The minimum time for completing the project, based on the critical path analysis, is 18 weeks. The critical path, which consists of activities with zero slack time, includes activities A, B, C, F, G, and H. By summing up the durations of these critical activities, we find that the minimum time for completing the project is 18 weeks.
To calculate the minimum time for completing the project, we need to identify the critical path, which consists of activities with zero slack time. Here are the step-by-step calculations:
1. Assign forward and backward pass values:
Start by assigning the project start time as Early Start (ES) = 0 for Activity A. Then, calculate the Early Finish (EF) for each activity by adding the duration to the ES. The backward pass starts from the project completion time, which is the Late Finish (LF) for Activity I, initially set at 26 weeks. Calculate the Late Start (LS) for each activity by subtracting the duration from the LF.
Activity A: ES = 0, EF = ES + 4 = 4, LS = LF - 4 = 26 - 4 = 22, LF = 26
Activity B: ES = 4, EF = ES + 3 = 4 + 3 = 7, LS = LF - 3 = 26 - 3 = 23, LF = 26
Activity C: ES = 7, EF = ES + 2 = 7 + 2 = 9, LS = LF - 2 = 26 - 2 = 24, LF = 26
Activity D: ES = 7, EF = ES + 6 = 7 + 6 = 13, LS = LF - 6 = 26 - 6 = 20, LF = 26
Activity E: ES = 13, EF = ES + 5 = 13 + 5 = 18, LS = LF - 5 = 26 - 5 = 21, LF = 26
Activity F: ES = 13, EF = ES + 4 = 13 + 4 = 17, LS = LF - 4 = 26 - 4 = 22, LF = 26
Activity G: ES = 18, EF = ES + 2 = 18 + 2 = 20, LS = LF - 2 = 26 - 2 = 24, LF = 26
Activity H: ES = 20, EF = ES + 3 = 20 + 3 = 23, LS = LF - 3 = 26 - 3 = 23, LF = 26
Activity I: ES = 9, EF = ES + 5 = 9 + 5 = 14, LS = LF - 5 = 26 - 5 = 21, LF = 26
2. Calculate slack time:
Slack time (ST) can be calculated by subtracting the EF from the LS or the ES from the LF for each activity.
Activity A: ST = LS - EF = 22 - 4 = 18
Activity B: ST = LS - EF = 23 - 7 = 16
Activity C: ST = LS - EF = 24 - 9 = 15
Activity D: ST = LS - EF = 20 - 13 = 7
Activity E: ST = LS - EF = 21 - 18 = 3
Activity F: ST = LS - EF = 22 - 17 = 5
Activity G: ST = LS - EF = 24 - 20 = 4
Activity H: ST = LS - EF = 23 - 23 = 0
Activity I: ST = LS - EF = 21 - 14 = 7
3. Identify the critical path:
The critical path consists of activities with zero slack time. In this case, the critical path includes activities A, B, C, F, G, and H.
4. Calculate the minimum project completion time:
Sum up the durations of the activities on the critical path to find the minimum time for completing the project.
Minimum Time = Duration of Activity A + Duration of Activity B + Duration of Activity C + Duration of Activity F + Duration of Activity G + Duration of Activity H
= 4 + 3 + 2 + 4 + 2 + 3
= 18 weeks
Therefore, the minimum time for completing the project is 18 weeks.
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A speed walker covered 4 1/2 mi in 3/4 hour. How far will he walk in 3/4 hour if he walks
a.1.5 times as fast
b.twice as slower.
Answer:
A=27/4 B=2.25
Step-by-step explanation:
4 and 1/2 also equals 18/4.
18/4+1/2(18/4)=18/4+9/4
18+9=27
Answer is 27/4
B)=4.5/2=2.25
Hilda adds 5 to a number, then multiplies the sum by negative 2. The result is 6. Write and solve an equation to find the number, x.
What is the number?
The unknown number will be -8 for the given expression.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Hilda adds 5 to a number, then multiplies the sum by -2. Let the number be x. Form the mathematical expression from the given information and solve for the value of x.
-2 ( x + 5 ) = 6
-2x - 10 = 6
-2x = 6 + 10
-2x = 16
x = 16 / -2
x = -8
Therefore, the unknown number will be -8 for the given expression.
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y=×+2
how do u solve this?
3 comic books for 3 dollars
Answer:
so 1 dollor for each comic book
Step-by-step explanation:
If you take 2 steps every minute, how long will 20 steps take?
Answer:
10 minutes
Step-by-step explanation:
just divide 20 by 2 to get the minutes also WHO WALKS THAT SLOW?!??!?!
