Answers
Answer: A Polar is (6√2, [tex]\frac{3\pi }{4}[/tex])
Step-by-step explanation:
Draw a line to point (see image). You need to find the length of that line and then the angle. Polar(length, angle)
Using pythagorean theorem
length² = (6)² + (-6)²
length² = 36 +36
length =√72
length = [tex]\sqrt{36 *2}[/tex]
length = 6√2
To find angle:
The triangle size is 6-6-6√2 Let's proportionally shrink so we can use unit circle numbers to figure angle. Becomes: 1-1-√2
So when we do sin x = opp/adj
sin x = [tex]\frac{1}{\sqrt{2} }[/tex] >get rid of radical on bottom
sin x = [tex]\frac{\sqrt{2} }{2}[/tex] > when is sin = [tex]\frac{\sqrt{2} }{2}[/tex] This happens at [tex]\frac{\pi }{4}[/tex] but we are in the 2nd quadrant so the angle is [tex]\frac{3\pi }{4}[/tex]
Polar is (6√2, [tex]\frac{3\pi }{4}[/tex])
The polar coordinates are (6([tex]\sqrt[]{2}[/tex], 3pi/4).
Rectangular coordinates are in the form of (x, y) and Polar coordinates are expressed in the form of (r, [tex]\theta[/tex]).
Relation between polar coordinates and rectangular coordinates-x = r cos([tex]\theta[/tex]), y = r sin([tex]\theta[/tex]) and x^2 +y^2 =r^2 ...(1)
So by using above formulas we can solve our question.
Here , x= -6 and y= 6
r^2 = (-6)^2 +(6)^2
=72
=>r = 6([tex]\sqrt[]{2}[/tex])
Put the values of x and y in the mentioned formula in eq(1)
-6 = 6([tex]\sqrt[]{2}[/tex] )cos[tex]\theta[/tex]
6 = 6([tex]\sqrt[]{2}[/tex] )sin([tex]\theta[/tex]),
=>-1/([tex]\sqrt[]{2}[/tex] = cos([tex]\theta[/tex]) , 1/[tex]\sqrt[]{2}[/tex]= sin[tex]\theta[/tex]
Here cos is negative and sin is positive so it lies in 2nd quadrant
so here [tex]\theta[/tex] lies between [tex]\frac{\pi}{2} \leq\theta\leq\pi[/tex]
[tex]\theta[/tex]= π-π/4
=3π/4
So,(r, [tex]\theta[/tex]) = ( 6√2, [tex]\frac{3\pi}{4}[/tex] )
Related Questions
PLEASE HELP MARKING AS BRAINLIST!
Answers
Hello :)
P(A) = 1/2
P(B) = 5 or greater = 5,6 => 2/6 = 1/3
P(A and B) = 1/2 x 1/3 = 1x1/2x3 = 1/6 ≈ 0.17
the answer is 0.17
Which of the following angles is not coterminal to
120°
A 180°
B. 240°
C. 840°
D. - 600°
Answers
Brainly needs this to be 20 characters long but it’s just c
All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sam
to make a statistical inference about the mean of the normally distributed population from which it was drawn?
ME-
Z.S
O The margin of error is multiplied by √0.5.
O The margin of error is multiplied by √√2-
O The margin of error is multiplied by 0.5.
O The margin of error is multiplied by 2.
Answers
Answer:
When you cut the sample size in half while making a statistical inference about the mean of a normally distributed population, the effect on the margin of error depends on the relationship between the sample size and the margin of error. Generally, the margin of error is inversely proportional to the square root of the sample size.
So, if you reduce the sample size by half, it means you are taking a smaller sample, which will result in a larger margin of error. In other words, the margin of error is multiplied by a factor greater than 1.
Among the given options, the correct answer is:
D. The margin of error is multiplied by 2.
This option correctly reflects the relationship between reducing the sample size by half and the resulting increase in the margin of error.
Alice was provided with the following trinomial: 3x² + 7x-12x - 34 - 2x² + 10 1 Provide Alice with a step-by-step guide on how to factorize the algebraic expression.
Answers
Hello!
