Step-by-step explanation:
If the order is relevant, the number of permutations is:
₁₀P₅ = 30,240
If the order is not relevant, the number of combinations is:
₁₀C₅ = 252
The number of ways to choose 5 letters among 10 without replacement will be 252 and with replacements will be 30240.
What are permutation and combination?When the order of the arrangements counts, a permutation is a numerical approach that establishes the total number of alternative arrangements in a collection.
The number of alternative configurations in a collection of things when the order of the selection is irrelevant is determined by combination.
The number of ways to choose r quantity among n without replacement is given as nCr = n!/(r!(n - 1)!)
n = 10 and r = 5
10C5 = 252
The number of ways to choose r quantity among n with replacement is given as, nPr = n!/(n - r)!
n = 40 and r = 5
10P5 = 10!/(10 - 5)! = 30240
Hence "The number of ways to choose 5 letters among 10 without replacement will be 252 and with replacements will be 30240".
For more about permutation and combination,
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Determine whether the experiment is blind or double blind.Is the aspirin produced by World's Best Pharmaceutical Company better than that of a competitor at relieving headaches? 200 headache suffers are chosen at random. Migraned Testing Service administers the experiment and provides the results evaluation. Three levels are made: participants receive contents from Bottle A, Bottle B, or Bottle C. Other than the fact that one bottle contains placebo aspirin (but not which particular bottle contains placebo aspirin), no other information is given to the testing service regarding the bottles' contents.a. Blindb. Double blindc. Neither
Answer:
The correct answer is:
Double-blind (b)
Step-by-step explanation:
A blind/blinded experiment is one in which information which may influence the participant or experimenter is withheld throughout the process of the experiment either by masking (giving false identity) or completely blinded, to avoid biases that may arise from such knowledge by the participant or experimenter.
Blinding is of three types: single-blind, double-blind and triple-blind experiements and this is named with respect to three categories involved in the experiment; participant, researcher or a third party, which may include: analysts, monitoring committees stakeholders etc. The blinding type is explained as follows
Blinding Type participant researcher Third-party
single-blind blinded unblinded unblinded
double-blind blinded blinded unblinded
triple-blind blinded blinded blinded
In this example, the 200 headache sufferers (participants) and the Migrane testing service (researchers) do not know the contents of the bottles being administered, whereas the pharmaceutical company (third-party knows), hence it is a double-blinded experiment.
What is the y intercept of the function f(x)=2•3^x
Answer:
[tex]\boxed{Option \ A}[/tex]
Step-by-step explanation:
[tex]f(x) = 2*3^x[/tex]
y intercept is when x = 0
So, Putting x = 0 in the above function
=> f(0) = [tex]2*3^0[/tex]
=> f(0) = 2*1
=> f(0) = 2
So, y-intercept is (0,2)
Answer:
A
Step-by-step explanation:
f(x) = 2 × 3^x
Plug x as 0 to find y-intercept.
2 × 3⁰
2 × 1
= 2
given the functions, f(x)=x^2 and g(x)=x+2, perform the indicated operation. when applicable, state the domain restriction. f(g(x)
Answer:
h(g(x)) = x²+4x+4
Domain restriction = [tex][-\infty, \infty][/tex]
Step-by-step explanation:
Given the functions h(x)=x^2 and g(x)=x+2, we are to find h(g(x)). To get the indicated operation we need to follow the steps;
Since the function in parenthesis g(x) = x+2
h(g(x)) can be written as h(x+2). Hence we are to look for the equivalent expression of h(x+2).
Since h(x) = x², h(x+2) can simply be gotten by simply replacing the variable x in h(x) as x+2 as shown;
h(x+2) = (g(x))²
h(x+2) = (x+2)²
We can open the bracket
h(x+2) = x²+4x+4
The domain restriction is the point where the function cannot exist for the value of x. The function can therefore exist on any real value R. The only domain restriction is at the interval [tex][-\infty, \infty][/tex]
Hence h(g(x)) is equivalent to x²+4x+4.
if sin theta = 2/3 which is possible
Answer:
C. cos theta = √5/3 and tan theta = 2/√5D. sec theta = 3/√5 and tan theta = 2/√5Step-by-step explanation:
According to SOH in SOH, CAH TOA;
SOH means sin theta = opposite/hypotenuse = 2/3
This shows that opposite = 2 and hypotenuse = 3. Before we can determine which of the expression is possible, we need to find the third side of the rigt angled triangle which is the adjacent.
