Answers
In solving the given question, we can say that ∠ZEFI and ∠ZJIK are equal parallel lines by co-exterior angles property.
what is parallel lines?Geometry parallel lines are coplanar infinite lines that do not intersect anywhere. In a given three-dimensional space, parallel faces are faces that never intersect. Curves with a constant minimum distance between them and no tangents or intersections are said to be parallel. Two lines that lie in the same plane, are equally spaced, and never intersect are called parallel lines in geometry. Can be applied horizontally or vertically. Parallel lines are found in everyday objects such as railroad tracks, rows of books, and crosswalks.
∠ZHIK and ∠ZEFI are equal by alternative angles property.
∠ZGFD and ∠ZEFD are equal by co-interior angles property.
∠ZGFD and ∠ZEFI are equal by interior alt. angles property.
∠ZEFI and ∠ZJIK are equal by co-exterior angles property.
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Related Questions
A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. Refer to Exhibit 7-4. The point estimate of the mean content of all bottles is? a) 0.22 b) 4 c) 121 d) 0.02
Answers
The point estimate of the mean content of 121 bottles with the average content of 4 ounces and the standard deviation 0.22 ounces is 4. Option B is the correct answer.
A point estimate is a statistic used to predict the corresponding population parameter. In a sense, a point estimate is a guess about a parameter that uses data from a sample as the basis of the guess. Point estimates can be used to estimate population parameters such as the population mean or population standard deviation.
The point estimate is a single numerical value that represents a guess for a parameter. The sample mean and sample standard deviation are examples of point estimates for the population mean and population standard deviation. If a point estimate is a good guess, it should be fairly close to the true value of the parameter.
Thus, option B is the correct answer.
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Suppose a random sample of 80 measurements is selected from a population with a mean of 65 and a variance of 300. Select the pair that is the mean and standard error of x. a) O [65, 2.236] b) O [65, 2.036] c) O [65, 2.436] d) O [80, 2.136] O [65, 1.936] f) None of the above
Answers
The pair that is the mean and standard error of x is [65, 2.236]. So, the correct option is a.
Suppose a random sample of 80 measurements is selected from a population with a mean of 65 and a variance of 300. We are required to select the pair that is the mean and standard error of x. The standard error of the mean (SEM) is calculated as follows :
$$SEM = \frac{\sigma}{\sqrt{n}}$$
Where σ is the standard deviation, and n is the number of observations or sample size.
Given that variance,
σ2 = 300
Therefore,
σ = √300 = 17.32.
Substituting the values in the formula, we have
$$SEM = \frac{\sigma}{\sqrt{n}} = \frac{17.32}{\sqrt{80}} = 1.9365$$
Therefore, the mean and standard error of x is [65, 1.936]. Option A is not the answer because the value of the standard error in that option is incorrect. Option B is not the answer because the value of the standard error in that option is incorrect. Option C is not the answer because the value of the standard error in that option is incorrect.
Option D is not the answer because the first value in that option is not the mean of x. Option E is incorrect because the value of the standard error is incorrect.
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13
Select the correct answer.
Solve the following equation for x.-
x²-36=0
Ο Α.
OB.
OC.
O D.
X = 1; x = -36
x= -1; x = 36
x = -6; x = 6
x=-18; x = 18
Answers
Answer:
C.
Step-by-step explanation:
x² - 36 = 0
x = 6
6² = 6 x 6 = 36
So..
36 - 36 = 0
As there are so many equations in mathematics, it is a very broad subject. These are a few illustrations of typical mathematical equations: [tex]x = -6; x = 6[/tex]. Thus, option C is correct.
What is the equation used in maths?To solve the equation [tex]x² - 36 = 0[/tex] , we can use the difference of squares formula:
A, B, and C are constants in the quadratic equation: ax2 + bx + c = 0. A quadratic function, often known as a function with the form f(x) = ax2 + bx + c, can be solved using this equation to get its roots.