[tex]3x^{2} + 7x-12x - 34 - 2x^{2} + 10\\\\3x^{2}- 2x^{2} + 7x-12x - 34 + 10\\\\x^{2} - 5x - 24\\\\x^{2} + 3x - 8x - 24\\\\(x^{2} + 3x) + (-8x - 24)\\\\x(x + 3) - 8(x + 3)\\\\\boxed{(x - 8)(x+3)}[/tex]
During a normal day, there are 782 passengers in average that
are late for their plane each day. However, during the
Christmas holidays, there are 1,835 passengers that are late for
their planes each day which caused delays of 14 planes. How
many more passengers are late for their planes in each day
during the Christmas holidays?
i picked 4th grade lol
Answers
During the Christmas holidays, there are 1,053 more passengers who are late for their planes each day compared to a normal day.
To solve this problemCalculating the difference between the quantity of late passengers on a typical day and the quantity of late passengers on holidays is necessary.
1,835 travellers were late over the Christmas break.
On an average day, there are 782 travelers who are late.
Difference = Number of late passengers during the Christmas holidays - Number of late passengers on a normal day
Difference = 1,835 - 782
Difference = 1,053
Therefore, during the Christmas holidays, there are 1,053 more passengers who are late for their planes each day compared to a normal day.
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Answer:
Step-by-step explanation:
During the Christmas holidays, there is an increase of 1,053 passengers who are late for their planes each day compared to the average daily number of 782 passengers who are late. This surge in late passengers during the holiday period contributes to delays in 14 planes.
The higher volume of travelers, combined with potential factors like weather conditions, congestion, and heightened travel demand, likely leads to a greater number of individuals encountering delays and difficulties reaching their departure gates on time.
Hope it helps! :)
Use the information above to answer the questions that follow.
2.2.1
2.2.2
2.2.3
2.2.4
sanitation in Johannesburg if a property is 175 m².
Write down, to the nearest ten cents and excluding VAT, the cost for
Calculate the cost for 4,1 ke sanitation in Cape Town before the increase.
Mr Jones lives in Johannesburg and Ms Brown lives in Cape Town. They
both own a property with an area of 550 m² and each was billed for 22 kl
sanitation.
Use the table above to determine the difference in the cost of sanitation
for the two properties.
Explain how the tariff system used in Johannesburg is beneficial to
home owners in terms of water usage.
(2)
(8)
(2)
[34]
mor
MO
ud.
0
0
Answers
Mr. Jones in Johannesburg is billed R9,767.12 and Ms. Brown in Cape Town is billed R680.24 for their respective properties.
From the provided information for Cape Town's sanitation tariffs:
0-4.2 kl: R16.03 per kl
Since 4.1 ke is equivalent to 4100 liters, which is less than 4.2 kl, we can use the tariff rate for the 0-4.2 kl range.
Cost for 4.1 ke of sanitation
= 4.1 ke x R16.03 per kl
= 4100 liters x R16.03 per kl
= R65.83
For Mr. Jones and Ms. Brown, who own properties with an area of 550 m² each and were billed for 22 kl of sanitation.
we need to determine the applicable tariff rate based on the property size and calculate the cost.
In Johannesburg, based on the provided information, the tariff rate for properties larger than 300 m² to 1,000 m² is R443.96.
Cost of sanitation for Mr. Jones in Johannesburg:
= 22 kl x R443.96 per kl
= R9,767.12
Cost of sanitation for Ms. Brown in Cape Town:
= 22 kl x R30.92 per kl = R680.24
Therefore, Mr. Jones in Johannesburg is billed R9,767.12 and Ms. Brown in Cape Town is billed R680.24 for their respective properties.
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Function c
is defined by the equation c(n)=50+4n
. It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits, n
.
True or False? The inverse function is as follows:
n=(c(n) − 50)×4
Responses
Answers
Answer:
False
Step-by-step explanation:
1. The inverse function should have c(n) isolated
2. When finding the inverse of a function, the variables c(n) and n are interchanged (and then c(n) is isolated).
It would look like this --->c(n)=50+4n--->n=50+4(c(n)) ---> c(n)=(n-50)/4
help please, i have a test tomorrow
Answers
The value of variables in the figure is,
⇒ x = 80
⇒ y = 70
We have to given that;
By using given figure we have to find the value of each variable.
