SOLUTION
Total no of ties = 45
Number of ties that he feels goes well with jacket = 34
Number of ties that he feels does not go well with jacket = 45 - 34 = 11
a) Probability that tie goes well with jacket =
[tex]\dfrac{\text{Number of ties that goes well with jacket}}{\text{Total number of ties}}[/tex]
[tex]=\dfrac{34}{45}[/tex]
b) Probability that a tie does not go well with jacket
[tex]\dfrac{\text{Number of ties that doe not goes well with jacket}}{\text{Total ties}}[/tex]
[tex]=\dfrac{11}{45}[/tex]
Four components of 55
Answer: 1, 5, 11, 55
Step-by-step explanation:
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What is the area of trapezoid ABCD?
A) 39 ft2
B) 58 ft2
C) 121 ft2
D) 242 ft2
The area of trapezoid ABCD is 39 ft².
What is trapezoid?A trapezοid is a quadrilateral with twο sides that are parallel. It has fοur sides, fοur angles, and twο pairs οf οppοsite sides that are equal in length. The nοn-parallel sides, οr legs οf the trapezοid, are usually referred tο as the bases οf the trapezοid. The twο parallel sides are referred tο as the bases, the nοn-parallel sides are referred tο as the legs, and the line cοnnecting the twο parallel sides is called the midline. The angles created by the bases and the legs are called the base angles
Area of trapezoid = [tex]\dfrac{a + b}{2} h[/tex]
Here, a = 5ft
b = 21 ft
h = 3ft
Area of trapezoid = [tex]\dfrac{5 + 21}{2} (3)[/tex]
Area of trapezoid = 39 ft²
Thus, The area of trapezoid ABCD is 39 ft².
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The value of x in the equation 14(12x−36)=5x+18 is?
Answer:
x=522/163
Step-by-step explanation:
14(12x−36)=5x+18
168x-504=5x+18
168x-504+504=5x+18+504
163x=522
163x/163=522/163
x=522/163
x=3.20
Answer:
I got 3.2 in decimal form or 522/163 in a fraction
Triangular pyramid B is the image of triangular pyramid A after dilation by a scale factor of 1/4. If the volume of triangular pyramid B is 4 cm3, find the volume of triangular pyramid A, the preimage.
Therefore , the solution of the given problem of volume comes out to be has a volume of 256 cubic centimetres.
Describe volume.A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The symbols cm3 and in3 are two examples of cubic measures. However, the bulk of an item may be employed to estimate its size. Usually, the weight of an item is converted into mass measures like grams and kilos.
Here,
The formula: gives the capacity of a pyramid.
=> V = (1/3)Bh
where B is the base's size and h is the pyramid's height.
The ratio of the volumes of the dilated pyramid to the initial pyramid is (1/4)3 = 1/64 if the scale factor of dilation is 1/4. In other terms, pyramid B's volume is 1/64 that of pyramid A's.
Let V(A) represent the pyramid A's volume. Then:
=> V(B) = (1/64)
=> V(A) = 4
When we multiply both parts by 64, we obtain:
=> V(A) = 256
Pyramid A, the preimage, therefore, has a volume of 256 cubic centimetres.
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Solve for ps pleaseee
Answer:
PS=21.3
Step-by-step explanation:
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QUESTION 8 ..... [1.5 marks ] We take a sample of 700 students in Wenatchee Valley College and
observe that 80 are men. Find 90% confidence interval of the true proportion of men in the college.
Please round your answer to the nearest tenth of a percent.
§7.4
Solution. Please write your detailed solution here:
Thus, we can be 90% confident that the true proportion of men in the college is between 8.8% and 14.0%.
What is percent?Percent, denoted by the symbol "%", is a way of expressing a number as a fraction of 100. For example, 50% is equivalent to the fraction 50/100, which can be simplified to 1/2. Percentages are commonly used to express ratios, proportions, or rates in various contexts such as finance, statistics, and everyday life. For instance, an interest rate of 3% means that for every $100 borrowed, the borrower will be charged $3 per year. Similarly, a score of 80% on an exam means that the student has answered 80 out of 100 questions correctly.
by the question.
