You have 140 tomatoes and 13 onions left over from your garden. You want to use these
to make jars of tomato sauce and jars of salsa to sell at a farm stand. A jar of tomato
sauce requires 10 tomatoes and 1 onion, and a jar of salsa requires 5 tomatoes and 1
onion. You will make a profit of $2 on every jar of tomato sauce and a profit of $1.50 on
every jar of salsa sold. The owner of the farm wants at least three times as many jars of
tomato sauce as jars of salsa. How many jars of each should you make to maximize
profit?
3. A company produces two types of tables, T1 and T2. It takes 2 hours to produce the parts
of one unit of T1, 1 hour to assemble and 2 hours to polish. It takes 4 hours to produce
the parts of one unit of T2, 2.5 hour to assemble and 1.5 hours to polish. Per month, 7000
hours are available for producing the parts, 4000 hours for assembling the parts and 5500
hours for polishing the tables. The profit per unit of T1 is $90 and per unit of T2 is $110.
How many of each type of tables should be produced in order to maximize the total
monthly profit?
Answers
1. To maximize the profit :
28 jars of salsa and
0 jars of tomato sauce should be made.
which make maximum profit of $42.
2. In order to maximize the total monthly profit
2300 units of T₁ type table and and
600 units of T₂ type table should be made
which provide maximum profit of $273000.
What is an Inequality?In Algebra, inequality is a Mathematical statement that shows the relation between two expressions using the inequality symbol. The expressions on both sides of an inequality sign are not equal. It means that the expression on the left-hand side should be greater than or less than the expression on the right-hand side or vice versa. If the relationship between two algebraic expressions is defined using the inequality symbols, then it is called literal inequalities.
1. Let x be the numbers of jars of tomato sauce
Let y be the number of jars of salsa sauce
Profit P(x, y)=2x+1.5y
x≥0
y≥0
10x+5y≤140
x + y ≤13
The solution set of the system of inequalities above the vertices of the feasible solution set obtained are shown below.
A at (0,13)
B at (0,28)
C at (14,0)
D at (15,0)
E at (15, -2)
Evaluate profit P(x, y) at each vertex
A at (0,13):P(0,13)=$19.5
B at (0,28):P(0,28)=$42
C at (14,0):P(14,0)=$28
D at (15,0):P(15,0)=$30
E at (15, -2):P(15,-2)=30-3=$27
The maximum profit of $42 is at vertex B.
Which means production of 28 jars of salsa and 0 jars of tomato sauce provides maximum profit of $42.
2. Let x be the number of tables of type T₁
and y the number of tables of type T₂
Profit P(x, y)=90x+110y
x≥0
y≥0
2x+4y≤7000
x+2.5y≤4000
2x+1,5y≤5500
The solution set of the system of inequalities above the vertices of the feasible solution set obtained are shown below.
A at (0,0)
B at (0,1600)
C at (1500,1000)
D at (2300,600)
E at (2750,0)
Evaluate profit P(x, y) at each vertex
A at (0,0):P(0,0)=0
B at (0.1600):P(0,1600)=90(0)+110(1600)=176000
C at (1500,1000):P(1500,1000)=90(2500)+110(1000)=245000
D at (2300,600):P(2300,600)=90(2300)+110(600)=273000
E at (2750,0):P(2750,0)=90(2750)+110(0)=247500
The maximum profit of $273000 is at vertex D.
which means production of 2300 tables of type T₁ and 600 tables of type T₂ makes maximum profit.
1. Hence, maximum profit is made by making
28 jars of salsa and
0 jars of tomato sauce getting
$42 of profit.
2. Hence the company needs to produce
2300 tables of type T₁ and
600 tables of type T₂,
in order to maximize its monthly profit which is equal to $273000.
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Related Questions
Clare spent $5.17 on apples. How many pounds of apples did Clare buy?
(round to the nearest tenth)
Answers
Answer: complete the question please
Step-by-step explanation:
How much is a pound/lb? Then do 5.17 divided by (however much is a pound/lb)
Scarlett is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if she spins a spinner with four equal-sized sections labeled Red, Green, Blue, Orange and rolls a fair die in the shape of a cube that has six sides labeled 1 to 6?
