Answers
Answer:
12 possible roots
Step-by-step explanation:
we can use the rational zeros theorem which says that in order to find the possible roots for a polynomial we need to divide the factors of the constant by the factors of the coefficient of the leading term
which in this case is:
±(1, 2, 3, 4, 6, 12)/(1)
±1, 2, 3, 4, 6, 12
so we have 12 possible roots
Related Questions
use a double- or half-angle formula to solve the equation in the interval [0, 2). (enter your answers as a comma-separated list.) tan 2 − sin() = 0
Answers
The solutions of the equation `tan(2x)-sin(x)=0` in the interval `[0, 2)` are:`x = 2πk ± 2arctan(√[(3+√5)/2]) ± 2arcsin(√[(1-cos(x))/2])` where `k` is an integer and `cos(x) = 1-2sin²(x/2)`
Given, `tan(2x)-sin(x)=0`.We can use the half-angle formula to solve this equation in the interval `[0, 2)` and obtain the solutions. The half-angle formula for tangent is: `tan(θ/2)= sin(θ)/(1+cos(θ))`The half-angle formula for sine is: `sin(θ/2)=±√[(1-cos(θ))/2]`Using the half-angle formula for tangent:`tan(2x)-sin(x)=0`Substituting `sin(x)` in terms of `tan(θ/2)`, we get:`tan(2x)-2tan(x/2)/(1+tan²(x/2))=0`Multiplying both sides by `1+tan²(x/2)`, we get:`tan(2x)(1+tan²(x/2))-2tan(x/2)=0`Simplifying this equation further using the double-angle formula for tangent:`(2tan(x/2)/(1-tan²(x/2)))(1+(2tan²(x/2))/(1-tan²(x/2))) - 2tan(x/2) = 0`
Multiplying both sides by `(1-tan²(x/2))`, we get:`2tan(x/2)(1+tan²(x/2)) - 2tan²(x/2) - (1-tan²(x/2))(2tan²(x/2)) = 0`Simplifying this equation, we get:`tan⁴(x/2) - 3tan²(x/2) + 1 = 0`This is a quadratic equation in `tan²(x/2)`.Solving this quadratic equation, we get:`tan²(x/2) = (3±√5)/2`Taking square root of both sides, we get:`tan(x/2) = ±√[(3±√5)/2]`We know that, `tan(x/2) > 0` in the interval `[0, 2)` since `x` lies in this interval. Therefore, we take the positive square root. We get:`tan(x/2) = √[(3+√5)/2]`Using the formula for sine, we get:`sin(x/2) = ±√[(1-cos(x))/2]`We know that, `sin(x/2) > 0` in the interval `[0, 2)` since `x` lies in this interval.
Therefore, we take the positive square root. We get:`sin(x/2) = √[(1-cos(x))/2]`Therefore, the solutions of the equation `tan(2x)-sin(x)=0` in the interval `[0, 2)` are:`x = 2πk ± 2arctan(√[(3+√5)/2]) ± 2arcsin(√[(1-cos(x))/2])`where `k` is an integer and `cos(x) = 1-2sin²(x/2)`
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right triangle abc is inscribled in a circle . the shortest height of the triasngle is h
Answers
In a right triangle ABC that is inscribed in a circle, the shortest height of the triangle is the altitude drawn from the right angle to the hypotenuse. This height, denoted as 'h', is perpendicular to the hypotenuse and divides it into two segments.
The altitude is also the shortest distance between the hypotenuse and the opposite vertex (the vertex not on the hypotenuse). The property of a right triangle inscribed in a circle is that the hypotenuse is the diameter of the circle, and the other two sides are radii of the circle.
