The linear programming problem is solved using the simplex method by constructing the simplex tableau, performing pivot operations, and obtaining the optimal solution. The optimal values of the decision variables are X1 = 11, X2 = 3, and X3 = 0, and the optimal objective function value is Z = 29. The other variables X4, X5, and X6 are equal to 0.
What is a linear constraint?
Linear constraint refers to a set of mathematical equations or inequalities that restrict the feasible region of a linear programming problem to a polyhedron, which is a bounded convex region in the n-dimensional space defined by the values of the decision variables.
The objective is to optimize a linear objective function subject to these linear constraints, subject to non-negativity constraints on the decision variables.
a) Write out the full set of linear constraints including the surplus variables:
x1 + 4x2 + 2x3 + x4 = 28
3x1 + 6x2 + x3 + x5 = 36
2x1 + x2 + 5x3 + x6 = 20
x1, x2, x3, x4, x5, x6 ≥ 0
Note: Assume that the third constraint was actually meant to be "2x1 + x2 + 5x3 + x6 ≤ 20" since the original inequality was not specified.
b) Write the problem in standard form:
Minimize Z = 2x1 + 3x2 + 2x3 + 0x4 + 0x5 + 0x6
Subject to:
x1 + 4x2 + 2x3 + x4 = 28
3x1 + 6x2 + x3 + x5 = 36
2x1 + x2 + 5x3 + x6 ≤ 20
x1, x2, x3, x4, x5, x6 ≥ 0
c) Write the problem in matrix form:
Minimize Z = [2 3 2 0 0 0] [x1 x2 x3 x4 x5 x6]T
Subject to:
[1 4 2 1 0 0] [x1 x2 x3 x4 x5 x6]T = 28
[3 6 1 0 1 0] [x1 x2 x3 x4 x5 x6]T = 36
[2 1 5 0 0 1] [x1 x2 x3 x4 x5 x6]T ≤ 20
[x1 x2 x3 x4 x5 x6]T ≥ 0
d) Write out the initial simplex tableau:
Basic x1 x2 x3 x4 x5 x6 RHS
Z 2 3 2 0 0 0 0
x4 1 4 2 1 0 0 28
x5 3 6 1 0 1 0 36
x6 2 1 5 0 0 1 20
Note: The initial tableau has the identity matrix as the coefficient matrix for the slack and surplus variables, and the objective coefficients are in the top row. The RHS column contains the right-hand side values of the constraints.
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In the diagram below, QP is tangent to a circle with the centre O. Rs is a straight line. T is a point on the circle. PS bisects TPQ and SPQ=22°
Answer:
In the given diagram, QP is tangent to a circle with centre O, RS is a straight line, T is a point on the circle, and PS bisects TPQ. We know that SPQ = 22°. Let's try to find out the value of the angle TPQ.
Since QP is tangent to the circle, the angle between RS and QP (i.e., angle RQP) is equal to the angle between QP and the radius drawn to the point of tangency (i.e., angle QOT). So, we can say that:
angle RQP = angle QOT
Also, since PS bisects TPQ, we can say that:
angle TPS = angle TPQ / 2
Now, let's consider the triangle TPQ. We know that:
angle TPQ + angle TQP + angle PTQ = 180° [Sum of angles in a triangle]
Substituting the values we have:
angle TPQ + angle TQP + (angle TPS + angle SPQ) = 180°
angle TPQ + angle TQP + (angle TPQ/2 + 22°) = 180°
Multiplying both sides by 2 to eliminate the fraction:
2(angle TPQ) + 2(angle TQP) + angle TPQ + 44° = 360°
Simplifying:
3(angle TPQ) + 2(angle TQP) = 316°
We don't know the values of angle TPQ and angle TQP, so we can't solve this equation exactly. However, we do know that these angles are both less than 180° (since they are angles in a triangle). Therefore, we can try some values for angle TPQ (let's call it x) and see if we can find a corresponding value for angle TQP that satisfies the equation.
If we take x = 40°, then we get:
3(40°) + 2(angle TQP) = 316°
120° + 2(angle TQP) = 316°
2(angle TQP) = 196°
angle TQP = 98°
Now, we can use the fact that angle TPS = angle TPQ / 2 to find angle TPS:
angle TPS = x/2 = 20°
Finally, we can use the fact that PS bisects TPQ to find angle PQT:
angle PQT = angle TPS
Step-by-step explanation:
Complete the following description for a graph that shows the distance Sam travels over time when she
runs at a constant rate.
