The equation of a line that passes through points (a,b) and (c,d) is (c-a)y = (d-b)x+b(c-a)-a(d-b).
What is equation of line?A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.
The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
Let the two points are (a,b) and (c, d)
To find the equation of line,
Use formula y- y₁ = (y₂-y₁/x₂-x₁) (x-x₁)
The equation of line,
y-b = (d-b/c-a)(x-a)
(c-a)(y-b) = (d-b)(x-a)
(c-a)y = (d-b)x+b(c-a)-a(d-b)
The required equation of the line is (c-a)y = (d-b)x+b(c-a)-a(d-b).
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What is an equation of the line that passes through the points (−7,−5) and (−4,−5)?
Answer:
y = -5
Step-by-step explanation:
The two points have the same y: it means that the line is parallel to x axis
Answer:
The slope of the given line is -3/2
Parallels have equal slopes
The new line y + 5 = (-3/2) (x - 4)
y + 5 = (-3/2)x + 6
y = (-3/2)x + 1
answer= y = (-3/2)x + 1
A freight train traveling along a certain route uses 12 units of fuel per mile plus an additional 2.2
units of fuel per mile for each railcar on the train.
Let N represent the number of railcars on the train. What is an expression for f (N), the total number
of units of fuel used per mile?
The total unit of fuel used per mile f (N)= 12+ 2.2N
What is a linear function?A linear function has the following form
y = f (x) = a + bx
A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
The graph of a linear function is a straight line.
The train uses 12 unit of fuel per mile and an additional 2.2 unit of fuel per mile for each railcar on the train.
Therefore the unit of fuel used per mile by N railcars is 2.2N
The total number of unit of fuel used per mile = 12+2.2N
therefore f(N)= 12+2.2N
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When checking for scene safety for the use of an AED Which of these best describes the dangers that would stop us?.
When checking for scene safety for the use of an AED the dangers that would stop us include
Combustible liquids close to the sufferer, flammable gases, a patient resting in standing waterWhat is an AED?An automated external defibrillator (AED) is a small, portable machine that shocks the heart with electricity through the chest.
After a sudden cardiac arrest (SCA), the shock may be able to stop an irregular heartbeat (arrhythmia) and restore a regular rhythm .
SCA happens when the heart develops a problem and abruptly stops beating. Without immediate treatment, it quickly results in death.
The dangers that would stop us from using a scene for an AED include
volatile gases, combustible liquids near the patient, and a patient lying in water
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Is mean absolute deviation the same as mean?.
The Mean absolute deviation and the mean are not same.
Given,
The mean;-
The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
Mean absolute deviation;-
The average distance between each data point and the mean is known as the mean absolute deviation of a dataset. It offers us a sense of how variable a dataset contains.
Therefore,
The Mean absolute deviation and the mean are not same.
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Would you use SSS or SAS to prove the triangles congruent?.
Answer:
SSS (side-side-side) and SAS (side angle side) both prove that two triangles are congruent, it depends on the data you have whether to use one or the other
a trophy company is setting up a nickel plating cell using an electrolyte containing nickel (iii) ions. predict the current required to produce metal at a rate of 5.00 g/min.
The current required to produce metal at a rate of 5.00 g/min is 274A
How to find the current in an electrolyte?The electrolyte ion equation is;
Ni²⁺ (aq) + 2e⁻ → Ni (s)
Faradays constant = 9.65 * 10⁴ C/mol
Molar mass of Nickel = 58.69 g/mol
Number of moles of nickel; n_ni = 5 g/min * 1 mol/58.69 g/mol = 0.0852 mol
n_e = 0.0852 mol * 2/1
n_e = 0.170 mol
I = nF/t
where;
t is in minutes
F is faradays' constant
Thus;
I = (0.17 * 9.65 * 10⁴)/(1 * 60)
I = 274 A
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Please answer this question.
Answer:
biggest size = 89 in ; smallest size = 30 in
Step-by-step explanation:
Tmax = 2 x 132 / 3 + 1
2 x 44 + 1
88 + 1
89 in
Tmin = 132/4 - 3
33 - 3
30 in
How do you find the x and y intercepts of an equation to find the x-intercept substitute 0 for X to find the y-intercept substitute 0 for X?.
Substitute 0 for y to find the x-intercept and Substitute 0 for x to find the y-intercept.
This is obvious because if y is set to 0, the only variable left is x (indicating that the x intercept has been found), and vice versa.
We set y = 0 and solve the equation for x to find the x-intercept. This is because the line crosses the x-axis when y=0. When an equation is not in the form y = mx + b, we can solve for the intercepts by plugging in 0 and solving for the remaining variable. Set x = 0 and solve for y to find the y-intercept.
