The number of slack variables in an initial tableau is equal to the number of "less than or equal to" constraints in the linear programming problem.
To determine how many slack variables are in an initial tableau, you need to consider the number of constraints in the linear programming problem. Here are the steps to follow:
Identify the number of constraints in the problem: These are the inequality constraints that typically involve "less than or equal to" (≤) or "greater than or equal to" (≥) symbols.
Assign a slack variable for each constraint: For each "less than or equal to" constraint, add a non-negative slack variable to convert the constraint into an equation. For each "greater than or equal to" constraint, you would add a non-negative surplus variable and an artificial variable.
Create the initial tableau: In the initial tableau, the columns will correspond to the decision variables, slack variables, and the objective function value (if needed). Each row will represent one constraint equation.
In summary, the number of slack variables in an initial tableau is equal to the number of "less than or equal to" constraints in the linear programming problem.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Yvonne put $4,000 in a savings account. At the end of 3 years, the account had earned $960 in simple interest. a. How much does she have in her account at the end of 3 years?b. At what annual simple interest rate did the account grow? C. How many more dollars would she have in her account if the interest rate were 1% greater?
Solution :
The amount invested by Yvonne = $ 4,000
Time of investment = 3 years
The simple interest earned by Yvonne in 3 years = $ 960
a). Therefore, the amount Yvonne earned by the end of three years is
= principal + interest earned
= 4,000 + 960
= $ 4,960
b). The formula for simple interest(S.I.) is given by :
[tex]$S.I. =\frac{P.T.R}{100}$[/tex]
or [tex]$R = \frac{SI \times 100}{P.T}$[/tex]
[tex]$ = \frac{960 \times 100}{4000 \times 3}$[/tex]
= 8%
c). Now if the interest rate is 1% greater, i.e. R = (8+1) = 9%
∴ [tex]$SI =\frac{P.T.R}{100}$[/tex]
[tex]$SI =\frac{4000 \times 3 \times 9}{100}$[/tex]
SI = $1,080
Therefore, the amount at the end of 3 years with 9% rate of interest will be
= 4000 + 1080
= $ 5080
Thus, Yvonne will have 5080 - 4960 = $ 120 money more in her account if the rate of interest was 1% greater.
uhhh just look at the screenshot then answer
Answer:
The Independent is the Number of Hours while the Dependent is the Number of Miles
Equation: y= 50x
Step-by-step explanation:
I Hope this helped
DEF is a right angled triangle calculate the length of EF correct to 3 sigificant figures
Answer:
[tex]\displaystyle EF \approx 15.9[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTrigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] cosθ = adjacent over hypotenuseStep-by-step explanation:
Step 1: Define
Angle θ = 28°
Adjacent Leg = EF = x
Hypotenuse = DF = 18
Step 2: Solve for x
Substitute in variables [Cosine]: [tex]\displaystyle cos28^\circ = \frac{x}{18}[/tex][Multiplication Property of Equality] Multiply 18 on both sides: [tex]\displaystyle 18cos28^\circ = x[/tex]Evaluate trig: [tex]\displaystyle 18(0.882948) = x[/tex]Multiply: [tex]\displaystyle 15.8931 = x[/tex]Rewrite: [tex]\displaystyle EF = 15.8931[/tex]Round: [tex]\displaystyle EF \approx 15.9[/tex]Robin was given a $40 monthly allowance. She wants to go to the movies as many times as possible and have at least $12.50 left at the end of the month to go to a concert. A movie ticket costs $5. How many times can she go to the movies?
Answer:
5 times
Step-by-step explanation:
5*5 is 25
40-25=15$ left
any more movie tickets would be too much money spent
If Robin was given a $40 monthly allowance. She wants to go to the movies as many times as possible and have at least $12.50 left at the end of the month to go to a concert. A movie ticket costs $5. Then she can go six times to the movies.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Robin was given a $40 monthly allowance.
She wants to go to the movies as many times as possible and have at least $12.50 left at the end of the month to go to a concert.
The amount spent on movies
40-12.5
$27.5
A movie ticket costs $5.
We need to find how many times can she go to the movies.
To find this we need to divide $27.5 by 5
$27.5/5=5.5
Robin can go 6 times to the movies.
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4. Calculate the mean of the data set {22, 34, 37, 23, 45, 21, 29, 37}. Round to the nearest tenth.
37
31.0
35.4
31.5
Answer:
31.0
Step-by-step explanation:
The mean of a given set of data is the ratio of the sum of the data to the number of units that make up the data set. It is also called the average of the data set.