Answers
Answer:
24 different outcomes
Step-by-step explanation:
The answer is 24 different possible outcomes. Since there are 4 colors and 6 numbers. Multiply the 4 by 6 to get 24. Hope this helps
1+1
2+2
3+3
Add all that up
Answers
Answer:
1+1
2+2
3+3= 12
Step-by-step explanation:
pls can I get branliest I need it
Answer:
12
Step-by-step explanation:
1+1+2+2+3+3
2+2+2+3+3
4+2+3+3
6+3+3
9+3
12
Identify the independent variable and the dependent variable. A pool store owner wants to determine the effect of algaecide brands on the treatment of pool water with algae. He contacts customers who have purchased the brands of algaecide and asks their opinion of the algaecide.
Answers
The independent variable is the brand of algaecide. The dependent variable is the treatment of pool water with algae.
What is the independent and dependent variable?
In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are investigated under the presumption or requirement that they are dependent on the values of other variables due to some law or rule.
Here, we have
Given
A pool store owner wants to determine the effect of algaecide brands on the treatment of pool water with algae. He contacts customers who have purchased the brands of algaecide and asks their opinion of the algaecide.
We have to determine the independent variable and the dependent variable.
We concluded that the independent variable is the brand of algaecide and the dependent variable is the treatment of pool water with algae.
Hence, the independent variable is the brand of algaecide and the dependent variable is the treatment of pool water with algae.
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The bars on a histrogram are side by side and do not touch each other.
True
False
SOMEONE PLEASE HELP AND NO LINKS OR FILES ASAP
Answers
What is the domain of the function y √ x?
Answers
The domain of the function y = √ x is x ≥ 0.
The domain of a function is the set of all input values for which the function is defined. The square root function, represented by √, is only defined for non-negative real numbers. This is because the square root of any negative number is not a real number, it becomes an imaginary number. Therefore, the domain of √ x is the set of all real numbers greater than or equal to zero.
This means that any input value less than zero would result in an undefined output for the square root function. In this case, since the square root is the only function, the domain of the function y = √ x is x ≥ 0. This means that the function can only take non-negative real numbers as input and will output a non-negative number.
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Carlos bought 515 Euros for his holiday to Germany. He spent £ 412 to obtain these Euros. How many Euros would Carlos have obtained if he spent £500 ?
Answers
Carlos needs a total of 400 Euros for buying 500 Euros.
The total amount available with Carlos for his holiday to Germany = 515 Euros
Amount spent to obtain these 515 Euros = £ 412
As it is clear that for buying 515 Euros he spent 412 Euros.
So, we will first find the Euros spent on buying 1 Euro.
For that, we will use Unitary Method:
So, the total Euros spent for buying 1 Euro will be = (412/515) = 0.8
So, for finding the total Euros spent for obtaining 500 Euros we will simply multiply the total Euros needed by the Euro spent for buying 1 Euro.
Thar will be equal to (0.8 * 500) = 400 Euros.
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What quadrant is 3 and 4 in a graph?
Answers
Both the x- and y-axes have negative values in this quadrant.
The x-axis in the fourth quadrant has positive values, whereas the y-axis has negative numbers.
A two-dimensional Cartesian system's axes split the plane into four infinite areas called quadrants, each of which is limited by two half-axes. These are frequently numbered from 1st through 4th and marked by Roman numerals: I (+; +), II (; +), III (; ), and IV (+; ).
The intersection of the x-axis (the horizontal number line) and the y-axis divides the coordinate plane into four equal pieces in the cartesian system (the vertical number line). These four regions are known as quadrants because they each account for one-quarter of the coordinate plane.
The third quadrant, known as Quadrant III, is located in the bottom left quadrant.
The fourth quadrant, indicated as Quadrant IV, is in the bottom right quadrant.
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helpppppppppppppppp!!!!
Answers
Answer:
69π m^2
Step-by-step explanation:
surface area of cylinder= 2πrh+2πr^2
However, the cylinder is open top
Therefore, the outer surface area of the cylinder
=2π(6/2)(10)+π(3)^2 m^2
=60π+9π m^2
=69π
i need help asap please
Answers
Step-by-step explanation:
the range is (-32, 28)
note that when the bubble is not filled in it should be an open bracket
1. Find the surface area of the cone in terms of pi.
A. 84pi cm
B. 98pi cm
C. 70pi cm
D. 119pi cm
Answers
The surface area of the cone is 119π
How to find the surface area of a cone?Surface area of a cone = πr(r + l)
where
r = radiusl = lengthTherefore,
r = 7 cm
l = 10 cm
Hence,
Surface area of the cone = 7π(7 + 10)
Surface area of the cone = 7π(17)
Surface area of the cone = 119π
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Answer: option D. 119
Step-by-step explanation:
surface area of cone =[tex]\pi[/tex] x r x l + [tex]\pi[/tex] x r^2
r =7 l =10
pi x 7 x 10 + pi x 7^2
A store sells jump ropes. Each jump rope costs the same amount. During a sale, the store reduces the price of each jump rope by $1.25. Jada
spends $15.08 on 2 jump ropes at the sale price.