The line crosses the x-axis when y=0. When an equation is not in the form y = mx + b, we can solve for the intercepts by plugging in 0 and solving for the remaining variable. Set x = 0 and solve for y to find the y-intercept.
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T/F according to semistrong form efficiency, an analyst who finds some unique information buried in a firm's published financial statements will be at an advantage to the rest of the market
On the basic of properties of Semi Strong form efficiency, we conclude the given statement that According to the Semi- strong form of efficiency, analysts who find unique information hidden in a company's published financial statements have an advantage over the rest of the market is False.
Semi Strong form :
The efficiency theory of the semi-strong format uses all publicly available information when calculating the current price of a stock, allowing investors to use either technical or fundamental analysis to find the best value in the market. We follow the belief that no higher return can be generated.
Those who agree with this version of theory believe that only information not available to the public can help investors drive returns to higher levels of performance than the general market. To test the semi -strong version of EMH, we can see if the stock price fluctuates up or down if private his message has been published before. For example, proposed mergers and ambiguous earnings announcements are known to insiders but not to the public. Therefore, this information will not be correctly reflected in the stock price until it is published. At this point, investors and traders take this new information into account, so the stock may bounce or fall depending on the nature of the news.
From the semi-strong efficiency information above, we can say that the information hidden in the company's published financial statements does not benefit the rest of the market.
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Please help me with this work it’s statements and reasons
The proof of ∠WVY = ∠XVZ for the given angles in the figure has been proved.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
In another word, the angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.
As per the given,
∠WVX = ∠YVZ
Since,∠WVX = ∠WVY - ∠YVX
∠YVZ = ∠XVZ - ∠YVX
Compare both,
∠WVY - ∠YVX = ∠XVZ - ∠YVX
∠WVY = ∠XVZ (proved)
Hence "The proof of ∠WVY = ∠XVZ for the given angles in the figure has been proved".
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Aven wants to buy a car in 4 years and needs a down payment of $2500. If she deposits $2000
now, with interest compounded continuously, what interest rate will she need to get her down
payment in time?
She needs to get her interest rate at will 5.592 %/year.
What is Compound interest?
Compound interest is the addition of interest to the principal sum of a loan or deposit or interest on interest plus interest.
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where,
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest is applied per time period
t = number of time periods elapsed
Solving for rate r as a decimal
r = n[(A/P)1/nt - 1]
r = 12 × [(2,500.00/2,000.00)1/(12)(4) - 1]
r = 0.0559158
Then convert r to R as a percentage
R = r * 100
R = 0.0559158 * 100
R = 5.592%/year
Hence, she needs to get her interest rate at will 5.592 %/year.
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you have set up a netflow collector using ip address 172.17.8.25 on udp port 2055. which of the following commands will redirect records to the new collector?
ip flow-export destination 172.17.8.25 2055 is the set up a netflow collector using ip address 172.17.8.25 on udp port 2055.
What is netflow collector?
A NetFlow-enabled router or switch can record statistical, infrastructural, routing, and other information about IP traffic flows using the NetFlow protocol, which was created by Cisco Systems. One of the three typical functional elements used for NetFlow analysis.A NetFlow exporter is a router, switch, probe, or host software agent that tracks important statistics and other information about IP packet flows and creates flow records that are delivered to a flow collector in the form of UDP packets.An application called NetFlow Collector is in charge of accepting flow record packets from one or more flow exporters, ingesting the data from the flow records, pre-processing and storing flow records.Hence, the ip flow-export destination 172.17.8.25 2055 is the set up a netflow collector using ip address 172.17.8.25 on udp port 2055.
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3) What is the value of the slope of the line
that passes through the points (3, 10) and
(4, 12)? Show all work.
The slope of the line is 2.
From the question, we have
the slope of the line that passes through two points is given by:
m = (y1 - y2) / (x1 - x2)
=(10-12)/(3-4)
=2
The slope of the line is 2.
Slope of a Line :
The ratio of the change in the y coordinate to the change in the x coordinate is known as a line's slope in mathematics.
Y and X, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate.
As a result, the formula for the change in y-coordinate with respect to the change in x-coordinate is m = change in y/change in x = y/x.
where the slope of a line is denoted by "m".
The graph of the equation y = mx + c has a slope of m, an intercept of m, and a y-intercept of c. In the slope-intercept version of the linear equation, m and c are real integer values.
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The slope of a line is -. find the slope of a line that is perpendicular to this line. -3 3
The required slope of line perpendicular to the given line is 1/3.
What are perpendicular lines and its slope?perpendicular lines have slants that are negative reciprocals of each other. The given line's incline is 5, and that implies that the slant of the other line should be its negative equal. Angle between perpendicular lines is 90 degree.
