given the following all-integer linear program: max 15x1 2x2 s. t. 7x1 x2 < 23 3x1 - x2 < 5 x1, x2 > 0 and integer a. solve the problem as an lp, ignoring the integer constraints. b. what solution is obtained by rounding up fractions greater than or equal to 1/2? is this the optimal integer solution? c. what solution is obtained by rounding down all fractions? is this the optimal integer solution? explain. d. show that the optimal objective function value for the ilp (integer linear programming) is lower than that for the optimal lp. e. why is the optimal objective function value for the ilp problem always less than or equal to the corresponding lp's optimal objective function value? when would they be equal? comment on the optimal objective function of the milp (mixed-integer linear programming) compared to the corresponding lp and ilp.

Answer:

  Horace

Step-by-step explanation:

You want to know if "base" refers to any particular side of a rectangle.

The formula for the area of a rectangle can be written ...

  Area = base × height

It can also be written ...

  Area = length × width

In each formula, the factors of the area refer to orthogonal dimensions of the rectangle. Any side of the rectangle can be considered to be the "base" or the "length" or the "width" or the "height". The other factor in the area formula is whatever dimension is orthogonal to that choice.

The commutative property of multiplication tells you that you get the same product if you reverse the order of the numbers.

So, you could have ...

  Area = AB·BC

or

  Area = BC·AB

If you insist that the fist of these numbers is the "base", then the base can be either AB or BC and the area will be the same.

The substitution property of equality tells you that you can substitute any equal values. Opposite sides of a rectangle are equal length, so either can be substituted for the other. In short, you can write the product for the area any of 8 ways:

  Area = AB·BC = AB·AD = BC·AB = AD·AB

  = CD·AD = CD·BC = AD·CD = BC·CD

If you want to distinguish between AB and BA, you can write this many more ways.

Horace seems to understand the fundamental interchangeability of the dimensions in the area formula. Horace has the right idea.

Bernice seems more attached to one particular understanding. We wonder what Bernice would call the "base" if the rectangle were drawn at a different angle to the grid.

Answer:

(a.)  8m

(b.) 12 cm

Step-by-step explanation:

a:

given: area of square = 64m²

formula of area of a square A = s²

We will reverse the formula to find the sum of the sides:

S = √A

S =√64

S = 8

b:

Given: perimeter of a square is 48 cm

formula for a perimeter of a square: P = 4 · s

We will reverse the formula to find the sum of the sides:

S = P ÷ 4

S = 48 ÷ 4

S = 12

The probability that the mean weight of two fruits picked at random falls between 360 grams and 491 grams is approximately 0.9554 or 95.54%.

To solve this problem, we need to use the formula for the sampling distribution of the sample mean:

x' = μ/√n

where x' is the sample mean, μ is the population mean, and n is the sample size.

Given that the population mean is 443 grams and the standard deviation is 34 grams, we can calculate the standard error of the sample mean:

SE = σ/√n

  = 34/√2

  ≈ 24.04 grams

Now we need to standardize the sample mean to a standard normal distribution using the z-score formula:

z = (x' - μ)/SE

The probability that the sample mean falls between 360 grams and 491 grams is equivalent to the probability that the z-score falls between:

z = (360 - 443)/24.04 ≈ -3.45 and z = (491 - 443)/24.04 ≈ 1.99

Using a standard normal table or calculator, we can find the probability that the z-score falls between -3.45 and 1.99, which is approximately 0.9554.

To learn more about distribution click on,

https://brainly.com/question/17355720

#SPJ4

The probability that at least three out of five randomly selected students will possess a GPA in excess of 3.0 is approximately 0.1772.

