The segment [P3, P4] satisfies the minimum requirements, and the minimal price value is $840.
Let X be the amount of mix A (in pounds), and Y be the amount of mix B.
The constraints are
20X + 10Y >= 400
10X + 30Y >= 960
5X + 10Y >= 210
X >= 0, Y >= 10.
The objective function to minimize is F(X, Y) = 20X+40Y.
In the equivalent form, the constraints are
2X + 1Y >= 40
X+ Y >= 33
X+2Y >= 42
The feasibility area is the infinite area in the first quadrant which lies ABOVE each of the following straight lines :
A red (which represents the constraint (1'));
The green (which represents the constraint (2')),
A blue (which represents the constraint (3')).
Plot 2X + 1Y = 40 (const. (1'), red);
X+Y = 33 (const. (2'), green)
X+2Y = 42 (const. (3'), blue)
The four corner points of the area are:
P1 = (0,40), P2 = (7,26), P3 = (24,9), P4 = (42,0)
As per the Linear Programming method, we can calculate and compare the values at these 4 points.
These values of P1, P2, P3,P4 are:
P1: F(0,40) = 0 + 40*40 = 1600
P2: F(7,26) = 20*7+40*26 = 1180
P3: F(24,9) = 20*24+40*9 = 840
P4: F(42,0) = 20*42+0 = 840.
By comparing the numbers, any value of (X, Y) that lies on the segment [P3, P4] satisfies the minimum requirements.
The segment [P3, P4] satisfies the minimum requirements, and the minimal price value is $840.
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Camden just accepted a job at a new company where he will make an annual salary of $43000. Camden was told that for each year he stays with the company, he will be given a salary raise of $2000. How much would Camden make as a salary after 7 years working for the company? What would be his salary after tt years?
The solution is, the salary of the Luke after 10 years is 98000 dollars & the salary of the Luke after t years is 53000+4500t .
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
Given data:
* The starting salary of the Luke in the new company was,
S1 = 53000
* The salary raise given to Luke each year is,
R = 4500
(a). The salary of the Luke after 10 years is,
S = S1 +R*10
S = 53000 + ( 4500* 10)
S = 98000
Thus, the salary of the Luke after 10 years is 98000 dollars.
(b). After the t years,
S = S1 +R*t
S = 53000 + ( 4500* t)
S = 53000+4500t
Thus, the salary of the Luke after t years is 53000+4500t .
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a store sells cereal for $2.99 and milk for $4.99. a shopper wants to spend at least $12 but no more than $25 on groceries. what is one possible combination of cereal and milk the shopper can buy and still stay in their budget?
The possible combination of cereal and milk the shopper can buy and still stay in their budget is:
12 ≤ 2.99x + 4.99y ≤ 25 (x , y ∈ N)
Inequality:The relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
"Information available from the question"
A store sells cereal for $2.99 and milk for $4.99.
A shopper wants to spend at least $12 but no more than $25 on groceries.
To find the possible combination of cereal and milk the shopper can buy and still stay in their budget.
Now, According to the question:
Let x represents the shopper buy and y represent the milk.
Then represents the inequality according to the information.
A store sells cereal for $2.99
It write 2.99x
And for the milk is 4.99y
So,
12 ≤ 2.99x + 4.99y ≤ 25 (x , y ∈ N)
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today the temperature is 75 degrees. yesterday was 65 degrees. what is the percentage of increase from yesterday to today?
The high temperature increased by 15.38% from yesterday to today.
First, you must find the actual increase in temperature. by using this formula:
Percentage increase = (Today's temperature - Yesterday's temperature) / Yesterday's temperature * 100
Percentage increase = (75 - 65) / 65 * 100 = 15.38%
Temperature is a physical quantity that indicates hot and cold. It is the manifestation of thermal energy, present in all matter, which is the inception of the occurrence of heat, a flow of energy when a body is in contact with another that is colder or hotter.
Temperature is measured with a thermometer.
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what is the volume of the triangle ?
Answer: 720
Step-by-step explanation:
Volume = l x w x h, so 9 x 10 = 90, 90 x 8 = 720.
Hope this helps.
