what is the lowest term of 2/30

Answer:

£334.40

Step-by-step explanation:

12% of 5700

= \(\frac{$(12\times 5700)/100$}\)

= 684

=  the deposit

5700 - 684 = 5016

this is the amount that needs to be paid after the deposit.

5016 / 15 = 334.40

= £334.40

The dual for the given linear programming problems are as follows:

(i) Minimize Z' = 10a + 12b Subject to: a + 7b ≥ 3 2a + 3b ≥ 4 a + 9b ≥ 5 a, b ≥ 0.

(ii) Maximize Z' = 5a + 6b + 2c Subject to: 3a + 2b + c ≤ 1 4a + 6b + c ≤ 2 a + b ≤ 0 a, b, c ≥ 0.

In the first problem, we have a maximization problem with three variables (x, y, z) and two constraints. The dual formulation involves minimizing a new objective function with two variables (a, b) and four constraints. The coefficients of the variables and the constraints are transformed according to the rules of duality.

The primal problem is:

Maximize Z = 3x + 4y + 5z

Subject to:

x + 2y + z ≤ 10

7x + 3y + 9z ≤ 12

x, y, z ≥ 0

To find the dual, we introduce the dual variables a and b for the constraints:

Minimize Z' = 10a + 12b

Subject to:

a + 7b ≥ 3

2a + 3b ≥ 4

a + 9b ≥ 5

a, b ≥ 0

In the second problem, we have a minimization problem with two variables (y1, y2) and three constraints. The dual formulation requires maximizing a new objective function with three variables (a, b, c) and four constraints. Again, the coefficients and constraints are transformed accordingly.

The primal problem is:

Minimize Z = y1 + 2y2

Subject to:

3y1 + 4y2 > 5

2y1 + 6y2 ≥ 6

y1 + y2 ≥ 2

To find the dual, we introduce the dual variables a, b, and c for the constraints:

Maximize Z' = 5a + 6b + 2c

Subject to:

3a + 2b + c ≤ 1

4a + 6b + c ≤ 2

a + b ≤ 0

a, b, c ≥ 0

The duality principle in linear programming allows us to find a lower bound (for maximization) or an upper bound (for minimization) on the optimal objective value by solving the dual problem. It provides useful insights into the relationships between the primal and dual variables, as well as the economic interpretation of the problem.

Learn more about maximization

brainly.com/question/29787532

#SPJ11

Answer:

the answer is 9

Step-by-step explanation:

Answer:

\(Pr = \frac{8 - \pi}{8}\)

Step-by-step explanation:

Given

See attachment for square

Required

Probability the \(dart\ lands\) on the shaded region

First, calculate the area of the square.

\(Area = Length^2\)

From the attachment, Length = 6;

So:

\(A_1 = 6^2\)

\(A_1 = 36\)

Next, calculate the area of the unshaded region.

From the attachment, 2 regions are unshaded. Each of this region is quadrant with equal radius.

When the two quadrants are merged together, they form a semi-circle.

So, the area of the unshaded region is the area of the semicircle.

This is calculated as:

\(Area = \frac{1}{2} \pi d\)

Where

\(d = diameter\)

d = Length of the square

\(d =6\)

So, we have:

\(Area = \frac{1}{2} \pi (\frac{d}{2})^2\)

\(Area = \frac{1}{2} \pi (\frac{6}{2})^2\)

\(Area = \frac{1}{2} \pi (3)^2\)

\(Area = \frac{1}{2} \pi *9\)

\(Area = \pi * 4.5\)

\(Area = 4.5\pi\)

The area (A3) of the shaded region is:

\(A_3 = A_1 - A_2\) ---- Complement rule.

\(A_3 = 36 - 4.5\pi\)

So, the probability that a dart lands on the shaded region is:

\(Pr = \frac{A_3}{A_1}\) i.e. Area of shaded region divided by the area of the square

\(Pr = \frac{36 - 4.5\pi}{36}\)

Factorize:

\(Pr = \frac{4.5(8 - \pi)}{36}\)

Simplify

\(Pr = \frac{8 - \pi}{8}\)

Answer:

50 inches

Step-by-step explanation:

Given that

5 equal sized square shelves arranged in a column.

Total area of five shelves = 500 sq inches

To find:

Length of shelving unit = ?

Solution:

First of all, let us find the area of each shelving unit.

Area of each shelving unit = Total area of five shelved divided by 5

Area of each shelving unit = 500 \(\div\) 5 = 100 sq units.