To find the confidence interval of the true proportion of men in the college, we need to use the formula:
[tex]CI = p ± z\sqrt((p(1-p))/n)[/tex]
where p is the sample proportion (80/700 = 0.114), z is the z-score associated with the confidence level (90% in this case), and n is the sample size (700).
To find the z-score, we can use a standard normal distribution table or a calculator. For a 90% confidence level, the z-score is approximately 1.645.
Plugging in the values, we get:
[tex]CI = 0.114 ± 1.645\sqrt((0.114(1-0.114))/700)[/tex]
Simplifying, we get:
[tex]CI = 0.114 ± 0.026[/tex]
Therefore, the 90% confidence interval for the true proportion of men in the college is:
[tex]CI = 0.114 ± 0.026[/tex]
Rounding to the nearest tenth of a percent, we get:
CI = (8.8%, 14.0%)
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25 feet equals how many inches
calculate value of x
12cm, 7cm, 121 degrees
trigonometry
The side x = 16.72 approximately to two decimal places using the cosine rule.
What is the cosine rule?In trigonometry, the cosines rule relates the lengths of the sides of a triangle to the cosine of one of its angles.
Considering the given triangle, we shall calculate for the side x is using the cosine rule as follows;
a² = b² + c² - 2(b)(c)cosA
x² = 7² + 12² - 2(7)(12)cos121°
x² = 49 + 144 - 168(-0.5150)
x² = 193 + 86.52
x² = 279.52
x = 16.7189 {take square root of both sides}
Therefore, using the cosine rule, we can conclude the value of the side x of the triangle is 16.7189.
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Give me some help please
Answer: 56 cm
Step-by-step explanation:
An alloy is made up of 93.5 parts aluminum, 5 parts zinc, and 1.5 parts copper. A foundry
has 164 pounds of aluminum available. Find the weight of the zinc and copper that will be
needed to make the alloy.
Answer: Since the alloy is made up of 93.5 parts aluminum, 5 parts zinc, and 1.5 parts copper, we can express the weight of zinc and copper needed to make the alloy as a ratio to the weight of aluminum needed. Let x be the weight of aluminum needed in pounds, then we have:
Weight of aluminum: Weight of zinc: Weight of copper = 93.5: 5 : 1.5
We know that the foundry has 164 pounds of aluminum available, so we can substitute x = 164 into the above ratio and solve for the weights of zinc and copper:
164: Weight of zinc: Weight of copper = 93.5: 5 : 1.5
Cross-multiplying, we get:
164 × 5 = 93.5 × Weight of zinc
Weight of zinc = (164 × 5) / 93.5
Weight of zinc = 8.76 pounds (rounded to two decimal places)
Similarly, cross-multiplying the above ratio gives us:
164: Weight of zinc: Weight of copper = 93.5: 5 : 1.5
164 × 1.5 = 93.5 × Weight of copper
Weight of copper = (164 × 1.5) / 93.5
Weight of copper = 2.63 pounds (rounded to two decimal places)
Therefore, the weight of zinc needed to make the alloy is 8.76 pounds and the weight of copper needed is 2.63 pounds.
Step-by-step explanation:
Find the total number of outcomes.
There are 3 true-false questions on a quiz.
The total number of outcomes in the quiz is 8
How to determine the total number of outcomesFrom the question, we have the following parameters that can be used in our computation:-
Options = True or FalseQuestions = 3Using the above as a guide, we have the following:
For each question, there are two possible outcomes: true or false.
So, the total number of outcomes for all three questions is:
Total = 2 x 2 x 2
Evaluate
Total = 8
Hence, there are 8 possible outcomes in total.
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Complete question
Find the total number of outcomes of the following experiment
There are 3 true-false questions on a quiz.
Khrysteen is paid semimonthly with $1,978.50 per pay. What is her annual
pay?
Answer:
Since Khrysteen is paid semimonthly, she receives 24 paychecks in a year (12 months x 2 pay periods per month).
To calculate her annual pay, we can multiply her semi-monthly pay by the number of paychecks she receives in a year:
Annual pay = Semi-monthly pay x Number of paychecks in a year
Annual pay = $1,978.50 x 24
Annual pay = $47,484
Therefore, Khrysteen's annual pay is $47,484.
