Answer:
A
Step-by-step explanation:
a) ✔️
This is the principle of mathematical induction. If P holds for the base case k=1 and we can show that if it holds for any arbitrary k (e.g. k=n) then it must also hold for the next value (e.g. k=n+1), then we have shown it holds for all natural numbers.
b) ❌
There is no guarantee that P holds for all natural numbers from the statement alone. It only guarantees that for any k where P does not hold, there exists a smaller number i where P does not hold.
c) ❌
This is the principle of weak mathematical induction. It only shows that if P holds for a given k and for all smaller values i then it must hold for k+1. It does not guarantee that P holds for all natural numbers.
d) ❌
This statement is the negation of the principle of mathematical induction. It is known as the "strong induction" principle, which assumes that if P does not hold for k, then there exists a smaller i where P does not hold. However, this principle is not sufficient to prove that P holds for all natural numbers k.
the expression when y=-6 y^2+8y-9
Answer:
-21
Step-by-step explanation:
y^2 + 8y - 9 y = -6
(-6)² + 8(-6) - 9
36 - 48 - 9
-21
So, the answer is -21
Answer:y=\frac{7}{12}-i\frac{\sqrt{167}}{12},\:y=\frac{7}{12}+i\frac{\sqrt{167}}{12}
Step-by-step explanation:y=\frac{7}{12}-i\frac{\sqrt{167}}{12},\:y=\frac{7}{12}+i\frac{\sqrt{167}}{12}
What is an equation of the line that passes through the point (4,1) and is perpendicular to the line 2x-y= 4?
Answer:
Point-Slope Form: y - 1 = -1/2(x - 4) or Standard Form: y = -1/2x + 3
Step-by-step explanation:
For a line to be perpendicular, you take the negative inverse of the slope of 2x - y = 4. To do this, rearrange the y to one side and you get y = 2x - 4. The slope of the line is 2. So, taking the negative inverse would be -1/m (with m being slope of the the equation given in the problem. This would give you -1/2.
Using point slope formula, y - y1 = m(x - x1), you can plug in the point given, (4,1) and the slope you found to get y - 1 = -1/2(x - 4). For standard form, isolating the y gets you y = -1/2x + 3.
You can check your answer by using Desmos by putting in the line 2x - y = 4, the point (4,1), and the equation you got as your answer. You will see that the equation is perpendicular to 2x - y = 4 and passes through point (4,1). Your equation of the line is y - 1 = -1/2(x - 4) or y = -1/2x + 3
(-6, -2) (-2, 0) what is solution to system of equations?
Note that the solution of the system of equations will be (-6, -2). (Option A)
What is a system of equation?
A system of equations is a collection of two or more equations with a shared set of unknown variables. The goal is to find the values of the variables that satisfy all the equations simultaneously.
Note that System of equations is represented by two straight lines on a graph.
And solution of the system of equations is the point of intersection of these lines, because that is the point where the values from both functions satisfy all the equations simultaneously.
From the graph attached, two straight lines represent the system of equations.
And the point of intersection of these lines is the solution.
Therefore, solution of the system of equations will be (-6, -2). (Option A)
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Full Question:
Although part of your question is missing, you might be referring to this full question:
What is the solution to the system of equations?
A (-6,2-)
B (-2, 6)
C (6,2)
D (-2,-6)? See attached image.
The summaries of data from the balance sheet, income statement, and retained earnings statement for two corporations, Walco Corporation, and Gunther Enterprises, are presented below for 2017.
Determine the missing amounts. Assume all changes in stockholders equity are due to changes in retained earnings
Walco Corporation Gunther Enterprise
Beginning of year Total assets $100,000 $159,000
Total liabilities 73,000 $_____ (d)
Total stockholders' equity $_____ (a) 67,500
End of year Total assets $_____ (b) 190,000
Total liabilities 128,000 50,000
Total stockholders' equity 54,000 $_____ (e)
Changes during year in retained earnings Dividends $_____ (c) 4,900
Total revenues 219,000 $_____ (f)
Total expenses 167,000 79,000
The missing amounts for Walco Corporation and Gunther Enterprises assuming all changes in stockholders equity are due to changes in retained earnings are
(a) Walco Corporation Total Stockholders' Equity = $54,000
(b) Walco Corporation Total Assets = $182,000
(c) Walco Corporation Dividends = $47,100
(d) Gunther Enterprises Total Liabilities = $140,000
(e) Gunther Enterprises Total Stockholders' Equity = $91,500
(f) Gunther Enterprises Total Revenues = $135,100
A balance sheet is a financial statement that reports a company's assets, liabilities, and stockholder equity on a specific date. Assets are resources a company owns that have monetary value, liabilities are obligations that must be paid in the future, and stockholder equity is the difference between a company's assets and liabilities. To calculate the missing amounts, you need to subtract the beginning of year figures from the end of year figures.