A line that starts at
with a constant (select)
slope.
D
A line starts at 0 with a constant positive slope.
The graph that shows the distance Sam travels over time is given below.
Here the graph starts at the point (0, 0).
So the line starts at 0.
Now the line is moving in such a way that as time increases, the distance travelled also increases.
So the slope is positive.
Hence the complete description is that line starts at 0 with a constant positive slope.
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HELP!!!!! WORTH 30 POINTS
The relation that is a function is given as follows:
Bottom left graph.
When does a graph represents a function?A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y. Vertically aligned points mean that a value of x is mapped to multiple values of y, that is, a single input is mapped to multiple outputs which disqualify the relation as a function.
Hence the bottom left graph is the only one with a relation representing a function, as a vertical line would not cross the graph of the function more than once no matter where it was plotted.
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The statements that are true about the triangle are
a) m∠5 + m∠6 = 180°
b) ∠ 2+ ∠ 3 = ∠ 6
c) m∠2 + m∠3 + m∠5 = 180°
Given data ,
Let the triangle be represented as ΔABC
Now , An exterior angle of a triangle is equal to the sum of the opposite interior angles.
For Exterior ∠ 1 we have
∠ 1 = ∠ 5 + ∠ 3 ( Exterior angle Property of Triangle )
Similarly,
For Exterior ∠ 4 we have
∠ 4 = ∠ 5 + ∠ 2 ( Exterior angle Property of Triangle )
Similarly,
For Exterior ∠ 6 we have
∠ 6 = ∠ 2 + ∠ 3 ( Exterior angle Property of Triangle )
From the triangle sum property , we get
Ina triangle sum of the measures of angles is equal to 180°
m∠2 + m∠3 + m∠5 = 180°
Hence , the triangle is solved
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The complete question is attached below :
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
What is the median of the data set?
I will give Brainliest to the best answer only if it is Brainly Expert
A. 10
B. 8.5
C. 8
D. 9
Answer:
The answer to your problem is, A. 10
Step-by-step explanation:
So first add up all the total number of ‘ X ‘
Which is:
4 + 3 + 2 + 1 = 10
Technically 10 is our answer.
Thus the answer to your problem is, A. 10
Not a 100% sure
Answer:
5, 8, 8, 8, 8, 9, 9, 9, 10, 10
The median of this data set is 8.5, so the correct answer is B.
Step-by-step explanation:
Since there are 10 observations, we are looking for the number halfway between the two middle observations (observations #5 and #6) when the data are arranged in order. Here, observation #5 is 8, and observation #6 is 9, so the median of this data set is (8 + 9)/2 = 8.5. B is the correct answer.
what is the next fraction in this sequence; 1/3, 5/12, 1/2, 7/12
Answer:2/3
Step-by-step explanation:
Since with each fraction, the value increases by an increment of 0.0833333333333, which we can figure out by subtracting the smaller values by the values that come directly after them in the string of fractions, we can find that the next value in the list is 2/3, which is 7/12 + 0.0833333333333.
Please help, check picture! Also please explain, I need to understand
I don’t even see triangles on the graph
Answer:
a first
Step-by-step explanation:
because I just don't
Determine 5^903 (mod60) and 17^342 (mod5)
The final value is 4 (mod5)
Hence, 17^342 ≡ 2^342 ≡ 4 (mod5).
To find 5^903 (mod60), we can use Euler's totient function. Since 60 = 2^2 × 3 × 5, we have φ(60) = 2^1 × 3^1 × 4 = 24. Therefore, we can use Euler's theorem to write:
5^24 ≡ 1 (mod60)
Raising both sides to the power of 37, we get:
5^(24*37) ≡ 1^37 ≡ 1 (mod60)
So 5^888 ≡ 1 (mod60).
Now, we can write:
5^903 = 5^888 * 5^15
Since 5^888 ≡ 1 (mod60), we just need to find 5^15 (mod60).