Now, We can formulate;
⇒ 55 = 1/2 (180 - y)
Solve for y;
⇒ 55 × 2 = 180 - y
⇒ 110 = 180 - y
⇒ y = 180 - 110
⇒ y = 70
And, The value of x is,
⇒ x = 180 - (60 + 40)
⇒ x = 180 - 100
⇒ x = 80
Thus, The value of variables in the figure is,
⇒ x = 80
⇒ y = 70
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Urgent please help I am running out of time thank you
Answers
Answer:
119
Step-by-step explanation:
Consider the equation x^3 - 3x^2 + 2x - 6 = 0. Find all the complex roots of this equation and represent them in the form a + bi.
Answers
Answer:
x=i[tex]\sqrt{2}[/tex], x=-i[tex]\sqrt{2}[/tex]
Step-by-step explanation:
This equation can be factored. In order to do so, we can split the expression into two parts: (x^3-3x^2) and (2x-6). The greatest common factor of the first group is x^2, factoring it out gives us x^2(x-3). The greatest common factor of the second group is 2, factoring it out gives us 2(x-3). Since both x^2 and 2 are being multiplied by x-3, we add them into a factored form of (x^2+2)(x-3)=0
x-3 provides us with one real root, so we can disregard it.
x^2+2=0 ---> x^2=-2--->x=±[tex]\sqrt{-2}[/tex]
Factoring out the imaginary number i (equals [tex]\sqrt{-1}[/tex]), we get x=±i[tex]\sqrt{2}[/tex]
The points on the graph represent both an exponential function and a linear function.
Complete this table by reading the values from the graph. Estimate any function values that are less than one.
x -3 -2 -1 0 1 2 3
Exponential function _____ _____ _____ _____ _____ _____ _____
Linear function _____ _____ _____ _____ _____ _____ _____
At approximately what values of x do both the linear and exponential functions have the same value for y?
Answers
We are given two curves on a graph paper and we have to find the y values for the given x.
From the graph we can check for a value of x, what is the value of y from the curve.
x -3 -2 -1 0 1 2 3
Exp 8 4 2 1 0.5 0.25 0.125
Lin. 7.5 6 4.5 3 1.5 0 -1.5
We find that the two have the same values where the two curves intersect.
From the graph we find that near to -3 and near to 2 both have the same values.
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The missing graph is attached below.
PLSSA HELP ME
Describe a way to transform to . Be specific
Answers
The way to transform A to B is (1,-1).
We are given that;
The coordinates (-1,1),(-3,1),(-1,3) and (1,-1),(3,-1),(1,-3).
Now,
To transform the coordinates (-1,1),(-3,1),(-1,3) to (1,-1),(3,-1),(1,-3), you can apply a reflection about the origin. This transformation can be represented by the matrix [-1 0; 0 -1]. When you multiply this matrix with the original coordinates, you will get the transformed coordinates.
First, represent the point (-1,1) as a column vector:
[-1]
[ 1]
Then, multiply this vector by the reflection matrix [-1 0; 0 -1]:
[-1 0; 0 -1] * [-1] = [ 1]
[ 1] [-1]
Therefore, by transformation the answer will be (1,-1).
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For which situations would it be appropriate to calculate a probability about the difference in sample means?
1) Both population shapes are unknown. n1 = 50 and n2 = 100.
2) Population 1 is skewed right and population 2 is approximately Normal. n1 = 50 and n2 = 10.
3) Both populations are skewed right. n1 = 5 and n2 = 10.
4) Population 1 is skewed right and population 2 is approximately Normal. n1 = 10 and n2 = 50.
5) Both populations have unknown shapes. n1 = 50 and n2 = 100.
6) Both populations are skewed left. n1 = 5 and n2 = 40.
Answers
It is generally appropriate to calculate a probability about the difference in sample means when the sample sizes are large (typically n ≥ 30) and the populations are approximately normally distributed.
