The area between the curves y = x^2 and y = 2x - 6 is 14.67 square units.
What is the measure of the area enclosed by the curves y = x^2 and y = 2x - 6?The region between the curves y = x^2 and y = 2x - 6 can be calculated by finding the points of intersection between the two curves. To determine these points, we equate the equations: x^2 = 2x - 6. By rearranging the equation, we get x^2 - 2x + 6 = 0. Solving this quadratic equation yields two real solutions: x = -1 and x = 3. These values represent the x-coordinates of the intersection points.
To calculate the area, we integrate the difference between the two curves within the given interval. The area A can be expressed as A = ∫[a,b] (f(x) - g(x)) dx, where f(x) represents the upper curve and g(x) represents the lower curve. In this case, A = ∫[-1,3] (2x - 6 - x^2) dx.
Evaluating this integral yields the area between the curves as approximately 14.67 square units. This represents the enclosed region between the curves y = x^2 and y = 2x - 6.
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(6. Factorise:
(a) 4a²-28ab-a+7b
(b) 2a²-366²
(c) 12ce-9c-8de+6d
(d) a² +b²+2ab-2a-2b-3
(e) 5-45a²
(f) p(y-2)-q(z-y)
(g)
³-y²z-y₂² +2³
J
Answer:
a. 1ab (4 -28+7)
b 2(a² - 183²)
c. cde(12-9-8+6)
d ab(a+b +2 -2-2 -3)
e 5(1- 9a²)
f py- 2p - qz -qy
pqy (1 - 2 -z -1)
The members of a cooking club are making cakes, which they will sell at a street fair for $8 apiece. It cost $30 for a booth at the fair, and the ingredients for each cake cost $2. At some point, the club members will sell enough cakes so that their sales cover their expenditures. How many cakes will they have sold?
They need to sell 5 pieces to cover their expenditures (have a profit of zero).
How many cakes will they have sold?
We know that the costs are:
$30 for the booth at the fair.$2 for each piece of cake they sell.And the revenue is:
$8 for each piece of cake.So, the profit (the difference between the revenue and the cost) for selling x pieces is:
p(x) = $8*x - $2*x - $30
p(x) = $6*x - $30
We want to find the value of x such that p(x) = 0, then:
0 = $6*x - $30
x = $30/$6 = 5
They need to sell 5 pieces to cover their expenditures (have a profit of zero).
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Find the length of side a.
sorry for the bad quality, camera is broken. the one on top is 13 and the one below is 12.
SOLUTION :
a² = hypo² - base²
a² = 13² - 12²
a² = 169 - 144 = 25
a = √25
a = 5 units.
________________________________
HOPE IT HELPS
Given y=-x^2 if the function is shifted 5 units up which equation describes the new function
The equation that describes the new function is y' = x^2 + 5
How to determine the new function?The function is given as:
y = x^2
Shifting the function up by 5 units, the rule is
(x, y) = (x, y + 5)
So, we have:
y' = x^2 + 5
Hence, the equation that describes the new function is y' = x^2 + 5
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In general, the arithmetic average return is probably too _____ (low/high) for longer periods and the geometric average is probably too _____ (low/high) for shorter periods.
The arithmetic average return is probably too high for longer periods and the geometric average is probably too low for shorter periods.
What is Arithmetic Average Return?
When we look at historical returns, the difference between the geometric and arithmetic average returns isn't too hard to understand.
To put it slightly differently, the geometric average tells you what you actually earned per year on average, compounded annually. The arithmetic average tells you what you earned in a typical year. You should use whichever one answers the question you want answered. A somewhat trickier question concerns forecasting the future, and there's a lot of confusion about this point among analysts and financial planners.
Now, If we have estimates of both the arithmetic and geometric average returns, then the arithmetic average is probably too high for longer periods and the geometric average is probably too low for shorter periods.
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In a movie theater, the number of seats in a row is 8 greater than the total number of rows. How many rows are in the movie theater, if the total number of seats in the theater is 884?