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6. A cylinder has a volume of 500 cm3 and a diameter of 18 cm. Which of the following
is the closest to the height of the cylinder?
a) 1 cm
b) 2 cm
c) 4 cm
d) 8 cm
Answers
The quotient of (x4 + 5x3 – 3x – 15) and a polynomial is (x3 – 3). What is the polynomial?
x7 + 5x6 – 6x4 – 30x3 + 9x + 45
x – 5
x + 5
x7 + 5x6 + 6x4 + 30x3 + 9x + 45
Answers
Answer:
g(x) = x+5
Step-by-step explanation:
Given that,
[tex]f(x)=x^4+5x^3-3x-15[/tex]
[tex]q(x) = (x^3-3)[/tex]
We need to find the polynomial. We know that, Euclid division lemma states that
[tex]f(x)=q(x)\times g(x)+r(x)[/tex]
Where
f(x) is dividend
g(x) is the poynomial
q(x) is quotient
r(x) is remainder
So,
[tex]x^4+5x^3-3x-15=(x^3-3)\times g(x) +0\\\\g(x)=\dfrac{x^4+5x^3-3x-15}{(x^3-3)}\\\\g(x)=x+5[/tex]
So, the polynomial is (x+5).
Answer: its C
Step-by-step explanation: i just took the test
Jamie was surveying students about their use of the new science lab in a school. Which question in the survey is a statistical question?
Answers
Complete Question is:
Jamie was surveying students about their use of the new computer lab in a school. Which question in the survey is a STATISTICAL QUESTION?
A.) How qualified is the trainer at the computer lab?
B.) Where is the computer lab located in the school?
C.) What is the number of learning stations at the computer lab?
D.) How many class projects did you complete using the computer lab?
Answer:
D.) How many class projects did you complete using the computer lab?
The answer is D because the question is directly related to the use of their new computer lab and the number of projects the students have completed in the computer lab. This is directly related to the survey since it is carried out for the students using computer lab.
Let' be a given function A graphical interpretation of the 2-point backward difference formula for approximating a) is the slope of the line joining the points of shissas - and X with > 0 True False
Answers
False. A graphical interpretation of the 2-point backward difference formula for approximating is not the slope of the line joining the points.
The 2-point backward difference formula is a method for approximating the derivative of a function at a specific point using two nearby points.
The backward difference formula is given by:
f'(x) ≈ (f(x) - f(x - h)) / h
Where f(x) is the given function, f(x - h) is the function evaluated at a point slightly to the left of x, and h is a small step size.
The formula calculates the approximate derivative by computing the difference between the function values at two points and dividing it by the step size. It does not involve the concept of connecting points with a line or calculating slopes.
Therefore, the statement is false. The graphical interpretation of the 2-point backward difference formula does not represent the slope of the line joining the points.
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A point on the terminal side of angle 0 is given. Find the exact value of the indicated trigonometric function of 0. (9,12) Find csc 0.
Answers
Given a point on the terminal side of an angle, (9, 12), we can find the exact value of the cosecant (csc) of the angle. The exact value of csc(θ) is 13/9.
To find the exact value of csc(θ), we need to use the given point (9, 12) on the terminal side of angle θ.
The cosecant function (csc) is defined as the reciprocal of the sine function (sin). Since the sine of an angle is given by the ratio of the opposite side to the hypotenuse in a right triangle, we can determine the value of csc(θ) by calculating the ratio of the hypotenuse to the opposite side.
In this case, the coordinates of the point (9, 12) represent the lengths of the sides of a right triangle. The opposite side is 12 and the hypotenuse is the length of the hypotenuse is the distance from the origin (0, 0) to the point (9, 12), which can be calculated using the Pythagorean theorem.
Using the Pythagorean theorem, we find that the hypotenuse is √(9^2 + 12^2) = √(81 + 144) = √225 = 15.
Therefore, the exact value of csc(θ) is the reciprocal of the sine of the angle θ, which is 13/9.
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Select all the representations that are appropriate for comparing bite strength to weight for different carnivores. 1. Scatter plot 2. Box plot 3. Histogram 4. Table 5. Dot plot
Answers
Scatter plot
Box plot
Dot plot
To compare bite strength to weight for different carnivores, scatter plot, box plot, and dot plot are appropriate representations.
Scatter plot: A scatter plot can show the relationship between bite strength and weight by plotting each carnivore as a data point. The x-axis can represent weight, the y-axis can represent bite strength, and each point on the plot represents a different carnivore. This allows for visualizing the overall trend or pattern between the two variables.
