The first 4-terms of sequence {aₙ} defined by recurrence-relation : aₙ₊₁ = 2aₙ²-1; a₁ = 0 are 0, -1, 1 and 1.
To find the first four terms of the sequence {aₙ} defined by the recurrence relation aₙ₊₁ = 2aₙ² - 1, with the initial-condition a₁ = 0, we apply the recurrence relation,
Starting with a₁ = 0, we can find the subsequent terms as follows:
⇒ a₂ = 2a₁² - 1 = 2(0)² - 1 = -1
⇒ a₃ = 2a₂² - 1 = 2(-1)² - 1 = 1
⇒ a₄ = 2a₃² - 1 = 2(1)² - 1 = 1
Therefore, the first four terms of the sequence are : a₁ = 0, a₂ = -1, a₃ = 1
and a₄ = 1.
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The given question is incomplete, the complete question is
Write the first four terms of the sequence {aₙ} defined by the following recurrence relation.
aₙ₊₁ = 2aₙ²-1; a₁ = 0.
Can someone please explain how to do this i am so confused i just want to pass this class please :(
Answer:
x=6√3
Step-by-step explanation:
In 30-60-90 triangles, if the hypotenuse is x, the longest leg is [tex]\frac{x}{2}[/tex], and the shortest leg is [tex]\frac{x\sqrt{3} }{2}[/tex].
If the longest leg is 6, then [tex]\frac{x}{2} =6[/tex]
Multiply by 2,
[tex]x=12[/tex]
If x=12,
[tex]\frac{12\sqrt{3} }{2}[/tex]
[tex]=6\sqrt{3}[/tex]
So, the shortest leg is 6√3.
PLEASE NEED HELP!!!
The wheel of a bicycle has a diameter of 54 inches. How far does the bicycle travel when the wheel completes 20 revolutions?
The following side lengths make a triangle: 5, 8, and 13.
True
False
Pls help me ‼️‼️‼️‼️
Answer:
no
Step-by-step explanation:
the first two numbers is not greater than 13 so no
What is the value of 24/25 divided by 4/5
Answer:
1.2
Hope it helps :)
[tex]\frac{24}{25}*\frac{5}{4}\\\\\\=\frac{6}{5}[/tex]
"Express the finite abelian groups tais
(a) Z36 x Z48 x Z60
(b) Z8 x Z9 x X Z11 X Z12
The finite abelian group Z36 x Z48 x Z60 can be expressed as Z2^6 x Z3^4 x Z5. The finite abelian group Z8 x Z9 x Z11 x Z12 can be expressed as Z2^3 x Z3^2 x Z11 x Z2^2 x Z3.
(a) The finite abelian group Z36 x Z48 x Z60 can be expressed as the direct product of its prime power factorizations. The prime factorization of 36 is 2^2 * 3^2, 48 is 2^4 * 3, and 60 is 2^2 * 3 * 5. Therefore, the group can be written as Z2^6 x Z3^4 x Z5.
(b) The finite abelian group Z8 x Z9 x Z11 x Z12 can be expressed as the direct product of its prime power factorizations. The prime factorization of 8 is 2^3, 9 is 3^2, 11 is a prime number, and 12 is 2^2 * 3. Therefore, the group can be written as Z2^3 x Z3^2 x Z11 x Z2^2 x Z3.
In both cases, the group is expressed as the direct product of cyclic groups of prime power orders. The order of the group is the product of the orders of the individual cyclic groups, and the structure of the group is determined by the prime factors and their powers.
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(q15) A supply of soaps available at different prices is given by the supply curve
, where x is the product quantity. If the selling price is $250, find the producer surplus.
The producer surplus at a price of $250 based on the supply curve, s(x) = 180 + 0.3·[tex]x^{\frac{3}{2} }[/tex] is about $1,326.5
What is a supply curve?The supply curve is the graphical representation of the price of a good or service and the quantity that manufacturers are willing to supply or provide.
