Answer:
Read carefully each step for your fully understand it.
Step-by-step explanation:
To find the equation of a line that is perpendicular to the line y = 2x - 3 and contains the point (-5, 3), we need to find the slope of the perpendicular line.
To find the slope, we use the negative reciprocal of the slope of the given line. The slope of the given line is 2, so the slope of the perpendicular line is -1/2.
We can then use the point-slope formula to find the equation of the line that is perpendicular to y = 2x - 3 and contains the point (-5, 3).
The point-slope formula is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values, we get:
y - 3 = -1/2 (x + 5)
We can then simplify this equation to get the final equation:
y = -1/2 x - 11/2
Therefore, the equation of the line that is perpendicular to y = 2x - 3 and contains the point (-5, 3) is y = -1/2 x - 11/2.
What is the amount of compound interest on #640.00 borrowed for 4years at 3%.
The amount of compound interest on #640.00 borrowed for 4years at 3% is #163, 840
How to determine the valueThe formula for determining compound interest is given as;
Compound interest = P ( 1 + r/n)^nt
Where;
P is the principal amount = #640. 00r is the rate e= 3%n is the number of times the amount appliedt is the length of timeNow, substitute the values
Compound interest = 640( 1 + 3/1)^(4×1)
expand the bracket
Compound interest = 640( 1 + 3)^4
Compound interest = 640(4)^4
find the exponential value
Compound interest = 640(256)
Multiply the value
Compound interest = #163, 840
Hence, the value is #163, 840
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How do you remove split infinitives?
To get rid of the split infinitive move the term that separates the infinitive from the split position.
In the given question we have to explain, how we remove split infinitives.
As we know that,
Split infinitives are grammatical constructions in which the "to" and "infinitive" halves of what is more often referred to as the to-infinitive in modern linguistics are separated by an adverb or adverbial phrase.
When an adverb is inserted between the word "to" and the infinitive verb, a split infinitive results. Move the term that separates the infinitive from the split position to get rid of the split infinitive.
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Which is the last sentence of the proof? because f e = 1, a2 b2 = c2. because f e = c, a2 b2 = c2. because a2 b2 = c2, f e = c. because a2 b2 = c2, f e = 1.
The last sentence of the proof is Because f+e=c, [tex]a^{2} + b^{2} = c^{2}[/tex]. Hence, option b is the correct answer to this question.
We have that △ABC and △CBD are right-angled triangles.
We have to prove [tex]a^{2} + b^{2} = c^{2}[/tex].
We are given the proof too.
Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA.
Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA.
The proportions and are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as
[tex]a^{2}[/tex] = cf and [tex]b^{2}[/tex] = ce.
Adding [tex]b^{2}[/tex] to both sides of the first equation, [tex]a^{2}[/tex] = cf, which results in the equation [tex]a^{2} + b^{2} = cf +b^{2}[/tex].
Because [tex]b^{2}[/tex] and ce are equal, ce can be substituted into the right side of the equation for [tex]b^{2}[/tex], resulting in the equation [tex]a^{2}+b^{2}[/tex] = cf + ce.
Applying the converse of the distributive property results in the equation [tex]a^{2}+b^{2}[/tex]= c(f + e).
Now Because f+e=c, [tex]a^{2} + b^{2} = c^{2}[/tex] .
Hence, the last sentence of this proof is Because f+e=c, [tex]a^{2} + b^{2} = c^{2}[/tex].
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The complete question is -
Which is the last sentence of the proof?
a. Because f + e = 1, [tex]a^{2} + b^{2} = c^{2}[/tex].
b. Because f + e = c, [tex]a^{2} + b^{2} = c^{2}[/tex].
c. Because [tex]a^{2} + b^{2} = c^{2}[/tex], f + e = c.
d. Because [tex]a^{2} + b^{2} = c^{2}[/tex], f + e = 1.
Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA. Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA. The proportions and are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as a2 = cf and b2 = ce. Adding b2 to both sides of first equation, a2 = cf, results in the equation a2 + b2 = cf + b2. Because b2 and ce are equal, ce can be substituted into the right side of the equation for b2, resulting in the equation a2 + b2 = cf + ce. Applying the converse of the distributive property results in the equation a2 + b2 = c(f + e).