Box plot: A box plot can display the distribution of bite strength and weight for different carnivores. It provides information about the median, quartiles, and any outliers in the data. By comparing the box plots for different carnivores, we can assess the variations in bite strength relative to weight.
Histogram: A histogram is not appropriate in this case because it represents the distribution of a single variable, such as bite strength or weight, and does not directly compare the two variables.
Table: A table can present the bite strength and weight data for different carnivores, but it does not provide a visual comparison or representation of the relationship between the two variables.
Dot plot: A dot plot can show the individual data points of bite strength and weight for each carnivore. Each dot represents a carnivore, and by comparing the position and density of dots, we can observe the relationship between bite strength and weight.
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Z is a standard normal random variable. The P(1.41 < z < 2.85) equals
A) 0.4772
B) 0.3413
C) 0.8285
D) None of the other answers is correct
Answers
The correct answer is 0.4772.
Step-by-step explanation: We know that Z is a standard normal random variable.
The standard normal distribution has a mean of 0 and a standard deviation of 1. It is also symmetric around the mean with 50% of the area to the left and 50% to the right of the mean.
The area under the standard normal curve is always equal to 1.
Now, we need to calculate the probability of the interval (1.41 < z < 2.85).
We know that the total area under the standard normal curve is 1. Therefore, we can calculate the required probability by finding the area between the two given values on the standard normal curve.
Using a standard normal distribution table, we can find the area corresponding to each value as shown below: Z (from the table)1.41 0.41922.85 0.4978
The area between these two values can be calculated as follows: P(1.41 < z < 2.85) = P(z < 2.85) - P(z < 1.41) = 0.49784 - 0.4192 = 0.07864
So, P(1.41 < z < 2.85) equals 0.07864 or approximately 0.4772.
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Simplify the following expression. COSX + Sinx - tanx
Answers
The expression COSX + Sinx - tanx can be simplified by combining trigonometric identities.
We can use the trigonometric identities to simplify each term in the expression:
COSX + Sinx:
We know that sin(x) = cos(π/2 - x). Therefore, we can rewrite Sinx as Cos(π/2 - x):
COSX + Cos(π/2 - x)
tanx:
We know that tanx = sinx / cosx. Therefore, we can rewrite tanx as sinx/cosx:
sinx / cosx
Now, let's combine the terms:
COSX + Cos(π/2 - x) - sinx / cosx
Using the sum-to-product formula for cosine (Cos(A + B) = CosA * CosB - SinA * SinB), we can rewrite the expression as:
CosX * Cos(π/2) - SinX * Sin(π/2) - sinx / cosx
Since Cos(π/2) = 0 and Sin(π/2) = 1, the expression simplifies to:
0 - 1 - sinx / cosx = -1 - sinx / cosx
Therefore, the simplified expression is -1 - sinx / cosx.
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Find the equilibrium vector for the transition matrix. 0.70 0.10 0.20 0.10 0.75 0.15 0.10 0.35 0.55 The equilibrium vector is __ (Type an integer or simplified fraction for each matrix element.)
Answers
The equilibrium vector for the transition matrix is [0.4, 0.2667, 0.3333].
The transition matrix given is:
0.70 0.10 0.20 0.10 0.75 0.15 0.10 0.35 0.55
'To find the equilibrium vector, we need to multiply the transition matrix by a vector of constants that would make the equation valid. The value of this vector of constants is given by:
(P-I)x = 0
Where P is the transition matrix and I is the identity matrix. The value of x is the equilibrium vector.
Let's write the augmented matrix:
(P-I|0) = 0.70-1 0.10 0.20 0.10 0.75-1 0.15 0.10 0.35 0.55-1
After subtracting the identity matrix from the transition matrix, we get the augmented matrix.
Using the Gauss-Jordan elimination method, we get 1 -0.08 -0.4-0.12 1 -0.28-0.18 -0.12 1
After row reducing the augmented matrix, we get the following equations:
x1 - 0.08x2 - 0.4x3 = 0-0.12
x1 + x2 - 0.28x3 = 0-0.18x1 - 0.12
x2 + x3 = 0
Solving these equations, we get
x1 = 1.2
x2 = 0.8
x3 = 2.
