The domain of discourse of the propositional function P(x) is {1,2,3,4}, by using negation, disjunction, and conjunction are:
a) "there does not exist an x in the domain for which P(x) is false."
b) "there exists an x in the domain for which P(x) is false."
c) "there exist exactly three x's in the domain for which P(x) is true."
d) -(E. P(x)) can be rewritten as “Every x is not P(x)”
We are given that the domain of discourse of the propositional function P(x) is {1, 2, 3, 4}. We need to rewrite each propositional function below using only negation, disjunction, and conjunction.
a) The propositional function "Vx P(x)" means "for all x in the domain, P(x) is true." To rewrite this using only negation, disjunction, and conjunction, we can use De Morgan's law and write:
-(Ex -P(x)), which means "there does not exist an x in the domain for which P(x) is false."
b) The negation of "Vx P(x)" is "there exists an x in the domain for which P(x) is false." Using De Morgan's law again, we can rewrite this as:
Ex -P(x).
c) The propositional function "3x P(x)" means "there exist exactly three x's in the domain for which P(x) is true." To rewrite this using only negation, disjunction, and conjunction, we can break it down into two statements:
There exists at least three x's in the domain for which P(x) is true.There does not exist a fourth x in the domain for which P(x) is true.Using the symbols for negation, disjunction, and conjunction, we can write this as:
(Ex_1 P(x_1) ∧ Ex_2 P(x_2) ∧ Ex_3 P(x_3)) ∧ -(Ex P(x)).
d) The propositional function "-(E. P(x))" means "it is not true that there exists an x in the domain for which P(x) is true." To rewrite this using only negation, disjunction, and conjunction, we can use De Morgan's law and write:
Ax -P(x),
which means "for all x in the domain, P(x) is false."
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give the position of C on this number line
The position of C on the number line is 1/8th position.
Define the term number line?A number line is a visual representation of the real numbers as points or marks on a straight line. The number line is usually represented horizontally, with zero in the middle and positive numbers to the right of zero and negative numbers to the left of zero.
From the given number line, there are total 8 points between 0 to 1
That means, it's fractions of 8.
Location of point C is on the 1st point,
So, position of C on this number line = (1/8) ÷ (1-0) = 1/8
Therefore, In the number line, C is located in the 1/8th place.
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g a second unit vector which is also orthogonal to both 8,-8,8 and 0,5,5 is the unit vector which points in the direction opposite to u1 -2/6.-1/6,1/6 this is the vector u2
The vector u2 is (0, √3/3, 2/3). It is a unit vector that is orthogonal to both 8,-8,8 and 0,5,5.
Given two vectors 8,-8,8 and 0,5,5, we need to find another unit vector that is orthogonal to both the given vectors. Let's call this vector u1.The vector u1 can be obtained by taking the cross product of the two given vectors:u1 = (8,-8,8) × (0,5,5)u1 = (-40,-40,40)
To get a unit vector, we need to normalize u1 by dividing it by its magnitude:|u1| = √((-40)² + (-40)² + 40²) = 60u1 = (-40/60, -40/60, 40/60) = (-2/3, -2/3, 1/3)Now we need to find another unit vector that is orthogonal to u1.
One way to do this is to take the cross product of u1 with another vector, and then normalize the result. We can choose any vector that is not parallel to u1. For example, we can choose the vector (1,0,0).u2 = u1 × (1,0,0)u2 = (-2/3, -2/3, 1/3) × (1,0,0)u2 = (0,1/3,2/3)
To get a unit vector, we need to normalize u2 by dividing it by its magnitude:|u2| = √(0² + (1/3)² + (2/3)²) = 1/√3u2 = (0, √3/3, 2/3)
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Please help with these Formal Logic questions;
8.1 Some cashmere sweaters are fashionable garments, so some cashmere sweaters are not suede jackets, for some suede jackets are not fashionable garments.
Which of the following correctly expresses the form of this argument?
a. Some C are F.
Some C are not S.
Some S are not F.
b. Some S are not F.
Some C are F.
Some C are not S.
c. Some C are not F.
Some C are not S.
Some C are F.
d. Some F are not S.
Some F are C.
Some S are not C.
e. Some C are F.
Some F are not S.
Some S are not S.
8.2 Some cashmere sweaters are fashionable garments, so some cashmere sweaters are not suede jackets, for some suede jackets are not fashionable garments.
