Answer:
[tex]slope=-\frac{1}{3}[/tex]
Step-by-step explanation:
Use the slope formula for two points:
[tex]\frac{y(2)-y(1)}{x(2)-x(1)}=\frac{rise}{run}[/tex]
Insert values
[tex]\frac{-12-(-10)}{11-5}[/tex]
Simplify
[tex]\frac{-12+10}{11-5} \\\\\\\frac{-2}{6} \\\\-\frac{2}{6}[/tex]
Simplify
[tex]-\frac{1}{3}[/tex]
The slope of the linear equation will be negative 1/3.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The points are given below.
(5, -10) and (11,−12)
The equation of the line that passes through (5, -10) and (11,−12) will be given as,
(y + 10) = [(-12 + 10) / (11 - 5)](x - 5)
y + 10 = - (1/3)x + 5/3
y = -(1/3)x + 5/3 - 10
y = -(1/3)x - 25/3
The slope of the linear equation will be negative 1/3.
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Rewrite the equation by completing the square 4x^2 +28x +49=0
The equation 4x^2 + 28x + 49 = 0 is already a perfect square trinomial, and when rewritten in completed square form, it is (x + 7/2)^2 = 0, resulting in the solution x = -7/2.
To rewrite the equation by completing the square for the given quadratic equation 4x^2 + 28x + 49 = 0, we must manipulate the equation so that the left side becomes a perfect square trinomial.
Steps to Complete the Square
Divide all terms by the coefficient of x^2, which is 4 in this case, to make the coefficient of the x^2 term equal to 1.
You now have x^2 + 7x + (49/4) = 0.
Find a number that, when added to x^2 + 7x, completes the square. This number is (b/2)
2, where b is the coefficient of x; thus, here it is (7/2)^2 = 49/4.
Since 49/4 is already present, it confirms that the equation is already a perfect square trinomial.
Therefore, you can rewrite the equation as (x + 7/2)^2 = 0.
Finally, solve for x by taking the square root on both sides of the equation and subtracting 7/2 from both sides to get x = -7/2.
The equation 4x^2 + 28x + 49 = 0 is rewritten in completed square form as (x + 7/2)^2 = 0, with the solution x = -7/2.
In how many ways can a quality-
control engineer select a sample
of 3 transistors for testing from a
batch of 100 transistors?
Answer:161700
Step-by-step explanation:
The number of ways for a quality-control engineer to select a sample of 3 transistors for testing from a batch of 100 transistors will be 161700.
What is combination?Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.
The number of ways for a quality-control engineer to select a sample of 3 transistors for testing from a batch of 100 transistors will be
¹⁰⁰C₃ = (100!) / [(100 – 3)! × 3!]
¹⁰⁰C₃ = (100 × 99 × 98 × 97!) / (97! × 3 × 2)
¹⁰⁰C₃ = 50 × 33 × 98
¹⁰⁰C₃ = 161700
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11: Jack is 10 years old.
Kylie is 17 years old.
Vanessa is 23 years old.
Kylie and Vanessa share £16 in the ratio of their ages.
Kylie gives 20% of her share to Jack.
Vanessa gives a quarter of her share to Jack.
How much money does Jack receive?
Answer:
£3.66
Step-by-step explanation:
17+23=40
40=16 what about 17
16×17=272÷40=£6.8
16-6.8=£9.2
20% of £6.8 = £1.36
1/4 of £9.2 = £2.3
1.36+2.3=£3.66
if 6th term of an ap is -10 and 10 th term is -26 then find thr 15 term plzzzzzzzzzzzzzzzzzzzzzzz answer i will give whatever you want
Answer:
-46
Step-by-step explanation:
We need to find the common difference of this arithmetic sequence:
[tex]\frac{-26-(-10)}{10-6} =\frac{-16}{4} =-4[/tex]
So, the common difference d = -4. We can now write the equation:
[tex]a_n=a_1+d(n-1)[/tex]
[tex]a_{15}=a_6+d(15-6)=-10-4(9)=-10-36=-46[/tex]
So, the 15th term is -46.
