A dairy farmer wants to mix a 80% protein supplement and a standard 55% protein ration to make 1400 pounds of a high-grade 60% protein ration. How many pounds of each should he use?

Answers

Answer 1

If the dairy farmer wants to mix a 80% protein. The amount of pounds of each that he should use is 80% 280 pounds and 55% 1120 pounds.

How to find the number of pounds?

Protein I 80% = x pounds

Protein II 55% = 1400 - x pounds

Mixture 60% = 1400

Hence,

80% x + 55% ( 1400 - x ) = 60% × 1400

80 x + 55 ( 1400 - x ) = 84000

80 x + 77000 - 55 x = 84000

Combine like terms

80 x - 55 x = 84000 - -77000

25 x = 7000

Divide both side by 25x

x= 7000/25

x =280 pounds ( Protein I)

Protein II

1400 - x pounds

1400 -280

=  1120 pounds

Therefore the farmer should use 280 pounds and 1120 pounds.

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Related Questions

Question content area top
Part 1
Find an equation for the line with the given properties. Express your answer using either the general form or the​ slope-intercept form of the equation of a line.
Perpendicular to the line y=
1
2x−2​; containing the point ​(−3​,6​)

Answers

The equation of the line  in slope-intercept form is y = -x/12 + 23/4

How to find the equation of the line?

Given that: the line is perpendicular to the line y= 12x−2 and it contains the (−3,6).

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system

The slope-intercept form of a straight line is:

y = mx + c,

where m is the slope and c is the y-intercept

When the two lines are perpendicular, the product of their slope is -1 i.e.

m₁ x m₂ = -1

where m₁ and m₂ represent the slope of the lines

Let the slope of the given line be m₁ and the slope of the unknown line be m₂

Line1(given):

y = 12x−2   and m₁ x m₂ = 12

m₁ x m₂ = -1

12 x m₂ = -1

m₂= -1/12

Line 2(unknown) with the point (−3,6):

y = mx + c

6 = -1/12 (-3) + c

6 = 1/4 + c

c = 6 -1/4 = 23/4

y = -x/12 + 23/4

Therefore, the slope-intercept form of the equation of the line is y = -x/12 + 23/4

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accounts recivable of 88000 and accounts payable of 39000 and has revenues of 121000 and expenses of 83000 what is the companies net income

Answers

The required net income of the companies is given as 49,000.

Given that,
Accounts receivable of 88000 and accounts payable of 39000 and have revenues of 121000 and expenses of 83000 what is the company's net income is to be determined.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Total income = 88000 + 121000 = 209000
Total outflow = 39000 + 83000 = 122000
Net income = 209000 - 122000 = 49000

Thus, the required net income of the companies is given as 49,000.

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Ken spends $344.76 before tax at a hardware store. If the sales tax rate in his city is 7.5%, what is the total cost of his purchase? Round to the nearest cent if necessary.

Answers

Answer:

$370.62

Step-by-step explanation:

Ken spends $344.76 before tax at a hardware store. If the sales tax rate in his city is 7.5%, what is the total cost of his purchase? Round to the nearest cent if necessary.

7.5% = 0.075

0.075 * $344.76  = $25.857 in tax so:

cost + tax

$344.76 + $25.857 = $370.617

rounded:  $370.62

Work out the values of a, b, c and d.
Justify each of your answers.

Answers

In the given circle, the values of required angles are as follow:

a = 51°, b = 28° , c = 31°, and d = 70°.

As given in the question,

In the given circle,

As we know by theorem , angles formed in the same arc are congruent.

Angle a° and angle 51° is formed in the same arc XY .

Value of a = 51°

Angle b° and angle 28° is formed in the same arc ZY .

⇒ Value of b = 28°

Angle c° and angle 31° is formed in the same arc WX .

⇒ Value of c = 31°

Angle d° and angle 70° is formed in the same arc WZ .

⇒ Value of d = 70°

Therefore, in the given circle the values of required angles are as follow:  a = 51°, b = 28° , c = 31°, and d = 70°.