[tex]a² - b² = (a + b)(a - b)[/tex]
In this case, a² = x² and b² = 36, so we can write:
[tex]x² - 36 = (x + 6)(x - 6)[/tex]
Setting this expression equal to 0 and solving for x, we get:
[tex](x + 6)(x - 6) = 0[/tex]
[tex]x + 6 = 0 or x - 6 = 0[/tex]
[tex]x = -6 or x = 6[/tex]
Therefore, the solutions to the equation [tex]x² - 36 = 0[/tex] are [tex]x = -6[/tex] and [tex]x = 6.[/tex]
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Isaiah is grounded and has to stay in his room all day. He made up a game where he throws balled-up paper called a "trashball" into his trash can. The diameter of the top of the trash can 1 the diameter of the top of is 12 in. Isaiah wants the "trashball" to have a diameter that is the trash can. > What should the diameter of Isaiah's "trashball" be? d Level G ? in. 12 in.
Answers
Answer:
Isiah Thomas
Step-by-step explanation:
I amazing fact
Answer:
the correct answer is 4
Step-by-step explanation:
yea sorry i don’t know step-by-step
Boxes is it a and B contain some counters box a contains more counters then box b what is the smallest possible value of K
Answers
The smallest possible value of k is 5. This is determined by setting up the equation 3k = (k + 8) + 1 and solving for k.
To find the smallest possible value of k, we need to determine the point where Box A has just one more counter than Box B. We can set up an equation to represent this:
3k = (k + 8) + 1
Simplifying the equation, we get:
3k = k + 9
2k = 9
k = 4.5
However, k must be a whole number, since we are dealing with counters. Therefore, the smallest possible value of k is 5.
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Complete question:
Boxes A and B contain some counters. Box A contains more counters than Box B. 3k counters in Box A and K+8 in Box B. What is the smallest possible value of K?
Identify and name congruent triangles
Answers
The answers are a) ASA congruence rule b) SSS congruence rule c) it is not necessary congruent.
What is Congruence ?Congruent refers to having the same height and shape. Congruent therefore involves comparing two numbers, and equivalent denotes the equality of two expressions. Therefore, to state two line segments are congruent implies that the two lines have equal measures.
According to question:a) ∠GIH is corresponding to ∠LJK
GH = KL
∠IHG = ∠KLJ
By ASA congruence rule
ΔGIH ≅ ΔJKL
b) AB = DF
AC = DE
BC = EF
By SSS congruence rule
ΔABC ≅ ΔDEF
c) Two Corresponding sides are congruent, which is not enough to make them congruent.
So, it is not necessary congruent.
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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 2 , 5 , 8 ,Find the 41st term.
Answers
The 41st term of the sequence is 121.
What is a sequence?In mathematics, a sequence is a list of numbers or objects that follow a certain pattern or rule. A sequence's terms are typically identified by subscripts, like a1, a2, a3,..., an, where n denotes the number of terms in the sequence.
Sequences can be arithmetic, geometric, or neither, depending on terms follow a static difference, constant ratio, or neither of these series, respectively. Algebra uses geometric sequences to represent exponential development or decay whereas arithmetic sequences are frequently employed to model linear connections.
The given sequence is 2 , 5 , 8 , ...
The common difference is:
d = 5 - 2 = 3
The nth term of a sequence is given as:
an = a1 + (n-1)d
Substituting the value we have:
an = 2 + (n-1)3
an = 3n - 1
a41 = 3(41) - 1 = 122 - 1 = 121
Hence, the 41st term of the sequence is 121.
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In this cartesian plane, I want you to make Ronaldo's face in it through the measuring!! In the 4 quartiles! I want you to send me back the document after you finish! or I will report you with 40 ACC I made
Answers
Answer:
answer is 091 accc h na tu
Which box plot represents data that contains an outlier?
A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 1 to 9, and the box ranges from 3 to 8. A line divides the box at 7. 5.
A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 1 to 10, and the box ranges from 6 to 8. 5. A line divides the box at 7. 5.
A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 1 to 9, and the box ranges from 2 to 7. A line divides the box at 4.
A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 3 to 9, and the box ranges from 5 to 7. A line divides the box at 6,
Answers
The box plot represents the data set 2, 4, 6, 8, 10, 12 is option (a) A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 1 to 9, and the box ranges from 3 to 8. A line divides the box at 7. 5.