Hope this helps!
Step-by-step explanation:
the answer and explanation is in the picture
please rate and mark as brainliest
please help Use elimination to solve each system of equations.
2x + 5y = 3
-x + 3y = -7
Q)David bed is 9 inches longer than his desk His desk is 66 inches long .
How long is David bed ?
-------inches.
Answer:75 inches
Step-by-step explanation: 9+66=75
=75 inches
Answer:
75 inches
Step-by-step explanation:
66+9=75
The price of a bracelet was decreased by 30% to £63.
What was the price before the decrease?
Answer:
90
Step-by-step explanation:
If the original price of a bracelet was a
70%a = 63
70/100a = 63
a = 63 × 100/70
a = 90
The price before the decrease is 90 euros.
What is decrease?The amount of decrease is the original amount minus the final amount. For example if you are looking for the percent of decrease from 9 to 6, the original amount is 9 and the final amount is 6.
GIVEN
Based on the given conditions, write z= 63/(1-0.3)
Calculate the sum or difference = 63/0.7
Divide a fraction by multiplying its reciprocal:[tex]=63*10/7 =90[/tex]
Hence, The price before the decrease is 90 euros.
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Sandra save 13% of her salary for retirement. This year her salary was $2000 more than in the previous year, and she saved $5590. What was her salary in the previous year?
Answer:
Sandra's salary the previous year was $41,000
Step-by-step explanation:
Please check the files attached for more explanation
Final answer:
By setting up an equation where 0.13 times Sandra's previous year's salary plus $2000 equals her savings of $5590, we solve to find that Sandra's previous year's salary was $41,000.
Explanation:
To solve the problem of finding Sandra's salary from the previous year, we need to use the information given about her savings and current year's salary increase. Since Sandra saved 13% of her salary and we know that the total amount saved this year is $5590, we can set up the following equation where S represents her salary from the previous year:
0.13(S + 2000) = 5590
Now we solve the equation:
Divide both sides of the equation by 0.13 to isolate S + 2000 on one side:
(S + 2000) = 5590 / 0.13
S + 2000 = 43000
Now subtract 2000 from each side to solve for S:
S = 43000 - 2000
S = 41000
Therefore, Sandra’s salary in the previous year was $41,000.
Using the circle below, if I double the radius in length, what affect does that have on the new circumference?
Answer:
it will also double the circumference
Step-by-step explanation:
c = 2πr
r' = 2r
c' = 2πr' = 2π x 2r = 4πr
How can you make the number 25 using 3,6,8 and 9.
Each number has to be used and can only be used once
6 ÷ 3 × 8 + 9
6÷3=2
2×8=16
16+9=25
If the área of a right is 6.22sq. In. And its base is 3.11 in. Write an equation that relates the área to the height, h, and the base. Solve the equation to determine the height.
In the given question one word is missing, the correct question is,
If the área of a right triangle is 6.22sq. In. And its base is 3.11 in. Write an equation that relates the área to the height, h, and the base. Solve the equation to determine the height.
The equation that relates the area(A) to the height (h) and the base(b) is [tex]Area = \frac{1}{2} bh[/tex]. Height of right trinagle is 4 inches.
Step-by-step explanation:
The given is,
Area of right triangle, A = 6.22 square inches
Its base is 3.11 inches
Step:1
Formula for area of right angle triangle is,
[tex]A = \frac{1}{2} bh[/tex]......................................(1)
Where, b - Base
h - Height
Equation (1), that relates the área (A) to the height (h) and the base (b).
Step: 2
From the given values,
Base, b = 3.11 inches
Area, A = 6.22 square inches
Equation (1) becomes,
6.22 = [tex]\frac{1}{2} (3.11)(h)[/tex]
(6.22) (2) = (3.11) (h)
12.44 = (3.11) (h)
[tex]h = \frac{12.44}{3.11}[/tex]
= 4
Height, h = 4 inches
Result:
The equation that relates the area(A) to the height (h) and the base(b) is [tex]Area = \frac{1}{2} bh[/tex]. Height of right trinagle is 4 inches.