Which of the following substitutions proves the argument invalid?
a. C = animals, F = cats, S = mammals.
b. C = dogs, F = animals, S = mammals.
c. C = dogs, F = mammals, S = fish.
d. C = mammals, F = animals, S = dogs.
e. C = cats, F = mammals, S = animals.
8.3 If cell phone companies screen text messages, then freedom of speech is threatened. Thus, freedom of speech is not threatened, because cell phone companies do not screen text messages.
Which of the following substitutions proves the argument invalid?
a. C = Abraham Lincoln was assassinated, F = George Washington was assassinated.
b. C = Joe Smith was beheaded, F = Joe Smith is dead.
c. C = Abraham Lincoln was beheaded, F = Abraham Lincoln is dead.
d. C = Abraham Lincoln was assassinated, F = Abraham Lincoln is dead.
e. C = Abraham Lincoln was beheaded, F = Abraham Lincoln is not dead.
8.4 If cell phone companies screen text messages, then freedom of speech is threatened. Thus, freedom of speech is not threatened, because cell phone companies do not screen text messages.
Which of the following correctly expresses the form of this argument?
a) If C then F.
C.
F.
b) Not F.
Not C.
If C then F.
c) All C are F.
C.
F.
d) If C then F.
Not C.
Not F.
e) If C then F.
Not F.
Not C.
8.5 All container ships that are ocean-going are air polluters. Hence, all container ships are air polluters.
Which of the following correctly expresses the form of this argument?
a) All C are A.
All C are O.
b) All C are A.
All C that are O are A.
c) All CS are O.
All CS are A.
d) All C are O.
All C are A.
8.6 All container ships that are ocean-going are air polluters. Hence, all container ships are air polluters.
Which of the following substitutions proves the argument invalid?
a. C = husbands, O = married, A = men.
b. C = men, O = humans, A = mammals.
c. C = men, O = married, A = husbands.
d. C = wives, O = divorced, A = women.
e. C = cats, O = animals, A = dogs.
8.17 All A are B. (T) Contrary
a. No A are B. (Und.)
b. All B are A. (Und.)
c. Some A are B. (T)
d. No A are B. (F)
e. No A are non-B. (T)
8.18 Some A are not non-B. (F) Contradiction
a. Some A are non-B. (T)
b. All A are non-B. (T)
c. Some B are not non-A. (F)
d. Some A are non-B. (T)
e. Some A are B. (T)
8.19 Some non-A are not B. (T) Subcontrary
a. Some non-A are B. (Und.)
b. No non-A are B. (Und.)
c. All non-A are B. (F)
d. Some A are B. (T)
e. Some non-B are not A. (T)
The answers for the questions given are mentioned below respectively.
Define the term expression?In mathematics, an expression is a combination of numbers, variables, and mathematical operations that are arranged in a specific way.
It can be a single number or variable, or a combination of them, along with mathematical operations like addition, subtraction, multiplication, division, exponents, and parentheses.
8.1 - The correct expression of the form of this argument is: a. Some C are F. Some C are not S. Some S are not F.
8.2 - The substitution that proves the argument invalid is: b. C = dogs, F = animals, and S = mammals.
8.3 - The substitution that proves the argument invalid is: e. C = Abrahamm Lincoln was beheaded, F = Abraham Lincon is not dead .
8.4 - The correct expression of the form of this argument is: d. If C then F. Not C. Not F.
8.5 - The correct expression of the form of this argument is: b. All C's are A. All C that are O are the A.
8.6 - The substitution that proves the argument invalid is: c. C=men, O=married, A=husbands.
8.17 - The correct truth value of the statement is: c. Some A are B. (T)
8.18 - The correct truth value of the statement is: e. Some A are B. (T)
8.19 - The correct truth value of the statement is: a. Some non-A are B. (Und.)
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can anyone help me please???
thank you xxxx
Using the property of a kite: the angles formed by two unequal sides of a kite are equal. The value of ∠BCD∠BCD is
∠BCD = ∠BAD ⇒ ∠BCD = 106°
What is the slope of the line passing through the points (4, -6) and (2, 3)?