To solve this problem, we need to use the binomial distribution with n = 5 and the probability of success p = P(GPA > 3.0), which can be found using the normal distribution table:

P(GPA > 3.0) = P(Z > (3.0 - 2.7)/0.7) = P(Z > 0.43) = 1 - P(Z < 0.43) = 1 - 0.6664 = 0.3336

Now we can use the binomial distribution to find the probability that at least three students out of five have a GPA greater than 3.0:

P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5)

Using the binomial formula and the probabilities of success and failure:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

we get:

P(X = 3) = (5 choose 3) * 0.3336^3 * 0.6664^2 = 0.1311

P(X = 4) = (5 choose 4) * 0.3336^4 * 0.6664^1 = 0.0421

P(X = 5) = (5 choose 5) * 0.3336^5 * 0.6664^0 = 0.0040

Therefore:

P(X ≥ 3) = 0.1311 + 0.0421 + 0.0040 = 0.1772

So the probability that at least three out of five students have a GPA greater than 3.0 is approximately 0.1772.

To know more about Probability:

https://brainly.com/question/11234923

#SPJ4

--The given question is incomplete, the complete question is given

"  The grade point averages (GPAs) of a large population of college students are approximately normally distributed with mean 2.7 and standard deviation 0.7. Suppose that five students are randomly selected from the student body. What is the probability that at least three will possess a GPA in excess of 3.0? "--

Answer:

120° and 60°

Step-by-step explanation:

5x - 10 + 3x - 18 = 180

8x = 180 + 10 + 18

8x = 208 / : 8

x = 26

.

(5x - 10)° = (5 × 26 - 10)° = 120°

(3x - 18)° = (3 × 26 - 18)° = 60°

Answer:

  output = -3n +1

Step-by-step explanation:

Given an input/output table for a linear function, you want an expression for the output when the input is n.

The input values count up from 1, so we can consider the output values to be the terms of an arithmetic sequence.

The first term of the sequence is a1 = -2 (when n=1).

The common difference of the sequence is d = (-5 -(-2)) = -3.

The general (n-th) term of an arithmetic sequence is given by the formula ...

   an = a1 +d(n -1)

For the known values of a1 and d, we find the n-th term to be ...

  an = -2 +(-3)(n -1)

  an = -2 -3n +3 . . . . . . . eliminate parentheses

  an = -3n +1 . . . . . . . . collect terms

The term corresponding to an input value of n is ...

  -3n +1

The area of a right triangle is given by the formula:

Area = 1/2 * base * height

Substituting the values given in the problem:

Area = 1/2 * 45 meters * 16 and 3/4 meters

To simplify the computation, we convert the mixed fraction 16 and 3/4 to an improper fraction:

16 and 3/4 = (16 * 4 + 3) / 4 = 67/4 meters

Substituting this value, we get:

Area = 1/2 * 45 meters * 67/4 meters

Simplifying:

Area = 843.75 square meters

Therefore, the area of the right triangle is 843.75 square meters.

Answer: 376 7/8

Step-by-step explanation: if you multiply the base and the height you'll get 754 3/4 since this is a triangle we are talking about it would be halved which would make it 376 7/8.

and im doing the exam and its correct.

Answer:

The answer is 22

Step-by-step explanation:

You would first start by solving for the x value. You would do 6x-7=2x+5, then start factoring out number and variable until the variable is on 1 side and the number are on the other, so it'd be 4x=12. After you would calculate for the x which is 3, which you did, then you would plug that back into the values. You'd plug 3 into 2(x)+5 which simplifies down to 6+5 which is 11 and since DB is half of AB you multiply by 2 to get 22.

The given graph is an illustration of a piecewise linear equation.

Jamie correctly described what the graph could be used for (a relay race)

Jamie wrongly described the axes of the graph, in both sections

The piece-wise function is: [tex]y=\left \{ {{\frac{1}{12}x, 0 < = x < 12} \atop {\frac{1}{8}x+\frac{1}2},12 < x < =20}} \right.[/tex]

See the attachment for the graph and Jamie's work

From the graph, we have:

Time (minutes) = x

Distance (miles) = y

(a) When the runner begins the race

From the graph, we have:

x=[0,12]

y=[0,1]

This means that the runner runs a distance of 1 mile in 12 minutes

So; Jamie's description here is wrong because he misrepresented the axes.

