The A-B-C department of a large company makes three products (A, B and C). To determine the best production schedule, the manager has formulated the following linear programming model: Decision variables: A = quantity of product A B = quantity of product B C=quantity of product C Objective function: Maximize 12 A+ 15 B + 16 C (total profit: coefficients are net profit per unit in dollars) Constraints: Material 1 3A + **B + 8C <= 720 pounds Material 2 2A + 3C <- 600 pounds Material 3 4A+ 6 B+ 4C <= 640 pounds Non-negativity A, B, C >= 0 The manager has solved this problem using Excel Solver and the sensitivity report is given below: - Variable Cells Cell | Name | Final Value | Reduced Cost | Objective Coefficient | Allowable Increase | Allowable Decrease $B$2 A 16 12 4 0.5
$C$2 B 0 -1 15 1 1E+30
$D$2 C 84 0 16 2 4
- Constraints Cell | Name | Final Value | Shadow Price | Constraint R.H Side | Allowable Increase | Allowable Decrease $E$6 Material 1 720 0.8 720 420
$E$7 Material 2 284 0 600 1E+30 316
$E$8 Material 3 400 2.4 400 560 40
Based on the information given (No need to implement this problem into solver), what is the optimal production quantity of product A? A. Can't be computed with the given information B. 16 C. 12 D. 4

The value of the expression is -5.

Given x = -1.5, let's evaluate the expression ⌊x⌋ + ⌈2x⌉ using the definition of the floor and ceiling functions.

The floor function ⌊x⌋ returns the largest integer less than or equal to x, while the ceiling function ⌈x⌉ returns the smallest integer greater than or equal to x.

For x = -1.5:

⌊x⌋ = ⌊-1.5⌋ = -2 (the largest integer less than or equal to -1.5)

⌈2x⌉ = ⌈2(-1.5)⌉ = ⌈-3⌉ = -3 (the smallest integer greater than or equal to -3)

Now, let's evaluate the expression ⌊x⌋ + ⌈2x⌉:

⌊x⌋ + ⌈2x⌉ = -2 + (-3) = -5

Therefore, ⌊x⌋ + ⌈2x⌉ is equal to -5 for x = -1.5.

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Answer:

The place value of 5 is HUNDREDTH

Explanation:

From the right-hand side, the place value of:

8 is Hundred

2 is Ten

6 is Unit

1 is Tenth

and finally, what we are required to tell,

5 is Hundredth.

Answer:

77

Step-by-step explanation:

cats:dogs

2:5

2x11=22

5x11=55

55+22=77

Answer:

77 animals

Step-by-step explanation:

Ratio = 2:5

2 = 22

5 = 5/2 ×22

= 55

=>There are 55 dogs in the animal shelter

Therefore the total number of animals = 55 +22

= 77

=> There are 77 animals at the animal shelter

1) The instantaneous rate of change of the function at x = 1 depends on the specific value of π.

2) The average rate of change of the function f(x) = x^2 - 5 over the interval [15, 25] is 40.

To find the momentary pace of progress of the capability at a particular point, we can compute the subsidiary of the capability and assess it by then.

Temporary rate of change:

We need to find the derivative of the function y = x + x5/3 - 8x + 25 and evaluate it at x = 1.

First, let's locate the function's derivative:

We differentiate each term using the power rule and the chain rule: y' = d/dx (x + x5/3 - 8x + 25).

Now, evaluate the derivative at x = 1: y' = x(-1) + (5/3)x(5/3-1) - 8.

Simplifying the expression will depend on the particular value of (pi) that you are employing. Instantaneous rate of change = y'(x=1) = (1)(-1) + (5/3)(1)(5/3-1) - 8.

Change at an average rate:

The average rate of change for the function f(x) = x2 - 5 can be determined by dividing the difference between the function's values over the interval [15, 25] by the difference between the x-values.

Normal pace of progress = (f(25) - f(15))/(25 - 15)

= (25^2 - 5 - (15^2 - 5))/(25 - 15)

= (625 - 5 - 225 + 5)/10

= 400/10

= 40

In synopsis:

The quick pace of progress of the capability at x = 1 relies upon the particular worth of π.

Over the [15, 25] interval, the function f(x) = x2 - 5 changes at an average rate of 40.

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The mathematical expression, an inequality to be more specific which represents the given word phrase; -3 * a number increased by 7 is less than -11 is; -3a +7 < 11.