Answer:
26 rows
Step-by-step explanation:
this is like a rectangle length×width situation.
seats per row = s
number of rows = r
s × r = 884
s = r + 8
so, we can use e.g. the second equation in the first :
(r + 8) × r = 884
r² + 8r = 884
r² + 8r - 884 = 0
the general solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = r
a = 1
b = 8
c = -884
r = (-8 ± sqrt(8² - 4×1×-884))/(2×1) =
= (-8 ± sqrt(64 + 3536))/2 = (-8 ± sqrt(3600))/2 =
= (-8 ± 60)/2 = -4 ± 30
r1 = -4 + 30 = 26
r2 = -4 - 30 = -34
a negative number did not make any sense for the number of rows, so r = 26 is our answer.
find the values of A and B
please help giving brainliest
Answer:
A=3Bz/2
B=2A/3z
Step-by-step explanation:
if you need more explanation you can ask me :)
Can someone help?
what do both of these functions have in common?
f(x) = 5e^x+5 - 5 g(x) = 0.5(x-5)^2 -5
o a. they have the same vertical stretch
ob. they have the same horizontal translation
c. they have the same vertical shift
d. they have the same end behavior
c. They have the same vertical shift.
A vertical shift is just an alternate within the y-price of each characteristic. it's miles literally picking up the entire characteristic or graph and moving the whole element up or down. If it's far moved up, we add to the y-cost, if it's far moved down, we subtract from the y-cost.
Vertical shift and lateral shift are phenomena because of the refraction of mild rays once they journey from one medium into every other. while light rays travel across two parallel surfaces, the emergent rays from the second one floor are parallel to the incident rays on the primary floor.
The segment Shift is how far the function is shifted horizontally from the standard position. The Vertical Shift is how long way the function is shifted vertically from the same old function.
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Show your steps in evaluating each of the following expressions. The steps count 4 points each, the answer is 1 point.
The steps in evaluating each of the following expressions is shown below.
What is an expression?An expression can be defined as a mathematical equation which shows the relationship existing between two or more numerical quantities or variables.
How to evaluate the given expressions?15 - 35/7 - 2 + 3 - 4
15 - (35/7) - 2 + 3 - 4 (bracket and division)
15 - 5 - 2 + 3 - 4 (regroup)
15 + 3 - 5 - 2 - 4 (subtract and add)
18 - 11 = 7.
Expression 2.10 + 2(9 - 5) - 16/18
10 + (2 × 4) - 8/9 (bracket and division)
10 + 8 - 8/9 (add)
18 - 8/9 (subtract)
162/9 - 8/9 = 17 1/9 or 154/9.
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Complete Question:
Show your steps in evaluating each of the following expressions. The steps count 4 points each, the answer is 1 point.
A. 15 - 35/7 - 2 + 3 - 4
B. 10 + 2(9 - 5) - 16/18
party planners recommend that, for every eight quests, two orders of appetizers be provided. which function reflects this ratio
The ratio guest to appetizers at the party was 4 guest per appetizer.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Ratio of guest to appetizers = 8 guest / 2 appetizers = 4 guest per appetizer.
The ratio guest to appetizers at the party was 4 guest per appetizer.
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40 points and I will choose brainlyist
below is the question.
Using proportions, the expected number of adults in Palm City whose main source of news is the internet or newspaper is of 19,413.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
From the table, the proportion of adults in Palm City whose main source of news is the internet or newspaper is found as follows:
p = (62 + 88)/(62 + 88 + 128 +24 + 38) = 0.4412.
Hence, out of 44,000 adults, the expected number is found as follows:
0.4412 x 44000 = 19,413.
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PLEASE HELP OUT ASAP!!!!!!
WILL GIVE 15 POINTS!!!!
a) The approximate area below the curve using five rectangles is 1280 square units.
b) The approximate area below the curve using ten rectangles is 1320 square units.
c) The approximate area below the curve using infinite number of rectangles is 1333.333 square units.