How did we arrive at this assertion?To determine if it is appropriate to calculate a probability about the difference in sample means, consider the assumptions and conditions for conducting a hypothesis test or constructing a confidence interval. The appropriateness of calculating a probability about the difference in sample means depends on the following factors:
1) Both population shapes are unknown. n1 = 50 and n2 = 100:
- It is generally appropriate to calculate a probability about the difference in sample means when the sample sizes are large (typically n ≥ 30) and the populations are approximately normally distributed. Since the population shapes are unknown in this case, it is difficult to assess this condition. However, the large sample sizes (n1 = 50 and n2 = 100) may suggest that it is reasonable to approximate the population distributions as normal. Therefore, calculating a probability about the difference in sample means could be considered.
2) Population 1 is skewed right and population 2 is approximately Normal. n1 = 50 and n2 = 10:
- In this case, the assumption of approximately normally distributed populations is violated for population 1, which is skewed right. When the population distributions are not approximately normal, it may not be appropriate to calculate a probability about the difference in sample means. The small sample size for population 2 (n2 = 10) may also limit the accuracy of any inference made based on this sample.
3) Both populations are skewed right. n1 = 5 and n2 = 10:
- Similar to the previous case, the assumption of approximately normally distributed populations is violated for both populations. Additionally, the small sample sizes (n1 = 5 and n2 = 10) may not provide sufficient information for reliable inferences. Therefore, it is generally not appropriate to calculate a probability about the difference in sample means in this situation.
4) Population 1 is skewed right and population 2 is approximately Normal. n1 = 10 and n2 = 50:
- Similar to case 2, the assumption of approximately normally distributed populations is violated for population 1, which is skewed right. In this case, the sample size for population 1 (n1 = 10) is also small, which may limit the accuracy of any inference made based on this sample. The larger sample size for population 2 (n2 = 50) might make it more reasonable to approximate the population distribution as normal. However, the violation of the assumption for population 1 suggests caution when interpreting the results. It is not generally appropriate to calculate a probability about the difference in sample means in this situation.
5) Both populations have unknown shapes. n1 = 50 and n2 = 100:
- Similar to case 1, the population shapes are unknown. However, the large sample sizes (n1 = 50 and n2 = 100) might suggest that it is reasonable to approximate the population distributions as normal. As mentioned before, calculating a probability about the difference in sample means could be considered in this case.
6) Both populations are skewed left. n1 = 5 and n2 = 40:
The assumption of approximately normally distributed populations is violated for both populations, as they are skewed left. Additionally, the small sample sizes (n1 = 5 and n2 = 40) may not provide sufficient information for reliable inferences. Therefore, it is generally not appropriate to calculate a probability about the difference in sample means in this situation.
Summarily, it is generally appropriate to calculate a probability about the difference in sample means when the sample sizes are large (typically n ≥ 30) and the populations are approximately normally distributed. However, when the population distributions are not approximately normal or when the sample sizes are small, it is generally not appropriate to calculate a probability about the difference in sample means.
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Help please, I need to get through geometry recovery class
Answers
To prove ∠AOW = 45°
Given,
∠WOZ = 90°
∠ZOB = 45°
Now,
∠XOA +∠AOW = 90°............(1)
∠XOA = ∠ZOB ( Vertically opposite angle )
∠XOA = 45°
Substitute in (1),
45° + 45° = 90°
Now,
∠WOX = ∠XOA +∠WOA
So,
∠WOA + ∠WOZ + ∠ZOB = 180°( Linear pair )
∠WOA + 90° + 45° = 180°
∠WOA = 45°
Hence proved.
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HELP!!!!!!!!!!!!!!!!!!
Answers
Answer:
D 0.89275
Step-by-step explanation:
Segment RT has endpoints R(-3,4) & T (-7,-3) what are the coordinates of the midpoint of RT?
Answers
Add the x coordinates from each set. Then divide the sum by 2. Resulting in: -5
Repeat this process with the y coordinates from each set. Resulting in: 0.5
The midpoint coordinates are: (-5, 0.5)
Show (AB)^-1 = B^-1 A^-1
Answers
The inverse of a product of matrices AB is given by:
(AB)-1 = B-1 A-1
where A and B are invertible matrices.
To find A-1, we need to solve the equation A x A-1 = I, where I is the identity matrix.
From the given information, we know that A = L'. The inverse of L' is L, so we have:
A-1 = L
To find B-1, we need to solve the equation B x B-1 = I. Since B is a scalar matrix with a value of 12, we have:
B-1 = 1/12
Now we can substitute the values of A-1 and B-1 into the formula for (AB)-1:
(AB)-1 = B-1 A-1
Substituting the values of A-1 and B-1, we get:
(AB)-1 = (1/12) L
Therefore, we have shown that (AB)-1 = B-1 A-1 is true.
find the first derivative with respect to x of the following function: f(x)=(7x+3)(4-3x)
Answers
You have the derivative of a product:
first limit (7x+3)
second limit (4-3x)
The Rule for the derivative of a product is:
(first limit × derivative of second limit) + (second limit × derivative of first limit)
f(x) = (7x+3)(4-3x)
f'(x)=(7x+3)×-3 + (4-3x)×7 = -21x- 9 + 28-21x
f'(x) = -42x + 19
PLSSS FIND BOTH x’s THANK YOUUU
Answers
Hello!
Solutions = -3 and 1.5
how to find the base area of a rectangular prism from length width and volume
Answers
If you want to find the base area of a rectangular prism, then all you need is length and width only.
[tex] \boxed{Volume = length \times width \times height} [/tex]
You don't need height. So, this is a must be easy.
[tex]\blue{\small{\mathfrak{That's \: it. \: Thanks \::)}}} [/tex]
Whose solution strategy would work?
Answers
Answer:c
Step-by-step explanation:
Translate the following phrase into an algebraic expression. Do not simplify. Use the variable names "x" or "y" to describe the unknowns.
the product of two numbers increased by 4
Answers
Answer:
The algebraic expression for the phrase "the product of two numbers increased by 4" can be written as `xy + 4`, where `x` and `y` represent the two unknown numbers.
Answer:
Step-by-step explanation:
To translate the phrase “the product of two numbers increased by 4” into an algebraic expression, we can use the variables x and y to represent the two numbers.
The product of two numbers is xy, and if we increase this by 4, we get:
xy + 4
Therefore, the algebraic expression for “the product of two numbers increased by 4” is: xy + 4
I hope this helps! Let me know if you have any other questions.
If KL = x + 8
, LM = 12
, and KM = 3x − 14
, what is KL?
Answers
Answer:
x = 17
Step-by-step explanation:
KL + LM = KM
x+8+12 = 3x-14
or, x+20 = 3x-14
or, 3x-x=20+14
or, 2x = 34
x = 17
Answer:
Step-by-step explanation:
3x-14=x+8+12
3x-x=8+12+14
2x=34
x=17
then
KL=(17)+8=25
What is the approximate volume of a cylinder with a radius of centimeters and a height of 4centimeters?
Use 3.14 for π and round the answer to the nearest tenth.
A. 150.7 cm3
B. 28.3 cm3
c. 113.0 cm3
d. 75.4 cm3
Answers
To calculate the volume of a cylinder, we use the formula:
Volume = π * radius^2 * height
Given:
Radius = cm
Height = 4 cm
π (pi) = 3.14
Let's substitute these values into the formula and calculate the volume:
Volume = 3.14 * (cm)^2 * 4 cm
= 3.14 * (cm^2) * 4 cm
= 12.56 * cm^3
Rounding the answer to the nearest tenth, we get:
Volume ≈ 12.6 cm^3
Among the answer choices provided, the closest option to 12.6 cm^3 is:
B. 28.3 cm^3
Therefore, the correct answer is B. 28.3 cm^3.
A normal distribution has a mean of 137 and a standard deviation of 6. Find the z-score for a data value of 155.
Round to two decimal places
Answers
Answer:
3
Step-by-step explanation:
To find the z-score for a data value of 155 in a normal distribution with a mean of 137 and a standard deviation of 6, you can use the formula:
z = (x - μ) / σ
where:
x is the data value,
μ is the mean, and
σ is the standard deviation.
Plugging in the values, we have:
z = (155 - 137) / 6
Calculating this expression:
z = 18 / 6 = 3
In Boston, a popular restaurant recently added a delivery option. In reviewing the sales for this new delivery service, the restaurant found the mean delivery orders in a random sample of Friday nights was x¯=48 orders, with a margin of error of 12 orders.
Answers
The 95% confidence interval for the mean number of delivery orders on a Friday night is 36 to 60 orders.
What is the confidence interval?The confidence interval for the mean number of delivery orders on a Friday night is constructed assuming a 95% confidence level.
Given data:
Sample mean (x) = 48 orders
The margin of error (E) = 12 orders
To calculate the confidence interval, we'll use the formula:
Confidence Interval = x ± E
Substituting the values:
Confidence Interval = 48 ± 12
The lower limit of the confidence interval:
Lower Limit = 48 - 12 = 36
The upper limit of the confidence interval:
Upper Limit = 48 + 12 = 60
Therefore, the 95% confidence interval for the mean number of delivery orders on a Friday night is 36 to 60 orders.
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Complete question:
In Boston, A Popular Restaurant Recently Added A Delivery Option. In Reviewing The Sales For This New Delivery Service, The Restaurant Found The Mean Delivery Orders In A Random Sample Of Friday Nights Was X¯=48 Orders, With A Margin Of Error Of 12 Orders. Construct A Confidence Interval For The Mean Number Of Delivery Orders On A Friday Night.
The cost of 1kg potatoes and 2kg tomatoes was 30 on a certain day. After two days the cost of 2kg potatoes and 4kg tomatoes was found to be 66.
Answers
Let's represent the cost of 1kg of potatoes as 'p' and the cost of 1kg of tomatoes as 't'.
From the first statement, we know that:
1p + 2t = 30 (Equation 1)
From the second statement, we know that:
2p + 4t = 66 (Equation 2)
We can now solve this system of equations to find the values of 'p' and 't'.
Multiplying Equation 1 by 2, we get:
2p + 4t = 60 (Equation 3)
Now, we can subtract Equation 2 from Equation 3 to eliminate 'p':
(2p + 4t) - (2p + 4t) = 60 - 66
0 = -6
This implies that there is no consistent solution for the given system of equations.
The cost of 3kg potatoes and 3kg tomatoes on the day was 54.
How many significant digits are in 26.04813?
Answers
7 significant figures.
Zeros that come at the start do not count as significant figures.
Eg. 0.0001 would only be 1 significant figure.
Zeros that come after is counted as a significant figure.
Eg. 2.20 Is three significant figures.
The product of two numbers is 1536.
If the HCF of the two numbers is 16.
find the LCM of these two numbers.
Answers
Work Shown:
LCM = (product of two numbers)/(HCF of the two numbers)
LCM = 1536/16
LCM = 96
An employee started a new job and must enroll in a new family health insurance plan. One of the plans involves prescription drug coverage. The employee estimates that the entire family will fill 10 prescriptions per month, totaling $1,250. The employee has two options to choose from:
Option A: $94 monthly premium; 80% coverage for all prescription costs
Option B: $42 monthly premium; 75% coverage for first $500 in prescription costs, then 85% coverage for all prescription costs over $500
Which option would result in the highest overall cost for the employee, and by how much?
A) Option A has the highest overall cost by $64.50.
B)Option B has the highest overall cost by $64.50.
C) Option A has the highest overall cost by $106.50.
D) Option B has the highest overall cost by $106.50.
Answers
Option B has the highest overall cost by $64.50.
To determine the option that would result in the highest overall cost for the employee
we need to compare the costs of both options based on the estimated prescription drug expenses.
Option A:
Monthly premium: $94
Prescription coverage: 80%
Option B:
Monthly premium: $42
Prescription coverage: 75% for the first $500, 85% for costs over $500
Let's calculate the costs for each option:
Option A:
Total prescription drug cost: $1,250
Employee's share (20%): 20% × $1,250 = $250
Monthly premium: $94
Total cost for Option A: $250 + $94 = $344
Option B:
Total prescription drug cost: $1,250
Employee's share for the first $500 (25%): 25% × $500 = $125
Employee's share for costs over $500 (15%): 15% × ($1,250 - $500) = $112.50
Monthly premium: $42
Total cost for Option B: $125 + $112.50 + $42 = $279.50
Comparing the total costs for each option, we see that Option B has a lower overall cost for the employee.
Hence, Option B has the highest overall cost by $64.50.
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