Given the data set {22, 34, 37, 23, 45, 21, 29, 37}. There are 8 numbers in the set. The total of these numbers
= 22 + 34 + 37 + 23 + 45 + 21 + 29 + 37
= 248
The mean = 248/8
= 31
Which expression is equivalent to (-3)x+ (-3) (-12)? A - 3x +36 KB - 3x - 36 c 3x - 36 3x +36
Answer:
-3x + 36
Step-by-step explanation:
A bike rental company rents beach bikes. They charge an initial fee plus $3 for each hour the
bike is rented. Charles rented a bike for 4 hours and was charged $22. Let x represent the
number of hours and y represent the total cost of the rental.
Use the key information above to find an equation that
represents this rental costs at the bike company. How much
would it cost someone to rent the same bike, with the same
fees, for 6 hours?
O $26
O $28
O $30
O $24
Since chad was charged 1 dollars for each hour for 6 hours, we can represent this as 1 x 6. Now subtract 6 dollars from the bill for the hours and it leaves the initial fee of $4 for rental.
Now check your work:
(1 x 6) + 4 = 10
Answer:
They would pay $28.
Step-by-step explanation:
4 x 3 = 12, 22-12= 10. $10 is initial fee.
6 x 3 = 18, 18+10= 28. $28 for 6 hours
For babysitting Nicole charges a flat fee of $7, plus $12 per hour. Write and equation for the cost, C, after h hours of babysitting. PLS HELP I WILL GIVE BRAINLIEST
Answer:
C=12h+7
Step-by-step explanation:
The total cost = 7 (flat rate) + 12h (12/hour)
It would be appreciated if you could may help me with this
Answer:
Answer for the first pic is 122.24
Answer for the second pic is A
Step-by-step explanation:
the rectangle is 72 in
the semi-circle is 50.24
Answer for the first pic: 122.24 in
Answer for the second pic: A
A car ride is drawn on a coordinate plane so that the first card is located at the point by (5,10) what are the coordinates of the first car after a rotation of 270° about the origin
Answer:
There are two possible solutions:
Clockwise rotation
[tex]P'(x,y) = (-10,5)[/tex]
Counterclockwise rotation
[tex]P'(x,y) = (10, -5)[/tex]
Step-by-step explanation:
There are two possible answers: (i) Clockwise rotation, (ii) Counterclockwise rotation. Vectorially speaking, rotation of point of rotation of a point about another point of reference is defined by:
[tex]P'(x,y) = O(x,y) + r_{OP}\cdot (\cos (\theta_{OP}\pm \theta'),\sin (\theta_{OP}\pm \theta'))[/tex] (1)
Where:
[tex]O(x,y)[/tex] - Point of reference.
[tex]r_{OP}[/tex] - Length of the segment OP.
[tex]\theta_{OP}[/tex] - Direction of segment OP, measured in sexagesimal degrees.
[tex]\theta '[/tex] - Angle of rotation, measured in sexagesimal degrees.
Please notice that clockiwise rotation occurs when [tex]\theta = \theta_{OP}-\theta'[/tex] and counterclockwise rotation when [tex]\theta = \theta_{OP}+\theta'[/tex]. In addition, we define length and direction of the segment below:
[tex]r_{OP} = \sqrt{(x_{P}-x_{O})^{2}+(y_{P}-y_{O})^{2}}[/tex] (1)
[tex]\theta_{OP} = \tan^{-1} \frac{y_{P}-y_{O}}{x_{P}-x_{O}}[/tex]
If we know that [tex]x_{O} = y_{O} = 0[/tex], [tex]x_{P} = 5[/tex], [tex]y_{P} = 10[/tex] and [tex]\theta' = 270^{\circ}[/tex], then the coordinates of the first car after rotation is:
[tex]r_{OP} = \sqrt{(5-0)^{2}+(10-0)^{2}}[/tex]
[tex]r_{OP} \approx 11.180[/tex]
Please notice that original point is located at first quadrant of the Cartesian plane centered at origin, then the direction of the segment OP is:
[tex]\theta_{OP} = \tan^{-1} \frac{10-0}{5-0}[/tex]
[tex]\theta_{OP} \approx 63.435^{\circ}[/tex]
The two solutions are finally presented:
Clockwise rotation
[tex]P'(x,y) = (0,0) + 11.180\cdot (\cos (-206.565^{\circ}),\sin (-206.565^{\circ}))[/tex]
[tex]P'(x,y) = (-10,5)[/tex]
Counterclockwise rotation
[tex]P'(x,y) = (0,0) + 11.180\cdot (\cos (333.435^{\circ}),\sin (333.435^{\circ}))[/tex]
[tex]P'(x,y) = (10, -5)[/tex]
From a point 114 m away from a building, Serena measures the angle between the
ground and the top of a building and finds it measures 43°. What is the height of the
building? Round to the nearest meter.