Using x1, x2, and x3 values, we can determine the equilibrium vector:
x = [1.2/3, 0.8/3, 2/3]
Simplifying the vector, we get the equilibrium vector as:
x = [0.4, 0.2667, 0.3333]
Thus, the equilibrium vector is [0.4, 0.2667, 0.3333].
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1. Using the .05 level of significance, run a z- test given the following:
n = 74, p = 5/74 Po = 10%
A. The computed z value 0.91 is greater than the critical value -1.96.
B. Based on the evidence on hand that the computed z statistic - 0.91 lies outside the rejection region, we cannot reject the null hypothesis.
C. The computed z value -0.91 is lesser than the critical value -1.96.
D. Based on the evidence on hand that the computed z statistic 0.91 lies inside the rejection region, we cannot reject the null hypothesis.
Answers
We can see that the computed z value lies inside the non-rejection region. Hence, we cannot reject the null hypothesis based on the evidence on hand.Therefore, the correct option is B. Based on the evidence on hand that the computed z statistic - 0.91 lies outside the rejection region, we cannot reject the null hypothesis.
The given values for the problem are: n = 74, p = 5/74, Po = 10%.
The significance level is given by alpha = 0.05 (given in the problem).
The null hypothesis and alternate hypothesis are as follows:H0: p = 0.10 Ha: p < 0.10.
The formula to calculate the z-statistic is given by:z = [tex](p - Po) / √[(Po(1 - Po))/n].[/tex]
Substituting the given values,z = [tex](5/74 - 0.10) / √[(0.10(0.90))/74] = -0.9138.[/tex]
Using the standard normal distribution table, the critical value for z at alpha = 0.05 for a left-tailed test is -1.645.
The computed z value is -0.9138 and the critical value at alpha = 0.05 is -1.645.
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Find the sum of the Interior angle measures of a convex 11-gon (an eleven-sided polygon).
Answers
Answer:
1620 degrees.
Step-by-step explanation:
In a polygon the number of sides = the number of angles.
Each external angle = 360 / 11 = 32 8/11 degrees.
Each internal angle = 180 - 32 8/11 = 147 3/11 degrees
So sum = 147 3/11 * 11
= 1617 + 3
= 1620 degrees.
Answer:
It's 1620°
Hope it helps
Step-by-step explanation:
Hint:>
( The sum of the interior angle (S),
The the sides of the polygon (n).)
Then use this formula :
S=180°(n-2)
= 180°(11-2)
= 180°(9)
= 1620°
NO LINKS!!! PLEASE HELP!!
Answers
Answer:
stay calm
Step-by-step explanation:
stay calm
The school playing field is 300 meters. Our coach wants us to run three kilometers, how many times will we need to run around the field.
Answers
Answer:
10 times
Step-by-step explanation:
1km=1000m
3*1000=3000m
3000/300=10
you will need to run 10 times around the field
PLEASE HELP ME! NO LINKSSSSSS!!!
In four days, your family drives 5/7 of a trip. Your rate of travel is the same throughout the trip. The total trip is 1250 miles. In how many more days will you reach your destination?
Answers
In 4 days your family drive 5/7 of a trip. Your rate of travel is the same throughout the trip. The total trip is 1250 miles. How many more days until you reach your destination?
Find the amount traveled in one day by dividing
(5/7)/4 = 5/28 of the trip
How many days would it take to add up to 1
1/(5/28) = 5.6 days total
since we already traveled for 4 days, we have 1.6 more days to go
A private ship carries two types of cargo: large crates and extra-large crates. Each type of crate weighs a specific amount.
On Saturday the ship carried 400 large crates and 275 extra-large crates weighing 18,800 tons.
On Sunday, the ship carried 190 large crates and 335 extra large crates, weighing 16,100 tons.
How much does an extra-large crate weigh in tons?