According to Pythagoras theorem; hyp² = opp²+adj²
adj² = hyp² - opp²
adj² = 3² - 2²
adj² = 9 - 4
adj² = 5
adj = √5
Hence the adjacent side is √5.
From the trigonometry identity above;
cos theta = adj/hyp = √5/3 and tan theta = opp/adj = 2/√5
Since sec theta = 1/cos theta then sec theta = 1/(adj/hyp)
sec theta = hyp/adj = 3/√5
From the above calculation, the following are possible:
cos theta = √5/3, tan theta = 2/√5 and sec theta = 3/√5
The correct options are C and D
At noon, ship A is 170 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing north at 15 km/h. How fast is the distance between the ships changing at 4:00 PM
Answer:
The distance between the ships is changing at 42.720 kilometers per hour at 4:00 PM.
Step-by-step explanation:
Vectorially speaking, let assume that ship A is located at the origin and the relative distance of ship B with regard to ship A at noon is:
[tex]\vec r_{B/A} = \vec r_{B} - \vec r_{A}[/tex]
Where [tex]\vec r_{A}[/tex] and [tex]\vec r_{B}[/tex] are the distances of ships A and B with respect to origin.
By supposing that both ships are travelling at constant speed. The equations of absolute position are described below:
[tex]\vec r_{A} = \left[\left(40\,\frac{km}{h} \right)\cdot t\right]\cdot i[/tex]
[tex]\vec r_{B} = \left(170\,km\right)\cdot i +\left[\left(15\,\frac{km}{h} \right)\cdot t\right]\cdot j[/tex]
Then,
[tex]\vec r_{B/A} = (170\,km)\cdot i +\left[\left(15\,\frac{km}{h} \right)\cdot t\right]\cdot j-\left[\left(40\,\frac{km}{h} \right)\cdot t\right]\cdot i[/tex]
[tex]\vec r_{B/A} = \left[170\,km-\left(40\,\frac{km}{h} \right)\cdot t\right]\cdot i +\left[\left(15\,\frac{km}{h} \right)\cdot t\right]\cdot j[/tex]
The rate of change of the distance between the ship is constructed by deriving the previous expression:
[tex]\vec v_{B/A} = -\left(40\,\frac{km}{h} \right)\cdot i + \left(15\,\frac{km}{h} \right)\cdot j[/tex]
Its magnitude is determined by means of the Pythagorean Theorem:
[tex]\|\vec v_{B/A}\| = \sqrt{\left(-40\,\frac{km}{h} \right)^{2}+\left(15\,\frac{km}{h} \right)^{2}}[/tex]
[tex]\|\vec r_{B/A}\| \approx 42.720\,\frac{km}{h}[/tex]
The distance between the ships is changing at 42.720 kilometers per hour at 4:00 PM.
The following data values represent a sample. What is the variance of the
sample? X = 8. Use the information in the table to help you.
х
12
9
11
5
3
(x; - x)²
16
1
9
9
25
Answer:
The variance of the data is 15.
σ² = 15
Step-by-step explanation:
The mean is given as
X = 8
х | (x - X) | (x - X) ²
12 | 4 | 16
9 | 1 | 1
11 | 3 | 9
5 | -3 | 9
3 | -5 | 25
The variance is given by
[tex]\sigma^2 = \frac{1}{n-1} \sum (x - X)^2[/tex]
[tex]\sigma^2 = \frac{1}{5 - 1} (16 + 1 + 9 + 9 +25) \\\\\sigma^2 = \frac{1}{4} ( 16 + 1 + 9 + 9 +25) \\\\\sigma^2 = \frac{1}{4} (60) \\\\\sigma^2 = 15[/tex]
Therefore, the variance of the data is 15.
Can someone help me with this question
Answer:
Product of given question is 6√5
Step-by-step explanation:
Given:
3√2(√10)
Find:
Product.