According to question:Slope of first line (m) = -3
let the slope of other line is n,
then, we know that
m×n = -1
-3×n = -1
n = 1/3
Thus the slope onother line is 1/3.
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Answer:
1/3
Step-by-step explanation:
suppose x is a binomial random variable with parameters n and p given below. compute the indicated probability in each of these cases. a) If n=4n=4 and p=0.4p=0.4 then P(X=0)=P(X=0)= . b) If n=4n=4 and p=0.1p=0.1 then P(X=4)=P(X=4)= . c) If n=5n=5 and p=0.1p=0.1 then P(X=0)=P(X=0)= . d) If n=3n=3 and p=0.3p=0.3 then P(X=0)=P(X=0)=
The probability of each of these cases when binomial random variable with parameters n and p are given:
a. 0.4116, b. 0.5625, c. 0.329, d. 0.375, e. 0.0046
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
Here,
The formula is,
P(x)=(n/x)(P)ˣ(1-P)ⁿ⁻ˣ
a. n=4, x=1, p=0.3
P(x)=0.4116
b. n=2, x=0, p=0.25
P(x)=0.5625
c. n=5, x=2, p=0.33
P(x)=0.329
d. n=4, x=2, p=0.5
P(x)=0.375
e. n=3, x=3, p=1/6
P(x)=0.0046
When a binomial random variable with parameters n and p is given, the probability of each of the following cases is given is: a. 0.4116, b. 0.5625, c. 0.329, d. 0.375, and e. 0.0046
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(1 point) how many anagrams can be created from the word 'accommodate' if the new words do not need to be meaningful?
The anagrams that can be created from the word accommodate is N=4989600.
What is meant by anagram?An anagram is a word or phrase made by rearranging the letters of another word or phrase, often using all of the original letters exactly once.
The original word or phrase is known as the anagram's subject. An anagram is any word or phrase that exactly duplicates the letters in a different order. An "anagrammatist" is someone who makes anagrams, and the purpose of a serious or expert anagrammatist is to make anagrams that reflect or remark on their subject.
Given word is
'accommodate'
Total number of letters= 11
Number of a = 2
c=2
m=2
0=2
The rest are one each.
Therefore, the number of possible arrangements can be written as;
N = 11!/(2!2!2!2!)
N = 39916800/8
N=4989600
Therefore, the anagrams that can be created from the word accommodate is N=4989600.
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In a random series, successive observations are probabilistically independent of one another. If this property is violated, the observations are said to be:
If this property is violated, the observations are said to be: autocorrelated
What is Random Series?
The results of an experiment are functions of an integer argument, and the results are described by a random series: U1, U2.. (or, simply, sequences of random values - 1st value, 2nd value, etc).
The term "time series" and, occasionally, "random processes with discrete time" are frequently used to describe random series. The Markov chain exemplifies a crucial category of random series.
In this question, it's asked when the property of independence is violated.
If the consecutive observations are correlated or linearly related, then they are said to be autocorrelated. This denotes that there will be an association of the current time period with the successive and preceding time periods. Violation of the autocorrelation assumption yields inaccurate results.
Hence, The observations are said to be: autocorrelated in the random series.
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What is the solution to the equation 3 m 3 m 3 m/m2 9 m2 9?.
This equation [tex]\frac{3}{m + 3}[/tex] - [tex]\frac{m}{3 - m}[/tex] = [tex]\frac{m^{2 } + 9}{m - 9}[/tex] has no solution.
Since we have given that
[tex]\frac{3}{m + 3}[/tex] - [tex]\frac{m}{3 - m}[/tex] = [tex]\frac{m^{2 } + 9}{m - 9}[/tex]
We need to find the solution of the above equation:
Since is a rational equation so, we will check for its extraneous solution.
[tex]\frac{3}{m + 3}[/tex] - [tex]\frac{m}{3 - m}[/tex] = [tex]\frac{m^{2 } + 9}{m - 9}[/tex]
[tex]\frac{3}{m + 3}[/tex] + [tex]\frac{m}{3 - m}[/tex] = [tex]\frac{m^{2 } + 9}{m - 9}[/tex]
[tex]\frac{3(m + 3) + m(m +3)}{m^{2} - 9}[/tex] = [tex]\frac{m^{2 } + 9}{m - 9}[/tex]
[tex]\frac{3m - 9 + m^{2} +3m }{m^{2}-9 }[/tex] = [tex]\frac{m^{2 } + 9}{m - 9}[/tex]
[tex]\frac{m^{2} -9+6m}{m^{2} -9}[/tex] = [tex]\frac{m^{2 } + 9}{m - 9}[/tex]
[tex]m^{2} +6m -9 = m^{2} + 9[/tex]
[tex]6m = 18[/tex]
[tex]m = \frac{18}{6} = 3[/tex]
Hence, the extraneous solution in case of rational equation is 3 , when we put m = 3, it becomes undefined so, it has no solution.