a) Total liabilities + Total stockholders' equity = Total assets
Total liabilities + $54,000 = $100,000
Total liabilities = $46,000
(b) Total assets = Total liabilities + Total stockholders' equity
Total assets = $128,000 + $54,000
Total assets = $182,000
(c) Changes during year in retained earnings = Total revenues - Total expenses - Dividends
Changes during year in retained earnings = $219,000 - $167,000 - $4,900
Changes during year in retained earnings = $47,100
The missing values for Gunther Enterprises:
(d) Total liabilities + Total stockholders' equity = Total assets
$67,500 + $(e) = $159,000
$(e) = $91,500
(f) Changes during year in retained earnings = Total revenues - Total expenses - Dividends
Changes during year in retained earnings = $(f) - $79,000 - $4,900
Changes during year in retained earnings = $(f) - $83,900
Using the balance sheet equation, we can find the missing values:
(d) Total liabilities = Total assets - Total stockholders' equity
Total liabilities = $159,000 - $67,500
Total liabilities = $91,500
(e) Total stockholders' equity = Total assets - Total liabilities
Total stockholders' equity = $190,000 - $50,000
Total stockholders' equity = $140,000
(f) Changes during year in retained earnings = Total revenues - Total expenses - Dividends
Changes during year in retained earnings = $219,000 - $79,000 - $4,900
Changes during year in retained earnings = $135,100
Therefore, the missing amounts are:
(a) Walco Corporation Total Stockholders' Equity = $54,000
(b) Walco Corporation Total Assets = $182,000
(c) Walco Corporation Dividends = $47,100
(d) Gunther Enterprises Total Liabilities = $140,000
(e) Gunther Enterprises Total Stockholders' Equity = $91,500
(f) Gunther Enterprises Total Revenues = $135,100
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in august 2012, tropical storm isaac formed in the caribbean and was headed for the gulf of mexico. there was an initial probability of .69 that isaac would become a hurricane by the time it reached the gulf of mexico (national hurricane center website, august 21, 2012). a. what was the probability that isaac would not become a hurricane but remain a tropical storm when it reached the gulf of mexico (to 2 decimals)? b. two days later, the national hurricane center projected the path of isaac would pass directly over cuba before reaching the gulf of mexico. hurricanes that reach the gulf of mexico have a .08 probability of having passed over cuba. tropical storms that reach the gulf of mexico have a .20 probability of having passed over cuba. how did passing over cuba alter the probability that isaac would become a hurricane by the time it reached the gulf of mexico? use the above probabilities to answer this question. p(c|h) (to 2 decimals) p(c|t) (to 2 decimals) p(h|c) (to 4 decimals) c. what happens to the probability of becoming a hurricane when a tropical storm passes over a landmass such as cuba? select (to 2 decimals) to (to 4 decimals).\
By using Bayes' theorem in probability.
a) The probability that isaac would not become a hurricane but remain a tropical storm when it reached the gulf of mexico is 0.31.
b) P(H|c) = 0.4493
c) It can be observed that the likelihood of a tropical storm developing into a hurricane decreases slightly when it passes over Cuba. This can be inferred from the fact that the conditional probability of a hurricane forming given that the storm has passed over Cuba (P(H|c) = 0.4493) is lower than the initial probability of 0.69.
a) The probability that Isaac would not become a hurricane but remain a tropical storm when it reached the Gulf of Mexico is:
P(not hurricane) = 1 - P(hurricane) = 1 - 0.69 = 0.31
So the probability is 0.31 (to 2 decimals).
b) We need to use Bayes' theorem to calculate the probabilities:
P(c|H) = P(H|c) * P(c) / P(H)
P(c|T) = P(T|c) * P(c) / P(T)
where c denotes passing over Cuba, H denotes becoming a hurricane, and T denotes remaining a tropical storm.
