How does the relative
frequency change between
when the spinner is spun 50
times vs. 100 times?
Answers
The relative frequency of an event is a way to estimate the probability of that event happening.
For example, if you spin a spinner 50 times and the spinner lands on red 20 times, the relative frequency of getting red would be 20/50 = 0.4. This is a statistical estimate of the probability of the spinner landing on red, and it's based on the limited number of trials (spinning the spinner 50 times). As you increase the number of trials, the relative frequency will become a more accurate estimate of the true probability of the event. So if you spin the spinner 100 times instead of 50 times, and the spinner lands on red 40 times, the relative frequency would be 40/100 = 0.4. This shows that as the number of trials increases, the relative frequency becomes a better estimate of the true probability of the event. The reason for this is that the more trials you have, the more representative your sample is of the population, and the closer your estimate will be to the true probability of the event. In this case, the true probability of the spinner landing on red is unknown, but as you spin it more times, the relative frequency will approach the true probability, providing a more accurate estimate.
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Related Questions
Find an equation of the tangent line at the given value of x. y= 0∫x sin(2t2+π2),x=0 y= ___
Answers
The equation of the tangent line at x=0 is y = x.
To find the equation of the tangent line at the given value of x, we need to find the derivative of the function y with respect to x and evaluate it at x=0.
Taking the derivative of y=∫[0 to x] sin(2t^2+π/2) dt using the Fundamental Theorem of Calculus, we get:
dy/dx = sin(2x^2+π/2)
Now we can evaluate this derivative at x=0:
dy/dx |x=0 = sin(2(0)^2+π/2)
= sin(π/2)
= 1
So, the slope of the tangent line at x=0 is 1.
To find the equation of the tangent line, we also need a point on the line. In this case, the point is (0, y(x=0)).
Substituting x=0 into the original function y=∫[0 to x] sin(2t^2+π/2) dt, we get:
y(x=0) = ∫[0 to 0] sin(2t^2+π/2) dt
= 0
Therefore, the point on the tangent line is (0, 0).
Using the point-slope form of a linear equation, we can write the equation of the tangent line:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
Plugging in the values, we have:
y - 0 = 1(x - 0)
Simplifying, we get:
y = x
So, the equation of the tangent line at x=0 is y = x.
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3. What are the 4 components of an
Atom?
Answers
Answer:
The parts of an atom are protons, electrons, and neutrons. A proton is positively charged and is located in the center or nucleus of the atom.
Step-by-step explanation:
Answer:
The parts of an atom are protons, electrons, and neutrons.
Step-by-step explanation:
Hope this helps! :3
plz mark as brainliest!
What is the solution to this inequality? −4m−3.65>4.35 Drag and drop a symbol and number to correctly complete the inequality. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. m Response area Response area
Answers
The solution to given linear inequality, -4m - 3.65 > 4.35, is m < -2
Solving Linear InequalitiesFrom the question, we are to solve the given linear inequality.
From the given information,
The given linear inequality is
-4m - 3.65 > 4.35
Solving the linear inequality
-4m - 3.65 > 4.35
Add 3.65 to both sides
-4m - 3.65 + 3.65 > 4.35 + 3.65
-4m > 8.00
Divide both sides by -4 and revert the signs
-4m/-4 > 8.00/-4
m < -2
Hence, the solution is m < -2
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The probability that an African American peron in the United State ha type O blood i 47%. Six unrelated African American people in the United State are elected at random
Answers
Six unrelated African American people in the United State are elected at random then the probability that all three have type O+ blood would be 0.103823
The probability that a person in the United States has type O+ blood is 47%. Three unrelated people in the United States are selected at random. Find the probability that all three have type O+ blood.
Since the probability of having a O+ blood is an independent event, so to find probability that all three have type O+ blood we will use multiplication rule of independent events as:
0.47*0.47*0.47= 0.103823
Therefore, the probability that all three have type O+ blood would be 0.103823
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Consider a one particle quantum system with the Hamiltonian of the form \[ H=\frac{p^{2}}{2 m}+V(\vec{r}) \] The system has eigenstates \( |n\rangle \) such that \[ H|n\rangle=E_{n}|n\rangle \] where
Answers
The states of a system that are not affected by time evolution and represent the stationary states are called eigenstates of the system. The eigenstates of a one-particle quantum system are defined by the equation, H|n⟩ = Eₙ|n⟩, where |n⟩ is the eigenstate of the system, Eₙ is the energy of the state, and H is the Hamiltonian of the system. We can find the energy eigenvalues and eigenstates of a one-particle quantum system using the Hamiltonian operator.