The function for the supply curve is; s(x) = 180 + 0.3·[tex]x^{\frac{3}{2} }[/tex]
When the selling price is $250, the quantity of the product supplied can be found from the equation; s(x) = 250 = 180 + 0.3·[tex]x^{\frac{3}{2} }[/tex]
0.3·[tex]x^{\frac{3}{2} }[/tex] = 250 - 180 = 70
[tex]x^{\frac{3}{2} }[/tex] = 70/0.3 = 700/3
x = (700/3)[tex]\frac{2}{3}[/tex] ≈ 37.9
The quantity of soap supplied when the price is $250, is therefore, about 37.9
The producer surplus can be calculated from the area of a trapezoid formula as follows;
A = (b₁ + b₂) × h/2
Where the length of the bases are; b₁ ≈ 37.9, b₂ = 0, and the height, h = (250 - 180) = 70
A = (37.9 + 0) × 70/2 = 1326.5
Therefore, at a selling price of $250, the producer surplus is about $1,326.5
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A bag contains colored tiles. • 3 tiles are red • 6 tiles are green • 3 tiles are blue A tile will be randomly selected from the bag. What is the probability in decimal form that the tile selected will be green? A bag contains colored tiles. • 3 tiles are red • 6 tiles are green • 3 tiles are blue A tile will be randomly selected from the bag. What is the probability in decimal form that the tile selected will be green?
Consider the function f(3) = 1/cose. Estimate the condition number for the problem of evaluating this function near the point 1.5708. Calculate the input and output relative errors whe
The condition number for the problem of evaluating the function f(x) = 1/cos(x) near the point x = 1.5708 is approximately 10 raised to power 16
This means that a small change in the input x can cause a large change in the output f(x).
The condition number of a function is a measure of how sensitive the function is to changes in its input. The larger the condition number, the more sensitive the function is to changes in its input. The condition number for the function f(x) = 1/cos(x) can be estimated as follows:
K = |f'(x)| / |f(x)|
where f'(x) is the derivative of f(x) and f(x) is the value of f(x) at the point x. At the point x = 1.5708, f'(x) = -1 and f(x) = 0.017453292519943295. Therefore, the condition number is approximately:
K = |-1| / |0.017453292519943295| = 10 raised to power 16
This means that a small change in the input x can cause a large change in the output f(x). For example, if the input x is changed by 1e raised to power of -16, the output f(x) will change by approximately 10 raised to power of 16.
This large condition number is due to the fact that the function f(x) = 1/cos(x) is very sensitive to changes in the input x near the point x = 1.5708. This is because the cosine function is very close to zero at this point.
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Which polynomial has (3x + 2) as a binomial factor?
6x3 + 3x2 + 4x + 2
12x2 + 15x + 8x + 10
18x3 – 12x2 + 9x – 6
21x4 + 7x3 + 6x + 2
Answer:
its option B : 18x3 – 12x2 + 9x – 6
Step-by-step explanation:
[tex]12( \frac{ -2 }{3}) {}^{2} +23( \frac{ - 2}{3} )+10= \frac{16}{3} − \frac{46}{3} +10=0[/tex]
12x² + 15x + 8x + 10 has a binomial factor of (3x+2).
What is a Quadratic equation?ax²+bx+c=0, with a not equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
We may utilize the factor theorem, which asserts that if a polynomial f(x) has a component (x - a), then f(a) = 0, to identify which polynomial has (3x + 2) as a binomial factor.
In this situation, finding a value of x that reduces 3x + 2 to zero is necessary since we are trying to discover a polynomial that contains (3x + 2) as a component. We obtain x = -2/3 by solving 3x + 2 = 0.
Let's try the polynomials one by one:
(a) 6x³ + 3x² + 4x + 2:
f(-2/3) = 6(-2/3)³ + 3(-2/3)² + 4(-2/3) + 2
= -8/3 - 4/9 - 8/3 + 2
= -32/9,
so (3x + 2) is not a factor.
(b) 12x² + 15x + 8x + 10:
f(-2/3) = 12(-2/3)₂ + 15(-2/3) + 8(-2/3) + 10
= 16/3 - 10 - 16/3 + 10
= 0,
so (3x + 2) is a factor.
(c) 18x³ - 12x² + 9x - 6:
f(-2/3) = 18(-2/3)³ - 12(-2/3)² + 9(-2/3) - 6
= -32/3 + 8/3 - 6 - 6
= -32/3,
so (3x + 2) is not a factor.