Write 13/12 as a mised number
Answer:
[tex]\frac{13}{12}=1\frac{1}{12}[/tex]
Step-by-step explanation:
You have 12/12 + 1/12 so it would end up being 13/12 so you can simplify the 12/12 to 1 and have [tex]1\frac{1}{12}[/tex]
which rule uses actual probability distributions to determine if hiring decisions have had adverse impact on minority groups? multiple choice question. the prima facie rule the standard deviation rule the four-fifths rule the bona fide occupational qualification rule
The prima facie rule uses actual probability distributions to determine if hiring decisions have had adverse impact on minority groups.
What do you mean by prima facie rule?The "prima facie" rule refers to a legal standard or a evidentiary standard used in the field of employment discrimination law. In the context of employment discrimination, a prima facie case refers to the minimum evidence required to establish a presumption of discrimination.
The term "prima facie" comes from Latin and means "at first sight" or "on its face." In other words, a prima facie case of discrimination is established if, at first sight, the evidence suggests that discrimination has taken place. Once a prima facie case has been established, the burden of proof shifts to the employer to provide a non-discriminatory explanation for the actions in question.
It is more commonly used in legal and ethical contexts to refer to a case or argument that is initially strong enough to establish a point, but may be challenged or overcome by further evidence or argument.
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convert 4582 base 10 to base 2
Answer:
458210 in binary
10001111001102
To convert decimal number 4582 to binary, follow these steps:
Divide 4582 by 2 keeping notice of the quotient and the remainder.
Continue dividing the quotient by 2 until you get a quotient of zero.
Then just write out the remainders in the reverse order to get binary equivalent of decimal number 4582.
Using the above steps, here is the work involved in the solution for converting 4582 to binary number:
4582 / 2 = 2291 with remainder 0
2291 / 2 = 1145 with remainder 1
1145 / 2 = 572 with remainder 1
572 / 2 = 286 with remainder 0
286 / 2 = 143 with remainder 0
143 / 2 = 71 with remainder 1
71 / 2 = 35 with remainder 1
35 / 2 = 17 with remainder 1
17 / 2 = 8 with remainder 1
8 / 2 = 4 with remainder 0
4 / 2 = 2 with remainder 0
2 / 2 = 1 with remainder 0
1 / 2 = 0 with remainder 1
Then just write down the remainders in the reverse order to get the answer, The decimal number 4582 converted to binary is therefore equal to :
1000111100110
The bearing of a fishing boat from a lighthouse is 118°.
Work out the bearing of the lighthouse from the fishing boat.
The bearing of the lighthouse from the fishing boat is 242
Hwo to determine the bearingFrom the question, we have the following parameters that can be used in our computation:
The bearing of a fishing boat from a lighthouse is 118°.
The bearing of the lighthouse from the fishing boat is calculated as
The bearing of the lighthouse from the fishing boat = 360 - The bearing of a fishing boat from a lighthouse
Substitute the known values in the above equation, so, we have the following representation
The bearing of the lighthouse from the fishing boat = 360 - 118
Evaluate
The bearing of the lighthouse from the fishing boat = 242
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Draw a rectangle on graph paper with vertices whose coordinates are (-1, 2), (-1, -4), (3, -
4), and (3, 2).
(Graph paper provided in the jamboard in Q1).
Part A: Find the perimeter and area of the rectangle. Show your work.
Part B: Multiply the coordinates of the vertices of the rectangle by 3. State the new vertices.
Part C: Draw the rectangle whose vertices are those you found in Part B. Find the perimeter and area of this new rectangle.
Show your work.
Part D: Compare the perimeter of the rectangle in Part C to the perimeter of the original rectangle. (list each and then compare).
Part E: Compare the area of the rectangle in Part C to the area of the original rectangle. (list each and then compare).
The area of the new rectangle is 9 times the previous area and the perimeter of the new rectangle is 3 times the previous area
Part A: Find the perimeter and area of the rectangle.From the question, we have the following parameters that can be used in our computation:
(-1, 2), (-1, -4), (3, -4), and (3, 2).
See attachment for the points, where we have
Length = 4 and width = 6
Using area and perimeter formulas, we have
Area = 4 * 6 = 24
Perimeter = 2 * (4 + 6) = 20
Part B: Multiply the coordinates by 3Here, we have
New = (-3, 6), (-3, -12), (9, -12), and (9, 6).