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find zeros f(x)=x^4-6x^3-21x^2=150x-100 given k=5

Answers

The zeros of the polynomial x⁴ - 6x³ - 21x² - 150x - 100  are 0.6511 and 8.262 respectively

Zeros of a Polynomial

Zeros of polynomial are the points where the polynomial equals zero on the whole. In simple words, we can say that zeros of polynomial are values of the variable such that the polynomial equals 0 at that point. Zeros of a polynomial are also referred to as the roots of the equation and are often designated as α, β, γ respectively.

The zeros of a polynomial f(x) are the values of x which satisfy the equation f(x) = 0. Here f(x) is a function of x, and the zeros of the polynomial are the values of x for which the f(x) value is equal to zero. The number of zeros of a polynomial depends on the degree of the equation f(x) = 0. All such domain values of the function, for which the range is equal to zero, are called the zeros of the polynomial.

To find the zeros of this polynomial function, we have to write the function appropriately.

x⁴ - 6x³ - 21x² = 150x - 100

x⁴ - 6x³ - 21x² - 150x - 100 = 0

The roots of this function is 0.6511 and 8.262 respectively

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Graph the following features:
Y-intercept=1
Slope- -2/3

Answers

The graph with the y-intercept of 1 and a slope of -2/3 is added as an attachment

What are linear equations?

Linear equations are equations whose slopes are constant average rates of change.

How to graph the equation of the line?

The given parameters are

y-intercept, c = 1Slope, m = -2/3

A linear equation is represented as

y = slope * x + y-intercept i.e. y = mx + c

Substitute the known values in the above equation

So, we have the following equation

y = -2/3x + 1

Hence. the linear equation is y = -2/3x + 1

See attachment for the graph

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0°F; drops 15° new temperature

Answers

The new temperature is -15 degrees

Mrs B invested $30,000, part at 5%, part at 8%. The total interest on the investment was $2100, how much did she invest at each rate?

(Please show working)

Answers

Answer:

$10,000 invested at 5%

$20,000 invested at 8%

Step-by-step explanation:

1. Let x = the amount of money invested at 5%, and y = the amount of money invested at 8%.

   x + y = 30,000 (the total amount invested)

   0.05x + 0.08y = 2,100 (the total interest earned)

2. Solve the system by whatever method you choose.

Which rule describes the transformation

Answers

R₀, 270° is the rule that describes the transformation

How to determine the rule that describes the transformation?

Rotation simply means turning. In a cartesian plane, if a point P, whose position vector is (x,y), is rotated through θ° about the origin, the position of the image P' is

a. (-y, x) for θ = 90°

b. (-x, -y) for θ = 180°

c. (y, -x) for θ = 270°

Given the: Triangle RST with vertices R(2, 0), S(4, 0), and T(1, -3). And the image of triangle RST after a rotation has vertices R'(0, -2). S'(0, -4), and T(-3, -1)

From the given vertices it is obvious that the relation between preimage and image is defined as

(x, y) => (y, -x)

Therefore, the rule that describes the transformation is (y, -x) for θ = 270° (i.e. when the figure rotates 270° counterclockwise). So the third option (R₀, 270° ) is the answer.

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A system consists of three identical components. In order for the system to perform as intended, all of the components must perform. Each has the same probability of performance. If the system is to have a .92 probability of performing, what is the minimum probability of performing needed by each of the individual components? Round your answer to three decimal places.

Answers

If each has the same probability of performance. If the system is to have a .92 probability of performing, The minimum probability of performing needed by each of the individual components is: 0.97126.

How to determine the probability:

Given data:

Number of identical component = 3

Probability of performing = .92

Now let determine the probability

Probability =  0.92 ^(1/3)

Probability = 0.92^0.3333

Probability =.9726

Therefore the probability is .9726.

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Graph the polygon with the given vertices and its image after a reflection in the line y=x.
A(2, -1), B(-1, 2), C(2, 3), D(4,2)

Answers

In the given picture the polygon ABCD is the formed polygon (in red color) and the reflection of the polygon is A'B'C'D' (in green color).

Graphing the polygon and reflection in a graph:

A polygon is a 2 - dimensional shape, that is formed by three or more straight edges. To graph, a polygon, plot the given points on the plane and connect the vertices using straight lines, without crossing any lines.

