer than he swims. Part A: Write a pair of linear equations to show the relationship between the number of minutes Melvin plays tennis (x) and the number of minutes he swims (y) every day. Part B: How much time does Melvin spend swimming every day? Show your work. Part C: Is it possible for Melvin to have spent 70 minutes playing tennis if he plays and swims for a total of exactly 110 minutes and plays tennis for 40 minutes longer than he swims? Explain your reasoning.
The answers to all the subparts using equations are shown:
(A) pair of linear equations: y + 40 = x and x + y = 110
(B) 75 minutes every day of swimming.
(C) The given statement is false as a result.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
So, (A):
Y indicates the volume of swimming
X denotes the quantity of tennis.
Making two equations now:
y + 40 = x
x + y = 110
(B)
X in the other equation is changed to match the first equation.
Please plug this in:
y + 40 + y = 110
2y = 70
35 minutes of swimming equals Y.
Including: 35
35 + 40 = 75 minutes every day of swimming.
(C)
No, given that equation: 70 + (70 - 40) = 100
This statement is false as a result.
Therefore, the answers to all the subparts using equations are shown:
(A) pair of linear equations: y + 40 = x and x + y = 110
(B) 75 minutes every day of swimming.
(C) The given statement is false as a result.
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please anyone help me with this question i need it ASAP!! all it’s asking is to Write the equation of a line perpendicular to y=2x-4 and
goes through the point (4,-1). please anyone help meee!!
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 2x - 4 ← is in slope- intercept form
with slope m = 2
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex] , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute (4, - 1 ) into the partial equation
- 1 = - 2 + c ⇒ c = - 1 + 2 = 1
y = - [tex]\frac{1}{2}[/tex] x + 1 ← equation of perpendicular line
-3/4 x 4/3 x -3/7
Just need the answer. Need by next Friday. 30 points for whoever answered.
Answer:-3/4x=-3x/4
4/3x -3/7 = 4x/3 - 3x
Step-by-step explanation:
You are bending a strip of metal into an isosceles triangle for a sculpture. The strip of metal is 28 inches long. The first bend is made 10 inches from one end. Describe two ways you could complete the triangle.
Answer:
2 ways below
Step-by-step explanation:
To complete the triangle, you would need to bend the other end of the strip of metal so that it is also 10 inches from the first bend. One way to do this would be to measure 10 inches from the first bend and mark the spot, then use a bending tool to carefully bend the metal at the mark.
Another way would be to hold the metal strip against a ruler or measuring tape, aligning the first bend with the 10-inch mark, then use the bending tool to make the second bend at the 20-inch mark. In either case, the resulting triangle would have two equal sides that are 10 inches long, and a base that is 8 inches long.
Your model train i 18 inche long. It i an exact model of a train that i 72 feet long. A window on the train i how many time wider than a window on the model?At the movie, ticket for a night how cot $9, and ticket for a day how cot $6. 75. What percent i the dicount you get for going to a day how?
The window on the train will be 48 times wider than a window on the model .
In the question ,
it is given that ,
the length of the model train is = 18 inches and
the length of the exact train is = 72 feet ,
on comparison , we need to convert it into inches .
we know that 1 feet is = 12 inches ,
So , 72 feet is = 72×12 inches = 864 inches
So , the length of the original train is = 864/18 = 48 times the model train .
the ratio will remain same for the width of the window .
So , the window on the train is 48 times wider than a window on the model .
Therefore , the window of the train is 48 times wider.
The given question is incomplete , the complete question is
Your model train is 18 inches long. It is an exact model of a train that is 72 feet long. A window on the train is how many time wider than a window on the model ?
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Required
Question 1- Which parallelogram has an area of 60 square units? *
A
12
15
10
C
15
15
12
B
10
10.2
6
D
6
6
10
Show your reasoning
Answer:
To find the area of a parallelogram, we can use the formula A = bh, where A is the area, b is the base, and h is the height. In this case, we are given that the area is 60 square units, so we can use this information to find the value of b and h for each of the options given.
Option A: 12 15 10
In this option, we can see that the base is 12 units and the height is 15 units, so we can plug these values into the formula to find the area: A = 12 * 15 = 180 square units. This is much larger than the given area of 60 square units, so option A cannot be correct.
Option B: 10 10.2 6
In this option, we can see that the base is 10 units and the height is 6 units, so we can plug these values into the formula to find the area: A = 10 * 6 = 60 square units. This matches the given area of 60 square units, so option B could be correct.
Option C: 15 15 12
In this option, we can see that the base is 15 units and the height is 12 units, so we can plug these values into the formula to find the area: A = 15 * 12 = 180 square units. This is much larger than the given area of 60 square units, so option C cannot be correct.
Option D: 6 6 10
In this option, we can see that the base is 6 units and the height is 10 units, so we can plug these values into the formula to find the area: A = 6 * 10 = 60 square units. This matches the given area of 60 square units, so option D could be correct.
Therefore, the correct answer is either option B or option D.
two dice are rolled what is the probability that the sum of the dice is atleast 5, given that one die is showing a 2
Answer:
Step-by-step explanation:
the sum of the dice is at least 5
one die is showing a 2
2 and 3
2 and 4
2 and 5
2 and 6
4 out of 36 ways to get the sum at least 5 and one die is always 2
Probability = 4/36 = 1/9
If it is known that one die is showing a 2, then the probability that the sum of the dice is at least 5, is the probability that the other die shows 3 or 4 or 5 or 6, i. e. 4/6=2/3=0.666.
