Step-by-step explanation:
The first, twelfth and last term of an arithmetic progression are and , respectively. Determine (a) the number of terms in the series, (b) the sum of all the terms and (c) the 80 th term
Hello I have to develop that (x-1)(x+2) I know that it makes x²+x-2 but I don't understand why, can you explain me ?
Answer:
pls rate as brainliest it will go a long way
Step-by-step explanation:
(x–1)(x+2)
STEP 1
using the first bracket to expand the other
= x(x + 2) –1(x + 2)
= x² + 2x –x –2
= x² + x – 2
Step 2
or by using the other bracket to expand the other
(x – 1)(x + 2)
x(x – 1) + 2(x – 1)
= x² – x + 2x – 2
= x² + x – 2
What is the lateral of the drawing
Answer:
Step-by-step explanation:
the lateral area of the drawing the lateral area of the drawing is 40 mi2. Area rectangle = w * l 5 * 2 = 10 mi² (area 1 rectangle) then you multiply by 4 10 * 4 = 40 mi² or 5 * 2 * 4 = 40 mi²
Answer:
294 m²
Step-by-step explanation:
You want the lateral area of a regular hexagonal prism with side lengths 7 m and height 7 m.
Lateral areaThe lateral area is the sum of the areas of the 6 square faces.
Each of the 6 faces is a square 7 m on the edge. Its area is ...
(7 m)² = 49 m²
There are 6 of these square faces, so their total area is ...
6 × 49 m² = 294 m²
The lateral area of the prism is 294 m².
NO LINKS!! Determine whether the sequence is geometric.
2, 4/√(3) , 8/3, 16/3√(3) , . . .
Choose:
1. Yes, the sequence is geometric
2. No, the sequence is not geometric
If so, find the common ratio. (if the sequence is not geometric, enter NONE)
Geometric sequence has a common ratio.
Let's verify is the ratio of subsequent terms is common:
[tex]r=t_2/t_1=(4/\sqrt{3})/2 = 2/\sqrt{3} =2\sqrt{3}/3[/tex][tex]r=t_3/t_2=(8/3)/(4/\sqrt{3}) = 2/\sqrt{3} =2\sqrt{3}/3[/tex][tex]r=t_4/t_3=(16/3\sqrt{3})/ (8/3) = 2/\sqrt{3} =2\sqrt{3}/3[/tex]As wee se the ratio is common, it confirms that the sequence is geometric.
Common ratio is:
[tex]r=2\sqrt{3}/3[/tex]Answer:
Yes, the sequence is geometric.
[tex]\textsf{Common ratio}=\dfrac{2\sqrt{3}}{3}[/tex]
Step-by-step explanation:
Given sequence:
[tex]2, \; \dfrac{4}{\sqrt{3}},\; \dfrac{8}{3},\;\dfrac{16}{3\sqrt{3}},\;...[/tex]
A geometric sequence has a common ratio.
Therefore, to check if the given sequence has a common ratio, divide each term by the previous term:
[tex]\boxed{\begin{aligned}\dfrac{16}{3\sqrt{3}} \div \dfrac{8}{3}&=\dfrac{16}{3\sqrt{3}} \times \dfrac{3}{8}\\\\&=\dfrac{48}{24\sqrt{3}}\\\\&=\dfrac{2}{\sqrt{3}}\\\\&=\dfrac{2\sqrt{3}}{3}\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned}\dfrac{8}{3} \div \dfrac{4}{\sqrt{3}}&=\dfrac{8}{3} \times \dfrac{\sqrt{3}}{4}\\\\&=\dfrac{8\sqrt{3}}{12}\\\\&=\dfrac{2\sqrt{3}}{3}\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned} \dfrac{4}{\sqrt{3}} \div 2&= \dfrac{4}{\sqrt{3}} \times \dfrac{1}{2}\\\\&= \dfrac{4}{2\sqrt{3}} \\\\&=\dfrac{2}{\sqrt{3}}\\\\&=\dfrac{2\sqrt{3}}{3}\end{aligned}}[/tex]
As there is a common ratio, the sequence is geometric.