From the problem, we have:
P(H) = 0.69
P(T) = 1 - P(H) = 0.31
P(c|H) = 0.08
P(c|T) = 0.20
To calculate P(c), we need to use the law of total probability:
P(c) = P(c|H) * P(H) + P(c|T) * P(T)
= 0.08 * 0.69 + 0.20 * 0.31
= 0.1228
Now we can calculate P(c|H) and P(c|T):
P(c|H) = 0.08 * 0.69 / 0.1228
= 0.4493 (to 2 decimals)
P(c|T) = 0.20 * 0.31 / 0.1228
= 0.5065 (to 2 decimals)
To calculate P(H|c), we use Bayes' theorem again:
P(H|c) = P(c|H) * P(H) / P(c)
= 0.08 * 0.69 / 0.1228
= 0.4493 (to 4 decimals)
c) Passing over a landmass such as Cuba can alter the probability of becoming a hurricane because it can either enhance or weaken the storm. In this case, we can see that the probability of becoming a hurricane is actually slightly lower when a tropical storm passes over Cuba, as P(H|c) = 0.4493 is lower than the initial probability of 0.69. However, it is important to note that this is just one example and the effect of passing over a landmass can vary depending on many factors.
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Write the expression in complete factored
form.
b2(p + 3) + q(P + 3) =
An assignment of probabilities to events in a sample space must obey which of the following? They must obey the addition rule for disjoint events. They must sum to 1 when adding over all events in the sample space. The probability of any event must be a number between 0 and 1, inclusive. All of the above
An assignment of probabilities to events in a sample space must obey all of the following: They must obey the addition rule for disjoint events, They must sum to 1 when adding over all events in the sample space, and The probability of any event must be a number between 0 and 1, inclusive. Hence, the correct option is All of the above.
What is probability?Probability is the branch of mathematics that deals with the likelihood of a random event occurring. Probability is concerned with quantifying the probability of different results in a certain event.
The possibility that a specific event will occur is calculated using probability. Probability is calculated using several methods in mathematics, including axioms, probability spaces, events, random variables, and expectation values.
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Blaine works for a battery manufacturing company. he wants to develop a method to test the batteries made each day to determine if they work. which method would provide the most valid results?
Random sampling 50 batteries throughout the day and testing to see if they would provide most valid results.
A sample is described as a smaller, more manageable representation of a larger group. A smaller population with characteristics of a larger one. A sample is used in statistical analysis when the population size is too large to include all participants or observations in the test.
The sample may be biased if it is taken from the first 25 batteries made each day or the last 25 batteries made each day.
The first and last battery made each day could not be an accurate representation of the total quality of the batteries produced that day if the battery manufacturing process is not consistent thought the day.
Although the battery quality can change during the day, sampling the first 50 batteries produced each day may also add bias into the sample.
The ideal course of action is to randomly select 50 batteries throughout the day, since this helps to ensure that the sample is reflective of the general calibre of batteries manufactured that day.
A more accurate image of the quality of the batteries manufactured can be obtained using this method, which is also more likely to capture any variations in battery quality over the day.
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Are the expressions -0.5(3x + 5) and
-1.5x + 2.5 equivalent? Explain why or why not.
These expression is not true .
What is a mathematical expression?
A mathematical expression is a sentence that consists of at least two numbers or variables, the expression itself, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations could be used: addition, subtraction, multiplication, or division.
For instance, the expression x + y is an expression with the addition operator placed between the terms x and y. Mathematicians utilize two different sorts of expressions: algebraic and numeric. Numeric expressions only contain numbers; algebraic expressions additionally incorporate variables.
-0.5(3x + 5) and -1.5x + 2.5 equivalent.
by distributing the 0.5 = -1.5x + 2.5
= -1.5x + 2.5
= 0.5(3*2 + 5 )
= - 1.5 * 2 + 2.5
= - 3 - 2.5 = -3 + 2.5
- 5. 5 = 0.5
this is not true. these expression is not true .
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suppose point p divides the directed line segment xy so that the ratio of xp to py is 3 to 5 . describe point r that divides the directed line segment yx so that the ratio of yr to rx is 5 to 3 .a. R and P are the same pointb. Point R is halfway between point P and point Xc. The distance from point X is the same as the distance prom point P to point Yd. Point R is three fifths of the way from point P to point Y along PY
For point, p divides the directed line segment xy so that the ratio of xp to py is 3 to 5 correct option is d. Point R is three-fifths of the way from point P to point Y along PY.
The directed line segments divide a line into ratios, and each ratio has different properties. The properties of ratios of points on a line are dependent on the way the line is divided. For instance, suppose point p divides the directed line segment xy so that the ratio of xp to py is 3 to 5. We can describe point r that divides the directed line segment yx so that the ratio of yr to rx is 5 to 3 as follows:
We can solve this problem using the concept of directed line segments and the properties of ratios of points on a line.
Since P divides the directed line segment XY in the ratio 3:5, we can write:
XP = (3/8)XY and PY = (5/8)XY
Now, let's consider the directed line segment YX. We want to find a point R on this segment such that YR:RX = 5:3.