To do this, we can use the repeated squaring method. Writing 15 in binary form, we have:
15 = 1111 (in binary)
So we can compute:
5^1 ≡ 5 (mod60)
5^2 ≡ 25 (mod60)
5^4 ≡ 25^2 ≡ 25 (mod60)
5^8 ≡ 25^2 ≡ 25 (mod60)
Therefore:
5^15 ≡ 5^8 * 5^4 * 5^2 * 5^1 ≡ 25 * 25 * 25 * 5 ≡ 25 (mod60)
Hence, 5^903 ≡ 5^15 ≡ 25 (mod60).
To find 17^342 (mod5), we can use the fact that 17 ≡ 2 (mod5). Therefore:
17^342 ≡ 2^342 (mod5)
Using the repeated squaring method again, we can compute:
2^1 ≡ 2 (mod5)
2^2 ≡ 4 (mod5)
2^4 ≡ 1 (mod5)
Therefore:
2^342 ≡ 2^2 * (2^4)^85 ≡ 4 * 1^85 ≡ 4 (mod5)
Hence, 17^342 ≡ 2^342 ≡ 4 (mod5).
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Which is the most accurate way to estimate 74% of 57?
Answer:
74% is about 75%, or 3/4.
57 is about 60.
So 74% of 57 is about 3/4 of 60, or 45.
74% of 57 is .74 × 57 = 42.18, so the estimate seems reasonable
Answer:
42.18
Step-by-step explanation:
[tex]\frac{57*74}{100} = 42.18[/tex]
A man is 4 years older than his wife and three times as old as his child. The sum of their ages three years ago was 54. Find the man's and wife's present ages
Lets take the variable x for the son.
Son: x
Dad: 3x
Mom: 3x-4
THREE years ago:
Son: x-3
Dad: 3x-3
Mom: 3x-4 -3
so, 3x-7
SUM=54
(x-3)+(3x-3)+(3x-7)=54
x-3+3x-3+3x-7=54
7x-13=54
7x=54+13
7x=67
so , x=67/7
x= 9.5
now lets see for the dad:
3x= 3*9.5
=28.5
Finally for the mom:
3x-4= 3*9.5 -4
= 28.5-4
= 24.5
The man's age is 32, his wife's age is 28.
Let's use algebra to solve this problem.
Let's represent the man's age as "M", his wife's age as "W", and their child's age as "C".
From the first sentence of the problem, we know that:
M = W + 4
From the second sentence, we know that:
M = 3C
Finally, from the third sentence, we know that the sum of their ages three years ago was 54:
(M-3) + (W-3) + (C-3) = 54
Substituting M = W + 4 and M = 3C into the third equation, we get:
(W+4-3) + (W-3-3) + (1/3M - 3) = 54
Simplifying this equation, we get:
2W + (1/3)(W+4) - 12 = 54
Multiplying both sides by 3 to eliminate the fraction, we get:
6W + W + 4 - 36 = 162
Combining like terms, we get:
7W - 32 = 162
Adding 32 to both sides, we get:
7W = 194
Dividing both sides by 7, we get:
W = 28
Substituting W = 28 into M = W + 4, we get:
M = 32
Finally, substituting M = 3C into the equation, we get:
32 = 3C
C = 32/3
Therefore, the man's age is 32, his wife's age is 28.
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Enter your answer and show all the steps that you use to solve this problem in the space provided. Use the 30°-60°-90° Triangle Theorem to find the answer.
Answer:
x = 5√3, and y = 10.
In a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg, and the length of the hypotenuse is twice the length of the shorter leg.
The objective of a study by LeRoith et al. (A-68) was to evaluate the effect of a 7-week administration of recombinant human GH (rhGH) and recombinant human insulin-like growth factor (rhIGF-I) separately and in combination on immune function in elderly female rhesus monkeys. The assay for the in vivo function of the immune system relied on the response to immunization with tetanus toxoid.
The study aimed to provide insights into the potential effects of rhGH and rhIGF-I, both separately and in combination, on the immune function of elderly individuals, as indicated by the immune response to tetanus toxoid immunization.
The study aimed to evaluate the impact of a 7-week administration of recombinant human growth hormone (rhGH) and recombinant human insulin-like growth factor (rhIGF-I), both separately and in combination, on immune function in elderly female rhesus monkeys. The researchers used the response to immunization with tetanus toxoid as an assay to measure the in vivo function of the immune system.
The study design likely involved the following steps:
Selection of elderly female rhesus monkeys as the study subjects: The researchers chose female monkeys of advanced age to represent the elderly population.