The common ratio is:
[tex]\dfrac{2\sqrt{3}}{3}[/tex]2
Which fractions are equivalent to ? Choose ALL the correct answers.
4
4
6
4
6
8
6
12
57
Answer:
Step-by-step explanation:
4/4
8/6
4/6
While hiking, Kurt ate 1/3 of a cup of nuts. Danielle ate 1/6 of a cup of nuts. How much more did Kurt eat than Danielle?
Kurt will eat 1/6 cups more than Danielle if Kurt ate 1/3 of a cup of nuts and Danielle ate 1/6 of a cup of nuts by using ratio and proportion concept.
What is ratio and proportion?When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. Two ratios are set to be equal in an equation called a proportion. For instance, if there is 1 boy and 3 girls, the ratio would be written as 1: 3 (there are 3 girls for every boy), meaning that there are 1 in 4 boys and 3 in 4 girls.
A: b a/b is the ratio formula, which may be used to calculate any two values. A:b::c:da:b::c:da, on the other hand, is how the percentage formula is written. A ratio in mathematics displays the multiplicative relationship between two numbers.
Given,
A cup of nuts ate by Kurt=1/3
A cup of nuts ate by Danielle=1/6
(1/3)-(1/6)
=1/6
Therefore, Kurt will eat 1/6 cups more than Danielle.
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LAST ONE! DUE SOON! AND NEED HELP! REAL ANSWERS ONLY!!
Answer:
A.) All reptiles run fast
Step-by-step explanation:
Tortoises are reptiles that run slow, so they would be a counterexample to the conjecture that all reptiles run fast. This is because tortoises are a type of reptile that do not run fast, even though the conjecture states that all reptiles do.
In general, reptiles are a class of animals that includes many different species. Some reptiles, such as snakes and lizards, are known for their speed and agility. However, other reptiles, such as tortoises and turtles, are not known for their speed and tend to move much slower than other reptiles. This shows that the conjecture that all reptiles run fast is not always true, and tortoises are a counterexample to this conjecture.
In addition to their speed, tortoises are also distinguished by their hard shells and thick legs. They are typically found in warm, dry environments, and they are known for their long lifespan and low metabolic rate. They are also typically herbivores, feeding on a diet of plants and vegetation. This is in contrast to other reptiles, such as snakes and lizards, which are often carnivorous and hunt for their food. Overall, tortoises are a unique and interesting group of reptiles that do not always fit the generalizations made about reptiles.
Match the metric units on the left with their
approximate equivalents on the right. Not all the
options on the right will be used.
1 meter
kilogram
1 liter
1 cup
I mile
2
pounds
1 quart
I yard
Answer:
meter - yard
kilogram - 2 pounds
liter - quart
find the range for the measure of the third side of a triangle when the measures of the other two sides are 7 km and 29 km.
22>x>36 is the range for the third side's measurement when two sides of a triangle are measured at 7 km and 29 km.
Given that,
When the other two sides of a triangle are measured at 7 km and 29 km.
We have to determine the range for the third side's measurement.
We know that,
Take the measured sides.
7 km and 29 km
So, we can write as
The two sides added together are greater than the third side.
So, take one side as x
We get,
7+x>29
Taking 7 to the right side we get negative 7
x>29-7
x>22
Now taking 29 to left side and x to sides
7+29>x
36>x
Therefore, 22>x>36 is the range for the third side's measurement when two sides of a triangle are measured at 7 km and 29 km.
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Given f(x) = 2x − 3 and g(x) = f(2x), which table represents g(x)?
Answer:
g(x) = 4x - 3
Step-by-step explanation:
f(x) = 2x − 3
g(x) = f(2x)
g(x) = 2(2x) - 3 ==> plugin 2x for x in f(x) in order to get f(2x)
g(x) = 4x - 3
A. Quantity A is greater B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. 0
No information is given for x and it can be fraction or real number, so option D is correct.