How to find the area below the curve by Riemann's sum
In this problem we must estimate the value of the area below the curve by finite number of rectangles using Riemann sums, whose expression is:
A ≈ [(b - a) / n] · ∑ f[a + i · (b - a) / n], for i = {0, 1, 2, 3, ..., n - 1} (1)
Where:
n - Number of rectanglesa - Lower limit of the interval.b - Upper limit of the interval.i - Index of the rectangle.The approximate area below the curve using five rectangles is: f(x) = 20 · x - x², a = 0, b = 20, n = 5
A ≈ [(20 - 0) / 5] · ∑ f[0 + i · (20 - 0) / 5]
A ≈ 4 · ∑ f(4 · i)
A ≈ 4 · [f(0) + f(4) + f(8) + f(12) + f(16)]
f(0) = 20 · 0 - 0² = 0
f(4) = 20 · 4 - 4² = 64
f(8) = 20 · 8 - 8² = 96
f(12) = 20 · 12 - 12² = 96
f(16) = 20 · 16 - 16² = 64
A ≈ 4 · (0 + 64 + 96 + 96 + 64)
A ≈ 1280
And using ten rectangles:
A ≈ [(20 - 0) / 10] · ∑ f[0 + i · (20 - 0) / 10]
A ≈ 2 · ∑ f(2 · i)
A ≈ 2 · [f(0) + f(2) + f(4) + f(6) + f(8) + f(10) + f(12) + f(14) + f(16) + f(18)]
f(0) = 20 · 0 - 0² = 0
f(2) = 20 · 2 - 2² = 36
f(4) = 20 · 4 - 4² = 64
f(6) = 20 · 6 - 6² = 84
f(8) = 20 · 8 - 8² = 96
f(10) = 20 · 10 - 10² = 100
f(12) = 20 · 12 - 12² = 96
f(14) = 20 · 14 - 14² = 84
f(16) = 20 · 16 - 16² = 64
f(18) = 20 · 18 - 18² = 36
A ≈ 2 · (0 + 36 + 64 + 84 + 96 + 100 + 96 + 84 + 64 + 36)
A ≈ 1320
And using infinite rectangles:
A ≈ [(b - a) / n] · ∑ f[a + i · (b - a) / n]
A ≈ (20 / n) · ∑ [20 · (20 / n) · i - (20 / n)² · i²]
A ≈ (20 / n) · ∑ [400 · i / n - 400 · i² / n²]
A ≈ ∑ (8000 · i / n² - 8000 · i² / n³)
A ≈ (8000 / n²) · ∑ i - (8000 / n³) · ∑ i²
A ≈ (8000 / n²) · [n · (n + 1) / 2] - (8000 / n³) · [n · (n + 1) · (2 · n + 1) / 6]
A ≈ (8000 / n²) · [(n² + n) / 2] - (8000 / n³) · [(n² + n) · (2 · n + 1) / 6]
A ≈ 4000 · (n² + 2) / n² - (8000 / n³) · [(2 · n³ + 3 · n² + n) / 6]
A ≈ 4000 · (1 + 2 / n²) - (4000 / 3) · [2 + 3 · (1 / n) + (1 / n²)]
As n → + ∞, then:
A ≈ 4000 - 8000 / 3
A ≈ 1333.333
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Help me out on this, ASAP!!! (Geometry)
Write formal proofs using the HL Theorm.
Answer:
Given PR is perpendicular to QS, and PQ and PS are congruent. Angle PRQ and angle PRS are right angles by the definition of perpendicular segments. Therefore triangle PRQ and triangle PRS are right triangles. Segment PR is congruent to segment PR by the reflexive property of congruence. By the HL Theorem, triangles PRQ and PRS are congruent.