Administration of recombinant human growth hormone (rhGH): The researchers administered rhGH to a group of monkeys for a period of 7 weeks. This hormone is known to stimulate growth and metabolism.
Administration of recombinant human insulin-like growth factor (rhIGF-I): Another group of monkeys received rhIGF-I, a hormone that mediates the effects of GH, for the same duration.
Combination treatment: A third group of monkeys received both rhGH and rhIGF-I simultaneously during the 7-week period.
Immunization with tetanus toxoid: After the 7-week treatment period, all monkeys were immunized with tetanus toxoid, which is a vaccine used to induce an immune response against tetanus.
Measurement of immune response: The researchers assessed the immune function by measuring the response of the monkeys' immune systems to the tetanus toxoid immunization. They likely examined parameters such as antibody production or T-cell response.
Data analysis: The researchers analyzed the immune response data to determine the effects of rhGH, rhIGF-I, and their combination on the immune function of the elderly female rhesus monkeys.
The study aimed to provide insights into the potential effects of rhGH and rhIGF-I, both separately and in combination, on the immune function of elderly individuals, as indicated by the immune response to tetanus toxoid immunization.
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Asemi annual coupon bond has a par value of $1,000 and matures in 10years. Today it sells for $887 and has a YTM of 10.9%. Solve forcoupon rate
The coupon rate for the semi-annual bond is approximately 11.96%.
Given the information provided, we have the following details:
- Par value: $1,000
- Maturity: 10 years
- Current price: $887
- YTM (Yield to Maturity): 10.9%
To solve for the coupon rate, we can use the bond pricing formula:
Bond Price = (C * (1 - (1 + r/2)^(-2n))) / (r/2) + (Par Value / (1 + r/2)^(2n))
Where:
- Bond Price = $887
- C = Coupon payment per period (which we need to find)
- r = YTM / 100 = 0.109
- n = Maturity in years = 10
Plugging in the given values:
$887 = (C * (1 - (1 + 0.109/2)^(-2*10))) / (0.109/2) + ($1,000 / (1 + 0.109/2)^(2*10))
Now, we can solve for the coupon payment, C:
C = (($887 * 0.109/2) - ($1,000 / (1 + 0.109/2)^(2*10))) / (1 - (1 + 0.109/2)^(-2*10))
C ≈ $59.80
Since this is a semi-annual bond, the annual coupon payment would be:
Annual Coupon Payment = C * 2 = $59.80 * 2 = $119.60
Finally, to find the coupon rate, we can divide the annual coupon payment by the par value:
Coupon Rate = (Annual Coupon Payment / Par Value) * 100 = ($119.60 / $1,000) * 100 = 11.96%
So, the coupon rate for the semi-annual bond is approximately 11.96%.
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Approximate the number to the nearest integer and tenth.
-√7
Estimating the square root of the number -√7 gives -2 and -2.6
Estimate the square root of the numberFrom the question, we have the following parameters that can be used in our computation:
-√7
To estimate the number is to approximate the number
When the square root of 7 is evaluated, we have
-√7 = -2.64575131106
Approximate to the nearest integer
-√7 = -2
Approximate to the nearest tenth.
-√7 = -2.6
Hence, the estimates are -2 and -2.6
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10) How many distinguishable permutations are there for the word sleepless
The word "sleepless" has 8 letters. To find the number of distinguishable permutations, we can use the formula for permutations of a set with no repeated elements, which is n!, where n is the number of elements.
Therefore, the number of permutations for the word "sleepless" can be calculated as 8!, which is equal to 40,320. This means that there are 40,320 different ways we can arrange the letters in the word "sleepless" while keeping all the letters distinct.
Note that if the word had repeated letters, we would have to divide the result by the factorials of the number of times each letter was repeated.
The pizza box measures 2/3 feet wide by 4/5 feet long. What is the area of the pizza box
The area of the pizza box measuring 2/3 feet wide by 4/5 feet long is 8/15 square feet.
The shape of the pizza box is a rectangle. The rectangle is a quadrilateral with opposite sides parallel and equal with an equal angle and of 90°.
The area of a rectangle is considered as:
A = L * B
where L is the length
B is the breadth
Given in the question,
L = 4/5 feet
B = 2/3 feet
The area is calculated by multiplying the fractions. For the multiplication of fractions, we multiply the numerators and denominators separately. And final answer is calculated by simplifying the resulting fraction.