Consider a one-particle quantum system with the Hamiltonian of the form, H = p²/(2m) + V(r).The system has eigenstates |n⟩ such that, H|n⟩ = Eₙ|n⟩, where p is the momentum, m is the mass, V(r) is the potential energy, |n⟩ is the eigenstate with the energy Eₙ, and H is the Hamiltonian.
We can find the energy eigenvalues and eigenstates of a one-particle quantum system with the Hamiltonian H, which is given by H = p²/(2m) + V(r).
The states of the system are the eigenstates |n⟩, and their energy is Eₙ. H|n⟩ = Eₙ|n⟩ defines the states of the system. The eigenvectors form an orthonormal basis for the Hilbert space.
For the energy eigenvalues and eigenstates of a one-particle quantum system, the operator H is represented by the Hamiltonian operator, which is given by the equation
\(\[\hat{H}=-\frac{\hbar^{2}}{2m} \frac{\partial^{2}}{\partial x^{2}}+V(x)\]\)
We can use this operator to find the eigenvalues and eigenstates of the system.
In quantum mechanics, the eigenstates of a system are defined as states that are not affected by time evolution and represent the stationary states. In other words, if the state of a system is an eigenstate, then it remains the same over time.
The eigenstates of a one-particle quantum system are defined by the equation, H|n⟩ = Eₙ|n⟩. Here, |n⟩ is the eigenstate of the system, Eₙ is the energy of the state, and H is the Hamiltonian of the system.
We can use the Hamiltonian operator to find the energy eigenvalues and eigenstates of a system. For a one-particle quantum system, the Hamiltonian operator is represented by the equation,\(\[\hat{H}=-\frac{\hbar^{2}}{2m} \frac{\partial^{2}}{\partial x^{2}}+V(x)\]\)
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A recipe calls for 40 ounces of rice. How many grams of rice does the recipe require?
Answers
Answer:
1133.98
Step-by-step explanation:
Answer:
1134
Step-by-step explanation:
There are 28.3495 grams per oz
28.3495 x 40 = 1133.98
i have 8 boxes of chocolate i eat 3 chocolates from each box i now have 72 chocolates in total
Answers
Answer: there were 12 chocolates in each box. (Originally, before any got eaten)
Step-by-step explanation: let x represent the total amount of chocolates in each box.
8x - 3(8) = 72
8x - 24 = 72 add 24 to both sides
8x = 96 divide both sides by 8
X = 12
Answer:
That means you had 48 chocolates in each box
Step-by-step explanation:
Since you eat 3 chocolates from all 8 boxes, you do this:
8 x 3 which = 24
Now since you have 72 chocolates left you do this:
72 - 24 which = 48
So, therefore, there were originally 48 chocolates in each box
(Don't eat so much chocolate lol you could get sick)
Determine if the following statements are true or false.
If the null hypothesis that the means of four groups are all the same is rejected using ANOVA at a significance level a = 0.05, then...
a. The standardized variability between the groups is higher than the standardized variability within the groups.
b. The appropriate a* to be used in pairwise comparisons of group means is 0.05/4 = 0.0125 because there are four groups.
c. We can then conclude that all of the group means are different from one another.
Answers
a. The statement is true.
b. The statement is false.
c. The statement is false.
a. When the null hypothesis of equal means for four groups is rejected using ANOVA at a significance level of 0.05, it implies that there is sufficient evidence to suggest differences between the group means. ANOVA compares the variability between groups to the variability within groups. If the null hypothesis is rejected, it means that the standardized variability between the groups is higher than the standardized variability within the groups.
b. The appropriate significance level for pairwise comparisons of group means, also known as post hoc tests, is not simply divided by the number of groups. Dividing the significance level by the number of groups, as stated in option b, is not a valid approach. To appropriately account for multiple comparisons, adjustments like the Bonferroni correction, Tukey's HSD, or the Sidak correction are commonly used. These methods ensure that the overall Type I error rate is controlled.
c. Rejecting the null hypothesis using ANOVA only indicates that there are differences between at least two group means. It does not provide information about which specific group means differ from each other. To identify which group means are significantly different, additional post hoc tests or pairwise comparisons are required. These tests allow for a more detailed analysis of specific group differences and provide insights into which pairs of group means are statistically significant.
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What are not exponential functions?.