Someone please help me
The top number is 18
Answer:
x = 24
Step-by-step explanation:
Since this is a right angle, we can use the Pythagorean Theorem to find x. In the formula, a^2 + b^2 = c^2, variables a and b represent the lengths of the legs, and variable c represents the length of the hypotenuse.
a^2 + b^2 = c^2
18^2 + x^2 = 30^2
324 + x^2 = 900
x^2 = 576
x = 24
I needed help solving this
Answer:
Answer C: m = 26, f = 22
there is a typo in answer D.
Step-by-step explanation:
There are 48 vehicles, so m + f = 48.
They have 140 wheels, so 2m+4f = 140.
You can rewrite the first as m = 48-f and then plug it into the second:
2(48-f) + 4f = 140 =>
96 - 2f + 4f = 140 =>
2f = 140 - 96 =>
2f = 44
f = 22
m = 48 - 22 = 26
Answer:
D
Step-by-step explanation:
Let m = motorcycles and c = cars
m + c = 48 2m + 4c = 140
m + c = 48 Multiple this equation through by -2
-2m -2c = -96 Add this to the second equation above
2m +4c = 140
2c = 44 Divide both sides by 2
c = 22. There are 22 cars. Plug this back into the top equation to find the number of motorcycles.
m + c = 48
m + 22 = 48 Subtract 22 from both sides
m = 26
Task 1—Non-Linear Systems of Equations Create a system of equations that includes: One linear equation And one quadratic equation
One linear equation y=x ......(i)
And quadratic equation y=x^2 .....(ii)
(1)Solving them
y=x=x^2
x-x^2=0
x(x-1)=0
If x=0 then y=0
if x=1 then y=1
(x,y)=(0,0),(1,1)
(2) graphically [refer in attachemet]
What is linear equation ?
A linear equation is one in which the variable's maximum power is always 1. It is also known as a one-degree equation. A linear equation in one variable has the conventional form Ax + B = 0. In this equation, x is a variable, A is a coefficient, and B is constant. A linear equation in two variables has the conventional form Ax + By = C. The variables x and y are variables, the coefficients A and B are coefficients, and the constant C is a constant.There are only one or two variables in a linear equation. In a linear equation, no variable is raised to a power larger than one or utilized as the denominator of a fraction. When you locate two values that satisfy a linear equation and display them on a coordinate grid, all of the points fall on the same line.To learn more about linear equation visit:
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What is the maximum number of consecutive odd positive integers that can be added together before the sum exceeds $401$
The maximum number of integers is 27 that can be added together before the summation of the A.P. Series exceeds 401.
According to the statement
We have a given that the maximum sum of the positive integers is 400.
And we have to find the value of n which is a maximum number of integers by which the value of sum become 400.
So, to find the value of the n we use the
A.P. Series'Summation formula
According to this,
S = n (n+1)/2
Here the value of s is 401
Then
S = n (n+1)/2
401 = n (n+1)/2
401*2 = n (n+1)
802 =n (n+1)
n (n+1) = 802
n^2 + n -802 =0
By the use of the Discriminant formula the
value of n becomes n = -28 and n = 27.
The negative value of n is neglected.
Therefore the value of n is 27.
So, The maximum number of integers is 27 that can be added together before the summation of the A.P. Series exceeds 401.
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3. A train travels 20 km at a uniform speed of 60 km/h and the next 20 km at a uniform speed of 80km/h. Calculate its average speed.
Answer:
Given,
Distance traveled = 20 km
Speed = 60 km/h
So, timetaken=DistanceSpeed=2060=13h
For the next journey
Distance traveled = 20 km
Speed = 80 km/h
So, timetaken=DistanceSpeed=2080=14h
Now,
Total distance traveled = 20 + 20 = 40 km
Total time taken = 13+14=712
We know,
Averagespeed=TotaldistancetraveledTotaltimetaken=40712=68.5 km/h
Hence the average speed of the train is 68.5 km/h
Which type of graph would you want to use to show the frequency of an interval?
line graph
histogram
box-and-whisker plot
stem-and-leaf plot
the product of 1540 and m is a square number. find the smallest possible value of m
Answer:
Step-by-step explanation:
the smallest value is 96.25 or rounded to the nearest whole number it is 96
what i did was put in my calculator 1540 divided by 4^2 because it is squared and has 4 sides
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2202, tysm for the help!