The equation of this part is calculated as follows:

Start by calculating the slope (m)

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{1-0}{12-0}=\frac{1}{12}[/tex]

The equation is then calculated using:

[tex]y=m(x-x_1)+y_1\\\\y=\frac{1}{12}(x-0)+0\\\\y=\frac{1}{12}x[/tex]

(b) When his partner takes over

From the graph, we have:

x=(12,20]

y=(1,2]

This means that his partner runs a distance of 1 mile in 8 minutes

So; Jamie's description here is also wrong because he misrepresented the axes, again.

The equation of this part is calculated as follows:

Start by calculating the slope (m)

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-1}{20-12}=\frac{1}{18}\\\\y=\frac{1}{8}(x-12}+1\\\\y=\frac{1}{8}x-\frac{1}{2}[/tex]

Hence, the piece-wise function can be represented as:

The piece-wise function is: [tex]y=\left \{ {{\frac{1}{12}x, 0 < = x < 12} \atop {\frac{1}{8}x+\frac{1}2},12 < x < =20}} \right.[/tex]

Read more about piece-wise equations at:

https://brainly.com/question/16984860

#SPJ1

Answer: $178.31

Step-by-step explanation:

To calculate Heidi's overtime pay, we first need to find out how many hours she worked overtime and then multiply those hours by her overtime pay rate. The standard workweek in the United States consists of 40 hours, and any hours worked beyond 40 hours are considered overtime.

Step 1: Calculate the number of overtime hours:

Total hours worked = 47.50 hours

Standard workweek = 40 hours

Overtime hours = Total hours worked - Standard workweek = 47.50 - 40 = 7.50 hours

Step 2: Calculate Heidi's overtime pay rate:

Hourly wage = $15.85

Overtime pay rate = Hourly wage * 1.5 (overtime is typically paid at 1.5 times the regular hourly rate) = $15.85 * 1.5 = $23.775

Step 3: Calculate Heidi's overtime pay:

Overtime pay = Overtime hours * Overtime pay rate = 7.50 hours * $23.775 = $178.31 (rounded to 2 decimal places)

Heidi's overtime pay for the week is $178.31.

Since the cost of each card is $ [tex]0.56[/tex], you can now multiply the total number of cards by the cost per card. the value of the inventory at the end of the month is $ [tex]343.28[/tex].

To find the value of the inventory at the end of the month, you need to start by calculating the total number of birthday cards that Marika's Cards and Gifts had at the end of the month.

First, you need to add the number of birthday cards that Marika's sold during the month (208) to the number of cards received from the distributor in two separate orders) [tex](144 \times 2) = 288[/tex]

[tex]117[/tex] (initial inventory) + [tex]208[/tex] (cards sold) +  [tex]288[/tex] (cards received from distributor) =  [tex]613[/tex] (total number of birthday cards at the end of the month)

Since the cost of each card is $0.56, you can now multiply the total number of cards by the cost per card to get the value of the inventory:

[tex]613 \times[/tex] $[tex]0.56 =[/tex] $[tex]343.28[/tex]

Therefore, the value of the inventory at the end of the month is $343.28.

To learn more about cost, visit

brainly.com/question/14094934

#SPJ1

Answer:

y = 23 degrees

Step-by-step explanation:

115° and 5y° are equal because they are alternate exterior angles

115 = 5y

Divide by 5 to isolate the y

23 = y

so y is 23°

1.  Perimeter of AARG = 1.6 × 4.4 cm = 7.04 cm

2.  The measure of SBH is 162°.

3. Area of AARG = 2.56 × 0.8 cm² = 2.048 cm²

4. The length of the circumference of circle B is approximately 13.01 cm.

The circumference of a this double shape's perimeter is its total length. In other terms, it is the total length of all a shape's sides. For instance, the circumference of a circle is equal to the distance around its outside, or circumference, whereas the perimeter of a rectangle may be computed by combining the measurements of all four sides.

To solve this problem, we can use the fact that all circles are similar. This means that corresponding lengths of the circles are proportional. In particular, if the ratio of the radii of two circles is k, then the ratio of their circumferences is also k, and the ratio of their areas is k².