Answer:
m = -9/2
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (4, -6) (2, 3)
We see the y increase by 9, and the x decrease by 2, so the slope is
m = -9/2
Describe the possible echelon forms of the following matrix. A is a 2x2 matrix with linearly dependent columns Select all that apply (Note that leading entries marked with an X may have any nonzero value and starred entries (*) may have any value including zero)
a. 0 0
0 0
b. 0 x
0 0
c. x *
0 0
d. x *
0 x
The possible echelon forms of the given matrix are:
A matrix is in echelon form when it has leading nonzero entries in each row, with each row starting further to the right than the row above it. In the given matrix, the first row does not have any nonzero entries, so it does not meet this criterion. The second row does have a nonzero entry (x) so it can meet the criterion, provided that it is the leading entry.
This is the case for b. 0 x
0 0, c. x *
0 0, and d. x *
0 x.
The other criterion for echelon form is that all starred entries (*) may have any value including zero. This criterion is met in all three cases.
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A production facility contains two machines that are used to rework items that are initially defective. Let X be the number of hours that the first machine is in use, and let Ybe the number of hours that the second machine is in use, on a randomly chosen day. Assume that X and Y have joint probability density function given by 3. f(x) = { 3/2(x^2 +y^2) 0
Answer:
Step-by-step explanation:
three cards are drawn with replacement from a standard deck of 52 cards. find the the probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card. express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability of drawing a diamond, then a black card, and then a face card from a standard deck of 52 cards with replacement is 3/104 or 0.028846 .
What is the probability?The probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card is given by the expression, `(13/52) × (26/52) × (12/52)`.
In a standard deck of 52 cards, there are 13 diamonds, 26 black cards (13 clubs and 13 spades), and 12 face cards (4 Jacks, 4 Queens, and 4 Kings).
To calculate the probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card, we use the formula of probability:
`P(E) = n(E) / n(S)`
where, P(E) = Probability of an event
n(E) = Number of favorable outcomes
n(S) = Total number of outcomes
Total number of outcomes = 52
First card will be a diamond
Number of diamonds in a deck of 52 cards = 13
Total number of outcomes after drawing the first card = 52
Probability of drawing a diamond in the first attempt = P(diamond)`= 13/52
Probability of drawing a black card in the second attempt, given that the first card is a diamond= `P(black/diamond)`= (26/52) = `(1/2)`
Probability of drawing a face card in the third attempt, given that the first card is a diamond and second card is a black card= `P(face/diamond and black)`= `(12/52)` = `(3/13)`
Therefore, probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card`= P(diamond) × P(black/diamond) × P(face/diamond and black) = (13/52) × (1/2) × (3/13)= 3/104`
Therefore, the required probability is 3/104 or 0.028846 rounded to the nearest millionth.
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Can someone please help me with these, I wasn’t able to attend school cause I have Covid and I don’t know what’s going on. Please please help me
Answer: The answer for the first question goes as follows: Which one(s) have both pairs of opposite sides that are parallel? Rectangle, Rhombus, and square. Which one(s) have both pairs of opposite sides that are congruent? Rectangle, square, and rhombus. Which one(s) have all four sides congruent? Square and rhombus.
The answers to the second question are:
Circumference = pi * diameter. So, the distance around it is 100pi.Area of a circle = pi * r^2. So the area of the theater is 7854.0 ft^2.Step-by-step explanation:
Essentially, all of these parallelograms have different properties and properties that they share. For example, a property they share by the definition of a parallelogram is that all of them have two pairs of opposing sides that are parallel. Another property they share from the definition of a parallelogram is that opposite sides are congruent.
As such, rectangles, squares, and rhombuses have the properties that all parallelograms have because they are all parallelograms. However, they also have their own properties.
Rectangles: A rectangle has the properties of a parallelogram, as well as the property of having all of its angles be right angles. This also makes all of its angles congruent.Rhombuses: Rhombuses have the properties of a parallelogram, and they also have all four of their sides congruent. Squares: Squares are like rhombuses and rectangles put together. They have all of their angles as right angles and they have all four of their sides congruent.Second Question Explanation:
1. The question is describing a theater that has a circular base. Therefore, you can use the formula for the circumference of a circle, pi * diameter, to find the circumference (or distance around) the theater. The diameter is given to you: 100 ft. So just multiply that by pi.