(d) 21x⁴ + 7x³ + 6x + 2:
f(-2/3) = 21(-2/3)⁴ + 7(-2/3)³ + 6(-2/3) + 2
= 64/27 - 56/27 - 4 + 2
= 2/27,
so (3x + 2) is not a factor.
Therefore, the only polynomial that has (3x + 2) as a binomial factor is 12x² + 15x + 8x + 10.
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23. The coordinates when the point (-4, 2) is reflected about the y-axis are: (a) (-2,4) (c) (4,2) (b) (4, -2) (d) (-4,-2) 24. The annual precipitation for one city is normally distributed with a mean
the coordinates of the reflected point are (4, 2).
When a point is reflected about the y-axis, the x-coordinate is negated while the y-coordinate remains the same.
The original point is (-4, 2). If we reflect this point about the y-axis, the x-coordinate becomes positive, and the y-coordinate remains unchanged.
Negating the x-coordinate, we get:
x-coordinate: -(-4) = 4
y-coordinate: 2 (unchanged)
Given the point (-4, 2), reflecting it about the y-axis would result in the x-coordinate changing its sign while the y-coordinate remains unchanged.
Therefore, the coordinates of the reflected point are (4, 2).
Among the options provided, the correct answer is (c) (4, 2).
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A large jar contains 500 marbles. All of the marbles in the jar are either blue or yellow, and there are 3 times as many blue marbles as yellow marbles. Which equation can be solved to find the number of yellow marbles in the jar?
Answer:
The equation to solve to find the number of yellow marbles =
3y + y = 500
4y = 500
The number of yellow marbles = 125
Step-by-step explanation:
Let the number of
Blue marbles = x
Yellow marbles = y
A large jar contains 500 marbles.
x + y = 500
All of the marbles in the jar are either blue or yellow, and there are 3 times as many blue marbles as yellow marbles.
3y = x
Hence, we substitute 3y for ymx in the above equation
3y + y = 500
4y = 500
y = 500/4
y = 125
The number of yellow marbles = 125
NO LINKS!! NO ONE WANT TO HELP ME PLEASE IM WASTING ALL MY POINTS PLSSS HELPPPP :((( Which of the following equations describe the line shown below? Check all
that apply MULTI CHOICE MORE THAN OND
(1,6) (-3,-6)
Answer:
Option E
Step-by-step explanation:
The two points are (1,6) and (-3,-6) . We can find the Equation of the line using two point form , as ,
[tex]\implies y - y_1 =\dfrac{y_2-y_1}{x_2-x_1}(x - x_1) \\\\\implies y - 6 = \dfrac{-6-6}{-3-1}(x-1) \\\\\implies y-6 = \dfrac{-12}{-4}(x-1) \\\\\implies \boxed{\boxed{y -6 = 3(x-1)}} [/tex]
On looking at options we see that option E is correct .
Hence the correct option is E.Please please help please please ASAP
a general solution of the differential equation x′(t)=ax is given by x(t)=c1x1(t) c2x2(t), where a matrix A = [0 -1; 1 0]?
The general solution of the differential equation x'(t) = Ax(t), where A is the matrix [0 -1; 1 0], is x(t) = [(c₁² - c₂² + 2ic₁c₂)[tex]e^{(it)[/tex] + (2c₁c₂ - c₁² + c₂²)[tex]e^{(it)[/tex]][1, i].
To solve the differential equation x'(t) = Ax(t), where A is the given matrix [0 -1; 1 0], we can use the method of finding the eigenvalues and eigenvectors.
Step 1: Find the eigenvalues λ of the matrix A by solving the characteristic equation |A - λI| = 0.
The characteristic equation for A is:
|0-λ -1| = 0
|1 0-λ|
Expanding the determinant gives:
(-λ)(-λ) - (-1)(1) = 0
λ² + 1 = 0
Solving the equation, we get two eigenvalues: λ₁ = i and λ₂ = -i.
Step 2: Find the eigenvectors corresponding to each eigenvalue.
For λ₁ = i:
(A - λ₁I)u₁ = 0
|0- i -1| |x₁| = |0|
|1 0- i| |x₂| |0|
Simplifying the equation gives:
-ix₁ - x₂ = 0
x₁ - ix₂ = 0
Solving this system of equations, we get the eigenvector u₁ = [1, i].