Answers
It is not of exponential order for h(t) = et2. F is of exponential order and has order. F is piecewise continuous. No function's Laplace transform is possible. g(t) = eat, where t [0,.
Non-exponential form:
To represent a scientifically notated number as a non-exponential quantity: • Remove the exponential component of the number by moving the decimal point the same number of places as the exponent's value. The decimal is moved to the right by the same number if the exponent is positive.
Here are a few instances of functions other than exponential ones. y = 3 1 x as a result. n = 0 3 p as a result. Because y = ( 4) x. Since b = 1, y = 6 0 x.
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Which describes the graph of y=-(x + 5)2 + 3?
A. Minimum at (-5,3)
B. Maximum at (5,3)
C. Minimum at (5,3)
D. Maximum at (-5,3)
Answers
Answer:
D
Step-by-step explanation:
Since there is a negative sign, the graph is a n shaped quadratic curve and hence, there can only be maximum point. Hence we can eliminate A and C.
For a curve in the completing the square form y = (x+a)²+b, the turning points are (-a,b). Hence in this case, turning point is at (-5, 3).
Hence the correct option is D
Answer:
D
Step-by-step explanation:
Hello there, can you please help me out with this question? thankyou
Answers
Answer:
y = 6
Step-by-step explanation:
Given the graph, we need to know that x is a vertical line while y is a horizontal line.
That being said, we also see that the horizontal line passes through 6 of y.
So if y is horizontal and the horizontal line passes through y of 6, our answer comes to be.
\([y = 6]\)
For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C. Use the box-and-whisker plot to answer the questions below. Average Life Span of Pets 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Years Part A: What is the range shown in the average life span of pets? Part B: What is the range of the middle 50% of the average life span of pets? Part C: Which quartile has the largest spread of life spans? Explain how you know with a complete sentence. B i U Font Family AA Ą OD == := IV ED
Answers
The range shown in the average life span of pets is 14 years.
The range of the middle 50% of the average life span of pets is 9 years.
The third quartile has the largest spread of life spans. I know this because the upper whisker of the box-and-whisker plot is longer than the lower whisker, indicating a greater range in the higher values of the dataset.
What is the range of the average life span of pets shown in the box-and-whisker plot?The first question seeks to clarify the specific range of the average life span of pets as depicted in the box-and-whisker plot. By understanding the range, we can determine the span between the minimum and maximum values represented in the plot.
How is the range of the middle 50% of the average life span of pets determined?The second question aims to explore how the range of the middle 50% of the average life span of pets is calculated. This range is derived from the interquartile range, which measures the spread of the data within the central 50% of the dataset.
Which quartile exhibits the largest spread of life spans in the box-and-whisker plot?The third question inquires about the quartile that exhibits the largest spread of life spans in the box-and-whisker plot. By examining the length of the whiskers in the plot, we can identify which quartile has a greater range of values, indicating a larger spread in life spans.
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Choose the composition of translations that maps the image ΔPQR onto ΔP′Q′R′.
Question 4 options:
(x,y) → (x + 6,y + 3)
(x,y) → (x – 6,y – 3)
(x,y) → (x + 6,y – 3)
(x,y) → (x – 6,y + 3)
Answers
Answer:
(x , y ) ---> (x + 6 , y - 3)
Step-by-step explanation:
(x , y ) ---> (x + 6 , y - 3)
P(-1 , 4) -----> P'(-1+6 , 4-3) = P'(5,1)
Comapre P and P' x-coordinate
-1 + a = 5
a = 5 +1 = 6
Q(-1, 2) ----->Q'(-1+6 , 2 -3)= Q'(5, -1)
R(3 , 1) ------> R'(3+6 , 1-3) = R'(9,-2)
Use digits to write the value of the 4 in this number.
842,963
Answers
Answer:
40,000
Step by step explanation:
842,963
840,000
40,000
Luke randomly selects 25 students from his school and asks each of them how many minutes they read each night to find out how much, on average, students at his school read. This represents which type of data collection
Answers
Answer:
Simple random sampling
Step-by-step explanation:
Luke wants to study average minutes students read each night. For that matter, he has selected a 'sample' of 25 students from entire 'population' of students in school.
He has selected the sample students randomly, for collecting data related to minutes of study each night. He also collects data from them directly ie with primary contact with them.
So, primary data collection, simple random sampling - has been used as a type of data collection.
Please help me ASAP!!!