2. The question is asking for the area of the theater. This means that you can use the formula for the area of a circle, A = pi * r^2. Note that it is asking you for the area, not the volume, so you would find the area of the circle, not the volume of the hemisphere. r represents the radius of the circle/theater. The diameter is given as 100 ft, and the radius is half of the diameter, so it is 50 ft. Now just plug the radius into the equation and you get the answer I showed.
The population of a place is increased to 54000 in year 2003 5% per annum find the population in the year 2001 what would be the population in the year 2005
Answer:
To find the population in the year 2001, we need to work backwards from the given population of 54,000 in 2003.
Let P be the population in the year 2001. From 2001 to 2003, there are two years, during which the population grows at a rate of 5% per annum. We can calculate the population in 2003 using the formula:
P * (1 + r)^n = 54,000
where r is the annual growth rate (5% or 0.05) and n is the number of years (2). Plugging in the values, we get:
P * (1 + 0.05)^2 = 54,000
Simplifying the equation, we get:
P = 54,000 / (1.05)^2
P = 48,543 (rounded to the nearest whole number)
Therefore, the population in the year 2001 was approximately 48,543.
To find the population in the year 2005, we can use the same formula with n = 2 + 2 = 4 (since we want to find the population four years after 2001):
P * (1 + 0.05)^4 = ?
Plugging in the value of P we just found, we get:
48,543 * (1 + 0.05)^4 = 60,723 (rounded to the nearest whole number)
Therefore, the population in the year 2005 would be approximately 60,723
(please could you kindly mark my answer as brainliest )
(x+2)^2=-16 This equation had no solution, why not?
Answer:
It has no solution within Real numbers. Its solutions are Complex/imaginary, since its discriminant is negative (-64).
Step-by-step explanation:
The normalized form of the equation
(x+2)^2= - 16
x^2 + 4x + 4 = - 16
x^2 + 4x + 20 = 0
We have in the form ax^2 + abx + c = 0
a = 1
b = 4
c = 20
Discriminant is b^2 - 4ac = 4^2 - 4*1*20 = 16 - 80 = - 64
Discriminant is negative, therefore, no Real solutions.
3. Find the distance from A to B. A(-2,2) B (4,-2)
The distance from points A(-2, 2) to B (4, -2) is equal to √52 units.
How to calculate the distance between the two points?Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical expression:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represents the data points (coordinates) on a cartesian coordinate.
Substituting the given points into the distance formula, we have the following;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(4 - (-2))² + (-2 - 2)²]
Distance = √[(6)² + (-4)²]
Distance = √(36 + 16)
Distance = √52 units.
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Solve each inequality (show work)
Answer:
5 less than or equal to x
Step-by-step explanation:
make x subject
Write this value in order , starting with the smallest 0. 2 1/2 2℅
0, 2%, 2 1/2 The values are ordered from smallest to largest, with 0 being the smallest, followed by 2%, and then 2 1/2.
0 is the smallest value because it represents nothing. It is the absence of a quantity, and therefore, it is always the smallest value.
2% is larger than 0 because it represents a percentage of a whole. Percentages are fractions out of 100, so 2% means 2 out of 100. It is larger than 0, but smaller than 2 1/2.
2 1/2 is the largest value because it represents a whole number and a fraction. It is larger than 2%, because 2 1/2 is equal to 250 out of 10,000 or 25 out of 1,000, which is a larger quantity than 2 out of 100.
Understanding the relative size of different values is an important skill in many areas, including mathematics, science, and finance. Being able to order values from smallest to largest helps us make sense of data and information, and it allows us to make informed decisions based on the relative size of different quantities. It is important to learn how to do this accurately and efficiently in order to be successful in these fields.
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Which operation is used to convert 245 liters to milliliters?
O Multiply by 1,000
O Multiply by 10,000
O Divide by 1,000
O Divide by 10,000
Edith's van can safely carry a maximum land of 920 kilograms.
She wants to use her van to carry
30 sacks of potatoes, each of mass 25 kilograms to the nearest kilogram
and
20 sacks of carots, each of mass 7. 5 kilograms to 1 decimal place
Can she definitely use her van safety in one journey?
You must show your working
(4 marks)
Yes, she can definitely use her van safety in one journey. The total weight is the weight of potatoes plus the weight of carots.