For λ₂ = -i:
(A - λ₂I)u₂ = 0
|0+i -1| |x₁| = |0|
|1 0+i| |x₂| |0|
Simplifying the equation gives:
ix₁ - x₂ = 0
x₁ + ix₂ = 0
Solving this system of equations, we get the eigenvector u₂ = [1, -i].
Step 3: Write the general solution as x(t) = c₁x₁(t) + c₂x₂(t), where c₁ and c₂ are constants.
The general solution to the differential equation x'(t) = Ax(t) is:
x(t) = c₁[1, i][tex]e^{(i\lambda_1 t)[/tex] + c₂[1, -i][tex]e^{(i\lambda_2 t)[/tex]
= c₁[1, i][tex]e^{(it)[/tex] + c₂[1, -i][tex]e^{(it)[/tex]
Expanding and simplifying the solution:
x₁(t) = c₁[tex]e^{(it)[/tex] + c₂[tex]e^{(it)[/tex]
x₂(t) = ic₁[tex]e^{(it)[/tex] - ic₂[tex]e^{(it)[/tex]
Therefore, the general solution is:
x(t) = c₁[c₁[tex]e^{(it)[/tex] + c₂[tex]e^{(it)[/tex]][1, i] + c₂[ic₁[tex]e^{(it)[/tex] - ic₂[tex]e^{(it)[/tex]][1, -i]
= (c₁c₁[tex]e^{(it)[/tex] + c₁c₂[tex]e^{(it)[/tex] + ic₁c₁[tex]e^{(it)[/tex] - ic₁c₂[tex]e^{(it)[/tex])[1, i] + (ic₁c₁[tex]e^{(it)[/tex] - ic₁c₂[tex]e^{(it)[/tex] - c₂c₁[tex]e^{(it)[/tex] - c₂c₂[tex]e^{(it)[/tex])[1, -i]
= [(c₁² - c₂² + 2ic₁c₂)[tex]e^{(it)[/tex] + (2c₁c₂ - c₁² + c₂²)[tex]e^{(it)[/tex]][1, i]
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The question is -
What's the general solution (c1x1(t) +c2x2(t)) of a differential equation x'(t) = Ax(t) with a matrix A = [0 -1; 1 0]?
SOMEONE PLEASE HELP ME!
Answer:
A
Step-by-step explanation
Please help me on #5. Both parts of possible please. Thank you for helping!
Answer:
5) No
The actual distance between the drone and the fossil is [tex]32\dfrac{3}{4}[/tex] ft
Step-by-step explanation:
3) A. -2/9
(2/3 - 5/6)/3/4 = (-1/6)/(3/4) = (-1/6) × (4/3) = -2/9
4) d. [tex]0.\overline {90}[/tex]
10/11 = 0.9090909...
∴ 10/11 = [tex]0.\overline {90}[/tex]
5) The height of the drone is flying above the ground = [tex]25\dfrac{1}{2}[/tex] ft.
The location of the fossil below the ground = [tex]7\dfrac{1}{4}[/tex] ft.
Taking the ground level as the origin on a number line, we have;
The location of the drone relative to the ground = + [tex]25\dfrac{1}{2}[/tex] ft. (The positive sign for a point above the origin)
The location of the fossil relative to the ground = [tex]-7\dfrac{1}{4}[/tex] ft. (The negative sign for a point below the origin)
Therefore;
The distance between the drone and the fossil = The difference between the location of the drone and the fossil
The distance between the drone and the fossil = [tex]25\dfrac{1}{2} - \left(-7\dfrac{1}{4} \right)[/tex]
[tex]25\dfrac{1}{2} - \left(-7\dfrac{1}{4} \right) = 25\dfrac{1}{2} + 7\dfrac{1}{4} = 32\dfrac{3}{4}[/tex]
The distance between the drone and the fossil = [tex]32\dfrac{3}{4}[/tex] ft.
Therefore;
The distance between the drone and the fossil > 32 ft.
CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM. I HAVE TO SOLVE FOR A AND B
Answer:
b is 10 degrees and a is 64 degrees.