What was the price of 1 jump rope before the sale? Enter the answer in the box.
Answers
Answer:
The jump rope cost $8.79 before the sale.
Step-by-step explanation:
She spent 15.08 on 2 while they were on sale. I divided 15.08 by 2 to find what each one cost individually on sale, which is $7.54. Then add $1.25 to $7.54= $8.79
hat is the product of the least common multiple and the greatest common factor of $22$ and $48$?
Answers
Answer:
1056
Step-by-step explanation:
You want the product of the LCM and the GCF of 22 and 48.
ProductOne way to find the LCM of two numbers is to start with their product, then divide out the extra factor:
LCM(A, B) = (A×B)/GCF(A, B)
Since we want the product of the LCM and the GCF, we can start with this and multiply by the GCF:
LCM(A, B) · GCF(A, B) = ((A×B)/GCF(A, B)) · GCF(A, B)
LCM(A, B) · GCF(A, B) = A×B
Using this for the given numbers, we get ...
LCM(22, 48)·GCF(22, 48) = 22·48 = 1056
__
Additional comment
If you want to go to the trouble of finding the LCM and GCF, you get ...
22 = 2·11
48 = 2·24
LCM(22, 48) = 2·11·24 = 528
GCF(22, 48) = 2
LCM·GCF = 2·528 = 1056
Write the equation of a line that is perpendicular to y=14x - 4 and passes through the point (28, 16)
Answers
The equation of the line perpendicular to {y = 14x - 4} and passes through the point (28, 16) is y = - (1/14)x + 18.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is the equation of the line as -
y = 14x - 4
The given equation of line is -
y = 14x - 4
Slope of the line perpendicular to the given line is -
m{p} = -1/14
The equation of this line will be -
y = -(1/14)x + c
For the point (28, 16), we can write -
16 = -(1/14) x 28 + c
c = 16 + 2
c = 18
So, the equation will be -
y = - (1/14)x + 18
Therefore, the equation of the line perpendicular to {y = 14x - 4} and passes through the point (28, 16) is y = - (1/14)x + 18.
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Write an equivalent expression by distributing the "-" sign outside the parentheses:
-(-10p - 0. 7q) – 4. 6
Answers
After distribution of the negative sing in the parenthesis, the equivalent expression is 10.7p - 4.6
The expression that is given to us is -(-10p - 0. 7q) – 4. 6.
Now, we know that the meaning of equivalent expression is the it has the same value as that of the original expression.
We have to use the "-" and distribute it over the expression to form an equivalent relation,
So, we know,
-(-10p - 0.7q) – 4.6
Here, p is a constant,
Multiplying the negative sign inside of the bracket,
= (-(-10p)-(-0.7p)-4.6
= 10p + 0.7p - 4.6
= 10.7p - 4.6
So, the equivalent expression is 10.7p - 4.6.
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Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answers
-4 +/- √ 16-4(1)(7)
_____________
2
-4 +/- 2i√3
_______
2
x= -2+/- i√3
Joe the hiker decided to take a rest at the gas station before Kingston. While sitting at the picnic table, he noticed that there were many cars in the parking area. There were three times more silver colour cars than red cars. There were 2 more blue cars than red and silver cars together. There were twice more white cars than red. Joe counted 42 cars altogether in the parking lot.
How many white cars were there?
how many blue cars were ther?
how many red cars were there?
how many silvers were there
Answers
There are 7 white cars, 16 blue cars, 14 red cars and 5 silver cars.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let w represents white cars
b represent blue carr
r represents red cars
s represents silver cars
There were three times more silver colour cars than red cars
3s=r...(1)
There were 2 more blue cars than red and silver cars together
b+2=r+s..(2)
There were twice more white cars than red.