Given,
Number of sacks of potatoes = 30
Mass of each potato = 25
Total weight of Potatoes = 30 * 25
= 750
Number of sacks of carrots = 20
Mass of each Carot = 7.5
Total weight of Carrot = 20 * 7.5
= 150
(The total weight is the weight of potatoes plus the weight of carrots.)
So, total weight = 750 + 150
= 900
The maximum land which Edith can carry safely in the van is 920 kilograms.
∵ 900 < 920
∴ She can use her van safely.
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1,500 decagrams = 150 kilograms.
True?
False?
Answer: FALSE
Step-by-step explanation:
1500 decagram = 15 kg
1 decagram = 0.01 kg
1500 decagram = 1500/0.01 kg
= 1500/100 kg
1500 decagram = 15kg
Find the greatest common factor and the least common multiple of the following terms. Submit all
solution steps and your final answers to earn full credit.
8a³b5
16a²b7
Answer:
To find the greatest common factor, we need to find the largest factor that divides both terms evenly. We can factor each term as follows:
8a³b5 = 2³ * a³ * b5
16a²b7 = 2⁴ * a² * b7
The greatest common factor is the product of the lowest exponent of each prime factor that appears in both terms. Therefore, the greatest common factor is:
GCF = 2³ * a² * b5 = 8a²b5
To find the least common multiple, we need to find the smallest multiple that both terms share. We can start by writing out the prime factorization of each term:
8a³b5 = 2³ * a³ * b5
16a²b7 = 2⁴ * a² * b7
The least common multiple is the product of the highest exponent of each prime factor that appears in either term. Therefore, the least common multiple is:
LCM = 2⁴ * a³ * b7 = 16a³b7
So, the greatest common factor is 8a²b5 and the least common multiple is 16a³b7.
Jen’s assignment is to read at least 85 pages of a novel. Jen has read 31 pages. How many pages p does Jen have left to read? Write an inequality that represents this situation. Then solve the inequality
Jen has 54 pages left to read to meet her assignment requirement.
The inequality that represents this situation is p ≥ 85 - 31
To find how many pages Jen has left to read, we can subtract the number of pages she has already read from the minimum number of pages she needs to read.
The minimum number of pages Jen needs to read is 85, and she has already read 31 pages. So, the number of pages she has left to read, p, can be found by:
p = 85 - 31
p = 54
Therefore, Jen has 54 pages left to read.
To represent this situation with an inequality, we can use:
p ≥ 85 - 31
This inequality states that the number of pages Jen still needs to read, p, must be greater than or equal to the difference between the minimum number of pages she needs to read (85) and the number of pages she has already read (31).
Solving for p:
p ≥ 85 - 31
p ≥ 54
This means that Jen must read at least 54 more pages to meet her assignment requirement.
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What is an abiotic factor that can prevent the organism from becoming preserved, AFTER it has been buried?
Answer options:
1. Groundwater
2. Predators & animals that eat bones.
3. Scavengers & plants that use the nutrients of fossils.
4. Other animals of the same species as the organism that died.
The abiotic factor that can prevent the organism from becoming preserved, AFTER it has been buried is groundwater.
What is an abiotic factor that can prevent the organism from becoming preserved, AFTER it has been buried?An abiotic factor refers to a non-living component of an ecosystem that influences the survival and growth of living organisms.
Groundwater can cause the dissolution of minerals present in the sediment that encases the buried organism.
This process can lead to the destruction of the fossilized remains, as the minerals provide the framework for the preservation of the organism's hard parts (such as bones or shells).
Groundwater can also cause the erosion of the sediment, which can expose the buried remains and make them vulnerable to biotic factors such as scavengers, predators, and decomposers.
Predators and animals that eat bones, scavengers and plants that use the nutrients of fossils, and other animals of the same species as the organism that died are all biotic factors that can affect the preservation of the organism, but they do so before or during the burial process.
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Please help me as I’m struggling
Therefore , the solution of the given problem of pie chart comes out to be number of adults who selected math (15) outnumbered the number of minors. (10).
Explain pie charts.
A pie chart, also referred to as a circle diagram, is a graphical representation of each of the values of a particular variable or a method to condense a collection of nominal data. (e.g. percentage distribution). A circle with many parts makes up this kind of chart. Each segment represents a particular group.
Here,
for a two-way table: Party A, Party B, and Party C
Men make up 12 8 % of the population while women make up 16 %.