Reflecting image in the line y = x

To reflect the image in the line y = x, switch the values of x to y and y to x. After switching the points, join the formed points and draw the reflected image.

Here we have

A(2, -1),  B(-1, 2),  C(2, 3),  D(4,2)

After switching the values of x to y and y to x the resultant points are

A'(-1, 2),  B'(2, -1),  C'(3, 2),  D'(2,4)

In the given picture the polygon ABCD is the formed polygon (in red color) and the reflection of the polygon is A'B'C'D' (in green color).

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Use Structure A shoe store buys packs of socks wholesale for $5 each and marks them up by 40%. The store decides to discount the packs of socks by 40%. Is the discounted price $5?



Multiple choice question.
cross out

A)
yes; The packs of socks are marked up to $7 and then discounted to $5.

cross out

B)
yes; The packs of socks are marked up to $9 and then discounted to $5.

cross out

C)
no; The packs of socks are marked up to $7 and then discounted to $4.20.

cross out

D)
no; The packs of socks are marked up to $5.20 and then discounted to $4.99.

Answers

The correct option regarding the price is C. no; The packs of socks are marked up to $7 and then discounted to $4.20.

How to calculate the price?

In this situation, a shoe store buys packs of socks wholesale for $5 each and marks them up by 40%. The price will be:

= Original price + Markup

= 5 + (40% × 5)

= 5 + 2

= $7

Then, the store decides to discount the packs of socks by 40%. This will give a price of:

= 7 - (40% × 7)

= 7 - 2.8

= $4.2

The price isn't discounted to $5.

In conclusion, the correct option is C.

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Sam is driving on the highway. He begins the trip with 12 gallons of gas in his car. The car uses up one gallon of gas every 35 miles.
Let G represent the number of gallons of gas he has left in his tank, and let D represent the total distance (in miles) he has
traveled. Write an equation relating G to D, and then graph your equation using the axes below.

Answers

equation and graph attached

the side length of a square is √8 find the area.
is the number rational or irrational?

Answers

The area of a square with a side length √8 represents a rational number, which is equal to 8 square units.

Is the number behind the area of the square a rational number?

Rational numbers are real numbers of the form m / n, where m and n are integers, where n ≠ 0. The rest of real numbers are irrational (i.e. π, √5, ∛7, e) Besides, the area of the square is determined by the following formula:

A = l²

Where l is the side length of the square.

First, substitute the side length of the square in the area formula:

A = (√8)²

Second, use algebraic properties to simplify the expression and find the corresponding result:

A = ([tex]8^{\frac{1}{2} }[/tex])²

A = 8

This number represents a rational number as 8 is equivalent to the rational number 8 / 1.

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If you cut a sheet of paper in half, stack one piece on top of the other, cut those in half, stack all the pieces together, repeating this process 20 times, how high will the stack of paper be?

Answers

The stack of paper will have the height of 1048576 papers

How to determine how high the stack of paper will be?

The first cut will produce 2 papers, the second cut will produce 4 papers, the third cut will produce 8 papers and the fourth cut will produce 16 papers.

If you examine the stages of cut and the number of papers, the relationship between them is:

1st cut: number of papers = 2¹ = 2  

2nd cut: number of papers = 2² = 4

3rd cut: number of papers = 2³  = 8

4th cut: number of papers = 2⁴  = 16

nth cut: number of papers = 2ⁿ

So if the  process is repeated 20 times, the number of papers will be:

Number of paper = 2²⁰ = 1048576

Therefore, the stack of paper will be as high as 1048576 papers

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Degree 5; zeros: 7, -i, 3+i; let a represent the leading coefficient

Answers

Therefore the required polynomial is [tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]

What is an leading coefficient?

The numbers placed in front of the variable with the biggest exponent are known as leading coefficients. They can be whole numbers, fractions, or decimals, as well as positive, negative, real, or imaginary, just like conventional coefficients.