Let's start with finding the radius of the larger circle. Since OB/OA = 2.25, we can write:

OA + AB = OB

OA + 1 = 2.25 OA

OA = 1 / 1.25 = 0.8

Therefore, the radius of the larger circle is 0.8 cm. Since the circles are similar, the ratio of the radii is 0.8/0.5 = 1.6.

1. The perimeter of ABSH is proportional to the radius of the circle, so we have:

Perimeter of ABSH = 1.6 × Perimeter of AARG = 1.6 × 4.4 cm = 7.04 cm

2. Let x be the measure of SBH. Then we have:

RAG + SBH + HBS = 360°

108° + x + 90° = 360°

x = 162°

Therefore, the measure of SBH is 162°.

3. The area of ABSH is proportional to the square of the radius of the circle, so we have:

Area of ABSH = 1.6² × Area of AARG = 2.56 × 0.8 cm² = 2.048 cm²

4. The circumference of circle B is proportional to the radius of the circle, so we have:

Circumference of circle B = 1.6 × Circumference of circle A ≈ 1.6 × 8.13 cm ≈ 13.01 cm

Therefore, the length of the circumference of circle B is approximately 13.01 cm.

To know more about perimeter visit:

brainly.com/question/6465134

#SPJ1

Answer:

It's 45.

Step-by-step explanation:

Same as the last question :)

Charlie can ensure that each sandwich contains 3 slices of turkey and 3 slices of ham, and can adjust the recipe as needed to suit his family's tastes and preferences.

Preparing food for a day at the beach can be a fun and fulfilling experience. Charlie decided to make sandwiches for his family to snack on when they get hungry. In this case, each sandwich contains 3 slices of turkey and 3 slices of ham.

The first step in making the sandwiches is to gather all the necessary ingredients. Charlie will need bread, turkey slices, ham slices, and any other desired condiments such as mayonnaise, mustard, lettuce, or tomato. He can choose any type of bread, but a sturdy bread such as a ciabatta, sourdough, or French bread would be ideal for a day at the beach.

To assemble the sandwiches, Charlie can follow these simple steps:

1. Lay out the bread slices. Charlie can choose to use one slice of bread per sandwich or two slices for a heartier sandwich.

2. Add a layer of mayonnaise or mustard if desired. Charlie can choose to spread the condiment on one or both slices of bread.

3. Add a layer of lettuce or tomato if desired. This can add some crunch and freshness to the sandwich.

4. Add 3 slices of turkey on one slice of bread, making sure they are evenly distributed. Charlie can choose to overlap the slices or lay them flat.

5. Add 3 slices of ham on top of the turkey slices, again making sure they are evenly distributed.

6. Top the sandwich with the other slice of bread, condiment-side down.

7. If desired, cut the sandwich in half or quarters for easy sharing and eating.

Charlie can repeat these steps for as many sandwiches as needed for his family. He can also customize the sandwiches by adding or subtracting ingredients, such as cheese, bacon, avocado, or pickles.

In terms of nutritional value, the sandwiches provide a good source of protein from the turkey and ham. The bread provides carbohydrates for energy, while the lettuce and tomato provide vitamins and minerals. The mayonnaise or mustard provides some fat and flavor, but can be skipped if desired.

Overall, making sandwiches for a day at the beach is a simple and convenient way to provide nourishing and satisfying food for the family. By following these steps, Charlie can ensure that each sandwich contains 3 slices of turkey and 3 slices of ham, and can adjust the recipe as needed to suit his family's tastes and preferences.

To know more about evenly distributed. click here:

brainly.com/question/31197941

#SPJ1

Charlie's family is going to relax at the beach all day! In preparation, Charlie made s sandwiches for them to eat when they get hungry. Charlie put 3 slices of turkey and 3 slices of ham on each sandwich how does he adjust the situation ?

There were 50 blue box at total in the box.

In mathematics, a cοmbinatiοn is a way οf selecting items frοm a cοllectiοn where the οrder οf selectiοn dοes nοt matter. Suppοse we have a set οf three numbers P, Q and R. Then in hοw many ways we can select twο numbers frοm each set, is defined by cοmbinatiοn.