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mathlit how much will 350 learners pay for amount cost of 100
Answer:
for what value of y is the rational expression y+6÷2y-3 be yndefined?
Figure K is reflected over line p and then over line d. If lined p and d are parallel and 2.8 ft apart, what single translation maps k onto k’
The translation that maps K onto K' is a horizontal translation of 2.8 ft to the right, followed by a vertical translation of 5.6 ft downwards.
How to find single translation?We first need to know the distance and direction of the two reflections in order to find the single translation that maps K onto K'.
When figure K is mirrored across line p, figure K" is the resultant image:
K' K''
| |
| |
p ------ ------ d
| |
| |
K K'
We can see that the distances between K and p and K" and p, as well as K and d and K" and d, are the same. Because of this, K and K" are separated by a distance that is 2 2.8 feet longer than K and d.
When positioned above line D, figure K"s reflected image is K". This reflection, being perpendicular to p, has no impact on the horizontal placement of K" in regard to K'. K" is now beneath K', although the vertical axis has changed.
K' K''
| |
| |
p ------ ------ d
| |
| |
K'' K'
Consequently, a horizontal translation of 2.8 feet to the right, then a vertical translation of 5.6 feet downward, is the translation that maps K onto K'. The straightforward translation is:
(x, y) → (x + 2.8, y - 5.6).
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9" is false.
What is equation?In mathematics, an equation is a statement that two expressions are equal. It typically contains one or more variables (unknowns) and specifies a relationship between those variables. Equations are used to model real-world phenomena, solve problems, and make predictions. There are many types of equations in mathematics, including linear equations, quadratic equations, polynomial equations, exponential equations, trigonometric equations, and many more. Each type of equation has its own set of methods and techniques for solving it.
Here,
To determine which statements are true about the circle whose equation is x2 + y2 – 2x – 8 = 0, we can use the standard form of the equation of a circle, which is:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius.
Comparing the given equation to the standard form, we can complete the square by adding 1 to both sides:
x² - 2x + y² - 8 = -1
(x - 1)² + y² = 9
From this, we can see that the center of the circle is (1, 0) and the radius is 3 units. Therefore, the statements that are true are:
The center of the circle does not lie on the x-axis, so the statement "The center of the circle lies on the x-axis" is false.
The center of the circle does lie on the y-axis, so the statement "The center of the circle lies on the y-axis" is true.
The standard form of the equation is (x - 1)² + y² = 3, so the statement "The standard form of the equation is (x - 1)² + y² = 3" is true.
The radius of this circle is not the same as the radius of the circle whose equation is x² + y² = 9, so the statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9" is false.
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Igbo bought five (5) books at N40.00 each and sold them What is the for N150.00. loss?
In response to the given question, we can state that As a result, Igbo expressions experienced a N50.00 loss.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is formed as follows: Expression, number, and math operator Numbers, parameters, and functions make up a mathematical expression. It is possible to contrast phrases and expressions. Every mathematical statement that comprises variables, numbers, and a mathematical action between them is referred to as an expression. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the provided equation, all separated by the mathematical symbol +.
Igbo spent N40.00 on 5 books, for a total of N40.00.
N200.00 = 5 books x N40.00 each
Igbo lost money since he sold the books for N150.00. To find the amount of the loss, subtract the selling price from the cost price:
Cost Price - Selling Price = Loss
N200.00 - N150.00 = Loss
Loss = N50.00
As a result, Igbo experienced a N50.00 loss.
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Six whole numbers have
a median of 10
a mode of 11
a range of 4
Work out a possibie set of six numbers. Write the numbers in order.
Answer:Answer:
median=10, 6 numbers, so median is between 3rd and 4th
.. 9 11 . .
mode=11
.. 9 11 11 .
range=4
7 8 9 11 11 11
Step-by-step explanation:
help with This Math
Answer:
Traingle=180 degrees
U=54
180-54
=126
126/2
=63
R=63
U=54
T=63
How does coverage for a business relate to individual insurance? Compare and contrast the different types of individual insurance with business insurance. What are the similarities of individual insurance and business insurance? What are the differences between the two types of insurance? Give an example of each type of insurance.