According to fundamental theorem of algebra , if a + bi be a zero of a polynomial with real coefficients then a-bi is also a zero

Now given that f(x) be a polynomial with degree 5 and with zeros -7,-i,-3+i

and f(x) be a polynomial with real coefficients.

therefore by fundamental theorem of algebra

+i and -3-i are also zeros of f(x)

so zeros of f(x) are 7, -i, -3 + i, i, -3 -i

Degree is 5, so there is at most 5 zeros therefore the required polynomial will be

f(x) = a(x + 7)(x + i )(x - i)(x +3- i)(x +3 +i)

= a[(x +7)(x² + 1)(x² +6x + 10)]

[tex]= a\left[x^5+ 13x^4 + 53x^3 +83x^2 + 52x + 70]\right[/tex]

[tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]

Therefore the required polynomial is [tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]

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Your office window is a 45 feet high. Looking out your window, you find that the top of a statue lines up exactly with the bottom of a building that is b = 600 horizontal feet
from your office. You know that the statue is c= 125 feet from the building. How tall is the statue? (See the figure below. Round your answer to two decimal places.)

Answers

The height of the statue that exactly with the bottom of a building is approximately 9.3926 feet tall.

height of the office window , a = 45 feet

the bottom of a building that is horizontal  from the office, b = 600 feet

let x represent the angle

tan(x) = a/b

tan(x) = 45/600

x = tan⁻¹(0.75)

x = 4.28 degree

the height of the statue, h  = ?

the statue is from the building, c = 125 feet

tan(45/600) = h/125

h = tan(0.075) x 125

h = 9.3926 feet

The height of the statue that exactly with the bottom of a building is approximately 9.3926 feet tall.

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How will the mode be affected if the outlier is removed from the data set below? 58, 60, 53, 54, 60, 35, 58, 60

will the mode decrease?

will the mode not change?

is there not enough information?

will the mode increase?​

Answers

The mode will not change.

Given data,

58,60,53,54,60,35,58,60

Outlier is the value in a set of data that much higher or lower than other values in data.

from given data, outlier is 35.

Mode is the value in a set of data that occurs more frequently in set of data.

from given data, 60 occurs more frequently.

Hence, 60 is the mode of data.

If outlier is removed from the data set then it will not affect the mode of the data

Thus, the mode will not change.

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. x^4 – 2x^3 – 7x^2 + 8x + 12 = 0

Answers

The Required Factors   (x + 1) (x - 3 ) (x + 2) (x - 2).

Given equation.
x^4 - 2x^3 - 7x^2+8x+12 = 0

Factors : factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

polynomial : an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable

Now, factorize the polynomial of degree 4 as follows.

= (x + 1) (x - 3) (x^2 - 4)

Then, again factorize polynomial of degree 2.

Therefore  (x + 1) (x - 3 ) (x + 2) (x - 2)

This is the required factors.

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3. Analyze and Persevere The height of
an experimental plant after x days can be
represented by the formula 3(4x + 2) The
height of a second plant can be represented
by the formula 6(2x + 2). Is it possible that
the two plants will ever be the same height?
Explain.
their pr
Р
$1

Answers

Two plants will never be of the same height.

Given, the height of an experimental plant after x days can be

represented by the formula 3(4x + 2).

The height of a second plant can be represented by the formula 6(2x + 2).

We have to state that will the two plants ever be of the same height,

Let assume that, the height of two plants be same,

So, 3(4x + 2) = 6(2x + 12)

On simplifying, we get

12x + 6 = 12x + 72

On subtracting 12x from both the sides, we get

12x + 6 - 12x = 12x + 72 - 12x

6 ≠ 72

It is an absurd condition, so we do not have any solution for x.

So, the two plants will never be of the same height.

Hence, two plants will never be of the same height.

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Solve the absolute value equation (3x-6)=12.
O a
Ob
Oc
Od
x=6,x=2

x=-6, x=-2
x=6₂x=-2
x=-6₂x=2

Answers

The solution of the absolute value equation |3x - 6| = 12 is x= 6 and x = -2

The absolute value equation is

|3x - 6| = 12

We can write the absolute value equation in two ways

3x - 6 = 12

-(3x - 6) = 12

We have to solve each equation

The first equation is 3x - 6 = 12

3x - 6 = 12

3x = 12+6

3x = 18

x = 18/3

x = 6

The second equation is -(3x - 6) = 12

Apply the distributive property

-3x + 6 = 12

-3x = 12 - 6

-3x = 6

x = 6/-3

x = -2

Hence, the solution of the absolute value equation |3x - 6| = 12 is x= 6 and x = -2

The complete question is:

Solve the absolute value equation |3x - 6| = 12 .