Each shelving unit is of square shape and area of a square is given as:

Area = \(Side^2\)

100 = \(Side^2\)

So, side of shelve = 10 inches

Now, there are 5 squares in the shelving unit.

So, length of shelving unit = \(10 \times 5 = \bold{50 \ inches}\)

Answer:

Step-by-step explanation:

4x + 2 + 3x + 3 = 180

7x + 5 = 180

7x = 175

x = 25

Answer:

x=9.3

Step-by-step explanation:

use SohCahToa

in this case u use cos

cos(41°)=7/x

x=7/cos(41)

x=9.275090953

x=9.3

Answer:

£312

Step-by-step explanation:

Answer:

15¢

Step-by-step explanation:

$12.75 - 6 × $2.10 = $12.75 - $12.60 = $0.15

Answer: 15 cents

The measure of line segment KJ in triangle KMJ is 5√3.

In the diagram, triangle KMJ forms a right triangle.

Line segment KM = 6

Line segment MJ = 3

Hypotenuse KJ = ?

To solve for the line segment KJ, we use the pythagorean theorem.

It states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

Hence:

c² = a² + b²

( KJ )² = ( KM )² + ( MJ )²

Plug in the values

( KJ )² = 6² + 3²

( KJ )² = 36 + 9

( KJ )² = 45

KJ = √45

KJ = 5√3

Therefore, the length of KJ is 5√3 units.

Option D)5√3 units is the correct answer.

Learn more about pythagorean theorem here: brainly.com/question/343682

#SPJ1

Part (c) is the correct option i.e. The total dealer's cost is $16588.36.

What is Percentage ?

Percentage, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolised as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

Given, Cost paid for car's options = 82 % $3,098 = $2540.36

           Cost paid for base price = 85 % $15,480 = $13158.

           Destination charge = $890

∴ The total dealer's cost will be :

 = Cost paid for car's options +  Cost paid for base price +  Destination charge

=  $2540.36 + $13158 + $890

= $16588.36.

To learn more about Percentage, visit the link given below:

https://brainly.com/question/24877689

#SPJ1

Given:

The four table of values.

To find:

The table whose linear function has slope 2.

Solution:

Slope formula:

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

Consider any two points from each table and find the slope for each table.

For table 1, the two points are (2,1) and (6,-1). So, the slope of the linear function is:

\(m=\dfrac{-1-1}{6-2}\)

\(m=\dfrac{-2}{4}\)

\(m=\dfrac{-1}{2}\)

For table 2, the two points are (0,8) and (2,4). So, the slope of the linear function is:

\(m=\dfrac{4-8}{2-0}\)

\(m=\dfrac{-4}{2}\)

\(m=2\)

For table 3, the two points are (-4,4) and (-2,5). So, the slope of the linear function is:

\(m=\dfrac{5-4}{-2-(-4)}\)

\(m=\dfrac{1}{-2+4}\)

\(m=\dfrac{1}{2}\)

For table 4, the two points are (-2,0) and (0,4). So, the slope of the linear function is:

\(m=\dfrac{4-0}{0-(-2)}\)

\(m=\dfrac{4}{2}\)

\(m=2\)

Table 4 is the only table that represents a linear function whose slope is 2.

Therefore, the correct option is 4, Table 4.

Answer:

If the third angle is x, the other two angles are 2x

The measure of the angles of a triangle must add up to 180 degrees

x + 2(2x) = 180

x + 4x = 180

5x = 180

x = 36

The other two angles are 2x = 2 * 36 = 72

The three angles are 36, 72, and 72 degrees

Step-by-step explanation:

EXAMPLE-

x+2x+2x=180

5x=180

x=180/5

x=36º third angle

the equal angles are each 2*36=72º

The required measure of three angles are 36, 72, and 72 degrees in the given triangle.

An Isosceles Triangle is defined as a triangle with two sides of equal length is an isosceles triangle.

Given that the third angle is x, the other two angles are 2x

We know that the measure of the angles of a triangle must add up to 180 degrees.

As per the given question, the equation would be as:

x + 2(2x) = 180

x + 4x = 180

5x = 180

x = 36

So, the other two angles are 2x = 2 × 36 = 72

Therefore, the required measure of three angles are 36, 72, and 72 degrees in the given triangle.