Total 28 15 19
32 ladies make up the group, to start with.
b) 16 female voters plan to support Party A.
Math, English, and science are studied by adults aged 15 to twenty-one and by children aged ten to ten.
Total 25 24 31
15 people selected math.
b) Reeshma is mistaken. The number of adults who selected math (15) outnumbered the number of minors. (10).
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Nonresponse bias occurs when ________.
A) the population has been divided into strata
B) portions of the population are excluded from the sample
C) cluster sampling is used instead of stratified random sampling
D) those responding to a survey or poll differ systematically from the nonrespondents
Nonresponse bias occurs when(D) those responding to a survey or poll differ systematically from the nonrespondents.
Nonresponse bias occurs when individuals who do not respond to a survey or poll differ systematically from those who do respond, resulting in a biased sample. This can lead to incorrect inferences about the population being studied.
Nonresponse bias can occur for various reasons, including lack of interest, inability to participate, or refusal to participate. It is important to understand and address nonresponse bias to ensure the accuracy and reliability of survey or poll results. Strategies such as follow-up contact attempts and incentives can help mitigate nonresponse bias.
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You purchased 40 shares for $3.95/sh. If you sold the shares for a total of $200. Did you net a profit or a loss?
Answer: profit
Step-by-step explanation:
3.95 (price of one share) multiplied by 40 (the amount of shares bought) would have cost $158. so selling all for $200 would be a $42 profit
A certain computer loses half of its value every four years. If the value of the computer after 6 years is $835, what was the initial value of the computer?
The PC is initially worth $3,340.
Given that a computer loses half of its worth after six years, and assuming that value is $835, we must determine the device's original value.
What does the term "starting value" mean?
The starting output value is the initial value.
Let's say that computer's starting value is x.
As a result, after four years,
It is X/2 for the fourth year.
It is X/2 for the fifth year.
It's X/4 in the sixth year.
We stated that the PC will be worth $835 after six years. Hence, we may express it as,
X/4 = $835
X=4( $835)
X= $3,340
Hence, the initial value of the computer is $3,340.
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The length of a rectangular room is 9 feet longer than twice the width. If the room's perimeter is 150 feet, what are the room's dimensions?
Answer:
Length = 53 feet
Width = 22 feet
Step-by-step explanation:
Perimeter = 2(length + width)
Then:
a = 2w + 9 Ec. 1
150 = 2(a + w) Ec. 2
a = length
w = width
From Eq. 1:
a - 9 = 2w Eq. 3
From Eq. 2:
150 = 2*a + 2*w
150 = 2a + 2w
150 - 2a = 2w Eq. 4
Equalizing Eq. 3 and Eq. 4
a - 9 = 150 - 2a
a + 2a = 150 + 9
3a = 159
a = 159/3
a = 53
From Eq. 1:
a = 2w + 9
53 = 2w + 9
53 - 9 = 2w
44 = 2w
44/2 = w
w = 22
Check:
From Eq. 2
150 = 2(a+w)
150 = 2(53+22)
150 = 2*75
4.1.60-(15)+(-13 4.2.-2(3)+27 ÷(-3)
Answer:
-15
Step-by-step explanation:
4.1.60 - (15) + (-13) = 32
4.2. -2(3) + 27 ÷ (-3) = -2(3) - 9 = -15
A square field has a side length of 6x10³ meters. Which of the following is its area in square meter
(1) 6x106
(3) 36x106
(2) 36×10⁹
(4) 6x10⁹
Answer:
36 × 10^6 m²
Step-by-step explanation:
Given the side length of a square = 6 × 10³m,
To solve for the area of a square, use the following formula:
A = S² where:
S = side of the square
Substitute the given value for the side into the formula:
A = S²
A = (6 × 10³)²
A = 36000000 or 36 × 10^6 m²
NOTE:
6 × 10³ is also the same as 6 × 1000 = 6000,
(6 × 10³)² is essentially 6,000² = 36,000,000
Therefore, its area in square meters is 36 × 10^6
please help!!
4.