The predicted value of y when x =7 is -8.5
How to predict the y value?Start by drawing the line of best fit through the points
See attachment for the graph.
From the attached graph, we have the following value
y = -8.5 when x = 7
Hence, the predicted value of y when x =7 is -8.5
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In a bag are three red marbles and three white marbles. If
two marbles are taken from the bag at the same time,
what is the probability that both marbles will be red?
The probability is 1/5.
How to find the probability?
There are 3 red marbles and 3 white marbles, for a total of 6.
The probability that the first marble is red is:
P(red) = 3/6
The probability that the second marble is also red is:
P(red') = 2/5 (because now there are 2 red marbles and a total of 5).
The joint probability is:
P = (3/6)*(2/5) = 1/5
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A poll worker analyzing the ages of voters found that mu = 65 and sigma = 5. what is a possible voter age that would give her zx = 1.14? round your answer to the nearest whole number.
If the value of μ is 65, σ is 5 and z is 1.14 then the value of possible voter age would be 70.6 years.
Given that value of μ is 65, σ is 5 and z is 1.14.
We have to calculate the possible voter age that can satisfy the given values of σ,μ and z.
We know that in z test,
z=X-μ/σ
in which μ is population mean,σ is population standard deviation.
We have to just put the values in the above formula to get the value of X which is our possible voter age.
Putting the values we get,
1.14=x-65/5
5.7=X-65
X=65+5.7
X=67.7
Hence the possible voter age is 67.7 which would satisfy the value of μ=65,σ=5 and z=1.14.
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Calculate the future value in five years of $8,000 received today if your investments pay future value a. 5 percent compounded annually $ b. 7 percent compounded annually c. 9 percent compounded annually d. 9 percent compounded semiannually e. 9 percent compounded quarterly.
The Future value is:
a) $10,210.25
b) $11,220.41
c) $12,308.99
d) $18,938.90
e) $44,835.28
What is future value?
The future value (FV) of any asset can be understood as an increase in its value at a fixed rate over a period of time. For a given principal sum P, rate of interest r, and time period t, the future value of an asset can be calculated as:
FV=P*(1+r) ^t
We can find future value as shown below:
P=$8,000
t=5 year
a) r=6%=0.06
FV=8000*(1+0.05) ^5
=8000*(1.0) ^5
=$10,210.25
b) r=7%=0.07
FV=8000*(1+0.07) ^5
=8000*(1.07) ^5
=$11,220.41
c) r=9%=0.09
FV=8000*(1+0.09) ^5
=$12,308.99
d) r=9% compounded semiannually
= 0.09
t=2*5=10
FV=8000*(1+0.09) ^10
=8000*(1.09) ^10
=$18,938.90
e) r=9 percent compounded quarterly
=0.09
t=5*4=20
FV=8000*(1+0.09) ^20
=8000*(1.09) ^20
=$44,835.28
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Which graph is the sequence defined by the function f(x) = 3(2)x-1?
On a coordinate plane, 5 points are plotted. The points are (0, 2), (1, 6), (2, 18), (3, 54), (4, 162).
On a coordinate plane, 5 points are plotted. The points are (1, 2), (2, 6), (3, 18), (4, 54), (5, 162).
On a coordinate plane, 6 points are plotted. The points are (0, 3), (1, 6), (2, 12), (3, 24), (4, 48), (5, 96).
On a coordinate plane, 5 points are plotted. The points are (1, 3), (2, 6), (3, 12), (4, 24), (5, 48).
Answer: On a coordinate plane, 5 points are plotted. The points are (1, 3), (2, 6), (3, 12), (4, 24), (5, 48).
Step-by-step explanation:
When x=1, f(x)=3. So, it passes through (1,3).