2w=r..(3)
42 cars altogether in the parking lot.
w+b+r+s=42
After solving the above equation we get
s=5, b=16, w=7 and r=14
Hence, there are 7 white cars, there are 16 blue cars, there are 14 red cars and 5 silver cars.
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Un prisma cuadrangular regular tiene 4 m de arista de la base y 6m de altura Calcula el area y el volumen
Answers
Answer:
El área y volumen del prisma cuadrangular mencionado son respectivamente:
Área = [tex]16m^{2}[/tex] Volumen = [tex]96m^{3}[/tex]Step-by-step explanation:
Para solucionar este ejercicio debes recordar que un prisma cuadrangular tiene como base y como superficie cuadrados, por lo tanto, para calcular el área de dicho cuadrado puedes utilizar la siguiente fórmula:
Área de un cuadrado = [tex]arista^{2}[/tex]Ya que el ejercicio nos da el valor de la arista (4 metros), podemos reemplazarla en la ecuación y calcular:
Área de un cuadrado = [tex](4m)^{2}[/tex]Área de un cuadrado = [tex]16m^{2}[/tex]Por último, para calcular el volumen debes multiplicar el área superficial, el área del cuadrado calculado, por la altura del prisma, cuyo valor dentro del enunciado es de 6 metros, de esta forma:
Volumen de un prisma cuadrangular = área superficial * alturaVolumen de un prisma cuadrangular = [tex]16m^{2}[/tex] * [tex]6 m[/tex]Volumen de un prisma cuadrangular = [tex]96m^{3}[/tex]Como puedes ver tras los cálculos, el área superficial del prisma es de [tex]16m^{2}[/tex] y su volumen es [tex]96m^{3}[/tex].
Pls help help help I’m failing help pls
Answers
Answer:
You must check the following boxes: whole number, integer, rational number, and real number.
Step-by-step explanation:
The answer to that expression is 3. It fits within the aforementioned boxes. Hope this helps; have a great day!
Answer:
EXCEPT IRRATIONAL NUMBER ALL ARE CORRECT.
SEE IMAGE FOR SOLUTION
Hope it helps
Have a great day
Why parallel algorithm is better than a sequential algorithm?
Answers
The capacity to complete complex tasks quickly enough to make them useful is the main benefit of choosing a parallel algorithm over a sequential algorithm.
What is the differences between parallel algorithm and sequential algorithm?The differences between parallel algorithm and sequential algorithm are-
Sequential algorithm
One by one, each instruction is carried out in order. It only has one processor.Due to the single processor, it performs poorly and puts a heavy burden on the processor.The format utilized for data transport is bit-by-bit.The entire process takes longer to finish.Low priceParallel algorithm
Every command is carried out simultaneously.There are several processors in it.Due to the several processor, it performs very fast and puts no burden on the processor.Transfers of data occur in bytes.The entire process takes less time to finish.Price is expensive.Due to capacity to complete complex tasks quickly enough to make them useful is the main benefit of choosing a parallel algorithm over a sequential algorithm.
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The ratio of apple juice to cranberry juice in a punch
is 27:51. Which ratio is equivalent to 27:51?
3:7
14 to 26
54:92
9 to 17
Answers
Answer:
9 to 17
Step-by-step explanation:
If you divide 21 by 3 you get 9. So divide 51 by 3 you get 17.
Hope it helps!
Answer: 9 to 17 never got Brandie’s pls give to me
Step-by-step explanation:
Please answer this question correctly please
Answers
Answer:
92
Step-by-step explanation:
Interesting question.
The given angle is 1/2 the central angle. The central angle is equal to the minor arcEG.
So the central angle = 46 *2
The central angle = 92
ArcEG = 92
H can be anywhere on the major arc EG and the answer would be the same.
How do I solve this I don't understand?
Answers
Answer:
The equation for this sequence will be 8 + 17n - 17 with n being replaced with the term number you are trying to find.
so 8 + 17(16) - 17
17 x 16= 272
8 + 272= 280
280- 17= 263
Thus, the 16th term will be 263.