Part C: Find the new perimeter and area of the rectangle.See attachment for the points, where we have
Length = 12 and width = 18
Using area and perimeter formulas, we have
Area = 12 * 18 = 216
Perimeter = 2 * (12 + 18) = 60
Part D: Comparison of the areasThe area of the new rectangle is 9 times the previous area
i.e. 216/24 = 9
Part E: Comparison of the perimetersThe perimeter of the new rectangle is 3 times the previous area
i.e. 60/20 = 3
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Help please (will mark as brainlest)
[tex] - a {x}^{2} + 2x + a - 5[/tex]
The value:[tex] - 183[/tex]
help on both problems
Answer:
the shape is different
Step-by-step explanation:
you draw the shapes
(Projectile Motion) Mary is outside her apartment building. She needs to pass her key to John, who is 6 m above the ground floor of the building. Mary has no time to run upstairs, so she throws the key towards John. Suppose the height, h m, of the key above the ground floor at time t seconds is given by h = -11t² + 20t + 1. Is it possible for John to catch the key? Justify your answer.
Using a standard deck of 52 cards, Lisa drew a card, recorded the suit of the card picked, then replaced it back in the deck. She continued this for a total of 40 draws. The table shows the frequency of each type of card drawn.
The experimental probability of not selecting a heart is (D)P(not heart) = 77.5%
How to find the experimental probability ?The experimental probability that a heart is selected is:
= Number of times hearts was selected / Number of times Lisa drew a card
= 9 / 40
This then means that the experimental probability of not selecting a heart is:
= 1 - experimental probability of selecting a heart
= 1 - 9 / 40
= 31 / 40
= 0. 775
= 77. 5 %
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The question is:
Determine the experimental probability of not selecting a heart.
(A) P(not heart) = 9%
(B) P(not heart) = 10%
(C) P(not heart) = 67.5%
(D)P(not heart) = 77.5%
something2730 (question 7 only)
Answer:2737
Step-by-step explanation:
B and D meet at a 75º, as does A and C
The double number line shows that Henrik has a mass of 60\,\text{kg}60kg60, start text, k, g, end text. A double number line with 2 tick marks. The line labeled Mass, kilograms, reads from left to right: 0, 60. The line labeled Percentage, reads from left to right: 0 percent, 100 percent. A double number line with 2 tick marks. The line labeled Mass, kilograms, reads from left to right: 0, 60. The line labeled Percentage, reads from left to right: 0 percent, 100 percent. Complete the table to show different percentages of Henrik's mass. Mass (\text{kg}kgstart text, k, g, end text) Percentage 100\%100%100, percent of 60\,\text{kg}60kg60, start text, k, g, end text 20\%20%20, percent of 60\,\text{kg}60kg60, start text, k, g, end text 40\%40%40, percent of 60\,\text{kg}60kg60, start text, k, g, end text
The double number line is discussed below.
What is number line?In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers.
Given is a double number line.
A double number line diagram uses a pair of parallel number lines to represent equivalent ratios.
The locations of the tick marks match on both number lines.
The tick marks labeled 0 line up, but the other numbers are usually different.
The lines in a double number line diagram are similar to the number lines students have seen in earlier grades in that -
Numbers correspond to distances on the line (so that the distance between, say, 0 and 12 is three times the distance between 0 and 4).We can choose what scale to use (i.e., whether each interval represents 1 unit, 2 units, 5 units, etc.).The lines can be extended as needed.Therefore, the double number line is discussed above.
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5 subtracted from 1/3 of 20
IN FRACTIONS
The least common multiple of 3 and 5 is 15, so we convert 5 to 15/3.So the answer is 5/3.
The calculation in fractions:
1/3 of 20 = (1/3) * 20 = 20/3
5 subtracted from 1/3 of 20 = 20/3 - 5
To simplify the expression 20/3 - 5, we need to subtract 5 from 20/3 by finding a common denominator between 5 and 20/3. The least common multiple of 3 and 5 is 15, so we convert 5 to 15/3:
20/3 - 5 = 20/3 - 15/3 = (20 - 15)/3 = 5/3
So the answer is 5/3.
Fractions are a way of representing numbers as ratios of two integers. The top number of a fraction is called the numerator, and the bottom number is called the denominator. The numerator represents the number of parts of the whole that are being considered, and the denominator represents the number of equal parts that make up the whole.
For example, the fraction 1/2 represents 1 part out of 2 equal parts that make up the whole.
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What is the answer to this problem solving for X? (12x-8=10x+6)
A new refrigerator has a price of $480.00. The store will discount the price by 15% if the purchaser pays in cash. What is the cash price of the refrigerator?
The cash price of the refrigerator is $408.