Answers
Answer:
the third one (2,-18)
Step-by-step explanation:
Determine whether the following statements are true and give an explanation or counterexample. projvu = projuv b. If nonzero vectors u and v have the same magnitude they make equal angles with u + v. (u.i)^2 + (u.j)^2 + (u.k)^2 = |u|^2. d. If u is orthogonal to v and v is orthogonal to w, then u is orthogonal to w. The vectors orthogonal to (1, 1, 1) lie on the same line. f. If proj v u = 0, then vectors u and v (both nonzero) are orthogonal.
Answers
The given statement is false and the explanation is given below:projvu = projuv This equation is equivalent to (proj v u).v = (proj u v).u.
Therefore, the given statement is not true. For example, consider the vectors u = (1, 0) and v = (0, 1). The projection of u onto v is zero, and the projection of v onto u is zero. In this case, projvu ≠ projuv, which implies that the given statement is not correct. Thus, the given statement is False.
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I need to know the answer to 2 1/3 x 4/5
Answers
Answer:
Simplify the expression.
Exact Form:
28/15
Decimal Form:
1.8¯6
Mixed Number Form:
1 13/15
Step-by-step explanation:
Answer:
Step-by-step explanation:
Convert 2 1/3 to improper fraction
\(2\dfrac{1}{3}*\dfrac{4}{5}=\dfrac{7}{3}*\dfrac{4}{5}\\\\\\=\dfrac{7*4}{3*5}\\\\\\=\dfrac{28}{15}\\\\= 1\dfrac{13}{15}\)
Find angle PRS in the image above
Answers
Answer:
142°
Step-by-step explanation:
Which of the following relations ia a function?
A
{(0,1), (0,2), (0,3), (0,4)}
B
{(1,6), (1,7), (7,8), (8,9)}
С
{(2,3), (3,2), (2,4), (4,2)}
D
{(1,1), (3,2), (6,3), (8,4)}
Answers
Answer:
i think the answer is c. hope it helps <3
Step-by-step explanation:
The reason that despite taking 1 hour and 40 minutes to fill a single bottle, bacteria took only ten minutes to fill another three bottles is:
a. The time consuming process which bacterias go through for their multiplication is binary fission.
b. Once the bacteria get multiplied by this process subsequently, same process occur in all the cells.
c. Once the container is filled, the cells filled in that bottle get multiplied simultaneously causing additional three bottles get filled in just a small duration of ten minutes.
Answers
The reason that despite taking 1 hour and 40 minutes to fill a single bottle, bacteria took only ten minutes to fill another three bottles is:
c. Once the container is filled, the cells filled in that bottle get multiplied simultaneously causing additional three bottles to get filled in just a small duration of ten minutes.
This is because the process of bacterial multiplication, binary fission, allows for rapid growth and expansion once the initial population has been established.
As more cells are present, the rate of multiplication increases, allowing for faster filling of subsequent bottles.
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Lucia checked her online bank statement which shows the current balance is $412.76, pending withdrawals are $481.23, and pending credits are $134.00. What is Lucia's current available balance? (4 points)
−$202.47
$65.53
$123.67
$777.20
Answers
Considering the withdraws and credits, Lucia's current available balance is of $65.53.
How do we find a balance?It is given by the sum of the money that the people has with the pending credits, and subtracted by the pending withdraws.
In this problem, we have that:
Lucia has $412.76, with pending credits of $134.00.She has pending withdraws of $481.23.Hence, her avaiable balance is given by:
412.76 + 134 - 481.23 = $65.53.
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The last dividend per share paid on a stock was $1.20. The dividend grows at 30% per year for one year (year 1) and at a constant rate of 6% thereafter. If the market capitalization rate is 12%, what is the estimated intrinsic value per share today? Enter your answer with two decimals.
Answers
The estimated intrinsic value per share today is approximately $27.39, calculated using the dividend discount model with a 30% dividend growth rate in Year 1 and a 6% constant growth rate thereafter, and a market capitalization rate of 12%.
To calculate the estimated intrinsic value per share today, we need to determine the present value of the future dividends using the dividend discount model.