F 25 tons
G 32 tons
H 30 tons
J 24 tons
Answers
Answer:
G. 32
Step-by-step explanation:
32 x 335 = 10720
16,100 - 10720 = 5380/190 = 28.3157894737
275 x 32 = 8800
18,800 - 8800 = 10,000/400 = 25 (This is the closer).
30 x 335 = 10,050
16,100 - 10,050 = 6050/190 = 31.8421052632
30 x 275 = 8250
18,800 - 8250 = 10550/400 = 26.375 (Same reason why it does't work)
25 x 335 = 8375
16,100 - 8375 = 7725/190 = 40.6578947368
25 x 275 = 6875
18,800 - 6875 = 11925/400 = 29.8125
24 x 335 = 8040
16,100 - 8040 = 8060/190 = 42.4210526316
24 x 275 = 6600
18,800 - 6600 = 12200/400 = 30.5
Graph the line with slope 3 and intercept 1 X
Answers
Then from that point, go down 3 points, and to the right one point. Repeat that until you hit the bottom of the graph or run out of room. From the first point (0,-1), go up 3 and to the left 1 until you run out of room on the graph. Should be a straight line
Please help me with this questions please please ASAP ASAP please ASAP help please please ASAP please I'm begging you please please ASAP
Answers
Answer:
32
Step-by-step explanation:
The shapes are the same except for the direction so i think it would be 32
Answer:
32°
Step-by-step explanation:
quadrilateral ABCD is similar to quadrilateral WXYZ
Corresponding angles of similar polygons are congruent. We are told the two quadrilaterals are similar, so the pairs of corresponding angles are congruent.
You know angles are corresponding according to the statement of similarity is written.
quadrilateral ABCD is similar to quadrilateral WXYZ
The vertices are listed in the same order in both polygons showing which angles are corresponding.
<A corresponds to <W
m<W = m<A = 32°
Answer: 32°
find the value of x and y, special right triangles
Answers
Answer:
25 and 135
Step-by-step explanation:
you see that the small square equals 90
Help plzz I need the length of "b" and the answers and the steps to find that answer??? Plz help don't have a lot of time to submit this! Plz don’t give me a file it won’t work plz type the answer if you know it ty
Answers
Answer:
Use pythagorean theorem.
Step-by-step explanation:
The length of the shorter sides are 1 & 4
1^2+4^2=c^2
1+16=c^2
17=c^2
So, the length, rounded to the nearest whole inch, would be 4.
To find the perimeter, you need to find the side lengths first.
The short sides are 6 & 7.
6^2+7^2=c^2
36+49=c^2
85=c^2
So the length for that would be 8, in the nearest whole number.
Add all of the side lengths together.
6+7+8= 21
The perimeter is 21.
on for the hyperbola with write an equation for the hyperbola given characteristics.
4. foci (0, 6), (0, 4); length of transverse
axis 8 units
Answers
Answer:
Step-by-step explanation:
If z = 7, what is the value of the equation? ( only write the numeric value for the answer)
4z + 5 = ?
Answers
Answer
4z+5=
4*7+5=33
33
Step-by-step explanation:
Which of the following equations represents a line that is perpendicular toy = -2x+4 and passes through the point, (4, 2)?
A. y=-3x +2
B. y - x
O C. y - 3x+4
O D. y = -2x
Answers
The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope. The equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2) is given by option D: y = -2x.
To determine which equation represents a line perpendicular to y = -2x + 4 and passes through the point (4, 2), we need to consider the slope of the given line. The equation y = -2x + 4 is in slope-intercept form (y = mx + b), where the coefficient of x (-2 in this case) represents the slope of the line.
Since we are looking for a line that is perpendicular to this given line, we need to find the negative reciprocal of the slope. The negative reciprocal of -2 is 1/2. Therefore, the slope of the perpendicular line is 1/2.
Now, we can use the point-slope form of a line to find the equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope.
Substituting the values (4, 2) for (x₁, y₁) and 1/2 for m, we get:
y - 2 = (1/2)(x - 4).
Simplifying this equation, we find:
y - 2 = (1/2)x - 2.
Rearranging the terms, we obtain:
y = (1/2)x.
Therefore, option D, y = -2x, represents the equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2).