In smaller cases, it is pοssible tο cοunt the number οf cοmbinatiοns, but fοr the cases which have a large number οf grοup οf elements οr sets, the pοssibility οf a set οf cοmbinatiοn is alsο higher.

The bοx will be represented as (x)

From the question, we form:

White tickets = (1 - 1/10 - 1/2 - 1/4)x = 30

Blue tickets = 3/20 x = 30

Blue tickets =  = 30 x 20 / 3 = 200

Blue tickets = 1/4 x 200 = 50

Thus, There were 50 blue box at total in the box

Learn more about cοmbinatiοn

https://brainly.com/question/20211959

#SPJ1

Consequently, 15 is the third partial total of the sequence.

The area of mathematics known as arithmetic deals with the mathematical study of numbers and the numerous procedures that can be performed on them. Addition, subtraction, multiplication, and division are the fundamental mathematical processes. The icons listed above stand in for these processes.

The given series is an arithmetic series with first term a1 = 2 and common difference d = 3.

To find the third partial sum, we need to add the first three terms of the series:

S₃ = 2 + 5 + 8

S₃ = 15

Therefore, the third partial sum of the series is 15.

To know more about Arithmetic visit:

brainly.com/question/11559160

#SPJ1

If the median of a set of scores is greater than the mean, then the distribution will be option (c) It is positively skewed.

The relationship between the median and mean of a distribution can give an indication of the shape of the distribution. If the median is lower than the mean, it suggests that the distribution is positively skewed.

Option a) It is leptokurtic refers to the degree of peakedness of the distribution, which is not directly related to the relationship between the median and mean.

Option b) It is platykurtic refers to a distribution that has less peakedness than a normal distribution, which is also not directly related to the relationship between the median and mean.

Option d) It is negatively skewed is the opposite of the correct answer and suggests that the median is higher than the mean, indicating a negatively skewed distribution.

Therefore, the correct option is (c) It is positively skewed.

Learn more about positively skewed here

brainly.com/question/17877219

#SPJ4

The given question is incomplete, the complete question is:

If the median of a set of scores is lower than the mean, what does that suggest about the shape of the distribution?

Group of answer choices

a) It is leptokurtic

b) It is platykurtic

c) It is positively skewed

d) It is negatively skewed

Therefore , the solution of the given problem of triangle comes out to be C is an 80-degree angle.

If a polygon has at least one additional segment, it is a hexagon. Its structure is a simple rectangle. Something like this can only be distinguished from a regular triangular form by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.

Here,

We can use the knowledge that a triangle's total angles equal 180 degrees to determine the missing angle measurements in the given triangle.

Angle A:

=> Angle A = 180 - (90 + 45) = 45 degrees

Angle B:

=> Angle B = 180 - (90 + 35) = 55 degrees

Angle C:

=> Angle C = 180 - (45 + 55) = 80 degrees

As a result, the triangle's sides' measurements are as follows:

=> A is a 45 degree angle.

=> B is a 55 degree angle.

=> C is an 80-degree angle.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Answer:

real and rational roots

Step-by-step explanation:

The discriminant of the given equation is [tex]7^2-4(2)(6)=1[/tex].

Since the discriminant is a perfect square, the equation has real and rational roots.

By following these steps, we will have a figure with 4-fold rotational symmetry around the given center point.

To complete the figure with 4-fold rotational symmetry around the center point, follow these steps:
1. Identify the center of rotation:

As mentioned, the given point is the center of rotation.
2. Determine the existing shape or pattern:

Observe the figure and identify the existing shape or pattern to replicate.
3. Divide the circle around the center point into four equal sections (quadrants):

This can be done by drawing two lines that intersect at the center point, dividing the area around it into four equal parts (90 degrees each).
4. Replicate the existing shape or pattern in each quadrant:

Copy the shape or pattern in the first quadrant to the other three quadrants, keeping them equidistant from the center point.
5. Check for symmetry:

Ensure that when you rotate the figure 90 degrees, 180 degrees, or 270 degrees around the center point, it remains identical in appearance.