The dividend discount model (DDM) formula is as follows:
Intrinsic Value = Dividend / (Discount Rate - Dividend Growth Rate)
Given the information provided:
Dividend in Year 1 = $1.20 * (1 + 30%) = $1.56
Dividend Growth Rate in Year 1 = 30%
Dividend Growth Rate from Year 2 onwards = 6%
Discount Rate = 12%
Now, let's calculate the present value of dividends for the perpetuity period (from Year 2 onwards) using the constant growth rate formula:
Present Value of Perpetuity Dividends = Dividend / (Discount Rate - Dividend Growth Rate)
Present Value of Perpetuity Dividends = $1.56 / (0.12 - 0.06) = $1.56 / 0.06 = $26.00
Next, we need to calculate the present value of the dividend in Year 1:
Present Value of Dividend in Year 1 = Dividend / (1 + Discount Rate)
Present Value of Dividend in Year 1 = $1.56 / (1 + 0.12) = $1.56 / 1.12 = $1.39
Finally, we can calculate the estimated intrinsic value per share today by summing the present value of dividends for Year 1 and the perpetuity period:
Intrinsic Value = Present Value of Dividend in Year 1 + Present Value of Perpetuity Dividends
Intrinsic Value = $1.39 + $26.00 = $27.39
Therefore, the estimated intrinsic value per share today is approximately $27.39.
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Part 2−20 Points - See Below Given this list of departments. 1. Receiving 2. Fabrication 3. Painting 4. Assembly \& Shipping 5. Offices 6. Restrooms \& lockers 7. Stores 1. Calculate how many relationship codes there will be in this chart. 2. Create an activity relationship diagram 3. Populate the diagram with codes for all the relationships 4. What is the percentage of codes in each category? Does it follow the standard percentages? 5. Provide at least 3 reason codes for the chart 6. Create a work sheet to assist in the creation of the dimensionless block diagram. 7. Create a dimensionless block diagram for your data B. Show the flow through the dimensionless block diagram
Answers
The task requires analyzing a list of departments and performing several tasks related to relationship codes, activity relationship diagrams, reason codes, a worksheet, and a dimensionless block diagram.
We need to consider the number of departments. Since we have 7 departments listed, the number of relationship codes can be calculated using the formula: (n * (n-1)) / 2, where n is the number of departments.
Substituting the value of n = 7, we get:
Relationship Codes = (7 * (7-1)) / 2
= (7 * 6) / 2
= 42 / 2
= 21
Therefore, there will be 21 relationship codes in the chart.
Create an activity relationship diagram:
An activity relationship diagram visually represents the relationships between departments. Here is a basic diagram representing the given departments:
Receiving --+
+-- Assembly & Shipping -- Offices
Fabrication--+
+-- Painting -- Stores
Restrooms & Lockers
Populate the diagram with codes for all the relationships:
To populate the diagram with codes, we can assign a unique code to each relationship. Here's an example of assigning codes to the relationships in the diagram:
Receiving (R) --+
+-- Assembly & Shipping (AS) -- Offices (O)
Fabrication (F)--+
+-- Painting (P) -- Stores (S)
Restrooms & Lockers (RL)
What is the percentage of codes in each category? Does it follow the standard percentages?
To determine the percentage of codes in each category, we need to count the number of codes in each category and calculate the percentage relative to the total number of codes (21).
In this case, we have the following categories and their respective codes:
Production: R, F, AS, P (4 codes)
Administration: O, S (2 codes)
Support: RL (1 code)
Percentage of Production codes = (4 / 21) * 100 ≈ 19.05%
Percentage of Administration codes = (2 / 21) * 100 ≈ 9.52%
Percentage of Support codes = (1 / 21) * 100 ≈ 4.76%
These percentages do not necessarily follow any standard percentages. The distribution of codes among categories can vary depending on the specific organization or context.
Provide at least 3 reason codes for the chart:
Reason codes are used to provide explanations or justifications for the relationships depicted in the chart. Here are three example reason codes for the given chart:
R01: Receiving department receives raw materials and supplies from external sources.
AS01: Assembly & Shipping department assembles products and prepares them for shipment.
O01: Offices department provides administrative support and management functions for the organization.
Create a worksheet to assist in the creation of the dimensionless block diagram:
Here's an example of a worksheet that can assist in creating the dimensionless block diagram:
Relationship Code From Department To Department
R Receiving Fabrication
F Fabrication Painting
AS Assembly & Shipping Offices
P Painting Stores
RL Restrooms & Lockers -
O Offices -
S Stores -
This worksheet lists the relationship codes along with the corresponding "From" and "To" departments.
Create a dimensionless block diagram for your data B. Show the flow through the dimensionless block diagram:
A dimensionless block diagram represents the flow of activities or information between different departments. Here's an example of a dimensionless block diagram based on the given data:
Receiving --> Fabrication --> Painting --> Stores
|
v
Assembly & Shipping --> Offices
|
v
Restrooms & Lockers
The arrows indicate the flow of activities or information from one department to another.