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Lightest weight
750g
0.7kg
7.5kg
705g
7.05kg

Answers

Answer:

.7 kg

Step-by-step explanation:

1. Convert answers in grams into kilograms

1000g = 1 kg

750g = .75kg

705g = .705 kg

2. Find smallest number of kg

= .7 kg

SOMEONE HELP ME.


A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building. What are the dimensions of this rectangular room in the actual building.

Answers

The dimension of the rectangular room in the actual building are 55 feet by 30 feet.

How to find the dimension of the rectangular room in the actual building?

Scale is used to represent the relationship between a measurement on a model and the corresponding measurement on the actual object.

A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building.

The dimensions of this rectangular room in the actual building can be found as follows:

let's find the length of the actual room

1 inches = 10 feet

3 inches  = ?

cross multiply

length = 30 ft

Let's find the width of the room

1 inches = 10 feet

5.5 inches  = ?

cross multiply

width = 55 ft

Therefore, the width and length of the room are 55 feet and 30 ft respectively.

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-3x + 6 = 4 - 6x

I kept getting 1.5 But it's not correct. ???

Answers

Answer:

-2/3 or -0.6666

Step-by-step explanation:

-3x + 6 = 4 -6x

Let's move the x to one side

-3x +6x=4-6

Combine like terms

3x = -2

Divide both sides by 3

-2/3=x

or -0.666666

Please help me with these thank you

Answers

The value of (2/3) ÷ (1/4) is 8/3 and the value of 7 ÷ (2/3) is 21/2.

This is a question from the division of fractions.

We know the property of fractions is given by:-

(m/n) ÷ (a/b) = (m/n)*(b/a) = mb/na

Hence, we can write,

(2/3) ÷ (1/4) = (2/3) * (4/1) = 2*4/3*1 = 8/3

7 ÷ (2/3) = (7/1)*(3/2) = 7*3/ 1*2 = 21/2

Fractions

A fraction represents a part of a whole or, more generally, any number of equal parts. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals.

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Evaluate the expression when m = -3.
2
m² -7m+6

Answers

Answer:

36

Step-by-step explanation:

substitute m = - 3 into the expression

m² - 7m + 6

= (- 3)² - 7(- 3) + 6

= 9 + 21 + 6

= 36

Desmond made a scale drawing of a house. The garage is 4 centimeters wide in the drawing. The actual garage is 5 meters wide. What is the scale factor of the drawing?

Simplify your answer and write it as a fraction.

Answers

The scale factor of the drawing that Desmond is illustrating is is 1/125.

What is a scale factor?

A scale factor is the ratio between rte scale of a particular object and the new object.

In this case, Desmond made a scale drawing of a house, the garage is 4 centimeters wide in the drawing and the actual garage is 5 meters wide.

100 centimeters = 1 meters

5 meters = 500 centimeters

Therefore, the scale will be:

= 4 / 500

= 1 / 125

= 1:125

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Start Fraction w superscript 12 baseline over w superscript 18 baseline End Fraction
A. w30
B. w–30
C. w6
D. w–6

Answers

Answer:

answer should be d

Step-by-step explanation:

it's d because if u fraction 6 u will get d


Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $25 and same-day tickets cost $15. For one performance, there were 55 tickets sold in all, and the total amount paid for them was $1025. How many tickets of each type were sold?

Answers

Answer:

advance: 20same-day: 35

Step-by-step explanation:

You have tickets that sell for $25 and $15, and you sold 55 tickets for $1025. You want to know the number of each sold.

Setup

Let 'a' represent the number of advance tickets sold. Then 55-a is the number of same-day tickets sold. The total revenue is ...