What is discount?A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.
Given that, a new refrigerator has a price of $480.00.
The store will discount the price by 15% if the purchaser pays in cash.
Now, the discount is
15% of 480
= 15/100 ×480
= 0.15×480
= 72
Now, 480-72
= $408
Therefore, the cash price of the refrigerator is $408.
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please help
thank you!!
Step-by-step explanation:
Hi joolin
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If the first 4 questions are True/False and the last 4 questions are Multiple Choice (a, b, c, or d). What is the probability that they will get them all correct?
The probability of getting all 8 questions correct is 1/4096 or approximately 0.024%.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
The probability of getting a True/False question correct is 1/2, since there are only two possible answers. The probability of getting a multiple-choice question correct is 1/4 since there are four possible answers.
So, for the first 4 True/False questions, the probability of getting them all correct is (1/2)⁴ = 1/16.
For the last 4 multiple-choice questions, the probability of getting them all correct is (1/4)⁴ = 1/256.
The total probability of getting all 8 questions correct is the product of the probabilities of getting each set of questions correct:
(1/16) x (1/256) = 1/4096
So, the probability of getting all questions correct is 1/4096 or about 0.024%.
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How many subsets are there of the set N = {1}?
Answer:
A Set With One Element
So any set with one element will have 2 subsets.
Step-by-step explanation:
Match the exponent expression to it's correct solution.
The matching is as follow:
x²³ / x³ --> [tex]x^{20[/tex]
[tex]x^{14}/ x^{17}[/tex] --> 1/x³
[tex]x^{19}/ x^{33}[/tex] --> 1/[tex]x^{14[/tex]
[tex]x^{16}/ x^7[/tex] --> [tex]x^9[/tex]
What are exponent and Power?Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.
Given:
We will use the Property of exponent and power
[tex]x^m/ x^n[/tex] = [tex]x^{m-n[/tex]
1. x²³ / x³
Using the property
x²³ - ³ = [tex]x^{20[/tex]
2. [tex]x^{14}/ x^{17}[/tex]
Using the property
= [tex]x^{14- 17}[/tex]
= [tex]x^{-3[/tex]
= 1/x³
3. [tex]x^{19}/ x^{33}[/tex]
Using the property
= [tex]x^{19-33}[/tex]
= [tex]x^{-14}[/tex]
= 1/[tex]x^{14[/tex]
4. [tex]x^{16}/ x^7[/tex]
Using the property
= [tex]x^{16-7}[/tex]
= [tex]x^9[/tex]
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7)
3)
5)
Determine if the two triangles are congruent. If they are, state how you know.
2)
1)
A
6)
SSS?
SAS?
Some triangle pairs are congruent triangles but some others are not, because:
Congruent; 2 pairs of corresponding angles and 1 corresponding side Congruent; 2 pairs of corresponding sides and 1 corresponding angleCongruent; 2 pairs of corresponding angles and 1 corresponding sideCongruent; 3 pairs of corresponding sidesNot congruent; only 2 pairs of corresponding sidesCongruent; 1 pair of corresponding side and 2 corresponding anglesNot congruent; only 3 pairs of corresponding anglesNot congruent; only 3 pairs of corresponding anglesA pair of triangles is congruent if they have one of these criterias:
SSS (three corresponding sides)SAS (2 pairs of corresponding sides and 1 pair of corresponding angle between those side pairs)ASA (2 pairs of corresponding angles and 1 pair of corresponding side between those angle pairs)AAS (2 pairs of corresponding angles and 1 pair of corresponding side not between the angles)HL (Congruent hypotenuse and 1 pair of corresponding side)Let's explore each triangle pairs we have:
Pair 1
We know that both triangle have a vertical angle on its connection, hence both angles are congruent. They also have another pair of corresponding angles and 1 pair of corresponding sides between the angles .
Pair 1 meet ASA rules --> Congruent triangles
Pair 2
Pair 2 has 1 corresponding angle and 2 pairs of corresponding sides
Pair 2 meets SAS rules --> congruent triangles
Pair 3
We know that both triangle have a vertical angle on its connection, hence both angles are congruent. They also have another pair of corresponding angles and 1 pair of corresponding sides between the angles.
Pair 3 meet ASA rules --> Congruent triangles
Pair 4
Pair 4 has 3 corresponding sides and meets SSS rules --> congruent triangles
Pair 5
Pair 5 only has 2 corresponding sides --> not congruent triangles
Pair 6
We know that both triangle have a vertical angle on its connection, hence both angles are congruent. They also have another pair of corresponding angles and 1 pair of corresponding sides not between the angles.