Two bikers meet at a park. Biker A needs to stop at the store that is 12 miles east of the park. Biker B heads southeast at a 61° angle at the same time for 24 miles. Once biker A leaves the store he heads southwest at an angle of 89° for 21 miles. Do NOT use the law of cosines, use your knowledge from the content of this course.
a. Use your knowledge of triangles to figure out if the two bikers will be able to meet up if each biker travels the distance given.
b. If they do not meet up, how much farther would one of the bikers have to travel to meet the other?
c. What is the measure of the angle between the bikers?
d. What is the relationship between the measure of the angles and the paths the bikers took?
e. Classify the triangle the paths created.
f. How many miles did they travel together?
a) Biker A follows the hypotenuse of the triangle on a straight path.
It is probable that the bikers will meet at the vertex located at the base of the triangle.
How to solve:The bikers have created a triangle with sides measuring 12, 21, and 24 miles and angles measuring 61, 89, and 30 degrees, respectively.
a) Biker A follows the hypotenuse of the triangle on a straight path.
It is probable that the bikers will meet at the vertex located at the base of the triangle.
They cover almost equal distances from their starting points:
24 miles ≈ √12²+21² miles
b) They encounter each other.
c) The angle at one vertex measures 30 degrees.
d) e) As shown in the attached picture, it is an almost right triangle.
f) Together, they cover a total distance of 57 miles (12+21+24).
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*9. The consultancy Imagination Inc. Is working with its manufacturing client Parts-R-Us to improve their on-time
performance. The firm can earn a bonus of up to $1,000,000 based on how much the on-time performance actually
improves. It's current (baseline) on-time performance is 90%.
The company typically completes approximately 1,000 orders per month, with approximately 100 orders delayed. The
bonus payment is prorated according to the following criteria:
• The on-time performance improvement is calculated based on a reduction in late events or an improvement in on-
time performance.
• No bonus is earned for the first 25% reduction in late events, say from 100 to 75. Maximum bonus is earned once
Parts-R-Us achieves 95% on-time performance.
Please answer the following:
Write down a formula to
determine the total bonus
amount to be received
Using your formula, show
how much bonus would be
paid if Parts-R-Us achieves
94% on-time performance
Parts-R-Us could be eligible for a $0 bonus if it achieves an on-time performance rate of 94% or more.
The company would have to maintain an order delivery rate of 95% in order to qualify for the bonus. If achieved, the bonus would be as follows: Bonus = 94% * (1 - 100).
The following is the calculation for the bonus:
Bonus = P * (1 - D)
Where:
P represents the proportion of orders that are delivered on time.
D represents the total number of orders placed late.
In the event that Parts-R-Us achieves an on-time performance rate of 94%, the bonus would be as follows:
Bonus = 94% * (1 - 100)
Bonus = $0
If the company only managed to complete its tasks 94% of the time, it will not be eligible for a bonus.
In order to qualify for the maximum bonus, Parts-R-Us would have to maintain an on-time delivery rate of 95%.
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60 identical machines in a factory pack 150 crates of limes per day
between them.
a) Write the ratio of the number of machines to the number of crates
packed per day in the form 1: n.
b) How many crates of limes would 70 of these machines pack per day?
Give any decimals in your answers to 1 d.p.
a) To write the ratio of the number of machines to the number of crates packed per day in the form 1: n, we need to find the number of crates packed per day per machine. We can do this by dividing the total number of crates packed per day by the number of machines:
Number of crates packed per day per machine = 150 crates/day ÷ 60 machines = 2.5 crates/machine/day
Therefore, the ratio of the number of machines to the number of crates packed per day in the form 1: n is 1:2.5 or 2:5.
b) To find out how many crates of limes 70 of these machines would pack per day, we can use the ratio from part (a) to set up a proportion:
1 machine : 2.5 crates/day = 70 machines : x crates/day
Solving for x, we get:
x = (70 machines × 2.5 crates/day) / 1 machine = 175 crates/day
Therefore, 70 of these machines would pack 175 crates of limes per day.
Step-by-step explanation:
a) The ratio of the number of machines to the number of crates packed per day can be written as:
60 : 150
To simplify this ratio, we can divide both sides by 10:
6 : 15
Finally, we can divide both sides by 3 to get the ratio in the form 1 : n:
1 : 2.5
Therefore, the ratio of the number of machines to the number of crates packed per day is 1 : 2.5.
b) If 60 machines can pack 150 crates per day, then one machine can pack:
150/60 = 2.5 crates per day
So, 70 machines can pack:
70 × 2.5 = 175 crates per day
Therefore, 70 machines can pack 175 crates of limes per day.