A = 4/5 * 2/3
= 4*2 / 5*3
= 8/15 square feet
Thus, the pizza box has an area of 8/15 square feet
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M is the midpoint of PQ. the diameter of circle O is 13 in. and RM = 4 in. Find PM
The PM of the circle is 6 in.
How to find the PM of the circle?Since the diameter of the circle divide the circle into two equal parts. We can say:
PM = MQ
Applying the Intersecting Chord Theorem (When two chords intersect each other inside a circle, the products of their segments are equal). That is:
SM * RM = PM * MQ
SM * RM = PM²
SM = 13 - 4
SM = 9 in
RM = 4 in
Substituting:
SM * RM = PM²
9 * 4 = PM²
PM² = 36
PM = √36
PM = 6 in
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Solve the following differential equation: (x² + y² + xy) dx + (xY) dy = 0 +
The solution to the given differential equation is:
[tex]$\frac{1}{2}x^4y + \frac{2}{3}x^3y^2 = C$[/tex]
To solve the given differential equation:
[tex]$(x^2 + y^2 + xy)dx + (xy)dy = 0$[/tex]
We will first check whether this is an exact differential equation or not.
[tex]$\frac{\partial M}{\partial y} = \frac{\partial }{\partial y}(x^2 + y^2 + xy) = 2y + x$[/tex]
[tex]$\frac{\partial N}{\partial x} = \frac{\partial }{\partial x}(xy) = y$[/tex]
Since [tex]$\frac{\partial M}{\partial y} \neq \frac{\partial N}{\partial x}$[/tex], this is not an exact differential equation.
Next, we will check if this differential equation is solvable using an integrating factor.
[tex]$\frac{1}{xy}(x^2 + y^2 + xy)dx + dy = 0$[/tex]
Let us assume the integrating factor as [tex]$u = u(x)$[/tex]
Multiplying both sides of the differential equation with the integrating factor, we get:
[tex]$\frac{1}{y}(x^2 + y^2 + xy)u(x)dx + u(x)dy = 0$[/tex]
Now, we can see that this is an exact differential equation.
[tex]$\frac{\partial }{\partial y}\left(\frac{1}{y}(x^2 + y^2 + xy)u(x)\right) = \frac{xu(x)}{y}$[/tex]
[tex]$\frac{\partial }{\partial x}\left(u(x)\right) = \frac{xu(x)}{y}$[/tex]
Solving this differential equation, we get:
[tex]$\ln |u(x)| = \frac{1}{2}\ln(x^2y^2) = \ln(xy)$[/tex]
[tex]$u(x) = xy$[/tex]
Multiplying the integrating factor to the original differential equation, we get:
[tex]$(x^3y + x^2y^2 + x^2y^2)dx + (x^2y^2)dy = 0$[/tex]
[tex]$(x^3y + 2x^2y^2)dx + (x^2y^2)dy = 0$[/tex]
This is now an exact differential equation and can be solved by finding the potential function:
[tex]$\frac{\partial }{\partial x}\left(\frac{1}{2}x^4y + \frac{2}{3}x^3y^2\right) = x^3y + 2x^2y^2$[/tex]
[tex]$\frac{\partial }{\partial y}\left(\frac{1}{2}x^4y + \frac{2}{3}x^3y^2\right) = x^2y^2$[/tex]
Therefore, the potential function is [tex]$\frac{1}{2}x^4y + \frac{2}{3}x^3y^2 = C$[/tex], where C is the constant of integration.
Hence, the solution to the given differential equation is:
[tex]$\frac{1}{2}x^4y + \frac{2}{3}x^3y^2 = C$[/tex]
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Solve for the series with center at 0 (Present up to 6th term): 1.1.e-2x 1.3. sin(2x – 1) 1 1.4. 1+3x2 1.2.cos(3x)
The series after solving the following term f(x) = [tex]e^{-2x}[/tex] is given as:
[tex]e^{-2x}[/tex] = 1 - 2x + 2x² - 4/3x³ + 2/3x⁴ - 4/15x⁵+....|x| < ∞.
The fundamental concepts in mathematics are series and sequence. A series is the total of all components, but a sequence is an ordered group of items in which repeats of any kind are permitted. One of the typical examples of a series or a sequence is a mathematical progression.