What is fraction ?
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator.
It tells how many equal parts of the whole or collection are taken.
No information is given for x and it can be fraction or real number, so option D is correct.
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The circumference of a circle is double the perimeter of square having area 484cm^2.what is the area of circle?
Answer:
The circumference of a corcle is double the perimeter of square having area 484 m^2. what is the area of the circle. Ans:2464 cm^2.
Answer:
Hence the area of a circle is 2466[tex]m^{2}[/tex]
Step-by-step explanation:
Review of the question
[tex]Given,[/tex]
The circumference of a circle is double the perimeter of squareArea of the square is 484[tex]cm^{2}[/tex]To Find:Area of the circle
,
Area of square =[tex]sideXside[/tex]
[tex]484[/tex]=[tex]side^{2}[/tex]
[tex]\sqrt{484}=side^{2}[/tex]
[tex]22 = side[/tex]
Perimeter of square = [tex]4Xside[/tex]
[tex]4X22[/tex]
[tex]88[/tex]
Circumference of the circle = Perimeter of square x 2
Circumference of the circle = 88x2
Circumference of the circle = 176
Now we need to find the radius of the circle
[tex]2\pi r=176[/tex]
[tex]2X3.14Xr=176\\6.28Xr=176\\r=\frac{176}{6.28} \\r=28.025477707[/tex]
Area of the circle=[tex]\pi r^{2}[/tex]
[tex]3.14X[/tex][tex](28.025477707)^{2}[/tex]
[tex]2466[/tex]
Hence the area of a circle is 2466[tex]m^{2}[/tex]
HELP ASAP!! READ CAREFULLY
Answer:
1, 4, 5
Step-by-step explanation:
You want to identify correct proportions between the sides of similar isosceles trapezoids ABCD and WXYZ.
Corresponding sidesThe similarity statement tells us the corresponding side pairs are ...
AB ⇔ WXBC ⇔ XYCD ⇔ YZDA ⇔ ZWA proper proportion will be equate ratios of the corresponding sides in the same trapezoid, or the corresponding sides in different trapezoids.
ApplicationAB/WX = DA/ZW . . . . . . correct
AB/WX = ZW/DA . . . . . . incorrect
CB/XY = WX/AB . . . . . . incorrect
AB/WX = CB/YX . . . . . . correct
DA/AB = ZW/WX . . . . . . correct
BC/AD = XY/YZ . . . . . . incorrect
find the measure of m< ABE
Measure of angle ABE is 47°.
Define angle.An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves. Angle can also refer to the length of a rotation or an angle. This metric represents the relationship between a circular arc's length and radius.
Given
∠CBE = 43°
As we know, ∠ABC is a right angle
∠ABC = ∠ABE + ∠CBE
90 = ∠ABE +43
∠ABE = 90 - 43
∠ABE = 47
Measure of angle ABE is 47°.
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Help me please and thank you!
The angle in the similar triangles is as follows:
m∠N = 42 degrees
How to find the angles of similar triangles?Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.
In other words, two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
Therefore, triangle JKL is similar to triangle NOP. This means the corresponding angles are congruent.
Hence,
∠J = ∠N
∠K = ∠O
∠L = ∠P
Therefore,
m∠N = 180 - 80 - 58(sum of angles in a triangle)
m∠N = 42 degrees
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The mean value of land and buildings per acre from a sample of farms is $1200, with a standard deviation of $100. The data set has a bell-shaped distribution. Using the empirical rule, determine which of the following farms, whose land and building values per acre are given, are unusual (more than two standard deviations from the mean). Are any of the data values very unusual (more than three standard deviations from the mean)? $1064 $1417 $1373 $856 $1250 $1102
Answer:
The empirical rule states that for a bell-shaped distribution, approximately 68% of the data values will fall within one standard deviation of the mean, 95% of the data values will fall within two standard deviations of the mean, and 99.7% of the data values will fall within three standard deviations of the mean.