We can express YR and RX in terms of XY using the fact that YX = -XY:
YR = (5/8)YX and RX = (3/8)YX
Substituting -XY for YX, we get:
YR = (-5/8)XY and RX = (-3/8)XY
To find the location of point R, we need to find the distance from Y to R along the directed line segment YX. We can do this by adding the distances from Y to P and from P to R:
YR = YP + PR
Using the ratios we derived earlier, we can express YP and PR in terms of XY:
YP = PY = (5/8)XY
PR = R - P = (3/8)XY - (3/8)XY = 0
Therefore, YR = (5/8)XY + 0 = (5/8)XY
This means that point R is located at a distance of 5/8 of the length of YX from Y. So, the correct answer is (d) Point R is three-fifths of the way from point P to point Y along PY.
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Math 4th 11-4 I need answers for 11-4 can you please help?
To make the table of 7, using the table of 4 and 3, we add the value of both table consecutively.
We have to make the table of 7, using table of 4 and 3.
As we know the table of 3 is:
3 6 9 12 15 18 21 24 27 30
As we know the table of 4 is:
4 8 12 16 20 24 28 32 36 40
To from the table of 7 using the table of 4 and 3 we add the consecutive value of both table respectively.
3 + 4 6 + 8 9 + 12 12 + 16 15 + 20 18 + 24 21 + 28 24 + 32 27 + 36 30+40
Now simplify
7 14 21 28 35 42 49 56 63 70
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The complete question is:
Math 4th 11-4: Help bunty to make the table of 7, using table of 4 and 3.
How could 1/5 + -4/5 be modeled on a number line
The expression 1/5 + -4/5 has plotted on the number line
To model 1/5 + (-4/5) on a number line, we can start by placing a point at 0 on the number line. Then we can represent 1/5 by placing another point to the right of 0, one-fifth of the distance from 0 to 1. We can represent -4/5 by placing a point to the left of 0, four-fifths of the distance from 0 to -1.
To add these two points together, we start at the point representing 1/5 and move four-fifths of the distance towards the left, since -4/5 is negative. The resulting point represents the sum of 1/5 and -4/5.
To solve this problem algebraically, we can add the two fractions together by finding a common denominator:
1/5 + (-4/5) = 1/5 - 4/5
= (1-4)/5
= -3/5
= -0.6
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Caris has a carton of 12 eggs, two of which have brown shells while the rest have white shells. Caris randomly chooses a brown egg from the carton. Which of the following statements is true? If she rejects this egg, returns it to the carton, and randomly picks again, these will be dependent events. If she uses this egg in a recipe and picks another one from the carton, these will be dependent events. Whether or not these are dependent or independent events depends on what color egg Caris chooses next. If she uses this egg in a recipe and picks another one from the carton, these will be independent events.
Answer:
Step-by-step explanation:
i think you have to times it
Find the equation of the line parallel to 2x + 5y = 10 which passes through (0,-3)
Answer: The given equation 2x + 5y = 10 can be rewritten in slope-intercept form (y = mx + b) by solving for y:
2x + 5y = 10
5y = -2x + 10
y = (-2/5)x + 2
where the slope is -2/5.
Since we want to find the equation of a line parallel to this one, the slope of the new line will also be -2/5. We can use the point-slope form of the equation of a line to find the equation of the new line, using the point (0,-3):
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point.
Substituting m = -2/5, x1 = 0, and y1 = -3, we get:
y - (-3) = (-2/5)(x - 0)
y + 3 = (-2/5)x
y = (-2/5)x - 3
Therefore, the equation of the line parallel to 2x + 5y = 10 which passes through (0,-3) is y = (-2/5)x - 3.
Step-by-step explanation:
Answer:
2x + 5y = - 15
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
2x + 5y = 10 ( subtract 2x from both sides )
5y = - 2x + 10 ( divide through by 5 )
y = - [tex]\frac{2}{5}[/tex] x + 2 ← in slope- intercept form
with slope m = - [tex]\frac{2}{5}[/tex]
• Parallel lines have equal slopes , then
y = - [tex]\frac{2}{5}[/tex] x + c
the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = - [tex]\frac{2}{5}[/tex] x - 3 ← equation of parallel line in slope- intercept form
multiply through by 5 to clear the fraction
5y = - 2x - 15 ( add 2x to both sides )
2x + 5y = - 15 ← in standard form
j by 9 and then multiply the quotient by 2
The sequence of the questions is [tex]J/9[/tex] when you multiply [tex]J[/tex] by [tex]9[/tex] and the quotient by [tex]2[/tex].
What in arithmetic is a quotient?In this example, the number being divided (15) is known as the result, and the number being divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division.