By using the formulae to solve issues, one may gain a deeper understanding of the principles. The main distinction between them and sets is that in a sequence, certain terms might appear again in different locations. A series can be finite or infinite in length and has length equal to the number of terms.
Given f(x) = [tex]e^{-2x}[/tex], center x = 0
f(x) = [tex]e^{-2x}[/tex] = [tex]1 - 2x + \frac{(2x)^2}{2!} +\frac{(2x)^3}{3!} +\frac{(2x)^4}{4!} +\frac{(2x)^5}{5!} +.....|x|[/tex]
[tex]e^{-2x}[/tex] = 1 - 2x + 4([tex]\frac{x^2}{2}[/tex]) - 8([tex]\frac{x^3}{6}[/tex]) + 16([tex]\frac{x^4}{24}[/tex]) - 35([tex]\frac{x^5}{100}[/tex])+.....|x| < ∞
[tex]e^{-2x}[/tex] = 1 - 2x + 2x² - 4/3x³ + 2/3x⁴ - 4/15x⁵+....|x| < ∞
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Claim. The standard deviation of pulse rates of adult males is less than 10 bpm. For a random samplo of 135 adult males, the pulse rates have a standard deviation of 9.2 bpm. Find the value of the tes
The value of the test statistics is 113.42.
To test the claim that the standard deviation of pulse rates of adult males is less than 10 bpm, we will use a chi-square test. Given a random sample of 135 adult males with a standard deviation of 9.2 bpm, let's find the value of the test statistic.
Step 1: State the null and alternative hypotheses.
H0: σ = 10 bpm (null hypothesis)
H1: σ < 10 bpm (alternative hypothesis)
Step 2: Determine the appropriate test statistic.
In this case, we will use the chi-square test statistic: χ² = (n-1)(s²/σ²), where n is the sample size, s is the sample standard deviation, and σ is the population standard deviation.
Step 3: Calculate the test statistic.
χ² = (135-1)(9.2²/10²) = (134)(84.64/100) = 134 * 0.8464 ≈ 113.42
The value of the test statistic is approximately 113.42. This value can be compared to the critical value from the chi-square distribution table with (n-1) degrees of freedom to determine whether to reject or fail to reject the null hypothesis.
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Larry and Susan work in an office near 2 Live Stew and Stew-topia, specialty stew restaurants on the same block. Larry notices that both places are charging only $2.00 for a bowl of stew,which is below the price of $4.00 that a bowl of stew typically costs elsewhere in the city Susan wonders if 2 Live Stew and Stew-topia are engaged in a price war. Over the past month, she has noticed that cach store has lowered its prices each week, but that Stew-topia always lowered its price first. She suggests that Stew-topia is engaging in predatory pricing Larry correctly replies that they cannot determine whether Stew-topia is guilty of predatory pricing because Choose one: o A to prove that Stew-topia engaged in predatory pricing, you would need to prove that the owner of Stew- o B. to prove Stew-topia engaged in predatory pricing, you would need to prove that Stew-topia priced 。C. to prove that Stew-topia engaged in predatory pricing, you would need to prove that the average variable topia threatened the owner of 2 Live Stew to keep him from matching the price cut. stew below average variable cost with the specific intention of driving 2 Live Stew out of business cost of a bowl of stew is $2.00 or less
Without additional evidence that shows Stew-topia's pricing strategy was intended to harm competition, it cannot be conclusively determined whether Stew-topia is guilty of predatory pricing.
To prove that Stew-topia engaged in predatory pricing, Larry would need to provide evidence that Stew-topia priced stew below average variable cost with the specific intention of driving 2 Live Stew out of business, or that the owner of Stew-topia threatened the owner of 2 Live Stew to keep him from matching the price cut. Simply observing that both 2 Live Stew and Stew-topia lowered their prices to $2.00 for a bowl of stew and that Stew-topia always lowered its price first is not enough to conclusively determine whether Stew-topia is engaging in predatory pricing.
Predatory pricing is a strategy used by a dominant firm in a market to deliberately set prices below the average variable cost (AVC) of production in order to drive competitors out of business and reduce competition in the long run. To prove that Stew-topia engaged in predatory pricing, Larry would need to show evidence that Stew-topia priced its stew below its average variable cost with the specific intent of driving 2 Live Stew out of business. This would require detailed financial data and documentation from Stew-topia, such as production costs, pricing decisions, and internal communications that demonstrate their predatory intent.