Computation:
⇒ 3√2(√10)
⇒ 3√20
⇒ 3√4×5
⇒ 3√2×2×5
⇒ 3×2√5
⇒ 6√5
Product of given question is 6√5
1/3 x =6 What would like match this answer
Answer:
x=18
Step-by-step explanation:
Answer:
x = 18
Step-by-step explanation:
Since 1/3x = 6,
x = 6 x 3
Thus, x = 18
Select the correct answer from each drop down menu.
The slope of diagonal OA is
A) 4/3
B) 3/4
C) 1
,and it’s equation is
A) 4x-y=0
B) x-3y=0
C) 4x-3y=0
Answer:
(A) [tex]\text{The slope of OA is }\dfrac{4}{3}[/tex]
(C) It’s equation is 4x-3y=0.
Step-by-step explanation:
Point O is at (0,0)
Point A is at (3,4)
[tex]\text{Slope of OA}=\dfrac{4-0}{3-0} \\m=\dfrac{4}{3}[/tex]
The equation of a straight line is in the form: y=mx+b
The y-intercept of the line OA=0
Therefore, we have:
[tex]y=\dfrac{4}{3}x+0\\3y=4x+0\\$Subtract 3y from both sides$\\4x-3y=0[/tex]
The equation of the line is: 4x-3y=0
Which of the following is not a solution to the inequality graphed below?
Answer:
C ( 1,-2)
Step-by-step explanation:
We can plot the points and see what point is not in the shaded section
If one number is five more than another number, and the smaller number is half of the larger number, what are the two numbers?
Answer:
Larger number = 10Smaller number = 5Step-by-step explanation:
Let larger number be x
Let smaller number be y
[tex]x = 5 + y[/tex]---> equation (i)
[tex]y = \frac{1}{2} x[/tex]
[tex]x = 2y[/tex]-----> equation (ii)
Equate equation (i) and (ii),
[tex]5 + y = 2y[/tex]
Move variable to L.H.S and change its sign:
Similarly, Move constant to R.H.S and change its sign
[tex]y - 2y = - 5[/tex]
[tex] - y = - 5[/tex]
The difference sign (-) will be cancelled on both sides
[tex]y = 5[/tex]
Putting the value of y in equation (ii) in order to find the value of X ( larger number)
[tex]x = 2y[/tex]
Plug the value of y
[tex] = 2 \times 5[/tex]
Calculate the product
[tex] = 10[/tex]
Hence,
Smaller number = 5
Larger number = 10
Hope this helps..
Best regards!!
Answer:
10 and 5
Step-by-step explanation:
Let the first number be x.
Let the second number be y.
x = 5 + y
y = 1/2x
Plug y as 1/2x in the first equation.
x = 5 + (1/2x)
Solve for x.
Subtract 1/2x on both sides.
x - 1/2x = 5 + 1/2x - 1/2x
1/2x = 5
Multiply both sides by 2.
2(1/2x) = 2(5)
x = 10
Plug x as 10 in the second equation.
y = 1/2(10)
Solve for y.
y = 5
x = 10
y = 5
The two numbers are 10 and 5.
10 is the larger number.
5 is the smaller number.
Find all of the angle measures in the image.
Answer:
Angle 2= 45
Angle 3= 45
Angle 4= 135
Angle 5= 135
Angle 6= 45
Angle 7= 45
Angle 8= 135
El precio de costo de “x” artículos es 60x + 4 000, además el precio de venta de los mismos es 80x. Determinar la cantidad de artículos que deben venderse si se quiere lograr una ganancia de S/. 12 000
Answer:
800 artículos.
Step-by-step explanation:
Sea x = la cantidad de artículos vendidos
De la pregunta,
Precio de costo = 60 x + 4000
Venta (precio de venta) = 80x
También nos dieron ganancias como S12000
Para determinar la ganancia
Precio de venta: precio de costo = beneficio (cuando el precio de venta es más alto que el precio de costo)
Por lo tanto,
12,000 = 80x - (60x + 4000)
12,000 = 80x - 60x - 4000
Recolectando términos similares
12,000 + 4,000 = 80x - 60x
16,000 = 20x
x = 16,000 / 20
x = 800
Por lo tanto, la cantidad de artículos que se venderán si desea obtener una ganancia de S12,000 es de 800 artículos.