A box-and-whisker plot is a graphical representation of a data set that displays the distribution of the data, as well as its quartiles and any outliers. The plot is made up of a rectangular box, which represents the middle 50% of the data, with a line in the box representing the median. Two lines, called whiskers, extend from the box to represent the range of the data outside of the box, excluding any outliers. Outliers are any values that fall outside of the whiskers.
In the given options, the box-and-whisker plot that represents the data set 2, 4, 6, 8, 10, 12 is the one that has a box ranging from 4 to 10, with a median line dividing the box at 7. This means that 50% of the data falls between 4 and 10, with the median value being 7. The whiskers range from 2 to 12, indicating that the data set has a minimum value of 2 and a maximum value of 12.
Therefore, the correct option is (a) A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 10. A line divides the box at 7.
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The given question is incomplete, the complete question is:
Which box plot represents the data set 2, 4, 6, 8, 10, 12?
A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 10. A line divides the box at 7.
A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 8. A line divides the box at 6.
A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 9. A line divides the box at 6.
A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 6 to 10. A line divides the box at 8.
Answer: (B)
Correct Answer 100%! Pls, give me brainliest. Thank You!
How can you tell if a point is a solution to a two variable inequality?
Answers
One way to determine whether a point is a solution to a two-variable inequality is to substitute the values of the variables in the inequality and determine whether the inequality is true or false. If the inequality is true, the point is a solution, and if the inequality is false, the point is not a solution.
For example, consider the inequality 2x + 3y > 7. Let’s see if the point (1,2) is a solution. To do so, substitute x=1 and y=2 into the inequality:2(1) + 3(2) > 7 Simplify to get:2 + 6 > 7 This is true, so the point (1,2) is a solution to the inequality. Conversely, let’s see if the point (4,-1) is a solution. To do so, substitute x=4 and y=-1 into the inequality:2(4) + 3(-1) > 7 Simplify to get:8 - 3 > 7 This is false, so the point (4,-1) is not a solution to the inequality .There are some general rules that can be followed to help determine which side of a line is shaded in an inequality. If the inequality is greater than or less than, the line should be dashed, and the shading should be above or below the line, respectively. If the inequality is greater than or equal to or less than or equal to, the line should be solid, and the shading should be above or below the line, respectively.
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Perimeter of a ______________ = side+side+side+side+side
Answers
Perimeter of a regular pentagon = side + side + side + side + side
A polygon is a two-dimensional shape with straight sides that are connected to form a closed figure. The perimeter of a polygon is defined as the total distance around the exterior of the shape.
To calculate the perimeter of a polygon, you add up the lengths of all its sides. For example, a regular pentagon has five sides that are all the same length. To find the perimeter of this pentagon, you would add up the length of all five sides:
Perimeter of a regular pentagon = side + side + side + side + side
= 5 × side
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Question 8 (4 points)
For a meat raffle, 100 tickets were sold.
The following were prizes:
number of winners
1
4
15
prize
grand prize - $1000 cash
$250 meat package
$50 meat package
What is the probability of winning the grand prize? 1/20
What is the expected value for someone buying a single ticket for $10.00 ? $
Answers
pls help as soon as possible
Answers
Answer:
42x-27
Step-by-step explanation:
cala used 4 2/3 cups of watermelon and 2 1/6 cups of cherries to make a fruit bowl how many cups of watermelon and cherries were used in all
Answers
Answer:
6 5/6 cups
Step-by-step explanation:
Add.
4 2/3 = 4 4/6
4 4/6 + 2 1/6 gives 6 5/6 cups were used in all.
Hope this helps!
sam wants to color the three sides of an equilateral triangle. he has five different colors to choose from. in how many different ways can sam color the sides of the triangle? (two colorings are considered the same if one coloring can be rotated and/or reflected to obtain the other coloring.)
Answers
There are 27 different ways for Sam to color the sides of the equilateral triangle, accounting for rotations and reflections.
We have,
To calculate the number of different ways Sam can color the sides of the equilateral triangle, we need to consider the symmetry of the triangle.