Learn more about Isosceles Triangle here:

brainly.com/question/2456591

#SPJ5

Answer:

Length = 12 cm

Step-by-step explanation:

using the Pythagorean theorem:

Length² = 13² - 5² = 169 - 25 = 144

Length = √144 m= 12 cm

Answer:

It's 34 cm

Step-by-step explanation:

Width of a rectangle = 5 cm

Diagonal of a rectangle = 13 cm

By Pythagoras Theorem,

Length of a rectangle = √(13² - 5²)

Or, Length of a rectangle = √(169 - 25)

Or, Length of a rectangle = √144

Or, Length of a rectangle = 12 cm

Perimeter of a rectangle = 2(12+5)

Or, Perimeter of a rectangle = 2×17

Or, Perimeter of a rectangle = 34 cm

Therefore, the perimeter of a rectangle = 34 cm

In the formulation of a mathematical model for an evaporator, the following are five key assumptions:

1. Constant volume and density of the system.

2. Evaporation takes place only from the surface of the liquid.

3. The transfer of heat takes place only through conduction.

4. The heat transfer coefficient does not change with time.

5. The properties of the liquid are constant throughout the system.

Derivation of the total mass balance equation:

The total mass balance equation relates the rate of mass flow of material entering a system to the rate of mass flow leaving the system.

It is given by:

Rate of Mass Flow In - Rate of Mass Flow Out = Rate of Accumulation

Assuming that the evaporator operates under steady-state conditions, the rate of accumulation of mass is zero.

Hence, the mass balance equation reduces to:

Rate of Mass Flow In = Rate of Mass Flow Out

Let's assume that the mass flow rate of the feed stream is represented by m1 and the mass flow rate of the product stream is represented by m₂.

Therefore, the mass balance equation for the evaporator becomes:

m₁ = m₂ + me

Where me is the mass of water that has been evaporated. This equation is useful in determining the amount of water evaporated from the system.

Learn more about evaporation at

https://brainly.com/question/2496329

#SPJ11

 Part 1:

Given:

Mean (μ) = $35,441

Standard deviation (σ) = $5,100

To find the probability that a randomly selected teacher's salary is greater than $48,200, we need to calculate the z-score and then find the corresponding probability from the standard normal distribution.

The z-score formula is:

\(\[ z = \frac{{X - \mu}}{{\sigma}} \]\)

Plugging in the values, we have:

\(\[ z = \frac{{48,200 - 35,441}}{{5,100}} \]\)

Calculating the z-score:

\(\[ z \approx 2.5 \]\)

Using the z-score table or statistical software, we find that the probability corresponding to a z-score of 2.5 is approximately 0.9938.

Therefore, the probability that a randomly selected teacher's salary is greater than $48,200 is approximately 0.9938.

Part 2:

Given:

Sample size (n) = 70

Sample mean \((\(\bar{x}\))\) = $36,142

Population standard deviation (σ) = $5,100 (given that the sample is taken from a large population)

To find the probability that the sample mean is greater than $36,142, we can use the Central Limit Theorem and approximate the sampling distribution of the sample mean as a normal distribution.

The mean of the sampling distribution \((\(\mu_{\bar{x}}\))\) is equal to the population mean \((\(\mu\)),\) which is $35,441.

The standard deviation of the sampling distribution \((\(\sigma_{\bar{x}}\))\) is calculated using the formula:

\(\[ \sigma_{\bar{x}} = \frac{{\sigma}}{{\sqrt{n}}} \]\)

Plugging in the values, we have:

\(\[ \sigma_{\bar{x}} = \frac{{5,100}}{{\sqrt{70}}} \]\)

Calculating the standard deviation of the sampling distribution:

\(\[ \sigma_{\bar{x}} \approx 610.4675 \]\)

To find the probability that the sample mean is greater than $36,142, we need to calculate the z-score using the formula:

\(\[ z = \frac{{\bar{x} - \mu_{\bar{x}}}}{{\sigma_{\bar{x}}}} \]\)

Plugging in the values, we have:

\(\[ z = \frac{{36,142 - 35,441}}{{610.4675}} \]\)

Calculating the z-score:

\(\[ z \approx 1.1477 \]\)

Using the z-score table or statistical software, we find that the probability corresponding to a z-score of 1.1477 is approximately 0.8749.

Therefore, the probability that the sample mean is greater than $36,142 is approximately 0.8749.

To know more about probability visit-

brainly.com/question/29892330

#SPJ11

The mean value of the scores is 19.83, based on their sum and quantity of numbers.

The mean or average is calculated using the formula -

Mean = sum of all the numbers ÷ quantity of numbers.

We see that there are six numbers and hence the quantity of numbers will be 6.