helppppppppp pleasee me give bralienst,stars and thanks
Answer:
(Going from left to right)
Box #1=3
Box #2=5
Box #3=7
Box #4=2
Step-by-step explanation:
For Box #4, there is nothing for the 2 to subtract from so it just goes down
For Box #3, it has to be 7, because nothing can be subtracted from 1 to get 3, so you would have to bring a 1 from the 4 to the left to make the 1 to a 10. 10-7=3
For Box #2 and 1, 3(we changed it in the last step) -9 = a negative number so we have to bring a 1 from the number to the left. This is a hard step but what you have to do it look at the bottom number, which is a 2, so that number had to be a 3 because 3-1=2. 4 becomes 14, and 14-9=5
Hope this helps, if it did, please consider giving me brainliest, it will help me a lot. If you have any questions, feel free to ask.
Have a good day! :)
help (6)(-1)(-3)(10)(-2)
Answer:
The answer is
- 360Step-by-step explanation:
(6)(-1)(-3)(10)(-2)
Multiply the terms in the bracket
That's
(6)(-1) = - 6
(-3)(10) = - 30
So we have
(-6)(-30)(-2)
= 180( - 2)
= - 360
Hope this helps you
11 ounces to 5 ounces
Answer: what is the question to this?
Step-by-step explanation: thanks let me know okay
Answer:
(11/5) (a ratio)
Step-by-step explanation:
11 ounces to 5 ounces could be rewritten as
11 oz.
---------- = (11/5) (a ratio)
5 oz
Fred has $26 to buy sketch paper for his art class. Each sketch pad costs $4.
How many sketch pads can he buy? Do not include units in your answer.
Answer:
6 pads
Step-by-step explanation:
Take the amount of money and divide by the cost per pad
26/4 = 6 with 1 dollar left over
He can buy 6 pads
Solve for X in the equation, where 4B = −2X − 2A
Answer:
X = [tex]\left[\begin{array}{ccc}2&-7&3\\13&0&2\end{array}\right][/tex]
Step-by-step explanation:
4B = -2X - 2A
Dividing both sides by -2
=> -2B = X + A
Subtracting A to both sides
=> X = -2B-A
Now, Let's Solve:
=> X = [tex]-2\left[\begin{array}{ccc}0&2&-2\\5&0&3\end{array}\right] -\left[\begin{array}{ccc}-2&3&1\\-3&0&4\end{array}\right][/tex]
=> X = [tex]\left[\begin{array}{ccc}-2*0&-2*2&-2*-2\\-2*5&-2*0&-2*3\end{array}\right] - \left[\begin{array}{ccc}-2&3&1\\-3&0&4\end{array}\right][/tex]
=> X = [tex]\left[\begin{array}{ccc}0&-4&4\\10&0&6\end{array}\right] - \left[\begin{array}{ccc}-2&3&1\\-3&0&4\end{array}\right][/tex]
=> X = [tex]\left[\begin{array}{ccc}0-(-2)&-4-3&4-1\\10-(-3)&0-0&6-4\end{array}\right][/tex]
=> X = [tex]\left[\begin{array}{ccc}2&-7&3\\13&0&2\end{array}\right][/tex]
What is the degree of the polynomial?
Answer: 3rd Degree
Step-by-step explanation:
Refer to the following wage breakdown for a garment factory:
Hourly Wages Number of employees
$4 up to $7 18
7 up to 10 36
10 up to 13 20
13 up to 16 6
What is the class interval for the preceding table of wages?
A. $4
B. $2
C. $5
D. $3
Answer:
The class interval is $3Step-by-step explanation:
The class interval is simply the difference between the lower or upper class boundary or limit of a class and the lower or upper class boundary or limit of the next class.
In this case for the class
$4 up to $7 18 and
$7 up to $10 36
The lower class boundary of the first class is $4 and the lower class boundary of the second class is $7
Hence the class interval = $7-$4= $3What is x when: |5x|=3
Answer:
3/5
Step-by-step explanation:
5x= 3
x= 3/5
hope you understand the answer
stay at home stay safe
keep rocking
pls mark me as BRAINLIEST
what is this one i cant seem to figure it out
Answer:
73
Step-by-step explanation:
Since DA is the diameter, this means that you can divide the circle into two half-circles. You will solve with the right half-circle. A half-circle has a 180 total degrees. Add up the values given and solve for x.