Answer: option b
Step-by-step explanation:
Garrick and Zan are measuring the heights of seedling plants for science class.
Use the drop-down menus to complete the statements about the measured heights and the actual heights of the plants.
The complete statements are
Garrick's plant is shorter than Zan's plant, each millimetre of error results in a 11.11% percent error.Garrick's measurement was 2 millimetres off and Zan's was 12 millimetres off. Garrick's measurement was 20% off and Zan's was 12% off.How to complete the statements?The complete question is added at the end of this solution
From the question, we have the following parameters that can be used in our computation:
Garrick's plant:
Actual height = 10 mmMeasured height = 8 mmZan's plant:
Actual height= 100 mmMeasured height = 88 mmGarrick's plant is shorter than Zan's plant and the difference in heights is
Actual difference = 100 mm - 10 mm = 90 mm
Measured difference = 88 mm - 8 mm = 80 mm
The percentage errors are calculated using
Percentage errors = Difference/Actual measurement * 100%
So, we have
Garrick's actual error = (10 - 8)/10 *100% = 20%
Zan's actual error = (100 - 88)/10 * 100% = 12%
Hence, Garrick's measurement was 20% off and Zan's was 12% off.
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Find the values of x and y.
The value of x is 5.
The value of y is 40°.
What is a triangle?It is a two dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
A composite figure that has three triangles.
Two equilateral triangles.
One isosceles triangle.
We see that,
Both equilateral triangles have the same sides and the same angles.
5x - 1 = 24
5x = 24 + 1
5x = 25
x = 5
We see that,
Let the opposite angle of 6y° = m
6y° + 60 + 60 + m = 360
6y + 120 = 360
6y = 360 - 120
6y = 240
y = 40°
Thus,
x = 5 and y = 40°
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1- For what values of x will the expression log x be undefined?
2- put the following in order from smallest to largest : log^2 16, log 100, log^3 30, log^5 40, log ^20 200
3- if you invested money into an account that pays 9% a compounded weekly, how many years would it take for your deposit to double?
9- The function S(d)= 86log d +112 relates the speed of wind, S, in miles per hour, near the centre of a tornado to the distance the tornado travels, d, in miles. Estimate the rate at which the speed of the wind at the centre of the tornado is changing the moment it has traveled its 50th mile.
When x0 x 0, log x is NOT defined (undefined). As a result, when x is in [(−∞,0]), log x is undefined.
1) We are aware that only when x is positive is a logarithmic function, log x, defined. i.e., x>0 . Therefore, when x0 x 0, log x is NOT defined (undefined). As a result, when x is in [(−∞,0]), log x is undefined.
2) Order from smallest to largest:
[tex]log^{200}_{20} < log 100 < log^{5}_{40} < log^{3}_{60} < log^{2}_{16}[/tex]
3)
[tex]\(2A=A(1+\frac{0.09}{52})^{n}\\\\ 2=(1+\frac{0.09}{52})^{n}\\\\ log2=log(1+\frac{0.09}{52})^{n}\\\\ log2=nlog(1+\frac{0.09}{52})\\\\ n=log2\div log(1+\frac{0.09}{52})\\\)[/tex]
log(2)/log(1+0.09/52 = 400.831511360387616 weeks
400.831511360387616/52 = 7.708298295392069538
7.7 years
Hence, It take 7.7 years for deposit to double.
4)
a)
[tex]S= 86 \ log d+112\\\\S= 86 log 50 +112\\\\S = 86*1.7+112\\\\S= 258.2[/tex]
S = 258.2 mph
b)
S = 258.2 mph ; find d
258 =86 log10 (d) + 112
146 = 86 log10 (d)
1.7 = log10 (d)
d = 50.118
Change from Log Form to Exponential Form
50.118 miles = d Rounded is 181 miles
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Paula bought a ski jacket on sale for $4 less than half its original price. She paid $89 for the jacket. What was the original price?