It follows from the task content that the mathematical expression which correctly represents the word phrase is to be determined.

Since the product of -3 and the number, a can be written as; -3 × a = -3a.

Hence, the word phrase as given in the task content can be written as;

-3a +7 < 11.

This follows from the concept of inequalities.

Ultimately, The mathematical expression, an inequality to be more specific which represents the given word phrase; -3 * a number increased by 7 is less than -11 is; -3a +7 < 11.

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a. The accumulated value of the annuity using the portfolio method is $19,454.11.

b. The accumulated value of the annuity using the yield-curve method is $34.33, rounded to 2 decimal places.

(A) To find the accumulated value of the annuity using the portfolio method, we need to calculate the accumulated value for each period separately based on the given effective interest rates.

For the first 15 periods with an 8% effective interest rate, we can use the formula for the accumulated value of an ordinary annuity:

Accumulated value = payment * [(1 + r)^n - 1] / r

where payment is $600, r is the effective interest rate per period (8% or 0.08), and n is the number of periods (15). Plugging in these values, we have:

Accumulated value (15 periods) = $600 * [(1 + 0.08)^15 - 1] / 0.08 = $10,092.94

For the following 16 periods with a 3% effective interest rate, we repeat the calculation using the same formula:

Accumulated value (16 periods) = $600 * [(1 + 0.03)^16 - 1] / 0.03 = $9,361.17

To obtain the total accumulated value of the annuity, we sum up the accumulated values for the two periods:

Total accumulated value = Accumulated value (15 periods) + Accumulated value (16 periods) = $10,092.94 + $9,361.17 = $19,454.11

Therefore, the accumulated value of the annuity due using the portfolio method is $19,454.11.

(B) To find the accumulated value of the annuity using the yield-curve method, we need to calculate the weighted average of the accumulated values based on the respective interest rates and periods.

First, we calculate the present value (PV) of each payment using the formula:

PV = payment / (1 + r)^n

where payment is $600, r is the effective interest rate per period, and n is the number of periods.

For the first 15 periods, with an 8% effective interest rate, the present value of each payment is:

PV (15 periods) = $600 / (1 + 0.08)^15 = $263.99

For the following 16 periods, with a 3% effective interest rate, the present value of each payment is:

PV (16 periods) = $600 / (1 + 0.03)^16 = $440.43

To calculate the accumulated value using the yield-curve method, we multiply each present value by the respective interest rate and sum them up:

Accumulated value = (PV (15 periods) * 8%) + (PV (16 periods) * 3%)

Accumulated value = ($263.99 * 0.08) + ($440.43 * 0.03) = $21.12 + $13.21 = $34.33

Therefore, the accumulated value of the annuity using the yield-curve method is $34.33, rounded to 2 decimal places.

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Answer:

Line down the middle

Step-by-step explanation:

There is only one line of symmetry in this shape because there is no rotational symmetry. Its a line down the middle.

Answer:

11/130

Step-by-step explanation:

The number of people who use any facility is:

N = 65 + 51 + 44 − 15 − 14 − 10 − 2(1)

N = 119

So the number of people who don't use any facility is 130 − 119 = 11.

And the probability is 11/130.

The probability of the arrow landing on an odd number is the number of odd numbers divided by the total number of possible outcomes. Therefore, the probability of the arrow landing on an odd number is  0.5 or 50%.


To find the probability that the arrow will point at an odd number on a circular board with 8 equal parts, we'll first determine the total number of odd numbers present and then divide that by the total number of possible outcomes.

Step 1: Identify the odd numbers on the board. They are 1, 3, 5, and 7. The game consists of spinning the arrow on a circular board with 8 equal parts, which means there are 8 possible outcomes or numbers. Since we want to know the probability of landing on an odd number, we need to count how many odd numbers are on the board. In this case, there are four odd numbers: 1, 3, 5, and 7.

Step 2: Count the total number of odd numbers. There are 4 odd numbers.

Step 3: Count the total number of possible outcomes. Since the board is divided into 8 equal parts, there are 8 possible outcomes.

Step 4: Calculate the probability. The probability of the arrow pointing at an odd number is the number of odd numbers divided by the total number of possible outcomes.