Pair 6 meet AAS rules --> Congruent triangles
Pair 7
We know that both triangle have a vertical angle on its connection, hence both angles are congruent. Pair 7 also has another 2 corresponding angles. In total, pair 7 has 3 corresponding angles.
Pair 7 is not congruent triangles because three corresponding angles might have different size of sides. A pair of triangles can be congruent only if there is at least one pair of corresponding side between them.
Pair 8
We know that both triangle have a vertical angle on its connection, hence both angles are congruent. Pair 8 also has another 2 corresponding angles. In total, pair 8 has 3 corresponding angles.
Pair 8 is not congruent triangles because three corresponding angles might have different size of sides. A pair of triangles can be congruent only if there is at least one pair of corresponding side between them.
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point p partitions directed segment AB in the part to part ratio of 4:4. If A(5,-7) and B(1,-1), find the y-coordinate of P. Round your answer to 2 decimals
Using the fact that P is the midpoint of the segment AB, we will see that its y-value is -4.
How to find the y-coordinate of P?We know that point P partitions directed segment AB in the part to part ratio of 4:4.
Notice that the ratio is equivalent to 1:1
So point P is just the midpoint of the segment, remember that for a segment whose endpoints are (a, b) and (c, d), the midpoint is:
M= ( [a+ c]/2, [b + d]/2)
P is the midpoint of (5,-7) and (1,-1), then the value of the y-coordinate of P is:
y = (-7 + (-1))/2
y = (-7 - 1)/2
y = -4
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The temperature in Duluth, Minnesota was -23F at sunrise. By noon, the temperature had risen 19 degrees. What was the temperature (in degrees Fahrenheit) at noon?
Answer:
Step-by-step explanation:
-23 + 19 = -4
At noon the temperature was -4 degrees F.
6 Find the area of the figure. 5. 3 in. 10 in. 4 in. 7 in. A 101. 8 square inches B 43. 9 square inches C 64. 9 square inches D 78. 6 square inches
The area of the rectangle would be equal to the sum of the areas of these 12 squares.
The area of a rectangle is a measure of the amount of space it covers. It is calculated by multiplying the length and the width of the rectangle.
For a rectangle with sides of 3 cm and 4 cm, the area can be found by multiplying 3 by 4. The formula for finding the area of a rectangle is
=> A = l * w,
where l is the length and w is the width.
So, for the rectangle with sides 3 cm and 4 cm, the area would be
=> A = 3 * 4 = 12 square centimeters.
To visualize this, imagine a rectangle with sides of 3 cm and 4 cm. If you placed 12 squares of 1 cm each inside this rectangle, it would fill up the entire rectangle without any space left.
Complete Question:
Find the areas of the rectangles whose sides are:
(a) 3 cm and 4 cm
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9=p-12;29,30,31 with one is the answer I said 29 and was wrong help me !!!
Answer: The equation 9 = p - 12 can be solved for p by adding 12 to both sides:
p = 9 + 12 = 21.
So the correct answer to the question "29, 30, 31 with one is the answer" would be 30, as it is the only one that equals 21.
Step-by-step explanation:
Please help me with this
The table that represents a linear relationship is the one in option 3.
Which table represents a linear relationship?A linear relationship can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we add 1 to the input we get:
y = a*(x + 1) + b
y = (a*x + b) + a
So for each increase of 1 unit on the input we have a constant increase on the value of y.
The table that represents a line is the number 3, where you can see that the increases in the f(x) values are constants.
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please can you solve the question
`
Answer:
x = 115°
y = 50°
Step-by-step explanation:
it is an isosceles triangle, the angles at the base are congruent, x is the opposite angle of 115°, therefore the same value, to find y we subtract the two 65° angles from the sum of the internal angles of the triangle (180°) and we have 50 ° which is the value of Y, look at the figure to understand better
What is the sum of the measures of the interior angles of a 20-sided figure?
Responses
3,240°
360°
3,600°
180°
Answer:
3,240°
Step-by-step explanation:
The sum of the measures of the interior angles of a polygon with n sides can be found using the formula:
(n-2) * 180°
So, for a 20-sided figure, the sum of the interior angles would be:
(20-2) * 180° = 18 * 180° = 3,240°