Which answer choice correctly represents an algebraic expression for 8 less than a number? i need help
The algebraic expression for 8 less than a number is x - 8
What is the algebraic expression for 8 less than a number?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations
Let the number be x.
The algebraic expression for 8 less than a number will be:
x - 8.
The expression is x - 8.
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Which integer represents the following situation:
The scuba diver is 30 feet below sea level.
Question 3 options:
A: -3
B: 33
C: 30
D: -30
Answer:
D. -30
Step-by-step explanation:
Let's say 0 is sea level. If the diver is 30 feet below 0, then they would by 30 below 0, or -30.
solve compound inequality -3a<6 or a-5<-2
The simplified form of the compound inequality - 3a < 6 Or a - 5< - 2
is a > 3 Or a < 3.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, - 3a < 6 Or a - 5< - 2.
∴ 3a > 6 Or a < - 2 + 5.
a > 6/3 Or a < 3.
a > 3 Or a < 3.
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The number of pages cameron reads varies directly with time in minutes. He can read 15 pages in 60 minutes. What is the constant of proportionality for the number of minutes to read 1 page.
The constant of proportionality is 0.25
What is Unitary Method ?Using the unitary approach, you can solve problems by first figuring out the value of a single unit, then multiplying that value by the number of units you need.
According to the given information
Applying Unitary Method
Pages have a direct relationship with time.
N ∝ t
N = k × t
k is constant of proportionality
Time taken to read 15 pages = 60 minutes
Time taken to read 1 page = [tex]\frac{15}{60}[/tex]
= 1/4
1/4 is constant of proportionality
k = 0.25
The constant of proportionality is 0.25
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As a young girl, Jennifer enjoyed watching her father make things in his woodworking shop.
Now that she's grown up, Jennifer builds wooden furniture for a living. Her most popular
product is a cedar porch swing.
There is a proportional relationship between the time (in days) Jennifer spends making porch
swings, x, and the number of swings she builds, y.
x (days) y (swings)5 1 10 2 15 3 20 4
What is the constant of proportionality? Write your answer as a whole number or decimal.
swings per day
Submit
Work it out
The constant of proportionality is 5 for the relation between x and y.
What is proportional relationship?
Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of the constant.
Given table is
x(days) 5 10 15 20
y(swings) 1 2 3 4
Since y is increasing with increase of days(x).
Thus the relation between y and x is in direct proportional.
Assume the relation be x ∝ y
x = ky, where k is constant proportionality.
Putting x = 5 and y = 1:
5 = k × 1
k = 5
Putting x = 10 and y = 2:
10 = k × 2
k = 5
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i need helpplsssssssssssssssssssssssssssssss−28+15=
Answer:
-13???
Step-by-step explanation:
Answer: −28+15=-13
Step-by-step explanation: -28 + 15 = -13
If you wanted information about a population, it could be impossible to ask everyone. One way to avoid asking everyone is to take a sample. There are many ways to take a sample, including a random sample.
Why might it be important to small subgroups of populations that you use a random sample?
The subgroup can be those who differ from the majority because of physical, ethnic, religious, or other differences. Include an example of a real-life situation that involves a subgroup that supports your response.
Read and reply to another student's post. Your reply should include questions and comments that add to the discussion. For example, you might point out additional reasons that subgroups benefit from random sampling, or how other subgroups might benefit in similar ways to those discussed in the post.
straightforward random sampling With simple random sampling (SRS), each sampling unit of a population has an equal chance of being included in the sample.