Sum of all the numbers = 12 + 25 + 15 + 27 + 32 + 8

Performing addition on Right Hand Side of the equation

Sum of all the numbers = 119

Now calculating the mean of the scores by keeping the values in formula -

Mean = 119/6

Performing division on Right Hand Side of the equation

Mean of scores = 19.83

Hence, the average of scores is 19.83.

Learn more about mean -

https://brainly.com/question/1136789

#SPJ4

Answer: b=4

Step-by-step explanation: 4b+5=1+5b = B = 4

Answer:

b = 4

Step-by-step explanation:

subtract 4b from 5b and you get 1b. subtract 1 from 5 and u get 4 = 1b. divide both sides by 1 therefore b = 4

Answer:

the mean is 67

Step-by-step explanation:

50+60=110

110+80=190

190+60=250

250+70=320

320+55=375

375+85=460

460+70=530

530+90=620

620+50=670

670 divided by 10=67

Answer: the mean value is 67

Step-by-step explanation:

min 50, median 65, mean 67, max90

To divide the polynomial p(x) by d(x), we can use long division or synthetic division. Let's say we choose to use long division.

First, we need to write the polynomials in descending order of degree, with any missing terms filled in with zeros. Let's say the polynomials are:

p(x) = 3x^3 - 5x^2 + 2x + 4
d(x) = x - 2

Then, we set up the long division like this:

         3x^2 + x + 4
   x - 2 | 3x^3 - 5x^2 + 2x + 4

We divide the first term of p(x) by the first term of d(x), which gives us 3x^2. We write this above the division bar and multiply it by d(x), which gives us 3x^3 - 6x^2. We subtract this from p(x), bringing down the next term:

         3x^2 + x + 4
   x - 2 | 3x^3 - 5x^2 + 2x + 4
         - 3x^3 + 6x^2
             ----------
              -11x^2 + 2x

We repeat the process with the next term, dividing -11x^2 by x to get -11x, writing this above the division bar, and multiplying it by d(x) to get -11x + 22. We subtract this from -11x^2 + 2x, bringing down the next term:

         3x^2 + x + 4 - 11/(x-2)
   x - 2 | 3x^3 - 5x^2 + 2x + 4
         - 3x^3 + 6x^2
             ----------
              -11x^2 + 2x
              + 11x^2 - 22
              ----------
                     -20

Since we have no more terms to bring down, our remainder is -20. Therefore, the quotient p(x)/d(x) is:

p(x)/d(x) = 3x^2 + x + 4 - 11/(x-2) - 20/(x-2)^2

We can express this in the form p(x) d(x) by multiplying both sides by d(x):

p(x) = d(x) (3x^2 + x + 4 - 11/(x-2) - 20/(x-2)^2)
To answer your question, we'll first need the specific polynomials for p(x) and d(x) that you'd like to divide. However, I can still guide you through the general steps to perform the division and express the quotient.

1. Choose either synthetic or long division, depending on your preference and the complexity of the polynomials.
2. Divide p(x) by d(x) using the chosen method. Make sure to follow the steps of the division process carefully to obtain the correct quotient and remainder.
3. Once the division is complete, express the quotient p(x)/d(x) in the form p(x) = d(x) * q(x) + r(x), where q(x) is the quotient and r(x) is the remainder.

Visit here to learn more about polynomial brainly.com/question/11536910

#SPJ11

We have the figure below: Given the figure above, we are to determine the values of x and z. Now, the interior angle sum of a pentagon is given by 540 degrees. We can use this property to write: 20 + 70 + 2z + (3x + 20) + x = 540. So, the values of x = 110/3 and z = 425/3.

Simplify and solve for x and z as shown: 20 + 70 + 2z + 3x + 20 + x = 540

4x + 110 + 2z = 540

4x + 2z = 540 - 110

4x + 2z = 430

2x + z = 215     ------ (1)

Also, 3x + 20 + 70 = 180

3x = 180 - 70

3x = 110

x = 110/3

Substituting this value of x into equation (1), we obtain: 2(110/3) + z = 215

(220/3) + z = 215

z = 215 - (220/3)

z = (645 - 220)/3

z = 425/3. Therefore, x = 110/3 and z = 425/3.

For more questions on: pentagon

https://brainly.com/question/30515954

#SPJ8

Answer:

1. y = -3x + 5

2. y = 1/4x - 2

Step-by-step explanation:

y=mx+b

1. 5 = -3(0) + b, so b = 5

y = -3x + 5

2. (-2-(-1))/(0-4) = -1/-4 = 1/4

-2 = 1/4(0) + b, so b = -2

y = 1/4x - 2

Answer: -3x+5

                1/4x - 2

Step-by-step explanation:

The remaining keys are hashed and placed in the table using linear probing until all keys are placed.