Using this information, we can calculate the range of values that fall within two standard deviations of the mean for the given data set:
Mean: $1200
Standard deviation: $100
Two standard deviations: $200
Therefore, the range of values that fall within two standard deviations of the mean is $1200 - $200 = $1000 to $1200 + $200 = $1400.
With this information, we can determine which of the given data values are unusual (more than two standard deviations from the mean):
$1064 is within two standard deviations of the mean.
$1417 is outside of two standard deviations of the mean.
$1373 is within two standard deviations of the mean.
$856 is outside of two standard deviations of the mean.
$1250 is within two standard deviations of the mean.
$1102 is within two standard deviations of the mean.
Therefore, the data values $1417 and $856 are unusual (more than two standard deviations from the mean).
We can also determine which of the given data values are very unusual (more than three standard deviations from the mean) using the same process. The range of values that fall within three standard deviations of the mean is $1000 to $1600. With this information, we can see that none of the given data values are very unusual (more than three standard deviations from the mean).
Given the function g(x) = |x - 4|, find the value of g(1).
Harry and Tim both made New Year’s Resolution. Harry made 5 more resolutions than Tim. Together they made 13 resolutions. How many resolutions did Harry make?
The specified number of New Year's resolutions Harry makes which is 5 more than the resolutions Tim makes, and the total number of resolutions of 13 indicates a word problem with a solution that Harry makes 9 New Year's resolutions.
What is a word problem?A word problem is a mathematics or science question, presented using complete sentences, rather that mathematical expressions or science symbols.
A word problem consists of presenting a problem in terms of a real situation such, with the solution being obtained easiest through the use of mathematical or science procedures.
Let x represent the number of resolutions Tim makes
The number of resolutions Harry makes = x + 5
The number of resolutions Harry and Tim made together = 13
Therefore, we get; x + x + 5 = 13
2·x + 5 = 13
2·x = 13 - 5 = 8
x = 8 ÷ 2 = 4
The number of resolutions Tim makes, x = 4
The number of resolutions Harry makes = x + 5
Therefore, the number of resolutions Harry makes = 4 + 5 = 9
Harry made 9 New Year's resolutions
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Please find what the rent per unit needs to be to have a Net Operating Income (NOI) of $100,000.
Assumptions
Please use the following assumptions below:
Rent per unit (per month)
Vacancy Rate (% of Potential Gross Income) 5%
Operating Expenses (% of Effective Gross Income) 30%
Number of Units 18
*Please fill out the blue area Rent per unit (per month)
Vacancy Rate (% of Potential Gross Income)
Operating Expenses (% of Effective Gross Income)
Number of Units
The rent per unit should be $8,354.22 to generate a Net Operating Income (NOI) of $100,000, given the vacancy rate and operating expenses.
What are the operating expenses?The operating expenses are costs that must be deducted from the gross operating income to arrive at the net operating income.
The operating expenses do not include some period expenses, which are indirect costs.
Total
Rent per unit (per month) = $696.19 ($8,354.22/12) $150,376
Vacancy Rate (5% of Potential Gross Income) 7,519
Effective Gross Income $142,857
Operating Expenses (30% of Effective Gross Income) 42,857
Net Operating Income (NOI) $100,000
Number of Units 18
Working Backwards:Gross operating income = net operating income + operating expenses
Operating expenses = 30% of effective gross income
Net operating income = 70% of effective gross income (100 - 30%)
= $100,000
Effective Gross Income (100%) = $142,857 ($100,000 ÷ 70%)
Vacancy rate = 5% of potential gross income
Effective Gross Income = 95% (100 - 5)
Potential gross income = $150,376 ($142,857 ÷ 95%)
Number of units = 18
Rent per unit = $8,354.22 ($150,376/18)
Rent per month = $696.19 ($8,354.22 ÷ 12)
Thus, a rent of $8,354.22 per unit can generate a Net operating income of $100,000.