What is simple random sampling?In other words, by looking at a smaller sample, you can draw conclusions about a larger population. To find trends in a variety of fields, including business and finance, statistical analysis is frequently utilized. Findings from statistical research can be used by people to improve the decisions they make with regard to their finances, enterprises, and investments.Simple random samples are a common place for researchers to start. As a result, they are able to statistically analyze a sample of people drawn from a larger population or group to get a rough idea of how the entire group will respond.Both pros and cons apply to this research methodology. In this article, we present a brief description of simple random sampling and highlight its benefits and drawbacks.A simple random sample is one of the techniques researchers employ to select a sample from a bigger population.If there is an equal likelihood that any subject will be selected from a population, this strategy will work.In order to draw general conclusions about a group, researchers choose basic random sampling.The simplicity and impartiality of it are two major benefits.Time, money, and the fact that bias may still exist are some of the drawbacks. Another is the difficulty of obtaining a list of a wider population.To Learn more About simple random sampling refer to:
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Please help me quick please it’s proofs and am really stuck on this question !!!
Answer:
Step-by-step explanation:
hey buddy thts supper easy just match the d and b
In AABC and ADEF, mZA = 68°,
m/C= m/F = 59°, mZE = 53°, and
AB = DE = 8 units. Can you prove that
AABC = ADEF? If so, write a proof. If not,
explain why not.
Answer:
It is impossible to prove that AABC = ADEF with the information given. In order for us to prove that these two figures are congruent, we would need to know the measures of all the angles in both figures and the lengths of all the sides. Since we only have the measures of some of the angles and the lengths of two sides, we cannot prove that the figures are congruent.
Can you solve for 3 variables with 3 equations?
Yes, three equations are needed to find the values of three variables. Then only it will have a unique solution. The solution of three variable equation is also known as the ordered triple.
There must be 3 equations, If there are 3 variables.
Lets consider A,B,C as our equations and x, y, and z as the variables.
We will now follow these following steps:
1) By using C, first write z in terms of x and y. Then, Replace z with its equivalent in B.
2) Then write y in terms of x.
3) In A, replace y with its equivalent and replace z with its equivalent then solve A for x. Now you should know the value of x. You should have written y in terms of x so plug x and you will find y.
4)Finally, you should have written z in terms of x and y so you can find the value of z.
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two numeric variables x and y exhibit a negative correlation if a. the value of y tends to decrease as the value of x decreases. b. the value of y tends to increase as the value of x decreases. c. the value of y tends to increase as the value of x increases. d. the values of x and y always have the same difference.
If x and y are two numerical variables, they will have a negative correlation. As the value of x declines, the value of y tends to do the same.
Statistics uses the terms correlation or dependency to describe any statistical relationship between two random variables or bivariate data, regardless of whether it is causal or not. When two variables are negatively correlated, one drops when the other grows.Therefore, if the value of x decreases, the value of y will decrease as well.A negative correlation between x and y means that when x increases, y decreases, and when x decreases, y also decreases. This is expressed by the formula y = -x.
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Last week cam's ice cream shop sold 525252 chocolate chip ice cream cones out of a total of 997997997 ice cream cones. Based on this data, what is a reasonable estimate of the probability that the next ice cream cone sold is a chocolate chip ice cream cone?.
The probability that next ice cream cone sold is a chocolate chip ice cream cone is 0.052. The result is obtained by dividing the chocolate chip ice cream cone sold by the total ice cream from the previous week data.
What is probability?Probability is a numerical description of how possible an event to happen. Probability of an event can be expressed as
P(A) = n(A) / n(S)
Where
P(A) is the probability of an event An(A) is the number of favorable outcomesn(S) is the total number of events in the sampleThe previous week data shows that
The number of chocolate chip ice cream cones, n(A) = 52The number of ice cream cones, n(S) = 997To estimate the probability that will happen in the future, we use the data happened in the past.
The probability that the ice cream cone sold for chocolate chip variant is
P(A) = n(A) / n(S)
P(A) = 52 / 997
P(A) = 0.052
Hence, the probability of next selling a chocolate chip ice cream cone is 0.052.
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Answer: 52/997
Step-by-step explanation: I checked on khan
Write an equation in standard form that has a y-intercept at (0,-3) and also contains the point (4,5).