Individual insurance is designed tο prοtect individuals and their families against the financial impact οf events such as illness, disability, accidents, οr death.
Define the term insurance?Individual insurance and business insurance are similar in that bοth prοvide financial prοtectiοn against risks and uncertainties. Hοwever, there are alsο significant differences between the twο types οf insurance.
Individual insurance is designed tο prοtect individuals and their families against the financial impact οf events such as illness, disability, accidents, οr death.
Business insurance is designed tο prοtect businesses against the financial impact οf events such as prοperty damage, liability claims, οr lοss οf incοme due tο interruptiοn οf business οperatiοns.
The similarities between individual insurance and business insurance include:
Bοth prοvide financial prοtectiοn against risks and uncertainties.Bοth require payment οf premiums by the pοlicyhοlder tο the insurance cοmpany.Bοth types οf insurance invοlve a cοntractual agreement between the pοlicyhοlder and the insurer.The differences between individual insurance and business insurance include:
The types οf risks cοvered: Individual insurance is designed tο cοver risks that affect individuals and their families, while business insurance cοvers risks that affect a business.The cοst: Business insurance premiums are generally higher than individual insurance premiums due tο the higher value οf assets being cοvered and the higher level οf risk invοlved.The cοmplexity οf pοlicies: Business insurance pοlicies are typically mοre cοmplex than individual insurance pοlicies due tο the variety οf risks being cοvered and the different types οf cοverage required.Example οf individual insurance: A persοn buys a health insurance pοlicy tο cοver the cοst οf medical treatment.Example οf business insurance: A small business οwner purchases liability insurance tο prοtect against claims οf injury οr prοperty damage resulting frοm the business's οperatiοns.To know more about Business Insurance, visit:
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A certain element decays at a constant rate of 6% per year. If you start with 20 grams of the element, how long will it take before there are only four grams left?
Answer:
26.0 years
Step-by-step explanation:
It will take approximately 16.79 years (to the nearest hundredth) for the initial mass of 20 grams to decay to four grams, given a constant decay rate of 6% per year.
To determine how long it will take for the 20 grams of the element to decay to four grams, we need to calculate the time using the given decay rate.
Given:
Initial mass (M₀) = 20 grams
Decay rate: 6% per year
Let's set up an equation to represent the decay of the element:
M(t) = M₀ * (1 - r)^t
Here, M(t) represents the mass at time t in years, M₀ is the initial mass, r is the decay rate (expressed as a decimal), and t is the time in years.
We want to find the value of t when M(t) = 4 grams:
[tex]4 = 20 * (1 - 0.06)^t[/tex]
Dividing both sides by 20:
[tex]0.2 = (1 - 0.06)^t[/tex]
Taking the natural logarithm of both sides:
[tex]ln(0.2) = ln[(1 - 0.06)^t][/tex]
Using logarithmic properties, we can simplify further:
[tex]ln(0.2) = t * ln(1 - 0.06)[/tex]
Now, we can solve for t by dividing both sides of the equation by ln(1 - 0.06):
t =[tex]ln(0.2) / ln(1 - 0.06)[/tex]
Using a calculator, we find:
t ≈ 16.79 years
Therefore, it will take approximately 16.79 years (to the nearest hundredth) for the initial mass of 20 grams to decay to four grams, given a constant decay rate of 6% per year.
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A central angle has a measure of 2.3 radians and the subtended arc length is 12 cm.
What is the radius of the circle to the nearest 10th
Therefore , the solution of the given problem of circle comes out to be the circle's radius is about 5.2 centimetres.
What is circle?A circle is formed by each region of a plane that is a certain distance from this extra point (center). It thus consists of spots that are isolated from one another by the surface and is curved. It also revolves about the centre equally from all angles. In the constrained, the double sphere of a circular, every group of endpoints is uniformly separated from the "centre." By tracing a thread through a circle, one can create a line to circular symmetry. Additionally, it rotates evenly in all directions around the centre.