Step-by-step explanation:
Properties of a parallelogram needed for this problem: Opposite angles are congruent and adjacent angles are supplementary, meaning they add to 180 degrees.
This means that in the picture, 2a and 12b+8 are equal, while 2a and 5b+2 are supplementary.
From this we can make two equations:
2a=12b+8
and
2a+5b+2=180
If we subtract 5b+2 in the second equation, both equations will equal 2a. I'll explain why that's good. We end up with:
2a=12b+8
and
2a=180-5b-2
Now, we can set the two equations equal to each other because they both equal the same thing. Then simplify.
12b+8=180-5b-2
17b=170
b=10
Knowing b is 10 degrees, we can easily plug that back into one of our original two equations. I'll choose 2a=12b+8.
2a=12(10)+8
2a=120+8
2a=128
a=64
b is 10 degrees and a is 64 degrees.
What is the answer when you simplify it?[tex]7^{2} +2(\sqrt{81} +\sqrt{49} )[/tex]
2. Quadrilateral ABCD was dilated with the origin as the center of dilation to create quadrilateral A'B'C'D. Which rule best represents the dilation that was applied to quadrilateral ABCD to create quadrilateral A'B'C'D ?
Answer:
[tex](x,y) => (2.5x,2.5y)[/tex]
Step-by-step explanation:
Given
See attachment for ABCD and A'B'C'D'
Required
Determine the dilation rule
Using AB and A'B' as points of references;
[tex]AB = (-1,2)\ to\ (2,1)[/tex]
[tex]A'B' = (-2.5,5)\ to\ (5,2.5)[/tex]
The dilation factor (k) is calculated as:
[tex]k = \frac{A'B'}{AB}[/tex]
This gives:
[tex]k = \frac{(-2.5,5)}{(-1,2)} \ or\ k = \frac{(5,2.5)}{(2,1)}[/tex]
Factorize
[tex]k = \frac{2.5*(-1,2)}{(-1,2)} \ or\ k = \frac{2.5*(2,1)}{(2,1)}[/tex]
[tex]k = 2.5 \ or\ k = 2.5[/tex]
Hence, the scale factor is 2.5
The dilation rule is:
[tex](x,y) => k(x,y)[/tex]
[tex](x,y) => 2.5(x,y)[/tex]
[tex](x,y) => (2.5x,2.5y)[/tex]
Can someone plz help me on this its due in 30 mins.
Answer:
A, C, and F
Step-by-step explanation:
Marianne and Roger are in good health and have reasonably secure careers. Each earns $45,000 annually. They own a home with a $125,000 mortgage; they owe $25,000 for their car loans and have $22,000 in student loans. If one should die, they think that funeral expenses would be $12,000. What is their total insurance need using the DINK method? O $86,000 O $12,000 O $217,000 O $98,000 O $172,000
Using the DINK method (Dual Income, No Kids), the total insurance need for Marianne and Roger is $172,000.
The DINK method calculates the insurance need based on the financial obligations and potential future expenses of a couple with dual incomes and no children. To determine their total insurance need, we consider their outstanding debts and potential expenses in case of death.
The calculations are as follows:
Mortgage: $125,000 (outstanding debt)
Car loans: $25,000 (outstanding debt)
Student loans: $22,000 (outstanding debt)
Funeral expenses: $12,000
The total outstanding debt and funeral expenses amount to $184,000.
However, the DINK method suggests subtracting the couple's annual incomes from the total insurance need since they have secure careers and can continue to generate income even in the event of the death of one spouse.
Both Marianne and Roger earn $45,000 annually, so we subtract $45,000 from the total, resulting in a total insurance need of $139,000.
Therefore, the correct answer is $172,000.
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Marcus goes to the park, which is 4 miles away. He walks 512 of the way and then jogs the rest of the way.
How many miles does he walk? Use the number line to help you.
Answer:
516 miles
Step-by-step explanation:
PLSSS HELP IMMEDIATELY!!!! i’ll mark brainiest if u don’t leave a link!
Answer:
A
Step-by-step explanation:
Answer: I would say it's B
Step-by-step explanation: The reason is because whiskers are primary to have, Sharp claws is a tool for animals to get food, and large beaks are used to pick at the food so they don't eat the wrong things.