Answer:
Below
Step-by-step explanation:
Find the slope between the two given points
(y1-y2) / (x1-x2) <==== does not matter which you assign as point 1 or 2
(-3-5) / (0-4) = -8/-4 = 2
now set up equation using point-slope form (use either point)
y-5 = 2 (x-4) re-arrange
y -5 = 2x - 8
2x - y = 3
what is the value of - 1.4x2 - 6.7
Answer:
Step-by-step explanation: Are you talking about negative numbers? If so, the answer is -9.5
If you aren't talking about negative numbers, then your answer is -3.9
Hope this helps.
PLEASE HELP‼️‼️‼️ TRIGONOMETRIC FUNCTIONS‼️‼️‼️
Sides of the given Right angle Triangle are 7.5,12.5,10.
What are basic theorems of Right angle Triangle?The Pythagoras Theorem defines the relationship between a triangle's perpendicular, hypotenuse, and base. The right-angled triangle theorem is another name for this. The Pythagoras theorem states that a triangle is said to be right-angled if the sum of the squares of the perpendicular and base is equal to the square of the hypotenuse. It can be said in the following way:
If Angle equals 90° then Hypotenuse = Perpendicular∧2+ Base∧2.
The base is the side that the right angle is connected to, the neighboring side of the right angle is connected to the hypotenuse by the perpendicular, and the side that the angle is opposite to is known as the hypotenuse. The legs of the hypotenuse are another name for the base.
Calculation:Given
Tan(B) = [tex]\frac{3}{4}[/tex]=[tex]\frac{NE}{BE}[/tex]
⇒BE=10;
NB^2=NE^2+BE^2;
⇒NB^2=156.25
⇒NB=12.5
Sides of the given Right angle Triangle are 7.5,12.5,10.
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Find all the zeros of the given function. State the multiplicity (If larger than 1)
#1. g(x)=2x^4 + 15x^3 - 17x^2 - 159x + 63
#2. h(x)=x^4 + 3x^3 + 8x^2 + 28x + 32
Answer:
#1. The zeros of the function g(x) are −3/2, 1, and 3 (all with multiplicity 1).
#2. The zeros of the function h(x) are −1 and −2 (both with multiplicity 2).
If you apply the following
translation:
(x, y) → (x + 3, y − 2)
to the point (0, 1), what are the
resulting coordinates?
Answer:
(3,-1)
Step-by-step explanation:
you have a graph and poin is (0,1) you have 0+3 to make 2 on the horizontil line and they y = -2 so you go down 2 to make (3,-1)
Answer:
(3, -1)
Step-by-step explanation:
Graphical TranslationGraphical Translation is about shifting the coordinates by a certain value towards the left/down (x and y coordinates respectively) for negative signs and towards the right/up (x and y coordinates respectively) for positive signs.
Eg. x is shifted by + 3 units, y is shifted by - 1 unit from the point (9 , 3) , the resulting coordinate will be:
(9 + 3, 3 - 1) = (12, 2)
SolutionGiven from the question:
x is shifted by + 3 units and y is shifted by - 2 units,
Therefore, the resulting coordinates will be:
(0 + 3, 1 - 2) = (3, -1).
11.
As of 1995, the human population was expected to double within 50 years. If we calculated r for the human population, we would get 1.39.
True
False
The answer is false just took the exam.
As of 1995, the human population was expected to double within 50 years. If we calculated r for the human population, we would get 1.39. statement is False.
To determine whether the statement is true or false, we need to calculate the doubling time (DT) based on the given growth rate (r) and see if it aligns with the expected doubling time of 50 years.
The formula to calculate the doubling time (DT) for a population with a constant growth rate (r) is:
DT = ln(2) / r
where ln is the natural logarithm (base e).
If the expected doubling time is 50 years, then:
DT = 50 years.
Now, we can calculate the value of r:
r = ln(2) / DT
Plugging in the values:
r = ln(2) / 50 ≈ 0.01386
Comparing the calculated value of r (approximately 0.01386) with the given value of 1.39, we can see that they are not the same.
Therefore, the statement is False. The calculated value of r (0.01386) does not match the given value of 1.39, and it would not result in the human population doubling within 50 years. In reality, with a growth rate of 1.39, the population would grow at an unsustainable rate, leading to an even faster increase in population over time.