Is quotient the same as answer?The result of dividing two integers is known as the quotient. Six divided into two results in the number three. Latin's "how many times" is the meaning of the word "quotient." It makes perfect sense: by dividing two numbers, you can determine "how many time" the two digits enters the first.
[tex]2 * (J/9)[/tex]
This means you first divide [tex]J[/tex] by [tex]9[/tex] to get the quotient, and then multiply the quotient by [tex]2[/tex]. So the order of operations is:
[tex]J/9[/tex]
Multiply the quotient by [tex]2[/tex]
For example, if [tex]J = 45[/tex], then:
[tex]J/9 = 45/9 = 5[/tex]
[tex]2 * (J/9) = 2 * 5 = 10[/tex]
So the result of multiplying [tex]J[/tex] by [tex]9[/tex] and then multiplying the quotient by [tex]2[/tex], when [tex]J = 45[/tex], is [tex]10[/tex].
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please answer the question in the photo (will mark brainliest + 15p)
we have
13x+6y=−30------------- > 6y=-30-13x--------------- > y=(-30-13x)/6
x−2y=−4-- > 2y=x+4-------- > y=(x+4)/2
Using a graphing tool---------- > see attached figure
the solution of the system is the point (-2.625,0688)
the best estimate pair for the solution to the system is (−2.5, 0.75)
What is the area of this figure?
6 mm
4 mm
3 mm
5 mm
3 mm
15 mm
3 mm
9 mm
Write your answer using decimals, if necessary. Square millimeters
Based on the given data, The shape's whole surface area is about 252 mm².
Based on the image, the shape appears to be a set of rectangles with different lengths and widths.
To find the area of this shape, we can break it down into smaller rectangles and add up their areas.
Starting from the bottom, we can see that the first rectangle has a length of 6 mm and a width of 4 mm. Its area is:
Area1
= 6 mm × 4 mm
= 24 mm²
Moving up to the second rectangle, we see that it has a length of 6 mm and a width of 3 mm. Its area is:
Area2
= 6 mm × 3 mm
= 18 mm²
The third rectangle has a length of 6 mm and a width of 5 mm. Its area is:
Area3
= 6 mm × 5 mm
= 30 mm²
The fourth rectangle has a length of 6 mm and a width of 3 mm. Its area is:
Area4
= 6 mm × 3 mm
= 18 mm²
The fifth rectangle has a length of 6 mm and a width of 15 mm. Its area is:
Area5
= 6 mm × 15 mm
= 90 mm²
The sixth rectangle has a length of 3 mm and a width of 9 mm. Its area is:
Area6
= 3 mm × 9 mm
= 27 mm²
Finally, the seventh rectangle has a length of 5 mm and a width of 9 mm. Its area is:
Area7
= 5 mm × 9 mm
= 45 mm²
To find the total area of the shape, we can add up the areas of all seven rectangles:
Total Area
= Area1 + Area2 + Area3 + Area4 + Area5 + Area6 + Area7
= 24 mm² + 18 mm² + 30 mm² + 18 mm² + 90 mm² + 27 mm² + 45 mm²
= 252 mm²
Therefore, the total area of the shape is approximately 252 mm².
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3
Each player on a softball team will get a uniform with a randomly selected
number between 1 and 30. No two players will have the same number.
The first player to get a uniform thinks the probability that she will
get a single-digit number is. Is the player correct? Explain
10
your reasoning.
30 percent chance
There are 30 possible numbers that a player can get on their uniform. Out of these, there are 9 single-digit numbers (1, 2, 3, 4, 5, 6, 7, 8, and 9) and 21 double-digit numbers (10, 11, 12, ..., 29, 30).
If no two players can have the same number, then the probability that the first player will get a single-digit number is simply the number of single-digit numbers divided by the total number of possible numbers:
P(single-digit number) = 9/30 = 0.3
So the player is correct that there is a 30% chance that she will get a single-digit number on her uniform.
Pls read ss
PLS HELPP
The slopes are,
1) 7/6
2)7/2
3) -1
4) -2
5) 10/9
What is slope?
Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line.Any two distinct places along the line can be used to determine the slope of any line.