Probability = (Number of odd numbers) / (Total number of possible outcomes)
Probability of landing on an odd number = Number of odd numbers / Total number of possible outcomes
Probability of landing on an odd number = 4 / 8

Step 5: Simplify the fraction. The probability of the arrow pointing at an odd number is 1/2 or 50%.

So, the probability that the arrow will point at an odd number is 1/2 or 50%.

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Answer: (1, 8)

Step-by-step explanation:

Substitute y = 3x + 5 into the equation 2x + 3y = 26:

2x + 3(3x + 5) = 26

2x + 9x + 15 = 26

11x = 26 - 15

11x = 11

x = 1

Substitute the value of x into the equation y = 3x + 5:

y = 3(1) + 5 = 3 + 5 = 8

Answer:

Wrong. If the line segment AB= 10, then the measure of AC= 10 as well. It's a right triangle. All the sides are the same.

Step-by-step explanation:

Answer: Not correct.  The tic marks on the angles mean that this is an equilateral triangle  

All the line segments are equal. If a length is given for one side of the triangle, the others are the same

All the angles are equal. The total of all the angles is 180. to find any one of them divide 180 ÷ 3

Step-by-step explanation:  This looks like a test item, so we are not supposed post answers.

So I hope this is enough to help you make the corrections yourself.

There is a 5/6 probability that you will remove pairs of socks to make sure you obtain a pair that is not navy.

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

Statistics is the study of events that follow a probability distribution.

So, we know that:

27 black socks.

18 grey socks.

9 navy socks.

Probability formula: P(E) = Favouravle events/Total events

Now, insert values in the formula as follows:

P(E) = Favouravle events/Total events

P(E) = 27+18/27+18+9

P(E) = 45/54

P(E) = 15/18

P(E) = 5/6

Therefore, there is a 5/6 probability that you will remove pairs of socks to make sure you obtain a pair that is not navy.

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Correct question:
in a pitch-black room, you have a drawer with 27 black socks, 18 grey socks, and 9 navy socks. What is the probability that you take out pairs of socks to ensure you get a pair that is not navy?

Answer:

Option A

Step-by-step explanation:

ƒ(x) = −x+2

g(x) = −4x² − 3x − 3

h(x) = f(x)g(x)

      =(−x+2)(−4x² − 3x − 3)

 h(x)  =4x^3+6x+3-8x^2 -6x-6

   h'(x)   =12x^2 -10x-3

If we solve option A then option A is same as  h'(x)

The number of strings where exactly two of the ones are next to each other, while the third one is not next to the other two, is (n-1) x (n-2).

In combinatorics, one of the fundamental concepts is counting the number of strings or sequences of symbols that satisfy certain conditions.

Let us first consider the case where the two ones that are next to each other are at the beginning of the string. In this case, we can place the third one in any of the remaining positions, which are n-2, where n is the total length of the string. Therefore, the number of such strings is (n-2).

Similarly, if the two ones are at the end of the string, we can place the third one in any of the n-2 remaining positions, and the number of such strings is again (n-2).

Now let us consider the case where the two ones are in the middle of the string. In this case, we can place the two adjacent ones in (n-2) ways, and the third one can be placed in any of the remaining n-3 positions, since it cannot be adjacent to the other two ones. Therefore, the number of such strings is (n-2) x (n-3).

To get the total number of strings that satisfy the given condition, we need to add up the number of strings in each of the three cases:

Total number of strings = (n-2) + (n-2) + (n-2) x (n-3)

Simplifying this expression, we get:

Total number of strings = (n-1) x (n-2)

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Answer:

54 and 36

Step-by-step explanation:

84

45% of 120 students chose the amusement park , then

45% of 120 = 0.45 × 120 = 54

54 students chose the amusement park

85

45% of 180 = 0.45 × 180 = 81

25% of 180 = 0.25 × 180 = 45

81 - 45 = 36

36 more students chose the amusement park than the water park

Answer:

54, 36

Step-by-step explanation:

84

45% of 120 students chose the amusement park

45% of 120 = 0.45×120=54

54 students chose the amusement park

85

45% of 180 = 0.45 × 180 = 81

25% of 180 = 0.25 × 180 = 45

81 - 45 = 36

36 students chose the amusement park than the water park

Answer:

99

Step-by-step explanation:

Triangles GJH and IJH are congruent, so GJ=IJ=99.

Answer:

2 : 7

Step-by-step explanation:

We can convert the 70mm of colored fabric to cm first:

Since 1 cm = 10mm, this means 70mm = 7 cm.

Now, we can set up a ratio with white:colored since they are both in cm now:

20 : 70

We can divide each side by 10 to simplify:

2 : 7

The amount Jamie got be x = $36,

The amount Nashwa got be y = $25.2

We can get Jamie and Nashwa got $10.8 altogether.

Based on the given conditions,

To find how much Jamie gets more than Nashwa.

First of all, we would have to solve for Jamie share from the money.

x : y = 10 : 7       (Equation-1)

But,

Jamie got amount = $36

We can substitute in x = $36 in equation-1,

Let us assume,

Jamie = x

Nashwa = y

So,

We can write,

x : y = 10 : 7  

$36 : y = 10 : 7  

\(\frac{36}{y} =\frac{10}{7}\)

We can cross-multiplying,

36*7 = 10y

252 = 10y

y = 252/10

We can divide the products,

y = 25.2

Hence,

Nashwa = $25.2

Difference of the Jamie and Nashwa,

Difference = x - y

Difference = $36 - $25.2

Difference = $10.8

We can write,

Jamie gets $36 more than Nashwa.

$25.2 + $10.8 = $36

$36 = $36

Therefore,

The amount Jamie got be x = $36

The amount Nashwa got be y = $25.2

We can get they got $10.8 altogether.

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If Joe borrowed $8000 at a rate of 14%, he will owe $11,992.18  after 3 years

We can use the formula for compound interest to calculate how much Joe will owe after 3 years:

A = P(1 + r/n)ⁿt

where:

A = the amount Joe will owe after 3 years

P = the initial principal (the amount Joe borrowed), which is $8000 in this case

r = the annual interest rate as a decimal, which is 0.14

n = the number of times the interest is compounded per year, which is 2 (since it's compounded semiannually)

t = the number of years, which is 3

Plugging in the values, we get:

A = 8000(1 + 0.14/2)²ˣ³

= 8000(1 + 0.07)⁶

= 8000(1.07)⁶

= 8000(1.499022)

= 11992.18

Therefore, Joe will owe approximately $11,992.18 after 3 years

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In business calculus, the term "functions" refers to mathematical relationships that associate inputs (typically denoted as x) with corresponding outputs (typically denoted as y). Functions can represent various aspects of business operations, such as revenue, cost, profit, demand, and supply.

The concept of "limits" in calculus deals with the behavior of a function as the input approaches a particular value. It determines the value that the function approaches or tends to as the input gets arbitrarily close to a specified value. Limits are essential for analyzing the behavior of functions near certain points, understanding rates of change, and evaluating derivatives and integrals.

"Continuity" of a function refers to its smooth and unbroken nature, without any abrupt jumps, holes, or vertical asymptotes. A function is continuous if its graph can be drawn without lifting the pen from the paper. Continuity ensures that small changes in the input correspond to small changes in the output, which is crucial for reliable analysis and prediction.

For example, consider the function f(x) = 2x + 1. This linear function represents a business scenario where x represents the number of units sold, and f(x) represents the total revenue generated. The limit of f(x) as x approaches 2 is 5, indicating that as the number of units sold approaches 2, the total revenue approaches $5. Since f(x) = 2x + 1 is a linear function, it is continuous across its entire domain.

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Answer:

1808 people

Step-by-step explanation:

Find 1% by dividing by 100.

1600/100=16

Multiply 16 by 13.

208

Add it to 1600.

1808

There are now 1808 people.

Answer:

42.667 mm to 42,673 mm

Step-by-step explanation:

42.67-0.003=42.667

42.67+0.003=42.673

Add and subtract the discreprency from the standard size.

Answer:

See below

Step-by-step explanation:

Sum of 18 and 6 = 24

1/4 of the sum of 18 and 6 is asking you what is the result of dividing 24 by 4

In  a way you can think of it as a fractional question but the answer is a whole number

\(\dfrac{1}{4} \cdot (18 + 6) = \dfrac{1}{4} \cdot 24 = \dfrac{24}{4} = 6\\\)

Step-by-step explanation:

The sum of two opposite interior angles equals an exterior angle

50+?=115

?=115-50=65°

Answer:

60 degrees

Step-by-step explanation:

angles on a straight line add up to 180 degrees.

so do 180-115=60

because its an equilateral triangle, you can check whether it adds up to 180

60+60+50=180

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