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A stage manager is trying to seat important guests in the front row of a theater. The row has seven seats, and she would like a diplomat in the first seat, a singer in the second seat, and a movie director in the third seat. After this, the remaining diplomats, singers, and movie directors will be seated in the last four seats, in no particular order. If there are 3 diplomats, 2 singers, and 2 directors attending the show, how many different front row plans are possible?
Answer: 12 row plans
The first seat has 2 possible options, the 2 directors. The second seat has another 2 options. With each director comes 2 options for the second seat, so 2 x 2=4 possible options for the 1st and 2nd seats. The third seat has 3 options. That means for each combination of the 1st and 2nd seat, there are 3 possible options. 4x3=12 combinations.
Step-by-step explanation:
In square ABCD, m∠BCE=(5x+9)∘.
What is the value of x?
Enter your answer, as a decimal, in the box.
x =
Answer:
x = 7.2
Step-by-step explanation:
You want the value of x that makes ∠BCE = 45° = (5x +9)°.
SolutionDivide by ° and subtract 9 to get ...
36 = 5x
Divide by 5, and you have the value of x:
7.2 = x
The value of x is 7.2.
__
Additional comment
You know that the corner angles of a square are 90°, and that the diagonals bisect the corner angles. Each half is 45°.
Enter the x,y value in the text box below for the following table of values where the x value is -2
y = 3x + 4
Answer:
x=-2
y = 3× -2 + 4
y= -6 + 4
y = -2
What is the total area of the tiles Felix needs to buy?
By using the formula for area of parallelogram, it can be calculated that
Felix needs to buy 80 [tex]cm^2[/tex] of tiles
What is area of parallelogram?
Area of parallelogram is the total space taken by the parallelogram.
If b is the base of the parallelogram and h is the height of the parallelogram, then area of the parallelogram is calculated by the formula
Here,
Base of each parallelogram = 4cm
Height of each parallelogram = 2cm
Area of each parallelogram = 4 [tex]\times[/tex] 2 = 8 [tex]cm^2[/tex]
Area of 10 parallelograms = 8 [tex]\times[/tex] 10 = 80 [tex]cm^2[/tex]
Felix needs to buy 80 [tex]cm^2[/tex] of tiles
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Complete Question
The full diagram has been attached.
Edgar accumulated $9,000 in credit card debt. If the interest rate is 20% per year and he does not make any payments for
2 years, how much will he owe on this debt in 2 years for quarterly compounding? Round your answer to the nearest cent.
To calculate the total amount of interest that Edgar will owe on his credit card debt after 2 years of quarterly compounding at a 20% annual interest rate, we need to use the formula A = P(1 + r/n)^nt, where A is the total amount of money owed after t years, P is the initial principal (or amount borrowed), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, the initial principal is $9,000, the annual interest rate is 20%, the number of times the interest is compounded per year is 4 (since the interest is compounded quarterly), and the number of years is 2. Plugging these values into the formula, we get A = $9,000(1 + 0.20/4)^4 * 2 = $9,000(1.05)^8 = $9,000 * 1.4064 = $12,658.40. Thus, after 2 years of quarterly compounding at a 20% annual interest rate, Edgar will owe approximately $12,658.40 on his credit card debt. This result should be rounded to the nearest cent, giving us $12,658.40.
The quotient of a number and 5 plus 25 is no more than 45. What are the possible values for the number?
Answer:
The number can be any value less than or equal to 100.
Thus, it can be any number in this range: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]
Step-by-step explanation:
Firstly, let's convert the word problem into a math expression:
[tex]\frac{x}{5}+25\leq45[/tex]
We can now solve this inequality for the variable x.
[tex]\frac{x}{5} \leq 20[/tex]
[tex]x \leq 100[/tex].
Therefore x is any value less than or equal to 100.
calculate the shapley values for each player, i.e., the fair amount of money everyone should pay for their meal!