1) The given points , [tex](x_1,y_1) =(0,1)[/tex] and [tex](x_2,y_2) = (6,8)[/tex] then,
=> slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{8-1}{6-0} = \frac{7}{6}[/tex]
2) The given points [tex](x_1,y_1) =(-1,10)[/tex] and [tex](x_2,y_2) = (-5,-4)[/tex] then,
=> Slope = [tex]\frac{-4-10}{-5+1} = \frac{-14}{-4}=\frac{7}{2}[/tex]
3) The given points [tex](x_1,y_1) =(-10,2)[/tex] and [tex](x_2,y_2) = (-3,-5)[/tex] then,
=> slope = [tex]\frac{-5-2}{-3+10} = \frac{-7}{7}=-1[/tex]
4) The given points [tex](x_1,y_1) =(-3,-4)[/tex] and [tex](x_2,y_2) = (-1,-8)[/tex] then,
=> slope = [tex]\frac{-8+4}{-1+3} = \frac{-4}{2}=-2[/tex]
5)The given points [tex](x_1,y_1) =(0,1)[/tex] and [tex](x_2,y_2) = (-9,-9)[/tex] then,
=> slope = [tex]\frac{-9-1}{-9+0} = \frac{-10}{-9}=\frac{10}{9}[/tex]
Hence the slopes are,
1) 7/6
2)7/2
3) -1
4) -2
5) 10/9
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match each of the following concepts with its definition: estimator answer 1 a random variable that depends on the information in the sample. estimate answer 2 a specific value of a random variable that approximates an unknown parameter. unbiasedness answer 3 when the expected value of the estimator is equal to the population parameter. bias answer 4 the difference between the expected value of the estimator and the population parameter. most efficient estimator answer 5 an unbiased estimator that has the minimum variance. relative efficiency
A relative efficiency greater than 1 means that the estimator is less efficient than the most efficient estimator. A relative efficiency less than 1 means that the estimator is more efficient than the most efficient estimator.
Estimator: A random variable that depends on the information in the sample.Estimate: A specific value of a random variable that approximates an unknown parameter.Unbiasedness: When the expected value of the estimator is equal to the population parameter.Bias: The difference between the expected value of the estimator and the population parameter.Most Efficient Estimator: An unbiased estimator that has the minimum variance.Relative Efficiency: Relative efficiency is a measure of the efficiency of an estimator. It is a ratio of the variance of an estimator to the variance of the most efficient estimator. A relative efficiency of 1 means that the estimator is as efficient as the most efficient estimatorfor such more questions on relative efficiency
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An automated car wash serves customers with the following serial process: pretreat, wash, rinse, wax, hand dry. Each of these steps is performed by a dedicated machine except for the hand-dry step, which is performed manually on each car by one of three workers. The steps of the process have the following processing times:
Pretreat: 2 minute per car
Wash: 7 minutes per car
Rinse: 1 minutes per car
Wax: 4 minutes per car
Hand dry: 6 minutes per car
Which resource is the bottleneck of this process? Round your answer to 2 decimal places. If the car wash has a demand of 14 cars per hour, what is the flow rate of the process? cut. customers per hour Round your answer to 2 decimal places. If the car wash has a demand of 14 cars per hour, what is the utilization of the machine that
The utilization of the machines is the processing time for the machines divided by the cycle time: 14 / 20 = 0.7 or 70%.
The bottleneck resource in this process is the hand-dry step, as it is the only step that is performed manually and thus has limited capacity. The processing time for the hand-dry step is 6 minutes per car, which is longer than any of the other steps.
To calculate the flow rate of the process, we need to determine the cycle time, which is the time it takes to process one car through all the steps. The cycle time is the sum of the processing times for all the steps, which is 2 + 7 + 1 + 4 + 6 = 20 minutes per car.
To convert this to customers per hour, we divide the number of minutes per hour (60) by the cycle time: 60 / 20 = 3 customers per hour.
Therefore, the flow rate of the process is 14 cars per hour x 3 customers per hour = 42 customers per hour.
To calculate the utilization of the machines, we need to calculate the total time that the machines are processing cars. Since all the steps except for the hand-dry step are performed by dedicated machines, the total processing time for the machines is 2 + 7 + 1 + 4 = 14 minutes per car.
Therefore, the utilization of the machines is the processing time for the machines divided by the cycle time: 14 / 20 = 0.7 or 70%.
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two people standing at different locations are looking at a tall building. person a angle of elevation to the building is 35 degrees. person b angle of elevation is 77 degrees. the building is 8 miles away from person b. how far away is person a from the building?
Therefore, Person A is approximately 95.17 miles away from the building.
To find out how far person A is from the building, we'll need to use trigonometry. The diagram below shows the situation.
Given that Person A's angle of elevation to the building is 35 degrees, we'll let angle BAC be 35 degrees.
Similarly, since Person B's angle of elevation is 77 degrees, we'll let angle ABC be 77 degrees. We'll also let AB be x, the distance from Person A to the building, and BC be 8 miles, the distance from Person B to the building.
First, we'll use the tangent function to find the height of the building. In triangle ABC, tan(77) = height/8. Solving for the height, we get:
height = 8tan(77) ≈ 61.23 miles.