Answer:
16ᵗʰ Term of the sequence is 263
Step-by-step explanation:
Here,
First Term = a₁ = 8
Second Term = a₂ = 25
Third Term = a₃ = 42
Now,
Common Difference (d)
d = a₂ - a₁ = 25 - 8 = 17
d = a₃ - a₂ = 42 - 25 = 17
Here, Common Difference is same everywhere
Now, For 16ᵗʰ term, n = 16
aₙ = a + (n - 1)d
a₁₆ = 8 + (16 - 1) × 17
a₁₆ = 8 + 15 × 17
a₁₆ = 8 + 255
a₁₆ = 263
Thus, 16ᵗʰ Term of the sequence is 263
-TheUnknownScientist
Is(1, 7)a solution to the inequality 3x + 11y ≤ 8? IXL
Answers
Answer: No, it is not a solution.
Step-by-step explanation:
We will substitute the point given, and if the inequality is true after simplifying then it is a solution.
Given:
3x + 11y ≤ 8
Substitue:
3(1) + 11(7) ≤ 8
Multiply:
3 + 77 ≤ 8
Add:
80 ≤ 8 ✗
How many ways can the train be made up?
Answers
Answer:
16c9
Step-by-step explanation:
First, we will add up the number of different car possibilities. This is:
6 + 7 + 3 = 16.
Then, we need to take 9 of these 16 cars, giving us 16c9.
Hope this helped!
Answer:
4,151,347,200
Step-by-step explanation:
6
2/3
15
13
Hit
Miss
2/5
3
5
215
2
Not score
Score
Find the probability that Ryan misses the target and does not score a goal,
(2 marks)
Not score
Answers
Answer:
Step-by-step explanation:
6
2/3
15
13
Hit
Miss
2/5
3
5
215
2
Not score
Score
Find the probability that Ryan misses the target and does not score a goal,
(2 marks)
Sarah has 3 bags of marbles. Each bag has 16 marbles. If 3/4 of the marbles are blue, what is the total number of blue marbles in the bags?
Answers
Answer: 12
Step-by-step explanation: 3/4 divid by 3
HELP DUE IN 10 MINS!
Find the sum of the interior angles 1. interior angle sum =?? degrees
Find the measure of one interior angle. 2. one interior angle: ?? degrees
Answers
Answer:
Sum of Interior Angles = 1,440º
Each Interior Angle = 144º
Step-by-step explanation:
Sum of Interior Angles = (n − 2) × 180°
Each Interior Angle (of a Regular Polygon) = (n − 2) × 180° / n
----------------------------
10 sided regular polygon
Sum of Interior Angles = (10 − 2) × 180º
Sum of Interior Angles = 1,440º
Each Interior Angle = (10 − 2) × 180º / 10
Each Interior Angle = 144º
Answer:
Sum of interior angles = 1440°
One of the interior angle = 144°
Step-by-step explanation:
This figure have 10 sides so it's called a Decagon
Sum of all interior angles of Decagon : 180 ( n - 2), where n = number of sides the polygon has.
=> 180 (10 - 2) = 1440
To find one of the interior angle : 1440 / 10 = 144
Hope this helps!
1. A state is considering adding another character to their vehicle license plates in order to increase the number of license plates available. Currently, a license plate must have exactly six character spaces. Each character space may be filled with any capital letter other than I or O or any number between, and including, 0 to 9. Letters and numbers may repeat on the plates.
(a) How many different license plate numbers are available under the current structure of exactly six characters per plate? Show your work.
(b) If the state required all license plates to have exactly seven characters instead of six, how many different license plate numbers would be available with the additional character requirement? Show your work.
(c) How many times bigger is the set of license plate numbers with exactly seven characters than that with the set of six characters? Show your work.
Answer:
Answers
9514 1404 393
Answer:
a) 1,544,804,416
b) 52,523,350,144
c) 34
Step-by-step explanation:
(a) Each character position can be any of 24 letters or 10 digits, so any of 34 characters. The number of possible characters sets increases by a factor of 34 for each added character. A six-character plate will have ...
34^6 = 1,544,804,416 . . . possibilities
__
(b) 34^7 = 52,523,350,144 . . . possibilities
__
(c) 34^7/34^6 = 34 . . . times as many
PLEASE HELP I WILL GIVE FIVE STARS AND BRAINLIEST Transformation and plot image.
Answers
Answer: You need to drew , this arrow , to each point K,L,M,N,
Drawing must be parallel to , this arrow, AND , exactly the same length, as the arrow .
step 2. when you drew it , then at the end are your new points, K",L",M",N".
Ok?
step 3.
Then you just read the coordinates. of new points .
I would gladly drew it , but I do not knew how to put picture in this , jet .
Step-by-step explanation: