A navy bean soup recipe requires 4 ounces of onion. If the EP
unit cost of the onions is $0.80 per pound, what is the total cost
of the ingredient?
Answers
The cost of onions is given as $0.80 per pound, so the cost of 0.25 pounds of onions is: 0.25 x $0.80 = $0.20
The total cost of 4 ounces of onions for the navy bean soup recipe is $0.20.
To calculate the total cost of 4 ounces of onions when the unit cost of onions is given in pounds, we need to convert the weight of onions from ounces to pounds.
There are 16 ounces in a pound, so 4 ounces is equal to 4/16 = 0.25 pounds.
The cost of onions is given as $0.80 per pound, so the cost of 0.25 pounds of onions is:
0.25 x $0.80 = $0.20
Therefore, the total cost of 4 ounces of onions for the navy bean soup recipe is $0.20.
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Related Questions
Determine if the triangles are similar
1. yes SSS
2. yes SAS
3. yes AA
4. No, not similar
Answers
Answer: 4. No, not Similar
Step-by-step explanation:
<QSR = 62
because of vertical angles
we have 3 different angles and no sides
a) Activity that should be crashed first to reduce the project duration by 1 day is (1) b) Activity that should be crashed next to reduce the project duration by one additional day is (2) c) Total cos
Answers
a) Activity that should be crashed first to reduce the project duration by 1 day is B.
b) Activity that should be crashed next to reduce the project duration by one additional day is C.
c) Total cost of crashing the project by 2 days = $10,000.
To determine the activities that should be crashed first and next, we need to consider the critical path method (CPM). The critical path is the longest sequence of activities that determines the total project duration. Crashing activities on the critical path will reduce the project duration.
Let's calculate the project duration and costs for each activity:
Activity A:
Normal Time: 7 days
Crash Time: 6 days
Normal Cost: $5000
Total Cost with Crashing: $5600
Activity B:
Normal Time: 4 days
Crash Time: 2 days
Normal Cost: $1500
Total Cost with Crashing: $3400
Immediate Predecessor(s): A
Activity C:
Normal Time: 11 days
Crash Time: 9 days
Normal Cost: $4200
Total Cost with Crashing: $6600
Immediate Predecessor(s): B
To find the critical path, we add the normal times of each activity:
Critical Path: A -> B -> C
a) Activity that should be crashed first to reduce the project duration by 1 day:
Since the critical path includes activities A, B, and C, we need to identify which activity's crash time can reduce the project duration by 1 day. The activity that can achieve this is B since its crash time is 2 days compared to activity A's crash time of 6 days. Therefore, activity B should be crashed first.
b) Activity that should be crashed next to reduce the project duration by one additional day:
After crashing activity B, the project duration will be reduced by 1 day. To further reduce the duration by an additional day, we need to determine which activity's crash time can achieve this. The activity that can achieve this is C since its crash time is 9 days compared to activity A's crash time of 6 days. Therefore, activity C should be crashed next.
c) Total cost of crashing the project by 2 days:
The total cost of crashing the project by 2 days is the sum of the total costs for the crashed activities:
Total cost of crashing = Total cost of crashing activity B + Total cost of crashing activity C
= $3400 + $6600
= $10,000
Therefore, the total cost of crashing the project by 2 days is $10,000.
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Complete Question:
Three activities are candidates for crashing on a project network for a large computer installation (all are, of course, critical). Activity details are in the following table.
a) Activity that should be crashed first to reduce the project duration by 1 day is
b) Activity that should be crashed next to reduce the project duration by one additional day is
c) Total cost of crashing the project by 2 days =
Determine whether the series converges or diverges. (n+4)! a) 4!n!4" b) 1 \n(n+1)(n+2) =
Answers
We have to determine whether the given series converges or diverges. The given series is as follows: `(n+4)! / 4!(n!)` Let's use the ratio test to find out if this series converges or diverges.
The Ratio Test: It is one of the tests that can be used to determine whether a series is convergent or divergent. It compares each term in the series to the term before it. We can use the ratio test to determine the convergence or divergence of series that have positive terms only. Here, a series `Σan` is convergent if and only if the limit of the ratio test is less than one, and it is divergent if and only if the limit of the ratio test is greater than one or infinity. The ratio test is inconclusive if the limit is equal to one. The limit of the ratio test is `lim n→∞ |(an+1)/(an)|` Let's apply the Ratio test to the given series.
`lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `lim n→∞ [(n+5)/4] * [1/(n+1)]` `lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `lim n→∞ (n^2 + 9n + 20) / (4n^2 + 20n + 16)`
As we can see, the limit exists and is equal to 1/4. We can say that the given series converges. The series converges. To determine the convergence of the given series, we use the ratio test. The ratio test is a convergence test for infinite series. It works by computing the limit of the ratio of consecutive terms of a series. A series converges if the limit of this ratio is less than one, and it diverges if the limit is greater than one or does not exist. In the given series `(n+4)! / 4!(n!)`, the ratio test can be applied. Using the ratio test, we get: `
lim n→∞ |(an+1)/(an)| = lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `= lim n→∞ [(n+5)/4] * [1/(n+1)]` `= lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `= 1/4`
Since the limit of the ratio test is less than one, the given series converges.
The series converges to some finite value, which means that it has a sum that can be calculated. Therefore, the answer is a).
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If I1 ⊇ I2 ⊇ .... In ⊇... is a nested sequence of intervals and if In = [an; bn], show that a1 ≤ a2 ≤ ....... ≤ an ≤ ........ and b1 ≤ b2 ≤..... bn ≤ ......
Answers
The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:
1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.
To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.
First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.
Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.
We can continue this process for all the intervals in the sequence, until we reach In. So we have:
a1 ≤ a2 ≤ ... ≤ an-1 ≤ an
and
b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn
This shows that the endpoints of the intervals are ordered in the same way.
Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:
Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:
1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.
Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .
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please help will give brainlist
Answers
(25.2 / 4.2) / 3
= 2
(2) following limits provided they exist: (i) lim [2 F(x) - 3 G(x)] (ii) lim [F(x)]³+ lim [G(x)]² x-3 Figure I F(x) -1 (A) (i)5 (ii) 9 (B) (i)3 (ii)-4 (c) (i)0 (ii) q (P) (i)5 (ii) 9 (E) none of the above Use the graphs of F and G in Figure I and the Limit Principles to find the (iii) lim lim [F(x)G(x)] +3 3 -3 -2 G(x) (iii) I (iv) 3 (iii) 4 (iv) I (iii) does not exist (iii) does not exist. 0 1 1 12 (iv) 3 (iv) 3 1 2 F(x) (iv) lim G(x)
Answers
(i) lim [2 F(x) - 3 G(x)] = 5
(ii) lim [F(x)]³ + lim [G(x)]² = 9
In the given problem, we are asked to find the limits of two expressions involving the functions F(x) and G(x).
In part (i), we have the expression 2 F(x) - 3 G(x). To find its limit, we evaluate the individual limits of F(x) and G(x) and then substitute them into the expression. The limit of F(x) is given as 3, and the limit of G(x) is given as -4. Substituting these values into the expression, we get 2(3) - 3(-4) = 5.
In part (ii), we are asked to find the limit of [F(x)]³ + [G(x)]². Again, we evaluate the individual limits of F(x) and G(x) and substitute them into the expression. The limit of F(x) is given as 3, and the limit of G(x) is given as -4. Substituting these values into the expression, we get (3)³ + (-4)² = 9.
These calculations are based on the Limit Principles, which state that the limit of a sum or difference of functions is equal to the sum or difference of their limits, and the limit of a constant times a function is equal to the constant times the limit of the function.
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evaluate 8g - f if f=4 and g = -1
Answers
Answer:
-12
Step-by-step explanation:
Step 1: Define
8g - f
f = 4
g = -1
Step 2: Substitute and Evaluate
8(-1) - 4
-8 - 4
-12
Sophia's school has 23 classrooms. Each classroom has 10 tables. How many tables are there in the school?
Answers
Answer:230
Step-by-step explanation: 23x10 i got by drawing out 23 lines and count by 10
can you guys answer these sequences?
Answers
b) 7, 17, 27, 37
-3,7,17,27,37
I need help with this question
Answers
Answer:
B (39)
Step-by-step explanation:
Using the Pythagorean theorem (a^2+b^2=c^2) and X=BC length
15^2+36^2=x
225+1296=x
√1521=x
x=39
Answer:
B.
Step-by-step explanation:
The Pythagorean Theorem
a^2+b^2=c^2
In this case it's c^2=a^2+b^2
c^2=15^2+36^2
c^2=225+1296
c^2=1521
c= the square root of 1521
c=39
So...
the length of line segment BC is 39
eamonn has just taken a statistics exam, and he wants to calculate a confidence interval to represent the exam scores in his class. the test mean was 75, with a standard deviation of 5. there are 30 students in the class. the 90% confidence interval for the class is:
Answers
The 90% confidence interval for the class is [73.49, 76.51].
Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.
CI = μ ± z x SD/√n
where CI = confidence interval
μ = sample mean = 75
z = found by using a z-score table
SD = sample standard deviation = 5
n = sample size = 30
At 90% confidence level, the area in each tail of the standard normal curve is 5, and the cumulative area up to the second tail is 95.
(100 - 90) / 2 = 5
100 - 5 = 95
Find 0.95 in the z-table to get the value of z.
At p = 0.95, z = 1.65
Plug in the values to the formula for confidence interval, CI.
CI = μ ± z x SD/√n
CI = 75 ± 1.65 x 5/√30
CI = 75 ± 1.51
CI = [73.49, 76.51]
Hence, for every 100 samples, at 90% confidence level, the mean will be between 73.49 and 76.51.
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Select the correct answer. What is the value of x in the equation 1,331x3 − 216 = 0? A. -6/11 B. 11/6 C. 1/6 D. 6/11
Answers
The value of x in the equation \(1331x^{3} - 216 = 0\) is \(-\frac{6}{11}\), the correct option is A.
To solve for x in the given equation, we can first isolate the variable term by adding 216 to both sides of the equation, which gives:
\(\frac{1331x^{3} }{3} = -216\)
Next, we can divide both sides of the equation by 1,331 to obtain:
\(x^{3} = - \frac{216}{1331}\)
We can simplify this expression by finding the prime factorization of both numbers. We can write 216 as 2³× 3³ and 1,331 as 11 × 11 × 11. Substituting these values, we get:
x³ = - (2³ × 3³) ÷ (11³)
x³ = - (8 ÷ 1331) × (27)
x³ = - 216 ÷ 1331
The result of taking the cube root of both sides is:
x = \(-( \frac{216}{1331})^{1/3}\)
x = \(- \frac{6}{11}\)
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rights answers only:)
Answers
The measure of angle 6 is 38°.
What are vertically opposite angles?
Vertically opposite angles are pairs of angles formed by two intersecting lines that are opposite to each other and share the same vertex but are not adjacent angles.
When two lines intersect, they form four angles at the intersection point. The vertical opposite angles are the pairs of angles that are opposite to each other and are not adjacent angles.
We know that, if two lies are parallel and a transversal cuts the lines.
then, the angle formed are corresponding angles ad the vertically opposite angles formed will be equal.
similarly, In the give figure,
we ca see that angle 6 ad angle 38 are vertically opposites angle.
so, angle 6 = 38°
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An instructor gives regular 28 - point quizzes and 100 - point exams in a mathematics course . Average scores for six students , given as ordered pairs ( x , y ) where x is the average quiz score and y is the average test score , are ( 12 , 49 ) , ( 14 , 54 ) , ( 15 , 58 ) , ( 10 , 43 ) , ( 18 , 65 ) , and ( 8 , 38 ) .
( c ) Use the regression line to predict the average exam score for a student with an average quiz score of 13. ( Round your answer to three decimal places.)
( e ) The instructor adds 4 points to the average exam score of everyone in the class . Describe the changes in the positions of the plotted points and the change in the equation of the line .
Answers
The slope of the line does not change but the y-intercept increases by 4.
c) Use the regression line to predict the average exam score for a student with an average quiz score of 13.
The equation of the regression line is given by: y = 3.225x + 9.129,
where y is the average test score, and x is the average quiz score.
Hence, substituting x = 13 gives:y = 3.225(13) + 9.129 ≈ 51.39
Therefore, the predicted average test score for a student with an average quiz score of 13 is approximately 51.39.
e) The instructor adds 4 points to the average exam score of everyone in the class.
The equation of the original regression line is y = 3.225x + 9.129.
Adding 4 points to the average test score of every student will change the y-intercept of the line.
The new equation will be y = 3.225x + 13.129.
Hence, The line's slope remains unchanged, but its y-intercept grows by 4 instead.
The plotted points will move up by 4 units, but their positions will not change with respect to each other.
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The slope of the line does not change but the y-intercept increases by 4.
c) Use the regression line to predict the average exam score for a student with an average quiz score of 13.
The equation of the regression line is given by: y = 3.225x + 9.129,
where y is the average test score, and x is the average quiz score.
Hence, substituting x = 13 gives:y = 3.225(13) + 9.129 ≈ 51.39
Therefore, the predicted average test score for a student with an average quiz score of 13 is approximately 51.39.
e) The instructor adds 4 points to the average exam score of everyone in the class.
The equation of the original regression line is y = 3.225x + 9.129.
Adding 4 points to the average test score of every student will change the y-intercept of the line.
The new equation will be y = 3.225x + 13.129.
Hence, The line's slope remains unchanged, but its y-intercept grows by 4 instead.
The plotted points will move up by 4 units, but their positions will not change with respect to each other.
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PLEASE HELP RIGHT NOW :(
Answers
Answer: C. and F.
Step-by-step explanation:
What is the average rate of change, please simplify your answer (PICTURE BELOW)
Answers
Answer:
\({ \tt{average \: \triangle = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ \)
x1 is -1; y1 is -3 [from graph (-1, -3)]x2 is 3; y2 is 5 [from graph (3, 5)]\({ \tt{ = \frac{5 - ( - 3)}{3 - ( - 1)} }} \\ \\ = { \tt{ \frac{8}{4} }} \\ \\ = 2\)
is this correct? helppp
Answers
Answer:
Yes its correct the unhighlighted is complement
Please help. Will give Brainliest
Answers
Answer:
A dilation
Step-by-step explanation:
I did this in math
Hope I helped! Have a nice day! Plz mar as brainliest!!! :D
-XxDeathshotxX
Answer:
This is a nonrigid transformation called a dilation.
Step-by-step explanation:
A dilation is when a pre-image's dimensions are altered in proportion with the pre-image. The image has a proportional relationship with the pre-image. The shape can get larger or smaller in size.
Help pls !!! Find the measure of the side indicated. Simplify your answer and write it as a whole number
Answers
Check the picture below.
Triangle X Y Z is shown. Line Z X is extended through point W to form exterior angle W X Y.
Which statement regarding the diagram is true?
m∠WXY = m∠YXZ
m∠WXY < m∠YZX
m∠WXY + m∠YXZ = 180°
m∠WXY + m∠XYZ = 180°
Answers
Answer:
C: m∠WXY + m∠YXZ = 180°
Step-by-step explanation:
edu is annoying to do, i got you :)
What is the result of dividing 2x3 x2 − 2x 8 by x 2?
Answers
The result of dividing 2x^3 + x^2 - 2x + 8 by x + 2 is:
Quotient: 2x^2 - 3x + 4
Remainder: 0
The given polynomial is 2x^3 + x^2 - 2x + 8.
First we choose a term to multiply with the first term of the divisor such that we get the first term of the polynomial.
(x)(2x^2) = 2x^3
Thus, we multiply the divisor (x + 2) by 2x^2 which gives 2x^3 + 4x^2.
Now we subtract this from the polynomial which gives -3x^2 - 2x +8.
Next we multiply the divisor by -3x which gives -3x^2 - 6x. Again we subtract the same from the remaining polynomial -3x^2 - 2x +8 and get 4x + 8.
Repeating the same we multiply the divisor by 4 which gives 4x + 8. Subtracting the same from the remaining polynomial 4x + 8 we get the remainder 0.
Thus, the quotient is 2x^2 - 3x + 4.
The question is incomplete, the complete question is:
What is the result of dividing 2x^3 + x^2 - 2x + 8 by x+2?
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consider the following problem: find two numbers whose sum is 23 and whose product is a maximum.
Answers
The problem is to find two numbers that satisfy two conditions: their sum is 23, and their product is maximized. In other words, we need to determine two numbers that maximize their product while their sum remains constant.
To solve this problem, we can use algebraic reasoning. Let's assume the two numbers are x and y. We know that their sum is 23, so we have the equation x + y = 23. To maximize their product, we can express one variable in terms of the other. Solving the equation for y, we have y = 23 - x. Substituting this value of y in terms of x into the equation for the product, we get P = x(23 - x). This is a quadratic equation in terms of x. To find the maximum product, we can determine the vertex of the parabola represented by the quadratic equation. The x-coordinate of the vertex represents the value of x that maximizes the product. By solving for x, we can then find the corresponding value of y.
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Which of the following functions has a graph that is a line? f(x) = |x| f(x) = x f(x) = x 2
Answers
Answer:
f(x) = x
Step-by-step explanation:
f(x) = |x| will give you V graph
f(x) = x will give you line graph (linear)
f(x) = x² will give you a curve graph
Answer:Answer:
f(x) = x
Step-by-step explanation:
f(x) = |x| will give you V graph
f(x) = x will give you line graph (linear)
f(x) = x² will give you a curve graph
Step-by-step explanation:
A chef at a restaurant uses 19 pounds of butter each day. About how many grams of butter does the chef use each day? use the conversion factors 16 ounces/1pound and 28.4 grams/1 ounce
Answers
Answer:
8,633.6 grams
Step-by-step explanation:
you do 16 times 19 because that will tell you how many ounces you have then you do 304 which is 16 times 19, 304*28.4 and there is your answer.