What is the equation represented by the table above?
A y = 8x
B y = x + 7
C y = 5x + 3
Dy = 3x + 5
Answer:
C: y = 5x + 3
Step-by-step explanation:
Note that if x changes from 1 to 3 (the "run"), y changes from 8 to 14 (the "rise"). Thus the slope of the line represented by the table is m = rise/run = 6/2, or m = 3. Answer choice D is the only one that displays a slope of 3.
Answer:
Answer is D
Step-by-step explanation:
A. 14=8(3), 14≠24
B. 14=3+7 , 14≠10
C. 14=5(3)+3, 14≠18
D.14=3(3)+5, 14=9+5 14=14
Which expression is equivalent to 2 (3x – 4)?
ОА) 3х - 4
O B) 5x - 6
Ос) 6x - 4
OD) 6x – 8
What is the volume of a sphere with a radius of 12 units?
A. 1447 units
B. 230410 units
C. 5767 units
D. 17287 units
Answer:
7238 units^3
Step-by-step explanation:
The formula for the volume of a sphere of radius 12 units is
V = (4/3)(pi)r^3.
Here, with r = 12 units,
V = (4/3)(pi)(12 units)^3 = 7238 units^3
Answer:
V = 2304π units³
Step-by-step explanation:
V = (4/3)πr^3
V = (4/3)π(12)^3
V = (4/3)π(1728)
V = 2304π units³
Which expression is equivalent to the series
shown?
125
Σ 45η
n=17
Answer:
its c ^u^ and the next to it is b :D
Step-by-step explanation:
edg 21
Answer:
It’s c and the next one is b
Step-by-step explanation:
Just took edge
A buyer for a grocery chain inspects large truckloads of apples to determine the proportion p of apples in the shipment that are rotten. Unless there is clear evidence that this proportion is less than 0.06, she will reject the shipment. To reach a decision she will test the hypotheses
 ,  . To do so, she selects an SRS of fifty apples from the over 20000 apples on the truck.
Suppose that only two of the apples sampled are found to have major defects, and she proceeds with the test. The P-value of her test is
Answer:
P value = 0.23527 which is greater than 0.10
Step-by-step explanation:
Given :
Phat = proportion of rotten apple = 2/50 = 0.04
1 - phat = 0.96
p = 0.06
Tstatistic = (Phat - p) / sqrt[(Phat(1-Phat))/n]
Tstatistic = (0.04 - 0.06)/sqrt[(0.04(0.96))/50]
Tstatistic = (-0.02) / 0.0277128
Tstatistic = - 0.7216
Pvalue of Tstatistic
P(Z < - 0.7216) = 0.23527 (Pvalue calculator)
What is the value of y?
2y°
y +10°
50°
A. 400
B. 60°
C. 500
D. 30°
Answer:
a part
Step-by-step explanation:
Attachment added....
Hope it helps :)
The following recipe is for 16 crepes: • 1/4 cup margarine, 3 tbs sugar, 1/2 cup orange juice, • 1 tbs grated orange rind, and 1/2 cup toasted almonds. You need to serve 5 crepes per person for 8 guests. How much of each ingredient is needed?
You need 5/2 times the amounts given in the recipe, so you need:
5/8 cup margarine 15/2 tbs sugar 5/4 cup orange juice 5/2 tbs grated orange rind5/4 cup toasted almonds.How much of each ingredient is needed?Here we have the recipe for 16 crepes:
1/4 cup margarine 3 tbs sugar1/2 cup orange juice 1 tbs grated orange rind1/2 cup toasted almonds.You want to make 5 crepes for person, for 8 persons, so you need:
8*5 = 40 crepes.
So you need to make the recipe N times:
16*N = 40
N = 40/16 = 10/4 = 5/2
So you need a fraction of 5/2 times each of the amounts in the recipes.
You will need:
(5/2)*1/4 = 5/8 cup margarine (5/2)*3 = 15/2 tbs sugar(5/2)*1/2 = 5/4 cup orange juice 5/2 tbs grated orange rind(5/2)*1/2 = 5/4 cup toasted almonds.Learn more about fractions at:
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