(2x) + (7x - 4) + (85) = 180
2x + 7x - 4 + 85 = 180
9x - 4 + 85 = 180
9x + 81 = 180
9x = 99
x = 11
Now that you have the value of x, solve for m∠CZB.
m∠CZB = 7x - 4
m∠CZB = 7(11) - 4
m∠CZB = 77 - 4
m∠CZB = 73
Imagine working in a freelance developer earning 80 USD per hour how many weeks you will have to take a 12 hour flight on a weekday you can either book a flight for ticket for 11 AM for 900 USD or 11 PM flight or 11 USD there is no Internet boards if you take the day off like you will lose a day of work what would you do
Answer:
pay the 11 AM ticket
Step-by-step explanation:
Note that the flight last for 12 hours, and assuming the freelance developer can still work (have access to the internet) on the airplane throughout the flight, he stand to earn $960 ($80*12), which will still cover the cost of the flight with a profit of $60 ($960-900).
However, if he decides to pay the $11 flight ticket and there is no Internet on boards; there by losing a day of work, he stand to have lost working time which would earn with $900.
Therefore, the best choice is to pay the 11 AM ticket.
Tabitha wants to hang a painting in a gallery. The painting and frame must have an area of 58 square feet. The painting is 7 feet wide by 8 feet long. Which quadratic equation can be used to determine the thickness of the frame, x? (5 points)
Answer:
4x² + 30x - 2 = 0
Step-by-step explanation:
Given:
Area = 58 square feet
Width = 7 feet
Length = 8 feet
Since the area is 58, writing the equation, we have:
(8 + 2x)(7 + 2x) = 58
Now expand the equation:
56 + 16x + 14x + 4x² = 58
56 + 30x + 4x² = 58
Collect like terms:
30x + 4x² + 56 - 58 = 0
30x + 4x² - 2 = 0
Rearrange the equation to a proper quadratic equation:
4x² + 30x - 2 = 0
The quadratic equation that can be used to determine the thickness of the frame, x is 4x² + 30x - 2 = 0
how many solutions does this linear system hacve y=2/3x+2 6x-4y=-10
Answer:
the linear system has two valid solution.
Answer:one solution
Step-by-step explanation:
In a random sample of 400 residents of Boston, 320 residents indicated that they voted for Obama in the last presidential election. Develop a 95% confidence interval estimate for the proportion of all Boston residents who voted for Obama.
Answer:
C.I = 0.7608 ≤ p ≤ 0.8392
Step-by-step explanation:
Given that:
Let consider a random sample n = 400 candidates where 320 residents indicated that they voted for Obama
probability [tex]\hat p = \dfrac{320}{400}[/tex]
= 0.8
Level of significance ∝ = 100 -95%
= 5%
= 0.05
The objective is to develop a 95% confidence interval estimate for the proportion of all Boston residents who voted for Obama.
The confidence internal can be computed as:
[tex]=\hat p \pm Z_{\alpha/2} \sqrt{\dfrac{ p(1-p)}{n } }[/tex]
where;
[tex]Z_{0.05/2}[/tex] = [tex]Z_{0.025}[/tex] = 1.960
SO;
[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.8(1-0.8)}{400 } }[/tex]
[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.8(0.2)}{400 } }[/tex]
[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.16}{400 } }[/tex]
[tex]=0.8 \pm 1.960 \sqrt{4 \times 10^{-4}}[/tex]
[tex]=0.8 \pm 1.960 \times 0.02}[/tex]
[tex]=0.8 \pm 0.0392[/tex]
= 0.8 - 0.0392 OR 0.8 + 0.0392
= 0.7608 OR 0.8392
Thus; C.I = 0.7608 ≤ p ≤ 0.8392
CAN ANYONE HELP ME PLEASE? Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $106. Two adults and three children must pay $75. Find the price of the adult's ticket and the price of a child's ticket.
Answer:
adult=18$ and children=13$
Step-by-step explanation:
a= adult. and. c= children
first change the statement into linear equation
3a+4c=106
2a+3c=75
then it just solving for a and y
3a+4c=106. a= 75-3c.
2
3(75-3c)+ 4c=106. solve for c
2
c=13
then find c by substituting the value you got into a . you can you either 3a+4c=106
or 2a+3c=75 to find the answer but the value of a is the same.
2a+3c=75. c=13
2a+3(13)=75
2a=75 -39
2a= 36
a=18
Answer:
Adults Ticket = $18
Child's Ticket = $13
Step-by-step explanation:
Let A denote the price of an adult's ticket
Let C denote the price of a child's ticket
It is given that the three adults and four children must pay $106.
Mathematically,
[tex]3A + 4C = 106 \:\:\:\:\:\:\:\:\:\:\: eq. 1[/tex]
It is also given that the two adults and three children must pay $75.
Mathematically,
[tex]2A + 3C = 75 \\\\2A = 75 - 3C[/tex]
[tex]$ A = \frac{(75 - 3C)}{2} \:\:\:\:\:\:\: eq\:. 2 $[/tex]
Substitute eq. 2 into eq. 1
[tex]3A + 4C = 106[/tex]
[tex]$ \frac{3(75 - 3C)}{2} + 4C = 106 $[/tex]
Simplify,
[tex]$ \frac{3(75 - 3C)}{2} + 4C = 106 $[/tex]
[tex]$ \frac{225 - 9C}{2} + 4C = 106 $[/tex]
[tex]$ \frac{225 - 9C + 2(4C)}{2} = 106 $[/tex]
[tex]$ \frac{225 - 9C + 8C}{2} = 106 $[/tex]
[tex]$ 225 - 9C + 8C = 2(106) $[/tex]
[tex]$ 225 - C = 212 $[/tex]
[tex]C = 225 - 212[/tex]
[tex]C = \$13[/tex]
Substitute the value of C into eq. 2
[tex]$ A = \frac{75 - 3(13)}{2} $[/tex]
[tex]$ A = \frac{75 - 39}{2} $[/tex]
[tex]A = \$18[/tex]
Therefore, the price of the adult's ticket is $18 and the price of a child's ticket is $13
A first number plus twice a second number is 14. Twice the first number plus the second totals 13. Find the numbers.
Answer: The first number is 4 and the second is 5
Step-by-step explanation:
Let's say the first number is x and the second is y:
x+2y=14
2x+y=13
I'll use the linear combination method to solve this.
2x+4y=28
- 2x+y=13
3y=15
y = 5
x = 4
Hope it helps <3
Answer:
y=1
x=12
Step-by-step explanation:
Let the first number be x
Let the first number be y
Given:
x+2y=14
2x+y=13
Substitution:
x=14-2y
Solution:
2x+y=13
14-2y+y=13
-2y+y=13-14
-y=-1
y=1
x=14-2y
x=14-2(1)
x=14-2
x=12
Proof:
1) x+2y=14
12+2(1)=14
12+2=14
14=14
Hope this helps ;) ❤❤❤
Let me know if there is an error in my answer
What is the rate of change of the function
The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.
Farmers Jay, Peter, and Sam own rectangular farms, as indicated in the figure. Jay owns 2 acres of land, Peter owns 4 acres and Sam owns 6 acres. Find the area of the common pasture. PLEASE HELP ASAP!
Answer:
Area of the common pasture = 12 acres
Step-by-step explanation:
Let the dimensions of the farm owned by Jay are 'a' units and 'b' units.
Area of the farm = ab = 2 acres
Similarly, areas of the farm owned by Peter with dimensions 'a' unit and 'c' unit = ac = 4 acres
And area of the farm owned by Sam with dimensions 'b' and 'd' units = bd = 6 acres
Now, [tex]\frac{ab}{ac}=\frac{2}{4}[/tex]
[tex]\frac{b}{c}=\frac{1}{2}[/tex] ---------(1)
[tex]\frac{ab}{bd}=\frac{2}{6}[/tex]
[tex]\frac{a}{d}=\frac{1}{3}[/tex] ---------(2)
[tex]\frac{b}{c}\times \frac{a}{d}=\frac{1}{2}\times \frac{1}{3}[/tex]
[tex]\frac{ab}{cd}=\frac{1}{6}[/tex]
cd = 6(ab)
cd = 6 × 2 [Since ab = 2 acres]
= 12 acres
Therefore, area of the common pasture will be 12 acres.