So, everything is eliminated except for option (4).
Answer:
D!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
PLEASE ANSWER QUICKLY
Answer:
Option (4)
Step-by-step explanation:
See attached image.
a vendor sold 25 dozens of mangoes. He was able to sell 3/5 of the total number of mangoes at 15.50 pesos and the remaining at 19.00 pesos each. How much was the total sales?
Answer: 422.5
Step-by-step explanation: To find how many mangoes were sold at 15.50 pesos, find 3/5 of the total number of mangoes. 3/5 of 25 is 15 because 3 (numerator) times 25 (mangoes) divided by 5 (denominator) is 15. 15 times 15.50 (price) is 232.5 pesos. Next we take the remaining mangoes (10) and multiply it by the price (19) to get 190 pesos. Add the sales and you get 422.5 pesos.
Answer:
422.50 pesos total
Step-by-step explanation:
3/5 ths of 25 = 15
(1/5th of 25 is 5, so we can multiply that number by 3 (3)(5) to get what 3/5ths of 25 are)
So, 15 mangoes were sold at 15.50 pesos
15 × 15.50 = 232.50
(why is this multiplication?
remember that repeated addition is multiplication. We are adding the cost of each mango (15.50) 15 times, which we could write as 15.50 + 15.50... 15 times, or we could simply multiply the two values :) )
Because this vendor has sold 15 of his mangoes, he has 10 left (25 - 15 = 10), so we multiply
10 × 19.00 to find the combined cost:
10 × 19.00 = 190.00
Now, we want to find the total sale (how much money he made in total, from all 25 mangoes)
So, let's add our two values together:
232.50
+ 190.00
422. 50
So, the vendor made 422.50 pesos total from his mangoes
hope this helps! have a lovely day :)
This Stem-and-Leaf Plot represents the heights of the students on Ralph’s basketball team. One student’s height is missing from the plot. If the mean height of all the students on the team is 61 inches, what is the missing height?
A. 55 in.
B. 59 in.
C. 61 in.
D. 65 in.
The missing height is 65.
What is the missing height?
Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
Missing height = (mean x total number of students) - sum of existing heights
Sum of existing heights = (54 + 55 + 56 + 61 + 63 + 64 + 70 ) = 423
Missing height = (8 x 61) - 423 = 64
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URGENT PLEASE ANSWER THESE
The distance of the cruise liner from me 20 seconds later will be; 2600ft.
How far will the cruise liner be in 20 seconds?a) Since, the speed of the liner is 30ft/sec, it follows that after 20secs, the liner would cover; (30×20)ft = 600ft more; and consequently, the distance is now; √(2000²+600²) = ft.
b) For the boat to be 2500 ft away given the speed 30ft per sec; Time taken = 2500/30 = 83.3seconds. Hence, the boat will be more than 2500 feets away after 2 minutes.
c) If the boat's distance is 2000ft from me; it follows that the distance covered is 10 seconds is; √(2000²-1500²) = 1322.9ft
Hence, the speed to attain this distance is; 1322.9/10 = 132.29ft/sec.
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Drag each expression to the correct location on the table.
Simplify each exponential expression using the properties of exponents and match it to the correct answer.
An exponential expression is one in which a number has been raised to a certain power.
What is an exponential expression?An exponential expression is one in which a number has been raised to a certain power.
Now;
1) 3^2 . (3^3)^2 . 3^-8 = 3^2 + 6 - 8= 3^0 = 1
2) (3^2) (2.3)^-3/2^-2 = 3^2 . 2^-3 . 3^-3/2^-3 = 1/3
3) (2^-1) . (3 . 2)^4/(3 . 2)^3 = 2^-1. 3^4 . 2^4/ 3^3. 2^3 = 3
4) 2^5 . 3^5 . 6^-5 = 32 * 243/7776 = 1
5) (2^3) . (2 . 3)^-1/2^2 = 2^3 . 2^-1 . 3^-1/2^2 = 1/3
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