Alternatively, Larry would need to provide evidence that Stew-topia used anti-competitive tactics, such as threatening the owner of 2 Live Stew to prevent them from matching the price cut or engaging in anti-competitive agreements or collusion. This would require concrete proof, such as emails, recordings, or witnesses, that demonstrate Stew-topia's anti-competitive behavior.
Simply observing that both 2 Live Stew and Stew-topia lowered their prices and that Stew-topia always lowered its price first is not enough to prove predatory pricing. There could be other reasons for the price cuts, such as seasonal promotions, cost reductions, or competitive pressures.
Therefore, without additional evidence that shows Stew-topia's pricing strategy was intended to harm competition, it cannot be conclusively determined whether Stew-topia is guilty of predatory pricing.
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a machine is used to fill 1-liter bottles of a type of soft drink. we can assume that the output of the machine approximately follows a normal distribution with a mean of 1.0 liter and a standard deviation of .01 liter. the firm uses means of samples of 25 observations to monitor the output, answer the following questions: determine the upper limit of the control chart such that it will include roughly 97 percent of the sample means when the process is in control. (3 decimal points are required)
The upper limit of the control chart such that it will include roughly 97 percent of the sample means when the process is in control is 1.008.
For a process with a normal distribution, the mean of the sample means is equal to the population mean and the standard deviation of the sample means is equal to the population standard deviation divided by the square root of the sample size. In this case, the mean of the output is 1.0 liter and the standard deviation is 0.01 liter, so the standard deviation of the sample means is 0.01 / √25 = 0.002.
To construct a control chart for the sample means, we need to determine the upper and lower control limits such that the process is in control when the sample means fall within these limits. Assuming the process is in control, we want to find the upper limit such that roughly 97% of the sample means fall below this limit.
Using the standard normal distribution, the Z-score corresponding to the 97th percentile is approximately 1.88.
Therefore, the upper control limit is 1.0 + 1.88(0.002) = 1.008. Any sample mean above this limit should be investigated for potential process issues.
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n² + n² + n² for n = -1
I need it fasttt
Substituting n = -1 in the given expression, we get:
n² + n² + n² for n = -1
= (-1)² + (-1)² + (-1)²
= 1 + 1 + 1
= 3
Therefore, n² + n² + n² for n = -1 is equal to 3.
Consider an electric circuit with an inductance of 0.05 henry, a resistance of 20 ohms, a condenser of capacitance of 100 micro farads and an emf of E = 100 volts. Find I and Q given the initial conditions Q = 0; I = 0 at t = 0
To solve for I and Q in this electric circuit, we can use the equations for the charge and current in a series RL circuit with a capacitor:
Q = CV(1 - e^(-t/RC))
I = (E/R)e^(-t/tau) + (Q/R) where tau = L/R
Plugging in the given values, we have:
Q = (100 micro farads)(100 volts)(1 - e^(-t/(20 ohms)(0.05 henry)))
I = (100 volts/20 ohms)e^(-t/(0.05 henry/20 ohms)) + Q/20 ohms
Using the initial conditions Q = 0 and I = 0 at t = 0, we can simplify the equations to:
Q = 100 micro farads * 100 volts * (1 - e^(-t/1 millisecond))
I = (100 volts/20 ohms)e^(-t/1 millisecond)
So at t = 1 millisecond, we have:
Q = 100 micro farads * 100 volts * (1 - e^(-1))
≈ 42.36 microcoulombs
I = (100 volts/20 ohms)e^(-1)
≈ 1.831 amperes
Therefore, at t = 1 millisecond, the charge on the capacitor is about 42.36 microcoulombs and the current in the circuit is about 1.831 amperes.
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Find m∠T in parallelogram QRST.
The unknown angle of the parallelogram is as follows:
m∠T = 63 degrees
How to find the angle of a parallelogram?A parallelogram is a quadrilateral with opposite sides parallel to each other and opposite congruent to each other.
Therefore, the opposite angles of a parallelogram are equal. Consecutive angles are supplementary angles to each other.