  25a +15(55 -a) = 1025

Solution

  10a + 825 = 1025 . . . . . simplify

  10a = 200 . . . . . . . . . . subtract 825

  a = 20 . . . . . . . . . . . divide by 10; the number of advance tickets

  55 -20 = 35 . . . . the number of same-day tickets

20 advance tickets and 35 same-day tickets were sold.

Can a normal approximation be used for a sampling distribution of sample means from a population with μ=52 and σ=9, when n=49?

Answers

Answer: Yes

Step-by-step explanation:It can because math works like that.

Other Questions
Can someone pls give me the answer to this??? #25 In a paragraph of 3-5 sentences, explain the causes and effects of American expansion during the late 1800s and early 1900s including how U.S foreign policy affected foreign relations during the early 1900s a 1.92 kg object on a frictionless horizontal track is attached to the end of a horizontal spring whose force constant is 4.77 n/m. the object is displaced 5.31 m to the right from its equilibrium position and then released, which initiates simple harmonic motion. what is the magnitude of the force acting on the object 3.72 s after it is released? answer in units of n. 5/3=?x1/3help please ASAP Which precedent was established by the Supreme Court's ruling in McCullochv. Maryland?A. The federal government has supremacy over the stategovernments.B. The citizens have the power to question their government and itsrepresentatives.C. The regulation of trade and the establishment of tariffs falls withinthe scope of the judicial branch.D. The Supreme Court has the power of judicial review and candetermine the constitutionality of laws. 3b(2x-z^3)=2h-7gx change the subject to x The crucible Playwright Arthur Miller said of the film: "One of the most persuasive moments of the film is when you see that ropetighten around Proctor's neck. That is a message." What message do you think is shown through this moment?Why do you think it was included in the film? Pls help Joshua borrowed $1,000 on January 1, 2021, and paid it all back at once on December 31, 2021. What was the APR? Juan always saves 30% of all his earnings. Last month he saved $141. How much did he earn last month? Schools A and B are competing in an academic contest. At the beginning of the final round, School A has 174 points and School B has 102 points. In the final round, correct answers earn 10 points and incorrect answers lose 6 points. School A gives the same number of correct and incorrect answers during the final round. School B gives no incorrect answers and the same number of correct answers as School A. The contest ends with a tie. Answer parts a and b. when moemoea sees her psychology professor in the grocery store, she does not immediately recognize her professor. based on perceptual principles, what is the most likely explanation for this lack of immediate recognition? what is superhero gloves molsty about. Add the detail to the chart IREADY Which of these is an independent variable? (Select all that apply)CO concentrationLight intensityPrepared plantAmount of liquid addedExperimental apparatusRun TimeO Produced bird bones have air pockets in them to reduce their weight. this also gives them an average density significantly less than that of the bones of other animals. suppose an ornithologist weighs a bird bone in air and in water and finds its mass is 45.0 g and its apparent mass when submerged is 3.60 g (the bone is watertight). what mass of water is displaced?mass of water displaced:kg what is the volume of the bone?volume of the bone:m3 what is its average density?average density of the bone:kg/m3 question credit: openstax college physics a company borrowed $28,000 by signing a 180-day promissory note at 6%. the total to be paid at maturity of the note is: ______Cannot control heat loss from the body you respond to the residence of a 55-year-old woman with a possible allergic reaction to peanuts that she ate approximately 30 minutes ago. the patient is conscious and alert, but has diffuse urticaria and the feeling that she has a lump in her throat. as your partner applies oxygen to the patient, you should: Pass journal entries using the perpetual system of inventory- Purchased 1000 units of shoes from Indiana International at $300 each on account Sold 200 units to Ceridian Corporation at $500 each on account Sold 500 units to Semed Inc. at 550 each on cash Paid cash in full to Indiana International Purchased 800 units of shoes from CITS at $450 each on cash Sold 100 units to Deeman Corp at $600 each on cash why does meitosis is called reduction division a short story includes a character who accomplishes amazing and, at times, unexpected, feats. in one paragraph, the character is described as a modern-day hercules. hercules was a greek hero who achieves twelve seemingly impossible tasks. what type of allusion does the author include