An engineer designs a satellite dish with a parabolic cross-section. The dish is 15 ft. wide at the opening and the depth is 4 feet. Find the position of the light source (the focus). How far is it from the deepest part of the dish?
The position of the light source(the focus) is at; (0, 3.516).
The distance from the position of light source to the deepest part of dish is; 3.516 ft.
We know that standard form of a parabola equation is;
x² = 4ay
Now, we are told the dish is 15 ft wide and the depth is 4ft.
This means that the edge of the parabolic cross section will have an x-coordinate of 15/2 = 7.5 ft
While the y-coordinate is the depth of 4ft.
Thus;
Since;
x² = 4ay
Plugging in 7.5 ft for x and 4 ft for y gives;
7.5² = 4a(4)
a = 7.5²/16
a = 3.516 ft
Thus, position of the light source which is the focus is; (0, 3.516)
And distance from the position of light source to the deepest part of dish = 3.516 ft.
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The position of the light source (the focus) in a satellite dish with a parabolic shape, with a 15 ft diameter opening and depth of 4 ft, is calculated using the formula for the focal length of a parabola. Plugging these values into the formula results in the finding that the focus is 14.0625 ft away from the base of the dish.
Explanation:The parabola can be described by the equation y = x2/4f, where f is the distance of the focus from the vertex. In a practical situation, to determine the position of the light source (the focus) in a satellite dish, which has a parabolic shape, we need to know the dish's width and depth. Here, the dish is 15 ft wide at the opening (which is the diameter of the dish) and the depth is 4 ft.
So, we can use these dimensions to calculate the position of the focus. First, we need to recall that in a parabola, the focus lies at the point (0, p), where p is the focal length. The focal length (p) of a parabolic dish can be calculated using the formula p = D2/16h, where D is the diameter of the dish and h is the depth of the dish. In this case, D = 15 ft and h = 4 ft.
Putting these values in the formula, we get p = (152)/16(4) = 14.0625ft. Therefore, the light source (focus) is placed 14.0625 ft away from the base of the dish.
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Elinor determined that a triangle with side lengths 6, 10, and 8 does not form a right triangle.
62 + 102 = 82
36 + 100 = 64
136 ≠ 64
Is her answer correct?
Answer
No, she should have added 62 and 82 and compared that to 102.
Answer:
The correct answer is C) No, she should have added 62 and 82 and compared that to 102.
Step-by-step explanation:
Her answer is incorrect because she did not follow the steps correctly, she should have added the two numbers. Good luck!
ооо
Choose the expression that shows the correct product for
Answer:
√36
Step-by-step explanation:
√(a·b) = √a·√b, so
√3·√12 = √(3·12) = √36 = 6
Answer:
√36
Step-by-step explanation:
√3*√12 = √36 = 6
This matches the second answer choice.
24-(-6) what the answer
Answer:
30
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
when you subtract a negative, you are basically adding the number.
*2 negatives equal a positive*
24 (- -) 6 = 30
combine negatives:
24 + 6 = 30
Sophia factored 81y^6 as (9y^3)(9y^2) Ahmed factored 81y^6 as (3y^6)(27y) Which of them factored 81y^6 correctly?
To find if either of them are correct just multiply each of them:
(9y^3)(9y^2)= (9)(9)(y^3)(y^2)
=81y^5
Sophia is incorrect.
(3y^6)(27y)=(3)(27)(y^6)(y)
=81y^7
Ahmed isn't correct either!
Both the persons Sophia and Ahmed do not factor in the expression correctly.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
It is given that, Sophia factored 81y⁶ as (9y³)(9y²) and Ahmed factored 81y⁶ as (3y⁶)(27y).
We have to find the correct factored form,
= (9y³)(9y²)
The expression is to be arranged in order to find the understand the property of exponent as,
=(9×9)(y³.y²)
=(81)(y³⁺²)
=81y⁵
Thus, both the persons Sophia nor Ahmed do not factor in the expression correctly.