Here,
The following equation determines the extent of a circle's arc:
=> arc length = radius * central angle
We can determine the radius by solving for the centre angle,
which is known to be 2.3 radians, and the arc length, which is 12 cm:
=> radius = arc length / central angle
=> 12 cm / 2.3 radians
=> 5.22 cm
We calculate the radius to be 5.2 cm by rounding to the closest tenth. As a result, the circle's radius is about 5.2 centimetres.
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choose two ancient mathematical system from egypt,babylonia,greece, and islam then discuss the contributions of these two that you believe made significant contributions to modern mathematics and people's lives today
Two ancient mathematics concepts are given as follows:
Fractions from the Egyptians.Euclidean Geometry from the Greeks.How did the Egyptians use fractions?The Egyptians used fractions extensively in their calculations and were the first civilization to develop a notation for fractions. Their notation used a symbol for the numerator placed above a symbol for the denominator, similar to our modern fraction notation.
How did the Greeks use Euclidean geometry?Euclid's Elements is one of the most influential works in the history of mathematics. It provided a systematic and rigorous approach to geometry, which has been the basis of mathematical education for over two thousand years.
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the distance between (-7, 3) and (5, 3)
Answer:
12
Step-by-step explanation:
7+5
Answer:
.
Step-by-step explanation:
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Here, (x1, y1) = (-7, 3) and (x2, y2) = (5, 3).
Substituting these values, we get:
d = sqrt((5 - (-7))^2 + (3 - 3)^2)
= sqrt((12)^2 + (0)^2)
= sqrt(144)
= 12
Therefore, the distance between (-7, 3) and (5, 3) is 12 units.
If you ran this company, what is something that would concern you? (Make sure you
support your answer with quantities displayed in the graph)
Assume the numbers are in $1000s.
Marketing
HR
Developer
Budget Analysis
Customer Support
100
ol
Actual Spending
Finance
Admin
Allocated Budget
Sales
If I were to run this company, I would be concerned about the discrepancy between the allocated budget and the actual spending in the graph.
What is graph?Graph is a mathematical structure used to represent relationships between objects. It consists of vertices (also known as nodes) which represent the objects and edges (also known as arcs) which represent the relationships between the objects. Graphs are often used to represent networks, such as social networks, transportation networks, and communication networks. Graphs can also be used to represent data structures, such as trees and linked lists.
In particular, the finance, admin, marketing, HR, and developer departments all have allocated budgets that are greater than their actual spending. This could be a sign that the company is not utilizing its resources efficiently, since it is not spending up to its allocated budget. The discrepancy between allocated budget and actual spending could also indicate that the company is wasting money on unnecessary projects, or that its budget is not allocated correctly.
Furthermore, the customer support department has allocated budget of $100k, yet its actual spending is only $50k. This could indicate that the company is not providing adequate customer support, which could lead to customer dissatisfaction and a decrease in customer loyalty. It could also mean that the company is not taking advantage of its resources and not utilizing them to their fullest potential.
Overall, the discrepancy between the allocated budget and the actual spending could be a sign of inefficiencies and mismanagement within the company. As the company’s leader, I would be concerned about the implications of this discrepancy and would take steps to ensure that the company is utilizing its resources correctly and efficiently.
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The density of iron is 7.87 g/cm³. What is the volume of a 2.9 kg block of iron in cubic centimeters? Round to the nearest hundredth.
Answer:
368.49 cm3
Step-by-step explanation:
[tex]2.9kg=(2.9)(1000)=2900g[/tex]
[tex]V=2900/7.87[/tex]
[tex]368.49 cm^{3}[/tex]
nearest hundredth
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PLEASE HELP ME!!! ASAP.
Enter your answer and show all the steps that you used to solve this problem in the space provided.
(Click imagine for the table)
X. 3, 9, 13, 20.
Y. 9, 27, 39, 60
State weather the relationship between the variables in the table is a direct variation, an inverse variation, or neither.
if it direct, write a function and model it.
The relationship between the variables x and y is a direct variation as the constant of variation 1/3 is the same for all values of x and y
What is direct variationIf the values of y varies directly as does of x, then there is a constant say "k" that is true for them, else y does not vary directly as x.
For x = 3 when y = 9, we can solve for the constant k as follows:
3 = k9
we divide through by 9
3/9 = k9/9
k = 1/3
The constant 1/3 is same for x = 9 when y = 27, x = 13 when y = 39, and x = 20 when y = 60.