The diameter of a circle is 4 feet. What is the circle's circumference?
Answer: Your answer will be 12.57.
Step-by-step explanation:
Using the formulas
C=2 x π x r
d=2 x r
Solving for C.
C = πd = π·4 ≈ 12.56637
State the vertex and the axis of symmetry
y = 3(x-5)^2
Answer:
Vertex = (5,0)
Axis of symmetry = x = 5
Explanation:
Y = 3(x-5)^2
Equal 3(x-5) to 0
y = 3 = 0
x-5 = 0
x = 5
Vertex = (5,0)
Formula for Axis of symmetry: x = -b/2a
Write 3(x-5)^2 in standard form
Y = 3x^2 - 30x + 75
x = -b/2a
x = -(-30)/2(3)
x = 30/6
x = 5
Find the correct expression to solve for z. A. z=8tan22° z = 8 tan 22 ° B. z=tan22°8 z = tan 22 ° 8 C. z=22(tan8) z = 22 ( tan 8 ) D. z=8tan22° z = 8 tan 22 °
Answer:
The correct expression to solve for z is z = 8 tan 22°. This expression uses the tangent function and the angle measure in degrees to find the value of z. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle, and the angle measure must be in degrees in order to use the tangent function. The other answer choices do not use the tangent function or the angle measure in degrees, so they are not correct.
Step-by-step explanation:
pls answer this questions for 15 points
Answer:
B
Step-by-step explanation:
by plugging in f, you can see that B, is the only correct answer
A fails at values greater than or equal to f = 2
C fails for all values
and D fails for all values
B works for all given values
2(1) + 3 = 5
2(2) + 3 = 7
2(3) + 3 = 3
2(4) + 3 = 11
2(5) + 3 = 13
What is the slope of ½?
The slope of ½ is 0. A line with a zero slope is neither rising nor falling when seen from left to right or the other way around. Simply put, the slope of a horizontal line is zero.
y=m x + b, where m is the slope and b is the y-intercept, is the slope-intercept form.
where y= 0 and
y = m x + b
The slope is 0 when expressed in the slope-intercept form, or m = 0.
A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x).
Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.
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28 seconds to 23 seconds
Answer:
5 if your doing subtraction or Percent Change from 28 to 23 ≈ -17.86%
Step-by-step explanation:
Here's a explanation for % of change.
1) Find the difference between 28 and 23 as a number.
2) Divide the result from Step 1 by the starting number 28.
3) Multiply the result from Step 2 by 100 to get it in terms of percent.
I hope this helped.
A 20-cm wrench is used to loosen a bolt. The force is applied 0. 20m from the bolt. It takes 100n to loosen the bolt when the force is applied perpendicular to the wrench. How much force would it take if the force was applied at a 30o angle from perpendicular? round-off your answer to the nearest whole number.
The force that it will take if applied perpendicular at 30° = 58 N
According to the formula of torque = τ and force = F,
τ = r x F x sinθ --- equation 1
Given, F = 100 N , r = 0.2 m (r = radius)
We have to find the force when θ (angle) = 30°
Putting value in equation 1,
τ = 0.2 x 100 x sin (30°)
τ = 10 Nm
Value of torque from here = 10 Nm
Now to calculate the force perpendicular at 30° the equation will change as,
τ = r x F x cosθ --- equation 2
10 = 0.2 x F x cos 30°
Taking τ on the right side and F on left,
F = 10/ (0.2 x cos 30°)
F = 57.73 N
F = 58 N
Therefore, The force that it will take if applied perpendicular at 30° = 58 N
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How do you calculate raw data?
Raw data can be calculated by using mathematical operations such as addition, subtraction, multiplication, and division.
This can be done manually or by using a calculator or a computer program .Additionally, statistical methods such as mean, median, mode, and standard deviation can be used to calculate raw data.Raw data can also be manipulated in various ways. For example, data can be sorted, filtered, and organized into categories or hierarchies. Data can also be visualized in graphs, charts, and diagrams to make patterns and trends easier to identify. Statistical methods such as correlation and regression can also be used to analyze and interpret raw data. Additionally, data can be combined with other data sets to create new insights and relationships. Finally, machine learning and predictive analytics can be used to make predictions about future outcomes based on existing data.
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Scientists studying dolphin echolocation simulate the projection of a bottlenose dolphin's clicking sounds using computer
models. The models originate the sounds at the focus of a parabolic reflector. The parabola in the graph shows the cross
section of the reflector with focal length of 1.3 inches and aperture width of 8 inches. Write an equation to represent the cross
section of the reflector. What is the depth of the reflector? Round your answer to the nearest hundredth.
The equation __ represents the cross section.
The depth is about __ inches.
Step-by-step explanation:
The equation of a parabola with focus at (h, k) and the directrix y = p is given by the following formula:
(y - k)^2 = 4 * f * (x - h)
In this case, the focus is at the origin (0, 0) and the directrix is the line y = -1.3, so the equation representing the cross section of the reflector is:
y^2 = 4 * f * x
= 4 * (-1.3) * x
= -5.2x
The depth of the reflector is the distance from the vertex to the directrix. In this case, the vertex is at the origin, so the depth is simply the distance from the origin to the line y = -1.3. Since the directrix is a horizontal line, this distance is simply the absolute value of the y-coordinate of the line, which is 1.3 inches. Therefore, the depth of the reflector is approximately 1.3 inches.