The figure shows the letter T and four of its transformed images—A, B, C, and D. Which of the four images was formed by a reflection of the letter T? (WILL MARK BRAINLIEST)
Answer:
C
Step-by-step explanation:
image C
reflection over the y axis
(x,y) ====> (-x,-y)
original points: ( -3,-1) , (-5,-1) , (-4,-3)
reflection over y axis :
(-3,-1) ===> (3,-1)
(-5,-1) ===> (5,-1)
(-4,-3) ===> (4,-3)
The student council needs to raise at least $950 to pay for their trip to Washington, DC. They have raised $589.55
so far. If they sell bagels to raise the rest of the money and charge $2 for each bagel sold, what is the minimum
number of bagels they need to sell to raise enough money?
168
181
294
295
Answer:
181 bagels
Step-by-step explanation:
Well how much money did they have to raise more to get to $950? It is $360.45. So now we take $360.45 and divide it by 2 and we get 180.225. But if we round 180.225 they would have to sell at least 181 bagels to raise $950 dollars.
Answer:
181 is the correct answer
Step-by-step explanation:
Did I do this equation correctly?
Answer:
It looks correct!!!!!!!!!
At the end of an experiment, a rat weighed 3.1 times its original weight. If the rat originally weighed 5.8 ounces, about how much did it weigh after the experiment?
A: 15 ounces
B: 18 ounces
C: 20 ounce
D: 24 ounces
Answer:
B
Step-by-step explanation:
5.8 multiplied by 3.1 equals 17.98, and you can round to 18 ounces.
Answer:
b.18 ounces
Step-by-step explanation:
i got it right on engnuity
Solve 48 = 5(2x - 7) + 3.
Justify each step.
Answer:
x=8
Step-by-step explanation:
48=5(2x-7)+3
Use the distributive property
48=10x-35+3
Combine like terms
48=10x-32
Add 32 to both sides to cancel out the negative 32
80=10x
x=8
Answer:
x = 8
Step-by-step explanation:
Step 1: Write equation
48 = 5(2x - 7) + 3
Step 2: Solve for x
Distribute 5: 48 = 10x - 35 + 3Combine like terms: 48 = 10x - 32Add 32 to both sides: 80 = 10xDivide both sides by 10: 8 = xRewrite: x = 8Step 3: Check
Plug in x to verify it's a solution.
48 = 5(2(8) - 7) + 3
48 = 5(16 - 7) + 3
48 = 5(9) + 3
48 = 45 + 3
48 = 48
What is 4 to the power of 3 simplified
Answer:
the answer is 64 because you should multiply it by it self for three times
Answer:
68
Step-by-step explanation:
because 4×4×4 =68
and I think it will helpful answer.
There are 9 water bottles in the refrigerator. I add 3 full boxes of water bottles to the refrigerator. Then i had two more boxes that each had 1 fewer bottle then the full box. Now that i'm done there's 67 bottles. What equation would find the number of bottles in a full box
Answer:
There are twelve 12 bottles in one full box.
Step-by-step explanation:
From the given information:
suppose there are 9 water bottles in the refrigerator,
and 3 full boxes of water are being added, we do not know the total number of bottles in a box, so let's represent it by b
i.e. 3b
However, two more boxes are being added which had 1 fewer bottle than the full box.
i.e. 2(b-1)
Now to determine the number of bottles in a full box, we have:
9 + 3b +2(b-1) = 67
9 + 3b + 2b - 2 = 67
5b + 7 = 67
5b = 67 - 7
5b = 60
b = 60/5
b = 12
Hence, there are twelve 12 bottles in one full box.
equation 1: 3x - 5y = 4
equation 2: -2x + 6y= 18
Answer:
1.x=4+5y/3
2.x=3y−9
Step-by-step explanation:
Which statement can be used to prove whether the conjecture is true or false?
What does the statement prove? (the picture)
Select one answer
A. The area of FCDE is 12 and CF×DE=16.
B. The area of ABDE is 24 and AB×AE=24.
C. The area of ABDE is 24 and AB×BD=24.
D. The area of FCDE is 12 and FE×DE=12.
The statement proves that the conjecture is..
A. True
B. False
Answer:
B and false
Step-by-step explanation:
Lol
The statement proves the conjecture which is the area of the rectangle ABDE and AB×AE=24 units.
What is the area of the rectangle?The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.
Given here: The triangle ABDE with AB and AE as the length and AB as the breadth.
Thus the area of the rectangle ABDE= 6×4
=24 units
Thus, The conjecture is True as the rectangle ABDE and the area of the rectangle is equal to 24 units.
Hence, The statement proves the conjecture which is the area of the rectangle ABDE and AB×AE=24 units.
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in δghi, h = 9.3 cm, g = 5.8 cm and ∠g=50°. find all possible values of ∠h, to the nearest 10th of a degree.
The given conditions cannot form a triangle. The sum of the angles in a triangle must be 180 degrees. In this case, the sum of the angles is 100 degrees (50 + 50). Therefore, there is no possible value for angle h.