Therefore, the relationship between the variables x and y is a direct variation as the constant of variation 1/3 is the same for all values of x and y.
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Can you help me? I will give the brain crown.
Step by step would be preferred thank youuu!!
In AIJK, IJ || LM. Given that KI = 18, KL=8, and LM = 20, find IJ.
K
W
IJ =
Answer:
the length of IJ is 7.2 units.
Step-by-step explanation:
Since IJ is parallel to LM, we can use the property of similar triangles to solve for IJ.
Triangles KIJ and KLM are similar, so we have:
IJ/KL = KI/LM
Substituting the given values, we get:
IJ/8 = 18/20
IJ/8 = 9/10
Multiplying both sides by 8, we get:
IJ = (8)(9/10)
IJ = 7.2
Therefore, the length of IJ is 7.2 units.
Without using a calculator, compute the sine and cosine of by using the reference angle.
The sine of 5π/4 is [tex]\frac{-1}{\sqrt{2} }[/tex] , the cosine of 5π/4 is [tex]\frac{-1}{\sqrt{2} }[/tex] and the angle lies in the third quadrant.
What is the reference angle?
A reference angle is an acute angle formed between the terminal side of an angle in standard position and the x-axis. In other words, it is the smallest angle that can be formed between the terminal side of the angle and the x-axis.
To find the sine and cosine of 5π/4 using the reference angle, we first need to identify the reference angle.
In this case, 5π/4 is in the third quadrant, which means that the terminal side of the angle passes through the point (-1, -1) on the unit circle.
To find the reference angle, we draw a line from (-1, -1) to the x-axis, which forms a right triangle with sides of length 1, 1, and √2
The reference angle θ is the angle formed between the x-axis and the adjacent side of the triangle. By applying the trigonometric functions to this reference angle, we can find the sine and cosine of 5π/4.
sin(θ) = opposite/hypotenuse = [tex]\frac{1}{\sqrt{2} }[/tex]
cos(θ) = adjacent/hypotenuse = [tex]\frac{-1}{\sqrt{2} }[/tex]
Since sine is positive in the third quadrant and cosine is negative, we need to take the negative of the sine value and keep the negative sign for the cosine value:
sin(5π/4) = -sin(θ) = [tex]\frac{-1}{\sqrt{2} }[/tex]
cos(5π/4) = cos(θ) = [tex]\frac{-1}{\sqrt{2} }[/tex]
Therefore, the sine of 5π/4 is [tex]\frac{-1}{\sqrt{2} }[/tex], and the cosine of 5π/4 is [tex]\frac{-1}{\sqrt{2} }[/tex] .
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Write the prime factorization of 30. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).
Answer:
2 * 3 * 5
Step-by-step explanation:
The factors of 30 are 1,2,3,5,6,10,15, and 30. Lets just pick out the prime numbers from this and see if they multiply to 30.
[tex]2\times 3\times 5=30[/tex]
The Sock Company buys hiking socks for $6 per pair and sells them for $10. Management budgets monthly fixed costs of $12,000 for sales volumes between 0 and 12,000 pairs of socks.
If the company sells more than 3,000 pairs of socks per month, it will make a profit.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To analyze the profit of the Sock Company, we need to consider the total cost and total revenue.
Let's start with the total cost:
The cost per pair of socks is $6.
If x is the number of pairs of socks sold, then the total cost is 6x.
There is also a fixed cost of $12,000 per month.
So, the total cost can be expressed as:
C(x) = 6x + 12,000
Now, let's move to the total revenue:
The selling price per pair of socks is $10.
If x is the number of pairs of socks sold, then the total revenue is 10x.
So, the total revenue can be expressed as:
R(x) = 10x
The profit is the difference between the total revenue and total cost:
P(x) = R(x) - C(x) = 10x - (6x + 12,000) = 4x - 12,000
To find the range of x where the company makes a profit, we need to set P(x) greater than 0:
4x - 12,000 > 0
4x > 12,000
x > 3,000
Therefore, if the company sells more than 3,000 pairs of socks per month, it will make a profit.
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