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1/3m - 1 - 1/2n evalute
Answers
Answer:
Step-by-step explanation:
1) Simplify 1/3m to m/3.
m/3 - 1 - 1/2n
2) Simplify 1/2n to n/2.
m/3 - 1 - n/2
for what value of x does 4^x=(1/8)^x+5?
Answers
Use main properties of powers
(a^m)^n=a^{m\cdot n};(am)n=am⋅n;
\dfrac{1}{a^n}=a^{-n}an1=a−n
to simplify given equation.
1.
4^x=(2^2)^x=2^{2x}.4x=(22)x=22x.
2.
\left(\dfrac{1}{8}\right)^{x+5}=\left(\dfrac{1}{2^3}\right)^{x+5}=(2^{-3})^{x+5}=2^{-3x-15}.(81)x+5=(231)x+5=(2−3)x+5=2−3x−15.
3. Then the equation is
2^{2x}=2^{-3x-15}.22x=2−3x−15.
The bases are the same, so equate the powers:
2x=-3x-15,
2x+3x=-15,
5x=-15,
x=-3.
Answer: for x=-3.
Estimate ΔyΔy using differentials.
y=cos(5x),=/30,x=0.055
(Give your answer to three decimal places.)
Answers
The estimated change in yy using differentials is -0.00679. This means that if xx is increased by 0.005, then yy is estimated to decrease by 0.00679. The differential of yy is dy=-5sin(5x)dxdy=−5sin(5x)dx. We are given that y=cos(5x)=π/30y=cos(5x)=π/30 and x=0.055x=0.055.
We want to estimate ΔyΔy, which is the change in yy when xx is increased by 0.005. We can use the differential to estimate ΔyΔy as follows:
Δy≈dy≈dy=-5sin(5x)dx
Plugging in the values of y, x, and dxdx, we get:
Δy≈-5sin(5(0.055))(0.005)≈-0.00679
Therefore, the estimated change in yy using differentials is -0.00679.
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factor the polynomial completely f(x)=x^4-6x^3-8x+48;x-6
Answers
Answer:
Factor x^3+8x^2+6x+48. x3+8x2+6x+48 x 3 + 8 x 2 + 6 x + 48. Factor out the greatest common factor from each group.
What is the factored form of m^6- 64n^3?
Answers
Step-by-step explanation:
Let x = m² and y = 4n.
Then m⁶ - 64n³ = x³ - y³
= (x - y)(x² + xy + y²)
= (m² - 4n)(m⁴ + 4m²n + 16n²).
in the figure, four long straigfht wires are perpendicular to the page, and their corss sections form a square edge length a. what is the magnitude of the net magnetic field at the square's center?
Answers
The magnitude of the net magnetic field at the square's center is \(= (7.94 * 10^{-4}N/m)i+(-7.94 * 10^{-4}N/m)j\).
Using \(dB=\frac{u_0i}{4\pi} \frac{sin\theta}{r^2}\) the force on say, wire 1 (the wire at the upper left of the figure) is along the diagonal (pointing toward wire 3, which is at the lower right). Only the forces (or their components) along the diagonal direction contribute. With θ=45°, we find the force per unit meter on wire 1 to be
\(f_1 = |F_{12}+F_{13}+F_{14}|\\\\= 2F_{12}cos\theta+f_{13}\\\\=2(\frac{u_0i^2}{2\pi a} )cos45^0+\frac{u_0i^2}{2\sqrt{2}\pi a }\)
\(=\frac{3}{2\sqrt{2}\pi }(\frac{u_0i^2}{0})\\\\=\frac{3}{2\sqrt{2}\pi } \frac{(4\pi*10^{-7}T.m/A)(15.0A)^2} {(8.50*10^{-2}m)}\)
\(= 1.12 * 10^{-3}N/m\)
The direction of F1 is along r^=(i^=j^)/sqrt2. In unit-vector notation, we have
\(F_1 = \frac{(1.12 * 10^{-3}N/m)}{\sqrt{2} }(i - j) \\\\= (7.94 * 10^{-4}N/m)i+(-7.94 * 10^{-4}N/m)j\)
Hence the answer is the magnitude of the net magnetic field at the square's center is \(= (7.94 * 10^{-4}N/m)i+(-7.94 * 10^{-4}N/m)j\).
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