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The Kamp family has twins, Rob and Rachel. Both Rob and Rachel graduated from college 2 years ago, and each is now earning $50,000 per year. Rob is an engineer. The mean salary for engineers with less than 5 years’ experience is $60,000 with a standard deviation of $5,000. Rachel works in the retail industry, where the mean salary for executives with less than 5 years’ experience is $35,000 with a standard deviation of $8,000.
Answer:
$38,000 is correct
Step-by-step explanation:
just took it
The z value is 1.875.
To compare Rob's salary as an engineer to the mean salary for engineers with less than 5 years of experience, we need to find the z-score of Rob's salary.
The z-score formula is
z = (x - μ) / σ,
where x is the given value,
μ is the mean, and
σ is the standard deviation.
Plugging in the values, we get z = (50,000 - 60,000) / 5,000 = -2.
For Rachel's salary as an executive in the retail industry, we use the same process.
The z-score formula is z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation.
Plugging in the values, we get z = (50,000 - 35,000) / 8,000 = 1.875.
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Please help me with this
Step-by-step explanation:
Putting values of c and r
4 + 4(10) - 3(10 - 3)
4 + 40 - 3(7)
44 - 21
23
How can you find f(2) if f(x)=−3x2−7?
Step-by-step explanation:
F(2)=3(2)²-7
=5
................
Answer:
Square 2. Multiply the result by -3, and then subtract 7.
Step-by-step explanation:
The answer is basically the explanation of the answer. You want to replace x with 2 then square it. You will have 4. Multiply 4 by -3 and you will have -12 then subtract it by 7 and you'll get the answer to f(x). The answer is the steps. Not the 'answer' answer. Hope this helps! (I did this question, and I got it right.)
Kim made 4 batches of this fruit punch recipe. Combine: 90 milliliters of strawberry juice 300 milliliters of pineapple juice 3 liters of apple juice How many liters of fruit punch did Kim make?
Answer:
13.56
Step-by-step explanation:
Each batch makes a total of ...
0.090 +0.300 +3 = 3.39 . . . liters
Then 4 batches makes ...
4 × 3.39 L = 13.56 L
Kim made 13.56 liters of punch.
Final answer:
Kim made a total of 13.56 liters of fruit punch by making 4 batches, with each batch including a combination of strawberry, pineapple, and apple juices.
Explanation:
Kim made 4 batches of fruit punch, each containing 90 milliliters of strawberry juice, 300 milliliters of pineapple juice, and 3 liters of apple juice.
To find the total amount of fruit punch made, we first convert all quantities to liters and then sum them up. Since there are 1,000 milliliters in 1 liter, 90 milliliters is equal to 0.09 liters and 300 milliliters is equal to 0.3 liters.
For one batch, the total liters of juice is:
Strawberry juice: 0.09 litersPineapple juice: 0.3 litersApple juice: 3 litersSo for one batch, the total is 0.09 + 0.3 + 3 = 3.39 liters.
Since Kim made 4 batches, the total amount of fruit punch is:
4 batches × 3.39 liters per batch = 13.56 liters
Therefore, Kim made 13.56 liters of fruit punch in total.
You roll a 6-sided die.
What is P(less than 6)?
Answer:
21
Step-by-step explanation:
0i s
If a 6-sided die is rolled then P(less than 6) is [tex]\frac{5}{6}[/tex]
What is probability?Probability refers to the chance of occurring of an event.Probability is always ≤ 1How to calculate probability ?Probability can be found by dividing the favourable cases by the total possible cases.
How to find P(less than 6)?P(less than 6) means the probability of getting a number which is less then 6 after the die is rolled.When a die is rolled each outcome has the probability of [tex]\frac{1}{6}[/tex]We know that if a die is rolled, the possible outcomes are {1,2,3,4,5,6}
Here, we should consider the outcomes {1,2,3,4,5}. These are favourable outcomes.To get the probability of getting a number which is less then 6 after the die is rolled, we can add the probabilities of each outcome.