Since two colorings are considered the same if one coloring can be rotated and/or reflected to obtain the other coloring, we need to account for these symmetries.
Let's analyze the possibilities:
- All three sides have the same color:
There is only one way to color the triangle in this case.
- Two sides have the same color, and the third side has a different color: Sam can choose the color for the two sides in 5 ways and the color for the remaining side in 4 ways (since it must be different from the other two colors).
However, we need to divide this by 3 to account for the different rotations of the equilateral triangle.
Thus, there are (5 x 4) / 3 = 20 / 3 = 6.67 (approx) ways to color the triangle in this case.
Since the number of colorings must be a whole number, we consider this as 6 ways.
- All three sides have different colors:
Sam can choose the color for the first side in 5 ways, the color for the second side in 4 ways (since it must be different from the first), and the color for the third side in 3 ways (since it must be different from the first two).
However, we need to divide this by 6 to account for the different rotations and reflections of the equilateral triangle.
Thus, there are (5 x 4 x 3) / 6 = 20 ways to color the triangle in this case.
In total, the number of different ways Sam can color the sides of the equilateral triangle is:
= 1 + 6 + 20
= 27.
Thus,
There are 27 different ways for Sam to color the sides of the equilateral triangle, accounting for rotations and reflections.
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I need help with answer this question
Answers
Answer:
y = 2x/15 + 6
Step-by-step explanation:
3y/2 = x/5 + 9
3y = (x/5 + 9) (2) The 2 that was dividing goes on to multiply on the other side.
3y= 2x/5 + 18
y = (2x/5 + 18) / 3 The 3 that was multiplying goes on to divide on the other side.
y = 2x/15 + 6
The vertical supports in this subdivided truss bridge are built so that ∆BAC ≅ ∆DAC, BC = BA, and CD = AD. Which statement is not true?
Answers
Answer: Not D
Step-by-step explanation:
Answer not available, but it is definitely not D.
Your welcome.
22 The regular selling price is a 22" tube television is $389. The markdown rate is 33%. Use the
percent paid to determine the sale price.
A. $245.34
C. $260.63
B. $267.89
D. $287.56
Answers
The Sale price is C. $260.63.
What is selling price?Selling price is the price at which a product or service is sold by a business or seller to a customer. It is the amount of money that a customer must pay in order to purchase the product or service. The selling price is typically determined by factors such as production costs, competition, supply and demand, and profit margins.
What is sale price?Sale price is the discounted price at which a product or service is sold for a limited period of time. It is usually a lower price than the regular price, and it is offered to customers as an incentive to make a purchase. Sale prices can be determined by applying a discount or markdown to the regular selling price.
In the given question,
To find the sale price, we need to first calculate the amount of the markdown:
Markdown = Regular Price x Markdown Rate
Markdown = $389 x 0.33
Markdown = $128.37
The sale price is then the regular price minus the markdown:
Sale Price = Regular Price - Markdown
Sale Price = $389 - $128.37
Sale Price = $260.63
Therefore, the answer is C. $260.63.
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stive efforts in
Eamples (finding slope in tables and graphs)
termine the slope of each linear equation. You may want to use the slope formula.
X O
1
2
3
y
S5
7
9
11
b)
566
X
-7
-6
-5
-4
y
10
7
4
1
c)
X
-2
0
2
4
y
I
3
5
can't
7
9
Answers
The slope of a linear equation is an important skill to have, as it can be used to identify the rate of change of the equation, and can be used to predict future values of the equation.
What is equation?An equation is an expression that states the equality of two things. It typically consists of an equal sign (=) and two expressions on either side of the equal sign that represent the same thing. Equations are used to describe relationships between different variables and can be used to solve mathematical problems. They can also be used to show the relationships between different quantities in physics and chemistry.
a)The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 6, and the run is 2, so the slope is 3.
b) The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 3, and the run is -7, so the slope is -3/7.
c) The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 4, and the run is 6, so the slope is 2/3.