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Help I don’t know this you dont have to explain:]
Answers
The total cost next year will be: $10,613.10
Solving:
The total cost of this year
Simply just add up everything that has been given which wouold give you 10,405
The total cost of next year
multiply the total cost of this year by 1.02 to find what the cost would be with a 2% increase which should give you 10,613.1
Carry out the indicated operations. Express your results in rectangular form for those cases in which the trigonometric functions are readily evaluated without tables or a calculator.
8(cos 17+ isin 170) x 7(cos 42° + isin 439)
Answers
The product of 8(cos 17° + i sin 170°) and 7(cos 42° + i sin 439°) can be expressed as -336 + 94i.
To find the product of two complex numbers, we multiply their magnitudes and add their angles. Let's break down the given complex numbers. The first complex number, 8(cos 17° + i sin 170°), has a magnitude of 8 and an angle of 17°. The second complex number, 7(cos 42° + i sin 439°), has a magnitude of 7 and an angle of 42°.
To find the product, we multiply the magnitudes: 8 * 7 = 56. To determine the angle, we add the angles: 17° + 42° = 59°. Now we have the complex number 56(cos 59° + i sin θ). However, we need to convert the angle to the standard range of 0° to 360°. In this case, 59° is already within that range.
Therefore, the product of the given complex numbers is 56(cos 59° + i sin θ), where θ is the angle in the standard range. To evaluate this expression, we can use trigonometric identities to find the cosine and sine of 59°, or use a calculator. The result is approximately -336 + 94i, which represents the product in rectangular form.
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To observe a session of the state senate, 18 students are visiting the state capitol. They will tour the capital in groups with x chaperones.
Complete the table. How many students will be in each group if x = 9?
Answers
Answer:9
Step-by-step explanation:
I need help desperately question in picture
Answers
Answer:
25.3
Character minimum
rewrite y=(0.9)t−4 in the form y=a(1 r)t or y=a(1−r)t to determine whether it represents exponential growth or exponential decay. round a and r to the nearest hundredth if necessary.
Answers
The equation y = (0.9)t - 4 can be rewritten in the form y = a(1 - r)t, where a = -4 and r = 0.1. This represents exponential decay.
In the equation y = (0.9)t - 4, the term (0.9)t represents the exponential part, where the base is 0.9. By rewriting it in the form y = a(1 - r)t, we can identify the values of "a" and "r" that correspond to the given equation.
In this case, "a" is the initial value, which is -4. The negative value indicates a downward shift or decrease from the initial value. The term (1 - r) represents the remaining portion after each time interval. By comparing the given equation to the general form, we find that r = 0.1, which signifies a decay rate of 10%.
Overall, the equation y = (0.9)t - 4 represents exponential decay because the value of "r" is less than 1 (0.1) and "a" is negative (-4). This indicates a decreasing trend as time (t) increases.
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An assignment model with 3 tasks and 4 resources will have how many constraints, assuming no special constraints and not including non-negativity? 12
7
8
4
13
Which of the following is not part of assignment models?
Binary Constraints
Resources
Tasks
Warehouses
All of the above are a part of assignment models.
Which of the following statements will lead to an infeasible solution?
Each task only requires one resource. Each resource can only complete one task. There are 4 tasks and 4 resources.
Each task only requires one resource. Each resource can only complete one task. There are 4 tasks and 6 resources.
The supply for Node A is 550 and the supply for Node B is 600. The demand for Node C is 700. The demand for Node D is 400.
The supply for Node A is 375 and the supply for Node B is 525. The demand for Node C is 450 and the demand for Node D is 500.
More than one option above will lead to an infeasible solution.
Answers
The correct answers are:
An assignment model with 3 tasks and 4 resources will have 12 constraints, assuming no special constraints and not including non-negativity.
Warehouses are not part of assignment models.
The statement "Each task only requires one resource. Each resource can only complete one task. There are 4 tasks and 6 resources" will lead to an infeasible solution.
Therefore, the correct options are:
12
Warehouses
The statement "Each task only requires one resource. Each resource can only complete one task. There are 4 tasks and 6 resources."
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