∴ Probability of getting a number which is less then 6 = ( [tex]\frac{1}{6}[/tex] + [tex]\frac{1}{6}[/tex] + [tex]\frac{1}{6}[/tex] + [tex]\frac{1}{6}[/tex] + [tex]\frac{1}{6}[/tex])
= [tex]\frac{5}{6}[/tex]
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What is the area of the following circle?
Either enter an exact answer in terms of
π
πpi or use
3.14
3.143, point, 14 for
π
πpi and enter your answer as a decimal.
To solve the problem we will first calculate the radius of the circle and substitute the value in the formula of the area of a circle.
Area of the circleArea of the circle [tex]=\pi r^2[/tex]
The area of the circle is 49π or 153.86 unit².
Given to usDiameter, d = 14π = 3.14SolutionRadius of the circleRadius,
[tex]\rm{ r = \dfrac{Diameter}{2} = \dfrac{d}{2}=\dfrac{14}{2} =7[/tex]
Thus, the radius of the circle is 7.
Area of the circleArea of the circle [tex]=\pi r^2[/tex]
[tex]=\pi\times (7)^2\\ = 49\pi[/tex]
Substituting the value of π = 3.14,
Area of the circle [tex]=49\pi\\ = 49 \times 3.14\\ = 153.86[/tex]
Hence, the area of the circle is 49π or 153.86 unit².
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The area of the circle is approximately 4.5m².
Explanation:The formula to find the area of a circle is A = πr², where π is approximately 3.14 and r is the radius. In this case, we have a radius of 1.2m. Using a calculator with an eight-digit output, we can calculate A = 3.14 x (1.2m)² = 4.5238934m².
However, since the radius only has two significant figures, we need to limit the calculated quantity to two significant figures. So, the area of the circle is approximately 4.5m² (rounded to two significant figures).
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work
18.) The temperature in Chicago is -11.8°F. The temperature in New York is 8.3°F. How much
warmer is it in New York than in Chicago? Show your work
"A firefighter stood on the middle rung of a ladder. When the smoke became less thick, the firefighter moved up 4 rungs. Then it got too hot, and the firefighter moved down 6 rungs. Later, the firefighter went up 7 rungs and stayed there till the fire was out. After the fire was out, the firefighter climbed the remaining 4 rungs and entered the building. How many rungs does the ladder have?"
Answer:
There are 18 rungs on the ladder.
Step-by-step explanation:
Given a firefighter who is standing on the middle of the ladder.
We have to find the number of rungs the ladder have.
Let the number of rungs be "2x" where "x" be the number of rungs from the middle of the ladder to the top of the ladder.
Rungs below the middle of the ladder is equal to rungs above the middle of the ladder.
According to the question:
Let the fire fighter be at "y" rungs this "y" will be the reference point.
⇒ Moved [tex]4[/tex] rungs from 'y' current position [tex]4[/tex] rungs above of 'y'.
⇒ Moved [tex]6[/tex] rungs down meaning that [tex](4-6)= -2[/tex] rung from 'y' below [tex]2[/tex] rung downward from 'y'.
⇒ Moved [tex]7[/tex] rungs upward from here meaning [tex](-2+7) = 5[/tex] rung above 'y'.
Now,
⇒ Further the firefighter climbed [tex]4[/tex] rungs from here [tex](5+4) = 9[/tex] rungs above 'y' .
Finally the firefighter have climbed [tex]9[/tex] rungs from 'y' that is the middle of the ladder so there is equal rungs below of it.
Total rungs of the ladder = '2x' = 2(9) = 18 rungs.
Carlos walked 16 of 20 of school days in February what is the value that is equivalent to the fraction of school days in February that Carlos walked to school . Math
Answer:
70%
Step-by-step explanation:
14 divided by 20
Answer:
6
Step-by-step explanation:
The price of a watch was increased by 10% to £660. What was the price before the increase?
Answer:
£600
Step-by-step explanation:
First take if 110% equals to £660 what about 100%
100×660 =66000 ÷ 110 =£600
The original price of the watch, before the 10% increase, was £600.