Finding slope in tables and graphs is a common mathematical skill that is used to identify the rate of change of a linear equation. This is determined by finding the change in the dependent variable (the y-axis) divided by the change in the independent variable (the x-axis). This is what is referred to as the slope of the equation. To find the slope in tables and graphs, you must look at the differences between the points on the x-axis and y-axis, and divide the change in the y-axis by the change in the x-axis. This will give you the slope of the equation. Finding the slope of a linear equation is an important skill to have, as it can be used to identify the rate of change of the equation, and can be used to predict future values of the equation.
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Question 8
Which division expression is the given figure modeling?
A
B
C
D
1
4÷3
3÷/1/1
1
12 ÷ 4
3 ÷ 1/1/
1
1
Answers
The division problem provided by the model shown here is [tex]3[/tex] ÷ [tex]\frac{1}{4}[/tex].
How are fractions divided?The first step of dividing fractions is to get the reciprocal of a second fraction, which involves flipping its numerator and denominator. Multiply all two numerators after that. Multiply the 2 denominators after that. Then finish, if required, simplify the fractions.
Simple division: What is it?Simple Division: Little numbers can be divided into groups and pieces using the simple division method in mathematics. Divide easy and basic division problems into terms that can be divided using simple division sums. Arithmetic, subtraction, multiplying, & division are the four fundamental mathematical operations.
Given:
We have three section [tex]1+ 1 + 1= 3[/tex]
[tex]= \frac{4}{12}[/tex]
[tex]= \frac{1}{3}[/tex]
In this case, the model yields the division issue.
[tex]3[/tex] ÷ [tex]\frac{1}{4}[/tex]
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How can I write this differently, 270 students don’t like carrots
Answers
Answer:
270 students dislike carrots.
Step-by-step explanation:
Angelfish need at least 7
gallons of water to live.
Four friends have four
different sized fish tanks
(rectangular prisms). If
each tank has the
following dimensions,
which children have a
tank big enough for an
angelfish?
Hint: 1 gallon = 231 cubic inches
Children
Caroline
Thomas
Henry
Kym
Tank dimensions (inches)
16 x 14 x 9
15 x 7 x 9.5
14 x 12 x 9.5
14 x 11 x 10.5
Answers
Answer: Caroline and Kym
Step-by-step explanation:
To determine which children have a tank big enough for an angelfish, we need to calculate the volume of each tank in cubic inches and convert it to gallons.
Caroline's tank: Volume = length x width x height = 16 x 14 x 9 = 2,016 cubic inches. Converting to gallons: 2,016 / 231 = 8.72 gallons. Caroline's tank is big enough for an angelfish.
Thomas's tank: Volume = length x width x height = 15 x 7 x 9.5 = 999.75 cubic inches. Converting to gallons: 999.75 / 231 = 4.32 gallons. Thomas's tank is not big enough for an angelfish.
Henry's tank: Volume = length x width x height = 14 x 12 x 9.5 = 1,596 cubic inches. Converting to gallons: 1,596 / 231 = 6.90 gallons. Henry's tank is not big enough for an angelfish.
Kym's tank: Volume = length x width x height = 14 x 11 x 10.5 = 1,683 cubic inches. Converting to gallons: 1,683 / 231 = 7.28 gallons. Kym's tank is big enough for an angelfish.
Therefore, Caroline and Kym have tanks that are big enough for an angelfish. Thomas and Henry do not.
What is the area in square feet of the shaded part of the rectangle below
Answers
Answer:
45 sqft
Step-by-step explanation:
Split the shaded area into a rectangle and a triangle. The area of the rectangle is 3x10=30 and the area of the triangle is 3x10/2=15 30+15=45
Or 10x6=60 10*3/2=15 60-15=45
A a varies partly with B and with another quantity C. If the to when B=2 and A= 28 and A = 12 when B = 3 and C=26. Find the value of A when B = 4 and C=6 Find the value of B when A= 38 and C=6
Answers
Let x be the part of A that varies with B, and y be the part of A that varies with C. Then we have:
A = xB + yC
Using the values given in the problem, we can write two equations:
When B = 2 and A = 28:
28 = 2x + 0y (since C is not mentioned)
When B = 3 and C = 26 and A = 12:
12 = 3x + 26y
Now we can solve for x and y by solving the system of equations:
2x = 28 => x = 14
3x + 26y = 12 => 42 + 26y = 12 => 26y = -30 => y = -15/13
Therefore, we have:
A = 14B - 15/13C
a) To find the value of A when B=4 and C=6, we can substitute B=4 and C=6 into the equation:
A = 14(4) - 15/13(6) = 56 - 45/13 = 383/13
Therefore, A is equal to 383/13 when B=4 and C=6.