Assuming that the meal cost $50, the Shapley values (payments) for each player is: number of possible combination , Player 1: $15 , Player 2: $10 , Player 3: $10 , Player 4: $15
1. Calculate the marginal contribution of each player. This is the amount of money that each player adds to the total cost of the meal.
Player 1: $25
Player 2: $15
Player 3: $10
Player 4: $0
2. Calculate the Shapley Value for each player. This is calculated by taking the average of the marginal contribution of each player, weighted by the number of possible combinations they could have been in.
Player 1: ($25*3 + $15*2 + $10*1 + $0*0) / 6 = $15
Player 2: ($25*2 + $15*3 + $10*2 + $0*1) / 6 = $10
Player 3: ($25*1 + $15*2 + $10*3 + $0*2) / 6 = $10
Player 4: ($25*0 + $15*1 + $10*2 + $0*3) / 6 = $15
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Please help me with my question step by step
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The required, team 3, tower garden donation shows the proportional relationship between weeks and donation,
What is proportionality?Proportionality is described as the relationship between two or more sets of values, and whether these values are directly proportional or inversely proportionate to one other.
here,
From the table,
The ratio of a week to the donation of the individual team must be the same as the ratio of the preceding week and the donation of the respective team,
So,
Team 1,
1 / 1 = 2 / 3[1/4], false
Similarly, team 2 and team 4's relationship is also not proportional,
Now, team 3
1 / [2 1 / 3] = 2 / [4 2/3 ]
3 / 7 = 3/7
Thus, The necessary, team 3, tower garden gift illustrates the proportional relationship between weeks and donation.
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A local manufacturing firm produces four different metal products, each of
which must be machined, polished and assembled. The specific time
requirements (in hours) for each product are as follows:
The firm has available to it on weekly basis, 480 hours of machining time, 400 hours of polishing time and 400 hours of assembling time. The unit profits on the product are Birr 360, Birr 240, Birr 360 and Birr 480, respectively.The firm has a contract with a distributor to provide 50 units of product I, and 100 units of any combination of products II and III each week. Through other customers the firm can sell each week as many units of products I, II and III as it can produce, but only a maximum of 25 units of product IV. How many units of each product should the firm manufacture each week to meet all contractual obligations and maximize its total profit? Make a mathematical model for the given problem. Assume that any unfinished pieces can be finished the following week.
Step-by-step explanation:
The firm should manufacture 50 units of product I, 100 units of product II, and 100 units of product III each week to meet all contractual obligations and maximize its total profit.
To set up the mathematical model for this problem, we can use variables to represent the number of units of each product that the firm manufactures each week. Let x1 be the number of units of product I, x2 be the number of units of product II, x3 be the number of units of product III, and x4 be the number of units of product IV.
The first constraint is that the firm has a contract to provide 50 units of product I and 100 units of any combination of products II and III each week. This can be represented as:
x1 = 50
x2 + x3 = 100
The second constraint is that the firm has a maximum of 480 hours of machining time, 400 hours of polishing time, and 400 hours of assembling time each week. The time required for each product can be represented as:
x16 + x28 + x34 + x410 <= 480 (machining time)
x14 + x26 + x32 + x48 <= 400 (polishing time)
x14 + x24 + x34 + x46 <= 400 (assembling time)
The third constraint is that the firm can sell as many units of products I, II, and III as it can produce, but only a maximum of 25 units of product IV. This can be represented as:
x1 >= 0
x2 >= 0
x3 >= 0
x4 <= 25
The objective is to maximize the firm's total profit, which is the sum of the profits for each product. The unit profits for each product are Birr 360, Birr 240, Birr 360, and Birr 480, respectively. The total profit can be represented as:
360x1 + 240x2 + 360x3 + 480x4
The complete mathematical model for this problem is:
Maximize: 360x1 + 240x2 + 360x3 + 480x4
Subject to:
x1 = 50
x2 + x3 = 100
x16 + x28 + x34 + x410 <= 480
x14 + x26 + x32 + x48 <= 400
x14 + x24 + x34 + x46 <= 400
x1 >= 0
x2 >= 0
x3 >= 0
x4 <= 25
This model can be solved using linear programming techniques to find the values of x1, x2, x3, and x4 that maximize the total profit while satisfying all of the constraints. In this case, the optimal solution is x1 = 50, x2 = 100, x3 = 100, and x4 = 0, which corresponds to manufacturing 50 units of product I, 100 units of product II, and 100 units of product III each week. This meets all of the contractual obligations and maximizes the total profit.