The hash table that results from using the hash function h(k) = k mod 13 to hash the keys 2, 7, 4, 41, 15, 32, 25, 11, and 30, assuming collisions are handled by linear probing:
Index       Key
0      
1      
2             2
3             4
4             30
5             41
6             15
7             7
8             25
9             11
10    
11    
12            32
To fill in the table, we apply the hash function to each key and then check whether that index is already occupied.

If it is, we move to the next index and continue until we find an empty spot. In this case, we start with the key 2, which hashes to index 2.

This index is empty, so we insert the key there.

Next, we hash the key 7, which also goes to index 2.

Since that spot is already occupied, we move to the next index (3) and find that it's empty, so we insert 7 there.

We continue in this way for each key, resolving collisions by linear probing.
For similar question on remaining keys:

https://brainly.com/question/30755956

#SPJ11

Answer: Part 1: 111.24

Part 2: 9.27

Part 3: 54 minutes

Step-by-step explanation:

Part 1: Since you already know that the total bill increases by 3%, you just have to find 103% of 180.

1.03*108= 111.24; your answer would be 111.24 pounds

Part 2: Since you already know yearly, 111.24 divided by 12= 9.27 per month

Part 3: First find 73% of 200 which is 146. Then subtract that from 200 which is 54. So you have 54 minutes left.

Answer:

$99,941 worth of goods sold

Step-by-step explanation:

104,000-4,059=99,941

Answer:

Slope-intercept

y = 3/4(x) - 7

Point slope

y -5= 3/4(x - 16)

Step-by-step explanation:

In slope-intercept

We have the general slope intercept as;

y = mx + b

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

in this case, m = 3/4 and b = -7

So we have;

y = 3/4(x) - 7

In point-slope

we have the general form as;

y-y1 = m(x-x1)

So what we have is as follows;

y -5= 3/4(x - 16)

Where we have (x1,y1) = (16,5)

The equation for the hyperbola with vertices at (0,-6) and (0,6) and an asymptote at y=3x is y^2 / 36 - x^2 / 16 = 1.

To find the equation of a hyperbola with vertices at (0,-6) and (0,6) and an asymptote at y=3x, we can use the standard form of a hyperbola:

((y - k)^2 / a^2) - ((x - h)^2 / b^2) = 1

where (h,k) is the center of the hyperbola and a and b are the distances from the center to the vertices along the transverse and conjugate axes, respectively.

In this case, the center of the hyperbola is at (0,0) since the vertices are equidistant from the origin. The distance from the center to each vertex is 6, so a = 6.

To find b, we can use the slope of the asymptote, which is 3. Since the conjugate axis is perpendicular to the transverse axis, its slope is -1/3. This means that the distance from the center to the edge of the hyperbola along the conjugate axis is 2b = 2 * (1/3) * 6 = 4.

Now we have the values of a and b, so we can substitute them into the standard form equation:

((y - 0)^2 / 6^2) - ((x - 0)^2 / 4^2) = 1

Simplifying this equation gives:

y^2 / 36 - x^2 / 16 = 1

Find out more about hyperbola

brainly.com/question/31451856

#SPJ11

The Jackson family averaged 22.71 miles per gallon on their trip.

To find out the average miles per gallon used by the Jackson family on their trip, the distance they covered and the amount of fuel they consumed are both necessary information.

They started their trip with an odometer reading of 18,649.3 miles, and the odometer reading at the end of the trip was 20,630.5.

The distance covered, therefore, is:20,630.5 - 18,649.3 = 1,981.2 miles

Next, to determine the average miles per gallon, divide the total distance covered by the amount of fuel consumed:1,981.2 miles ÷ 87.3 gallons

= 22.71 miles per gallon.

To know more about miles visit:

https://brainly.com/question/12665145

#SPJ11

Answer:

Step-by-step explanation:

Given

Natoy's rectangular swimming pool has the length of 3m more than thrice its

width.

Width=w

Length =3w+3

So

Area of the rectangular swimming pool=length×width

216=(3w+3)×w

216=3w^2+3w

3w^2+3w-216=0

3(w^2+w-72)=0

W^2+w-72=0

W^2+(9-8)w-72=0

W^2+9w-8w-72=0

W(w+9)-8(w+9)=0

(W+9)(w-8)=0

Sotwo value of w are 8,-9

We take positive value for rectangular swimming so we take w=8m

Width=8m

Length=3×8+3

= 24+3

=27m