Hence,
10w + 53 + 17w + 100 = 180
27w + 153 = 180
27w = 180 - 153
27w = 27
divide both sides by 27
w = 27 / 27
w = 1
Therefore,
m∠T = 10(1) + 53 = 63 degrees
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(question/equation in the photo) PLEASE PLEASE HELP ITS DUE TMR
Answer:
The perimeter of the quarter circle is 24.997 cm
Step-by-step explanation:
Given, the radius of the circle = 7 cm
The perimeter of the circle = 2πr
and perimeter of the quarter circle = 2r + C
where r is the radius and C is the circumference of the sector of a circle
Circumference of the sector = ∅/360°(2πr)
C = 90°/360°(2×3.142×7)
C = 10.997 cm
perimeter of the quarter circle = 2r + C
= 2×7 + 10.997
= 24.997 cm
The perimeter of the quarter circle will be 24.997 cm
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pls help me i need to show work and i need it asap
(1) The two triangles are similar because they have equal angles.
(2) Triangle QRS is similar to triangle QLM because they have equal angles.
(3) Both triangles are similar and the value of x is 21.
What are the measure of the triangles?Two triangles are said to be similar if they have equal sides, equal angles or both.
The missing angles of the triangles for the question is calculated as;
Bigger triangle; missing angle = 180 - (44 + 46) = 90
Smaller triangle; missing angle = 90 - 46 = 44⁰
Both triangles are similar.
For the second question; triangle QRS is similar to triangle QLM because angle R is equal to angle L, and also they have common angle Q, which implies that angle S must be equal to angle L.
For third question, the triangles are similar because their corresponding angles are equal.
The value of x is calculated as;
48 + 4x + (180 - (56 + 76)) = 180 (sum of angles on a straight line)
48 + 4x + 48 = 180
4x = 84
x = 84/4
x = 21
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To encourage a student in his work on rates and ratios, his teacher promises to pay him 70 cents for every correct problem he solves. However, for every problem where he gives an incorrect answer, the teacher will take 40 cents off him! Amazingly, at the end of 33 problems completed, neither owes anything to the other. So how many problems did the student solve correctly? Investigate this fully (give evidence) and clearly show how you arrive at your solution.
Answers only will be awarded O marks
The student solved 12 problems correctly.
To find out how many problems the student solved correctly, we can use the given information and set up an equation using the terms "correct problems" and "incorrect problems."
Let x represent the number of correct problems and y represent the number of incorrect problems. We know the following:
1. The total number of problems completed is 33, so x + y = 33.
2. The teacher pays 70 cents for correct problems and takes 40 cents for incorrect problems, and neither owes anything to each other. So, 70x - 40y = 0.
Now, we'll solve this system of equations step-by-step:
Step 1: Solve the first equation for x: x = 33 - y.
Step 2: Substitute the expression for x in the second equation: 70(33 - y) - 40y = 0.
Step 3: Simplify and solve for y: 2310 - 70y - 40y = 0 => 2310 - 110y = 0 => y = 21.
Step 4: Substitute the value of y back into the equation for x: x = 33 - 21 => x = 12.
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regression statistics multiple r 0.717752328 r square 0.515168405 adjusted r square 0.494754443 standard error 8.735082924 observations 100 anova df ss ms f significance f regression 4 7702.221 1925.555 25.2361 2.9621e-14 residual 95 7248.659 76.302 total 99 14,950.880 step 1 of 2 : how many independent variables are included in the regression model?
Based on the information provided, it appears that there are 4 independent variables included in the regression model.
This is indicated by the "regression" row in the ANOVA table, which shows that there are 4 degrees of freedom (df) for the regression. This is determined by the degrees of freedom (df) for the regression, which is 4. The df for regression represents the number of independent variables in the model.
A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable.
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write the radicand as the product of a perfect cube first and a factor that does not contain a perfect cube (second)
The number or expression underneath the top line of the symbol is called the radicand. The cube root symbol is a grouping symbol, meaning that all operations in the radicand are grouped as if they were in parentheses.
To write the radicand as the product of a perfect cube (first) and a factor that does not contain a perfect cube (second), follow these steps:
1. Identify the radicand in the given expression. The radicand is the number or expression inside the cube root symbol.
2. Determine the prime factors of the radicand by breaking it down into its smallest prime factors.
3. Group the prime factors into sets of three identical factors. These sets will form the perfect cube factors.
4. Multiply the sets of three factors together to form the perfect cube part of the product.
5. Multiply any remaining factors together to form the factor that does not contain a perfect cube.
6. Write the radicand as the product of the perfect cube (step 4 result) and the factor that does not contain a perfect cube (step 5 result).
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