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which dimconstraint option allows you to create a dimensional constraint that has extension lines perpendicular to an angled surface?
Aligned Dim constraint option allows you to create a dimensional constraint that has extension lines perpendicular to an angled surface.
What are constraints?In CAD software, a constraint is a restriction or limitation placed on geometric properties by a designer or engineer: An entity in a design model that keeps its structure when the model is altered is referred to as type 203. In addition to relative length and angle, these properties may also include size, shift, and displacement.
The term "plural form constraints" refers to the delineations of geometrical characteristics between two or more entities or solid modelling bodies; these delimiters are definitive for properties of hypothetical physical position and motion, or displacement in parametric design. However, a CAD programme vendor may use different terminology than another.
CAD software for solid modelling, computer-aided architectural design (including building information modelling), computer-aided engineering, assembly modelling, and other CAD subfields frequently uses constraints.
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suppose that a and b are independent events with p(a) 5 .5 and p(b) 5 .6. can a and b be mutually exclusive events?
Yes, Since a and b are independent event then therefore, a and b are mutually exclusive events.
P(a) +P(b) = 0.5+0.5
therefore, P(a ∪b) = 1.0
Mutually exclusive events are events that do not occur at the same time. For example, when you toss a coin, the result is either heads or tails, but you cannot get both results. Such events are also called disjoint events because they do not occur at the same time. If A and B are mutually exclusive events, their probabilities are given by P(A or B) or P(A U B).
According to the question:
P(a) = 0.5 and P(b)=0.5
therefore,
P(a) +P(b) = P(a ∪ b)
⇒ 0.5 +0.5 = 1.0
Therefor a and b are mutually exclusive events.
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9) y=3x+1
y=1/3x + 1
Answer:
y = 3 ; x = -3
Step-by-step explanation:
[x + 1 x y = 1/3x + 1] y = 3
SUBSTITUTE
[ x + 1 x 3 = 1/3x + 1
SIMPLIFY
[ x + 3 = 1/3x + 1]
ISOLATE X FOR X + 3 = 1/3X + 1: X = -3
100 passengers board an airplane with exactly 100 seats. everyone has a ticket with an assigned seat number. however, the first passenger has lost their ticket and takes a random seat. every subsequent passenger attempts to choose their own seat, but takes a random seat if theirs is taken. suppose you are the very last passenger to board the plane. what is the probability that you will get your assigned seat?
Thus , probability of very last passenger getting seat comes out to be
P = 0.5 .
What is the process of probability?
Mathematics' field of probability deals with numerical representations of the possibility that an event will take place or that a statement is true. An event's probability is a number between 0 and 1, with 1 generally denoting certainty and 0 generally denoting impossibility.
Here,
If everyone chose at random, you would only have a 1/100 chance of receiving your own seat on a plane with 100 seats. However, in the context of this riddle, each participant does not make a random selection; rather, they only do so if all available seats have been occupied.
This indicates that half of the scenarios will resolve themselves (i.e., someone takes the mystery ticket holder's assigned seat allowing every subsequent passenger to take their assigned seat), while the other half will not resolve themselves and you will be seated in the incorrect location, making the probability of any plane occupancy equal to half.
Thus , probability of very last passenger getting seat comes out to be P = 0.5 .
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consider the data set below. what are the factors? what is the response variable? how many levels of factor a are there and how many levels of factor b are there? what is the value of n (replicates per combination or treatment)?
Data set: Factor A: Brand of Car Factor B: Type of Fuel Response Variable: Fuel Efficiency Levels of Factor A: 4 (Toyota, Honda, Ford, Chevrolet) Levels of Factor B: 2 (Gasoline, Diesel) Value of n: 3 (3 replicates per combination or treatment)
The data set has two factors: Brand of Car and Type of Fuel. The response variable is Fuel Efficiency, which is the value that is being measured in response to the two factors. There are four levels of Factor A (Toyota, Honda, Ford, Chevrolet) and two levels of Factor B (Gasoline, Diesel). Finally, the value of n is 3, meaning there are 3 replicates or treatments per combination of the two factors.
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