Next, we'll use the tangent function again to find x. In triangle ABC, tan(35) = height/x + 8. Solving for x, we get:
x = (height)/(tan(35)) - 8
≈ 103.17 miles - 8
≈ 95.17 miles.
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the cylinder has a volume of 45 cubic inches and a height of 5 inches what is the raduis of the cylinder
The radius of the cylinder is 3 inches.
What is the volume of a cylinder?
A cylinder is a three-dimensional solid with two parallel circular bases and a curved lateral surface connecting the two bases. The volume of a cylinder is given by the formula [tex]V = \pi r^2h[/tex], where r is the radius of the base, h is the height of the cylinder, and π is a constant value approximately equal to 3.14.
Calculating the value of radius :
We are given that the cylinder has a volume of 45 cubic inches and a height of 5 inches. Using the formula for the volume of a cylinder, we get:
[tex]V = \pi r^2h[/tex]
Substituting the given values, we get:
[tex]45 = \pi r^2(5)[/tex]
Simplifying the equation, we get:
[tex]9 = r^2[/tex]
Taking the square root of both sides, we get:
[tex]r = \pm 3[/tex]
Since the radius cannot be negative, we take the positive value of r, which is:
r = 3 inches
Therefore, the radius of the cylinder is 3 inches.
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Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 5 inches.
(a) What is the probability that an 18-year-old man selected at random is between 70 and 72 inches tall? (Round your answer to four decimal places.)
(b) If a random sample of eight 18-year-old men is selected, what is the probability that the mean height x is between 70 and 72 inches? (Round your answer to four decimal places.)
(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?
The probability in part (b) is much higher because the mean is larger for the x distribution.
The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.
The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.
The probability in part (b) is much higher because the mean is smaller for the x distribution.
The probability in part (b) is much higher because the standard deviation is larger for the x distribution.
The probability that an 18-year-old man selected at random is between 70 and 72 inches tall is approximately 0.0793 and the probability that the mean height of a sample of eight 18-year-old men is between 70 and 72 inches is approximately 0.9057 and the probability in part (b) is much higher because the standard deviation is smaller for the x distribution.
What do you mean by normally distributed data?
In statistics, a normal distribution is a probability distribution of a continuous random variable. It is also known as a Gaussian distribution, named after the mathematician Carl Friedrich Gauss. The normal distribution is a symmetric, bell-shaped curve that is defined by its mean and standard deviation.
Data that is normally distributed follows the pattern of the normal distribution curve. In a normal distribution, the majority of the data is clustered around the mean, with progressively fewer data points further away from the mean. The mean, median, and mode are all the same in a perfectly normal distribution.
Calculating the given probabilities :
(a) The probability that an 18-year-old man selected at random is between 70 and 72 inches tall can be found by standardizing the values and using the standard normal distribution table. First, we find the z-scores for 70 and 72 inches:
[tex]z-1 = (70 - 71) / 5 = -0.2[/tex]
[tex]z-2 = (72 - 71) / 5 = 0.2[/tex]
Then, we use the table to find the area between these two z-scores:
[tex]P(-0.2 < Z < 0.2) = 0.0793[/tex]
So the probability that an 18-year-old man selected at random is between 70 and 72 inches tall is approximately 0.0793.
(b) The mean height of a sample of eight 18-year-old men can be considered a random variable with a normal distribution. The mean of this distribution will still be 71 inches, but the standard deviation will be smaller, equal to the population standard deviation divided by the square root of the sample size:
[tex]\sigma_x = \sigma / \sqrt{n} = 5 / \sqrt{8} \approx 1.7678[/tex]
To find the probability that the sample mean height is between 70 and 72 inches, we standardize the values using the sample standard deviation:
[tex]z_1 = (70 - 71) / (5 / \sqrt{8}) \approx -1.7889[/tex]
[tex]z_2 = (72 - 71) / (5 / \sqrt{8}) \approx 1.7889[/tex]
Then, we use the standard normal distribution table to find the area between these two z-scores:
[tex]P(-1.7889 < Z < 1.7889) \approx 0.9057[/tex]
So the probability that the mean height of a sample of eight 18-year-old men is between 70 and 72 inches is approximately 0.9057.
(c) The probability in part (b) is much higher because the standard deviation is smaller for the x distribution. When we take a sample of eight individuals, the variability in their heights is reduced compared to the variability in the population as a whole. This reduction in variability results in a narrower distribution of sample means, with less probability in the tails and more probability around the mean. As a result, it becomes more likely that the sample mean falls within a given interval, such as between 70 and 72 inches.