Here is the calculation:
Angle G + Angle H + Angle I = 180
50 + Angle H + Angle I = 180
Angle H + Angle I = 180 - 50
Angle H + Angle I = 130
Since the sum of angle h and angle i is 130 degrees, there is no possible value for angle h that will result in a triangle with a total angle measure of 180 degrees.
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Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left. Write an equation to determine the number of friends (x)(x)left parenthesis, x, right parenthesis at Jack's party.
Answer:
3x + 2 = 50
16
Step-by-step explanation:
According to the given situation, the equation to determine the number of friends is shown below:-
We assume the number of friends is x
50 - 3x = 2
-3x = -48
3x = 48
x = 16
So, the equation is
3x + 2 = 50
and the number of friends is 16
Therefore, the equation to determine the number of friends we just solved the above equation.
Answer:
3x+2=50 and the number of friends is 16
Step-by-step explanation:
what two numbers can add to 4 but multiple to -12
Answer:
Numbers: 6 and -2
Step-by-step explanation:
Equations
This question can be solved by inspection. It's just a matter of factoring 12 into two factors that sum 4. Both numbers must be of different signs and they are 6 and -2. Their sum is indeed 6-2=4 and their product is 6*(-2)=-12.
However, we'll solve it by the use of equations. Let's call x and y to the numbers. They must comply:
[tex]x+y=4\qquad\qquad [1][/tex]
[tex]x.y=-12\qquad\qquad [2][/tex]
Solving [1] for y:
[tex]y=4-x[/tex]
Substituting in [2]
[tex]x(4-x)=-12[/tex]
Operating:
[tex]4x-x^2=-12[/tex]
Rearranging:
[tex]x^2-4x-12=0[/tex]
Solving with the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
With a=1, b=-4, c=-12:
[tex]\displaystyle x=\frac{-(-4)\pm \sqrt{(-4)^2-4(1)(-12)}}{2(1)}[/tex]
[tex]\displaystyle x=\frac{4\pm \sqrt{16+48}}{2}[/tex]
[tex]\displaystyle x=\frac{4\pm 8}{2}[/tex]
The solutions are:
[tex]\displaystyle x=\frac{4+ 8}{2}=6[/tex]
[tex]\displaystyle x=\frac{4- 8}{2}=-2[/tex]
This confirms the preliminary results.
Numbers: 6 and -2
Which equation is represented by line j?
Answer: its letter c or 3
Step-by-step explanation:
Please help!! Each pair of points lies on a line with the given slope. Find the missing value that results in the given slope:
Answer:
i think -12,9 and you multiply it by x,-2
Fun
+
Moon
—————
Scare
Can you replace the letters above with a digit from 0-9 to make the math equation correct?
The two Ns and two O’s must be represented by the same digit.
HINT: N=4, F=5, U=7
Please help me on this escape room! The answer has to be 5 digits!,
Answer:
574 + 9664 = 10238Step-by-step explanation:
GivenFUN + MOON = SCAREN= 4, F = 5, U = 7SolutionSubstituting given numbers:
Step 1
574 + MOO4 = SCAR8, E = 8 as 4+4M + 1 = S ⇒ M = 9, S = 1, C = 0 as single digit becomes 2-digitO > 4 as O + 5 should be 2 -digit numberStep 2
574 + 9OO4 = 10AR8Digits used so far: 0, 1, 4, 5, 7, 8, 9
Digits left: 2, 3, 6
Step 3
5 + O = A, O = 6 as it should be > 4, then we get A = 2 and R = 3574 + 9664 = 10238The difference of twice a number and five is three. Find the number.
Translate the word problem to an equation. Which steps describe how to solve the equation?
subtract 5 then multiply by -
add 5 then multiply by
add 2 then multiply by
multiply by then add 5
Answer:
the second option would be the answer add 5 then multiply by
max object z=11x+x+6w
6x+15x−3w≥60
3x+2x+w≤21
2x+3x−w=34
x≥0,y≥0,w≥0
solve the dual of the siven prislem usin the dual simplex algorithm
If you have access to a linear programming solver or software like Excel Solver or MATLAB's Optimization Toolbox, you can enter the dual problem and use the solver to obtain the optimal solution.
To solve the dual of the given problem using the dual simplex algorithm, we first need to rewrite the primal problem in standard form. The primal problem is as follows:
Maximize: z = 11x + x + 6w
Subject to:
6x + 15x - 3w ≥ 60
3x + 2x + w ≤ 21
2x + 3x - w = 34
x ≥ 0, y ≥ 0, w ≥ 0
The dual problem will have the following form:
Minimize: w = 60y + 21z + 34u
Subject to:
6y + 3u + 2v ≥ 11
15y + 2u + 3v + u + v ≥ 1
-3y + v = 6
y ≥ 0, u ≥ 0, v unrestricted
Now, we can apply the dual simplex algorithm to solve the dual problem. The steps involved in the dual simplex algorithm include:
Start with an initial feasible solution.