Answer:
4900
Step-by-step explanation:
so what you're going to do first is you're going to do 114* 43 which equals 4902 then you round that and you're going to have 4900I am not a hundred percent sure
Y=x^4-4x^3.FInd the value of u when x=-1
What is the x-value of the solution to the system of equations?
5x + 4y =8
2x -3y = 17
-3
O -2
O 4
O5
Answer:
-234
Step-by-step explanation:
5x + 4y =8 2x -3y = 17 -3 O -2 O 4 O5=234
Terry is building a rectangular pen for her sheep. She wants the perimeter of the pen to be no more than 65 feet, and the length of the pen to
be at least 17 feet.
Which system can be used to find the possible values for the length (l) and width (w) of a rectangular pen for Terry's sheep?
Answer:D!
Step-by-step explanation: i’m taking the test rn!
By selling a watch for Rs 1275, Javed lost 15%. At what price should he sell to make a profit of 10%
Answer: Rs. 1,650
Step-by-step explanation:
First find the original price of the watch.
If the watch is sold at Rs. 1,275, there is a 15% loss.
Assume the watch is x.
(1 - 15%) * x = 1,275
0.85x = 1,275
x = 1,275 / 0.85
x = Rs. 1,500
Now add a 10% markup on the original:
= (1 + 10%) * 1,500
= 1.1 * 1,500
= Rs. 1,650
What is the slope and y-intercept of the following equation: y = -4 +2x
Answer:
slope = 2, y- intercept = - 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 4 + 2x , that is
y = 2x - 4 ← is in slope- intercept form
with slope m = 2 and y- intercept c = - 4
Find the distance between the two points. Leave
your answer exact. (-8, 10) and (-6, 7)
A. V13
B. 3.6
C. V169
D. 13
Answer:
A. V13
Step-by-step explanation:
Janna works at a lab with a huge circular particle accelerator. It has a radius of 4 kilometers. What is the accelerator's diameter?
Step-by-step explanation:
since it is a circle the diameter is two times larger than radius.So 4×2=8km
I will mark you brainiest if you can answer this
Answer:
I believe it's eighteen.
Step-by-step explanation:
Determine the value of y, if x is 4.
PLEASE HELP
Two ships leave Liverpool at the same time one travel north- west at an average speed of 10.5 km/h while the other travels at an average speed of 14km/h in a bearing of 280
Answer:
нечего не понятно но очень интересно да, очень
50 apples cost $25. How much would 75 apples cost?
Answer:
[see below]
Step-by-step explanation:
50 apples cost 25 dollars.
25/50 = 0.5
Each apple cost half a dollar.
0.5 * 75 = 37.50
75 apples should cost $37.50.
Hope this helps.
Question 3 , HELP! PLEASE!
Answer:
12mlies
Step-by-step explanation:
just add 7 + 5 and boom you have you answer
Diego drank 0.162 liters of water from a 1-liter bottle. How much water is left in the bottle?
A circular race track is 62.8 miles around. A driver is moving at 5 miles an hour driving from the outside to the center of the track. How long will it take for him to arrive?
Calculate the time it takes to travel to the center.
G I V E N
Speed of driver = 5 miles/hours
Distance to be covered = 62.8 miles
F O R M U L A ~ U S E D
Speed = Distance/Time
S O L U T I O N
Time = Distance/Speed
= 62.8 miles / 5 miles / hour
= 12.56 hours
It will take 12.56 hours to cover 62.8 miles, if the driver is moving
with 5 miles/hours
PLEASE HELP 16 POINTS is math
PLEASE SOLVE! Also how do you properly solve them ( please include steps)
Solve the equation for x:
2(8x – 16) = 48
Answer:
The answer would be 5
Step-by-step explanation: Plz mark brianliest
Evaluate the expression
27²
⁻⁻⁻⁻
27^4/3
Answer:
The answer is 9
Step-by-step explanation:
27^2 =729
729/27^4/3
Solve for the value of p.
2 Xp=44
Answer:
p=22
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