b) To find the value of B when A=38 and C=6, we can rearrange the equation to solve for B:
A = 14B - 15/13C => 13A = 182B - 15C => 13A + 15C = 182B
Substituting A=38 and C=6, we have:
13(38) + 15(6) = 182B => 494 = 182B => B = 247/91
Therefore, B is equal to 247/91 when A=38 and C=6.
In a hat, you have index cards with the numbers 1 through 10 written on them. Find how many of the 10 possible numbers you can pick match the described event, then drag and drop each of the numbers into the correct box to order the events from least likely to happen (1) to most likely to happen (8) when you pick one card at random.A. You pick a number greater than 0.B. You pick an even number.C. You pick a number that is at least 2.D. You pick a number that is at most 0.E. You pick a number divisible by 3.F. You pick a number divisible by 5.G. You pick a prime number.H. You pick a number less than the greatest prime number among the numbers 1 through 10.
Answers
The order of events from least likely to most likely are as follows:
D. You pick a number that is at most 0A. You pick a number greater than 0C. You pick a number that is at least 2B. You pick an even numberE. You pick a number divisible by 3F. You pick a number divisible by 5G. You pick a prime numberH. You pick a number less than the greatest prime number among the numbers 1 through 10The reason for this order is because of the chances of each event occurring. Event D has the least chance of occurring because no numbers in the set have a value less than or equal to 0. Event A is the next least likely because only one number in the set is greater than 0, which is the number 1. Event C is the next least likely because only two numbers in the set are at least 2 (2 and 3). Event B is the next least likely, as there are only five even numbers in the set (2, 4, 6, 8, and 10). Events E, F, G, and H are the most likely to occur, because of the number of numbers that are divisible by 3, and 5, and are prime numbers.
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Measure the diameter of the tin mm and write down the real diameter in mm
Answers
Answer:
Step-by-step explanation:
Use the numbers to place the companies in order of greatest comparative advantage to least comparative advantage in
producing large tubes of toothpaste.
O 2.1.3.4
O 4.1,2,3
O 4,3,1,2
Answers
The companies in order of greatest comparative advantage to least comparative advantage in producing large tubes of toothpaste is 4, 3, 1, 2 that is option C.
Use the numbers to place the companies in order of greatest comparative advantage to least comparative advantage in producing large tubes of toothpaste.
Toothpaste company
Large tubes
Small tubes
1) Sparkling
100 per hour
200 per hour
2) Bright White
100 per hour
250 per hour
3) Fresh!
200 per hour
250 per hour
4) Mint
150 per hour
150 per hour
Formula for comparative advantage is
CA=rate of producing large tubes/rate of producing small tube
For 1 Sparkling:
CA = 100/200
CA = 0.5
For 2 Bright White:
CA = 100/250
CA = 0.5
For 3 Fresh:
CA = 200/250
CA = 0.8
For 4 Mint:
CA = 150/150
CA = 1
thus, to place the companies in order of greatest comparative advantage to least comparative advantage in producing large tubes of toothpaste is 4, 3, 1, 2.
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Complete question:
Use the numbers to place the companies in order of greatest comparative advantage to least comparative advantage in
producing large tubes of toothpaste.
2.1.3.4
4.1,2,3
4,3,1,2
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Sunflower canola oil is a cooking oil sold in south african supermarkets a 750ml bottle cost R28 and a 2litre bottle cost R63 evaluate which option will be the most cost effective option
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Therefore, the 2-liter bottle is the more cost-effective option as it has a lower cost per milliliter.
What are millimeters?Millimeters (mm) is a unit of length in the metric system. It is a subunit of a meter, with one meter being equal to 1000 millimeters. Millimeters are commonly used to measure small distances such as the thickness of paper, the width of a fingernail, or the diameter of a small object. The abbreviation for millimeters is "mm".
by the question.