Check for optimality.
If not optimal, select a pivot column and pivot row.
Perform row operations to make the pivot element 1 and all other elements in the pivot column 0.
Repeat steps 2-4 until the optimal solution is reached.
The detailed calculations and iterations involved in the dual simplex algorithm can be quite lengthy and involve complex matrix operations. It would be best to use a specialized software or linear programming solver to perform these calculations accurately and efficiently.
If you have access to a linear programming solver or software like Excel Solver or MATLAB's Optimization Toolbox, you can enter the dual problem and use the solver to obtain the optimal solution.
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If you use the eight digits 1,2,3,4,5,6,7 and 9 each once and ONLY once to form 4 two-digit prime numbers. What will be the sum of the four prime numbers you created?
Answer:
190
Step-by-step explanation:
You want the sum of four 2-digit prime numbers that can be formed from the set of digits {1, 2, 3, 4, 5, 6, 7, 9} using each digit only once.
PrimesThere are 18 primes in the range 13-97 that have unique digits. These can be paired by the digits they use:
{23, 59} and {29, 53} . . . . number total = 82
{41, 67} and {47, 61} . . . . . number total = 108
Sets of 4A set of 4 primes with unique digits can be formed by choosing one of the first two pairs together with one of the second two pairs. For example, one possible choice is ...
{23, 59, 47, 61}
However you do this, the sum of the four primes will be ...
82 +108 = 190
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Find the product (-2/5)(-12/7)
Answer:
[tex]\frac{24}{35}[/tex]
Step-by-step explanation:
1. First turn (-2/5)(-12/7) into one fraction -> (* = multiply)
[tex]\frac{-2*-12 }{5*7}[/tex]
2. Simplify the top and bottom
[tex]\frac{-2*-12 }{5*7}[/tex] = [tex]\frac{24}{35}[/tex]
notice that negative times negative is equal to positive
Ex: -2 * -12 = +24
The sum of 6+0.413+0.173 is
Cans someone please help me I’m really confused?? and I’ll mark brainlist
Answer:
A. 1/2
Step-by-step explanation:
3/16 / 3/8
3/3 = 1
16/8 = 2
1/2
Answer: 1/2
Step-by-step explanation:
3/16 divided by 3/8
To divide by a fraction multiply by the reciprocal of that fraction
3/16 x 8/3
Reduce the numbers with the GCF (3)
1/16 x 8
Reduce the numbers with the GCF (8)
1/2 or 0.5
What is the length of the diagonal, d, of the rectangular prism shown below
The length of the diagonal of the rectangular prism is 8.31
Length of Diagonal in a Rectangular PrismThe diagonal length is calculated using the formula:
Diagonal = √(l² + h² + w²
Using the parameters given for our compuation:
length = 7
height = 2
width = 4
Inputting the values into our formula:
Diagonal = √(7² + 2² + 4²
Diagonal = √(49 + 4 + 16
Diagonal = √69
Diagonal = 8.31
Therefore, the length of the diagonal is 8.31
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On November 1, 2020 Starstruck Inc. signed a $300,000,8 month, 8% note payable. At due date, the principal and interest will be paid. Calculate the amount of interest expense that Starstruck Inc. should report on its income statement for the year ended December 31,2021. (round to the nearest dollar) Answer: \$.
Starstruck Inc. should report approximately $8,767 as the amount of interest expense on its income statement for the year ended December 31, 2021.
To calculate the amount of interest expense that Starstruck Inc. should report on its income statement for the year ended December 31, 2021, we need to determine the interest accrued for the 14-month period from November 1, 2020, to December 31, 2021.
The formula to calculate interest expense is:
Interest Expense = Principal * Interest Rate * Time
Principal = $300,000
Interest Rate = 8% per year
Since the note is an 8-month note, we need to calculate the interest for the 14-month period.
We can use the following formula to calculate the time in years:
Time = Number of days / Days in a year
Number of days from November 1, 2020 to December 31, 2021 = 426 days
Days in a year = 365 days
Time = 426 / 365
Now we can calculate the interest expense:
Interest Expense = $300,000 * 8% * (426 / 365)
Interest Expense ≈ $8,767.12
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simplify expression
8x-6+x-1
Answer:
9x -7
Step-by-step explanation:
8x-6+x-1
Combine like terms
8x +x -6-1
9x -7
Mrs. Lopez had $150.55 in her checking account. She wrote checks for the following amounts: $45.76, $35.82, and $79.00. What is the new balance in Mrs. Lopez’s checking account?
-11.03
10.03
11.03
-10.03
Answer:
-10.03
Step-by-step explanation:
45.76+35.82+79= 160.58
150.55-160.58= -10.03