For similar question on rotational.

https://brainly.com/question/26249005

#SPJ11

Answer: 8

Step-by-step explanation:

The work required to pump the water out of the hemispherical tank is 5,930,818.125 ft-lb.

To find the work required to pump the water out of the hemispherical tank, we need to consider the following steps:
Step 1: Determine the volume of the hemispherical tank.
The formula for the volume of a hemisphere is (2/3)πr³,

where r is the radius.

Given the radius is 13 ft, we can calculate the volume as follows:
Volume = (2/3)π(13³)

= (2/3)π(2197)

= 14603.86 ft³.
Step 2: Calculate the weight of the water in the tank.
Given the water weighs 62.5 lb/ft³, we can determine the weight of the water in the tank by multiplying the volume by the water weight:
Water weight = Volume × Weight/ft³

= 14603.86 ft³ × 62.5 lb/ft³

= 912741.25 lb.
Step 3: Determine the average height at which the water must be pumped out.
Since the tank is hemispherical, the average height for pumping the water is half the radius (13 ft).

So, the average height is:
Average height = 13 ft ÷ 2 = 6.5 ft.
Step 4: Calculate the work required to pump the water out of the tank.
Work = Weight × Distance × Force of gravity.

where Force of gravity = 1 (as we're working with pounds and feet, the force of gravity is already accounted for).
Work = 912741.25 lb × 6.5 ft × 1 = 5930818.125 ft-lb.

For similar question on hemispherical.

https://brainly.com/question/29521548

#SPJ11

Answer:

The probability of selecting an orange chew is 25/62, and the probability of selecting a peach chew is 13/62. To find the probability that the next chew Lydia removes from the bag will be orange or peach, we add these probabilities:

P(orange or peach) = P(orange) + P(peach) = 25/62 + 13/62 = 38/62

To express this probability as a percent, we divide the numerator by the denominator, then multiply by 100:

P(orange or peach) = 38/62 = 0.6129...

0.6129... × 100 ≈ 61

Therefore, the probability that the next chew Lydia removes from the bag will be orange or peach, expressed as a percent to the nearest whole number, is 61%

There were 90 grapes in the container at first.

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

Let's assume that there were x grapes in the container at first.

Arianna ate 0.45 of the grapes, which means she ate 0.45x grapes.

Alex ate 35% of the grapes, which means he ate 0.35x grapes.

The total number of grapes eaten is the sum of what Arianna and Alex ate:

0.45x + 0.35x = 0.8x

This means that 0.8x grapes were eaten, and the number of grapes left is x - 0.8x = 0.2x.

We know that there were 18 grapes left, so we can set up an equation:

0.2x = 18

Solving for x, we get:

x = 90

Therefore, there were 90 grapes in the container at first.

To know more about percentage visit:

https://brainly.com/question/24877689

#SPJ9

Answer:

To find the percentage of residents who participated in the recycling drive, we need to divide the number of participants by the total number of residents and then multiply by 100 to get the percentage. Total number of residents in Percy's town = 5,320 + 1,680 = 7,000 Number of residents who participated = 5,320 Percentage of residents who participated = (Number of participants / Total number of residents) x 100 = (5,320 / 7,000) x 100 = 76% Therefore, 76% of the residents of Percy's town participated in the recycling drive.

Answer:

The correct answer is 76%.

Step-by-step explanation:

To find the percentage of Percy's town that participated in the recycling drive, we must divide the number of people that participated by the total number of residents.

To do this, we should first find the total number of residents. Since residents either participated or did not participate, the total number of residents is the sum of these two values. This is modeled below:

Total number of residents = 5,320 + 1,680 = 7,000 total residents

Now, we can continue with the percentage calculation.

% participation = # of participants/# of residents * 100

% participation = 5,320/7,000 * 100

% participation = 76%

Therefore, we can conclude that 76% of Percy's town participated in the recycling drive.

For more information about percentages, check out these other questions on Brainly:

https://brainly.com/question/24877689

https://brainly.com/question/25656758