The objective is to maximize total profit, which is given as
P = 360 [tex]x_1[/tex]+ 240[tex]x_2[/tex]+ 360[tex]x_3[/tex] + 480[tex]x_4[/tex]
What is Linear Programming Problem?The goal of the Linear Programming Problems (LPP) is to determine the best value for a given linear function. The ideal value may be either the highest or lowest value. The specified linear function is regarded as an objective function in this situation.
Let[tex]x_1[/tex] , [tex]x_2[/tex], [tex]x_3[/tex] and [tex]x_4[/tex] be the number of units of product I, II, III and IV to be produced, respectively.
The constraints are that the time requirements for each product should not exceed the available time, the firm is contractually obligated to produce 50 units of product I and 100 units of products II and III, and the firm can sell at most 25 units of product IV.
These constraints can be written mathematically as:
3[tex]x_1[/tex] + 2 [tex]x_2[/tex]+ 2 [tex]x_3[/tex] + 4[tex]x_4[/tex] ≤ 480 (Machining)
[tex]x_1[/tex] + [tex]x_2[/tex] + [tex]x_3[/tex] + 3[tex]x_4[/tex] ≤ 400 (Polishing)
2[tex]x_1[/tex] + [tex]x_2[/tex]+ 2 [tex]x_3[/tex] + [tex]x_4[/tex] ≤ 400 (Assembling)
and, [tex]x_1[/tex] ≥ 50 (Product I)
[tex]x_2[/tex] + [tex]x_3[/tex] ≥ 100 (Products II and III)
[tex]x_4[/tex] ≤ 25 (Product IV)
[tex]x_1[/tex] , [tex]x_2[/tex], [tex]x_3[/tex] , [tex]x_4[/tex] ≥ 0
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Solve for <1. (Will mark as brainiest!)
Answer:
< 1 = 64°
Step-by-step explanation:
First at all the sum of 2 angles should be 180°
< 3 + 116° = 180°
< 3 = 180 - 116
< 3 = 64°
Then, the sum of intern angles of a triangle must sum 180°, so:
< 1 + 52° + < 3 = 180°
< 1 +52 + 64 = 180
< 1 = 180 - 64 -52
< 1 = 64°
7. A material in which thermal energy is transferred slowly is a conductor.
True or False
Answer:
False
Step-by-step explanation:
False. A material in which thermal energy is transferred slowly is actually an insulator. A conductor is a material that easily allows the transfer of thermal energy. This is because conductors have loosely bound electrons that can move freely through the material, allowing heat to be easily transferred. Examples of good conductors include metals such as copper, aluminum, and silver. On the other hand, insulators have tightly bound electrons that do not move easily, making them poor conductors of heat. Examples of good insulators include materials like glass, plastic, and rubber.
What are the values of t and u?
t = ?°
u= ?
By using properties of triangle, it can be calculated that-
t = 60°
u = 8
What is a triangle?
A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles.
Based on the sides of a triangle, triangle may be classified as equilateral, isosceles and scalene
Triangle whose all three sides are equal is called equilateral
Triangle whose two sides are equal is called isosceles
Triangle whose all sides are unequal is called scalene
Here,
[tex]\angle[/tex]FGE = 90°
[tex]\angle[/tex]GFE = 30°
[tex]\angle FEG[/tex] = 180 - (90 + 30)
= 180 - 120
= 60°
t = 60°
Since FE = HE and [tex]\Delta[/tex]FGE and [tex]\Delta[/tex]FGE are right angle triangles,
So FG = FH
u = 8
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