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Jaxon is flying a kite, holding his hands a distance of 3.25 feet above the ground and
letting all the kite's string play out. He measures the angle of elevation from his hand
to the kite to be 24°. If the string from the kite to his hand is 105 feet long, how many
feet is the kite above the ground? Round your answer to the nearest tenth of a foot if
necessary.
Answer: 46.0 ft
Step-by-step explanation:
[tex]\text{sin} \ 24^o=\dfrac{x}{105}[/tex]
[tex]x=105 \ \text{sin 24}^o[/tex]
So, the distance above the ground is [tex]\text{105 sin} \ 24^o+3.25\thickapprox \boxed{46.0 \ \text{ft}}[/tex]
compute the zeros of the polynomial 4x2 - 4x - 8
Answer:
(2, 0) and (-1, 0)
Step-by-step explanation:
[tex]4x^2 - 4x - 8 = 0 \text{ // Divide by 4} \\x^2 - x - 2 = 0\\\\x_{1, 2} = \frac{-(-1) \pm \sqrt{(-1)^2 - 4 \times 1 \times (-2)}}{2\times1}\\\\x_{1, 2} = \frac{1 \pm \sqrt{1 + 8}}2\\\\x_{1, 2} = \frac{1 \pm \sqrt9}2\\\\x_{1, 2} = \frac{1 \pm 3}2\\\\x_1 = \frac{1 + 3}2 = \frac42 = 2\\\\x_2 = \frac{1 - 3}2 = \frac{-2}2 = -1[/tex]
Therefore, the zeroes are (2, 0) and (-1, 0).
Write a quadratic equation that goes through the points (0,5), (2,1), and (1,2). y = ax^2 + bx + c
a person pays $1 to play a certain game by rolling a single die once. if a 1 or 2 comes up, the person wins nothing. if, however, the player rolls a 3, 4, 5, or 6 he or she wins the difference between the number rolled and $1. find the expectation of this game. is the game fair?
A person pays $1 to play a certain game by rolling a single die once. if a 1 or 2 comes up, the person wins nothing. if, however, the player rolls a 3, 4, 5, or 6 he or she wins the difference between the number rolled and $1, this means that the game is not fair, based on the expected value
How do we determine the expected value of the game?We can see that the expected value of the game can be found by multiplying each payout by its probability of occurring and then summing up the results:Expected value = (0.2)($1) + (0.2)($1) + (0.2)($2) + (0.2)($3) + (0.2)($4) + (0.2)($0) + (0.2)($0)Expected value = $0.40 Since the expected value of the game is positive, it means that, over the long run, players are expected to make money on average. This means that the game is not fair.
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IN A BOX PLOT , IF THE MEDIAN IS TO THE LEFT OF THE CENTER OF THE BOX AND THE RIGHT WHISKER IS SUBSTANTIALLY LONGER THAN THE LET WHISKER, THE DISTRIBUTION IS SKEWED LEFT OR RIGHT?
The distribution is skewed to the right.
How to find distribution is skewed?If the median is to the left of the center of the box and the right whisker is substantially longer than the left whisker in a box plot, then the distribution is skewed to the right.
This means that the majority of the data is clustered on the left side of the box plot and there are some extreme values on the right side that are causing the right whisker to be longer.
The median being to the left of the center of the box indicates that the data is not symmetric and is pulled to the left by the majority of the values.
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Triangle lmn will be dilated with respect to the origin by a scale factor of 1/2
what are the new coordinates of L’M’N’
The triangle LMN, with vertices L(6, −8), M(4, −4), and N(−12, 2), dilated with respect to the origin by a scale factor of 1/2, results in triangle L'M'N', with vertices L'(3, -4), M'(2, -2), and N'(-6, 1)
To dilate a triangle with respect to the origin, we need to multiply the coordinates of each vertex by the scale factor. In this case, the scale factor is 1/2, so we multiply each coordinate by 1/2.
The coordinates of L' are obtained by multiplying the coordinates of L by 1/2:
L'((1/2)6, (1/2)(-8)) = (3, -4)
The coordinates of M' are obtained by multiplying the coordinates of M by 1/2:
M'((1/2)4, (1/2)(-4)) = (2, -2)
The coordinates of N' are obtained by multiplying the coordinates of N by scale factor 1/2:
N'((1/2)×(-12), (1/2)×2) = (-6, 1)
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The given question is incomplete, the complete question is:
Triangle LMN with vertices L(6, −8), M(4, −4), and N(−12, 2) is dilated with respect to origin by a scale factor of 2 to obtain triangle L′M′N′. What are the new coordinates of L′M′N′ ?