Explanation:The price of a watch was increased by 10% to £660, and we are asked to find the price before the increase. We can solve this problem by considering that the increased price is 110% of the original price. To calculate the original price, let's set up the equation:
660 = 1.10 * Original Price
To solve for the Original Price, we divide 660 by 1.10:
Original Price = £660 / 1.10
This gives us the original price of the watch which is £600.
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what is 11/12 of a full rotation
Answer:
Turn-0.9166666666666666
Degree-330.00000000081860208
Final answer:
11/12 of a full rotation equates to 330 degrees or approximately 2.91 radians.
Explanation:
11/12 of a full rotation in a mathematical context refers to completing 11 out of 12 equal parts of a circle. Since a circle has 360 degrees, we can calculate this portion of a rotation by finding 11/12 of 360 degrees, which is 330 degrees. In terms of radians, since a full rotation is 2π radians, the same portion in radians would be 11/12 of 2π radians, which is approximately 2.91 radians.
please hellllllllppppppppppppppppppppppppppp
Answer:
[tex]21^{10}[/tex]
Step-by-step explanation:
First, multiply the 3 and the 7 together, and then "multiply" the exponents -8 and 3. (However, when "multiplying exponents, you're really just adding them together: -8 + 5)
([tex]21^{-5}[/tex])^2
Then, multiply the -5 and -2 together, giving you:
[tex]21^{10}[/tex]
Image: ( A regular hexagon has an apothem of 4 and a side length of
8√3 /3 Its area is:_____)
Answer
A) 16√3 sq units
B) 48√3 sq units
C) 64√sq units
D) 32√3 sq units
Answer:
D: 32[tex]\sqrt{3}[/tex]
Step-by-step explanation:
8/3[tex]\sqrt{3}[/tex] * 1/2 * 4 = 16[tex]\sqrt{3}[/tex]/3
16[tex]\sqrt{3}[/tex]/3 * 6 = 32[tex]\sqrt{3}[/tex]
You manage a health food store and budget $80 to buy ingredients to make 30 pounds of trail mix. Peanuts cost $2.50 per pound, raisins cost $2.00 per pound, and granola costs $4.00 per pound. If you use twice as many pounds of peanuts as raisins, how many pounds of each ingredients should you buy?
Answer:
8 pounds of raisin, 6 pounds of granola and 16 pounds of peanuts
Step-by-step explanation:
Lets form equations first.
->Peanuts cost $2.50 per pound, raisins cost $2.00 per pound, granola costs $4.00 per pound
2.50p + 2.00r + 4.00g= 80 -->eq(1)
-> bought ingredients to make 30 pounds of trail mix
p+ r+ g= 30 -->eq(2)
->If you use twice as many pounds of peanuts as raisins
2r=p
eq(1)=> 2.50p + 2.00r + 4.00g= 80
2.5(2r) + 2r +4g =80
5r + 2r + 4g =80
7r + 4g =80
eq(2)=>
2r+ r+ g= 30
3r + g =30
-4(3r + g =30)
7r + 4g =80
_______________
-5r = -40
r= 40/5 =>8
For 'g':
3(8) + g =30
g= 6
For 'p':
2r=p
p=16
therefore, 8 pounds of raisin, 6 pounds of granola and 16 pounds of peanuts should be bought
The solution to the problem is to buy 20 pounds of peanuts, 4 pounds of raisins and 6 pounds of granola.
Explanation:This problem requires the use of algebra. Let's denote the amount of peanuts as x, the amount of raisins as y and the amount of granola as z. We have certain constraints according to the problem that need to be satisfied. These are:
2*y = x (since the amount of peanuts is twice that of raisins)x + y + z = 30 (total weight should equal 30 pounds)2.5x + 2y + 4z = 80 (total price should not exceed $80)First, substitute x = 2y from the first equation into the other two equations. This gives you the new equations y + z = 10 and 9y + 4z = 80. Next, solve these simultaneous equations. The solutions are y = 4, z = 6. Substituting y into the first equation gives us x = 2*4 = 20. So, you should buy 20 pounds of peanuts, 4 pounds of raisins and 6 pounds of granola.
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