Please help me thanks a lot
Answers
Answer:
C
Step-by-step explanation:
Plot your point at (-9,0) then draw your line with your slope (plot some other points first). Using algebra rearrange your y=mx+b formatted equation.
y=-5/3x-15, 3y = -5x - 45, 5x + 3y = -45
how to know if a function has a vertical asymptote
Answers
To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.
A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:
Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.
Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.
For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.
In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.
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If Maya’s crew paints the platform at a rate of 720 feet per hour, determine how long to the nearest hour it will take them to paint the entire platform. ( read and respond)
Answers
Answer:
400/2.5 = 720/x
400x = 720 x 2.5
x = 4.5
Step-by-step explanation:
The required hours it would take to paint the entire platform is given as x/720. Where x is the length of measure of the platform.
What is rate of change?Rate of change is defined as the change in value with rest to the time is called rate of change.
Here,
Maya’s crew paints the platform at a rate of 720 feet per hour,
Let the length of the platform be x,
Now,
Divide the length with the rate, giving the time to paint the complete platform,
Time = length/rate
Time = x / 720
Thus, the required hours it would take to paint the entire platform is given as x / 720. Where x is the length of measure of the platform.
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what is the main reason why you would want to remove individual differences by using a repeated-measures anova?
Answers
The main reason for using a repeated-measures ANOVA (Analysis of Variance) is to remove or control for the effects of individual differences when studying the effects of an independent variable on a dependent variable.
Here, we have,
we know that,
By using a repeated-measures design, where the same participants are measured under different conditions or at different time points, individual differences are considered within the analysis. This design allows researchers to examine the effects of the independent variable while minimizing the impact of individual variability, which can include factors such as age, gender, personality traits, cognitive abilities, and other individual characteristics.
By removing or accounting for individual differences, a repeated-measures ANOVA helps to increase the internal validity of the study by reducing the influence of confounding variables. It allows researchers to focus on the effects of the independent variable by controlling for the variability attributable to individual differences. This helps in drawing more accurate conclusions about the specific effects of the independent variable on the dependent variable, as it reduces the possibility that the observed effects are solely due to individual differences rather than the manipulation of the independent variable.
Overall, using a repeated-measures ANOVA helps researchers to isolate and examine the effects of the independent variable by minimizing the impact of individual differences and increasing the internal validity of the study.
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5s=13 what is the answer
Answers
I hope it’s help u !
find an equation for F minus one the inverse function. Verify that your equation is correct by showing that
Answers
Explanation
We are to first find the inverse of the function:
\(f(x)=\frac{x+12}{x-4}\)\(\mathrm{A\:function\:g\:is\:the\:inverse\:of\:function\:f\:if\:for}\:y=f\left(x\right),\:\:x=g\left(y\right)\:\)To do so, we will follow the steps below:
Step 1:
\(\begin{gathered} write\text{ the function interms of y} \\ y=\frac{x+12}{x-4} \end{gathered}\)Step2: Interchange x with y
\(x=\frac{y+12}{y-4}\)Step 3: solve for y
\(\begin{gathered} xy-4x=y+12 \\ xy-y=12+4x \\ y(x-1)=12+4x \\ y=\frac{12+4x}{x-1} \end{gathered}\)Thus, the inverse of the function is
\(\begin{gathered} f^{-1}(x)^=\frac{12+4x}{x-1} \\ \\ for \\ x\ne1 \end{gathered}\)Part 2
\(f(f^{-1}(x))=f(\frac{12+4x}{x-1})\)Simplifying further
\(\begin{gathered} f(\frac{12+4x}{x-1})=\frac{\frac{12+4x}{x-1}+12}{\frac{12+4x}{x-1}-4}=x \\ Thus \\ f(\frac{12+4x}{x-1})=x \end{gathered}\)Also
\(f^{-1}(f(x))=f^{-1}(\frac{x+12}{x-4})\)Simplifying further
\(\begin{gathered} f^{-1}(\frac{x+12}{x-4})=\frac{12+4\times\frac{x+12}{x-4}}{\frac{x+12}{x-4}-1}=x \\ \\ Thus \\ f^{-1}(\frac{x+12}{x-4})=x \end{gathered}\)