To evaluate which option is the most cost-effective, we need to compare the cost per milliliter of each option.
Calculate the price per liter: To compare the cost of the two options, you'll need to calculate the price per liter of each. You can do this by dividing the price of the bottle by its volume in liters. For example, if the 2-liter bottle costs $4, the price per liter would be $2 ($4/2 liters). If the 750ml bottle costs $2.50, the price per liter would be $3.33 ($2.50/0.75 liters).
Compare the price per liter: Once you have the price per liter for each option, you can compare them. In this example, the 2-liter bottle is cheaper at $2 per liter compared to the $3.33 per liter for the 750ml bottle.
Consider the convenience: While the 2-liter bottle may be cheaper, you should also consider if it's more convenient for you. If you won't be able to use all the 2-liters before it goes bad, or if it's difficult to carry around, then multiple 750ml bottles may be a better option for you despite the higher cost per liter.
For the 750ml bottle:
[tex]Cost per milliliter = R28 /750ml[/tex]
[tex]Cost per milliliter = R0.0373/ml[/tex]
For the 2-liter bottle:
[tex]Cost per milliliter = R63 / 2000ml[/tex]
[tex]Cost per milliliter = R0.0315/ml[/tex]
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The circle graph describes the distribution of preferred music from a sample of 400 randomly selected middle school students.
a circle graph titled preferred music, with five sections labeled rock 13 percent, hip hop 25 percent, pop 35 percent, classical 13 percent, and jazz 14 percent
Which of the following conclusions can we draw from the circle graph?
Pop is the preferred music for 35 students.
Jazz is the preferred music for 56 students.
Together, Hip Hop, Rock, and Jazz are the preferred music for less than half the students.
Together, Hip Hop and Pop are the preferred music for 260 students.
Answers
The conclusion we can draw from the circle graph is (2) Jazz is the preferred music for 56 students.
Which of the conclusions can we draw from the circle graph?From the circle graph, we can draw the following conclusions:
Pop is the preferred music for 35% of the sample, which is equivalent to 0.35 x 400 = 140 students.
Therefore, conclusion (1) is incorrect.
Jazz is the preferred music for 14% of the sample, which is equivalent to 0.14 x 400 = 56 students.
Therefore, conclusion (2) is correct.
The combined percentage of Hip Hop, Rock, and Jazz is 13% + 25% + 14% = 52%, which is more than half of the sample.
Therefore, conclusion (3) is incorrect.
Hip Hop and Pop are the preferred music for 25% + 35% = 60% of the sample, which is equivalent to 0.6 x 400 = 240 students.
Therefore, conclusion (4) is incorrect.
Therefore, the only correct conclusion that can be drawn from the circle graph is that Jazz is the preferred music for 56 students.
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How to reduce dimension using PCA?
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PCA (Principal Component Analysis) is an unsupervised learning technique used to reduce dimensionality. It is a commonly used dimensionality reduction technique. This technique is used to discover patterns in data that have multiple features. PCA is used to reduce the dimensionality of data.
Compute the mean of each feature. For every feature, compute the mean μ=1/nΣxi where n is the number of data points and xi is the feature vector. Calculate the covariance matrix compute the covariance matrix from the mean-adjusted data: X=X−μ,Covariance matrix: C=1/nXTX where X is the mean-adjusted data matrix.
Now find the eigenvectors and eigenvalues of the covariance matrix. Sort the eigenvectors in order of decreasing eigenvalues. These eigenvectors represent the principal components. The first eigenvector represents the direction of the maximum variance.
Create the projection matrix. Only the top k principal components are used for dimensionality reduction. The projection matrix can be computed by stacking the eigenvectors of the top k principal components: W=[u1u2…uk]where ui represents the eigenvector.
Project the data onto the lower-dimensional subspace. The original data can be projected onto the lower-dimensional subspace using the projection matrix: Z=X×WPCA is a commonly used dimensionality reduction technique that involves computing the principal components of a dataset. This technique can be used to find the most important patterns in the data.
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