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What is the approximate average rate of change of the function f(x)=50(1.021)^x over the interval of x=7 to x=10
The average rate of change of the function, f(x)=50(1.021)^x over the interval of x=7 to x=10 is calculated as: 1.24.
How to Find the Average Rate of Change of a Function?The average rate of change = f(b) - f(a) / b - a.
Given the following:
The function is: f(x) = 50(1.021)^x
Interval is: x = 7 to x = 10
Therefore:
a = 7
b = 10
f(a) = f(7) = 50(1.021)^7
f(a) = f(7) = 57.83
f(b) = f(10) = 50(1.021)^10
f(b) = f(10) = 61.55
Therefore:
Average rate of change = (61.55 - 57.83) / 10 - 7
= 1.24.
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A random sample of 40 ucf students has a mean electricity bill of $110. Assume the population standard deviation is $17. 90. Construct a 90% confidence interval for the mean electricity bill of all ucf students. Round final answer to two decimal places. No $ needed in your answer.
Using the t-distribution, it is found that the 90% confidence interval for the mean electricity bill of all ucf students is (108.79, 121.21).
It is referred to as the simple random sampling technique when each member of a population has an equal likelihood of being chosen. This sampling technique relies solely on chance to determine the selection. A random number generator or any other approach that relies solely on chance can be used to carry out such a sampling strategy.
Using the t-distribution, it is found that the 90% confidence interval for the mean electricity bill of all ucf students is (105.25, 114.75).
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The function g(x) is a transformation of the parent function f(x). Decide how
f(x) was transformed to make g(x).
f(x)
g(x)
x
-2
-1
2
لیا
у
619
9
-13
9
27
81
-2
-1
2
3
4
9
3
110
27
81
OA. Horizontal or vertical stretch
B. Horizontal or vertical shift
C. Horizontal or vertical reflection
D. Reflection across the line y=x
f(x) was transformed to make g(x) by B) Horizontal or vertical stretch.
How does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
Given that the function g(x) is a transformation of the parent function f(x).
To Decide how f(x) was transformed to make g(x).
The reflection of the point (x,y) across the line y = 1/2 x is the point (y, x).
By the given tables we can see that;
g(x) = 1/2 f (x)
Therefore, f(x) was transformed to make g(x) by B) Horizontal or vertical stretch.
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-
12-
Speed
(metres per
second)
0
1
Time (minutes)
5
A tram leaves a station and accelerates for 2 minutes until it reaches a speed of 12 metres per
second.
It continues at this speed for 1 minute.
It then decelerates for 3 minutes until it stops at the next station.
The diagram shows the speed-time graph for this journey.
Calculate the distance, in metres, between the two stations.
In meters
The value of the total distance between the two stations is 2520m
How to calculate distance in meters ?The train runs with the following acceleration:
v = u + at
12 = 0 + a(120)
a = 0.1 m/s2.
Distance covered by the train in first part:
S = 1/2at^2
S = 1/2×0.1×(120)^2
S = 720m
Distance covered in second part:
S = ut
S = 12×60 = 720m
Train deceleration is given by
v = u+ at
0 = 12+a (180)
a = -1/15
Distance covered by the train in last part:
S = ut- 1/2at^2
S = 12(180) - 1/2(1/15)(180)^2
S = 2160 - 1080
S = 1080m
Therefore, The value of the total distance between the two stations is 720+720+1080 = 2520m.
The complete question is :A tram leaves a station and accelerates for 2 minutes until it reaches a speed of 12 meters per second. It continues at this speed for 1 minute. It then decelerates for 3 minutes until it stops at the next station .Calculate the distance, in meters, between the two stations.
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write 60:52 in the form n:1.
Converted form of ratio 60:52 in form n:1 is 10/7 : 1.
How to write a ratio in n:1 form?
In order that a ratio is written in the form n:1 we must make the right hand side equal to one.
n can be expressed as a decimal or a fraction.
According to the given question:
Convert ratio 60:52 in n:1 form
So, divide both sides of ratio with 52 to get 1 on right side of ratio.
60/52 : 1
10/7 : 1
Hence 10/7 : 1 is the converted form.
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Which is not a power function?.
A function containing a variable base raised to a fixed power is considered to be a power function.
when a function has a constant base raised to a variable power. This can be called an exponential function, not a power function A power function may be a function with a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real number. It is in the form of f(x)=kx^p, where k and p are the real numbers whereas k is the coefficient.
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Eden and Kember are reading the same book. Eden says she has read 1/6 of the book.
Kimber says she has read 32 more pages than Eden. If Kimber is on page 60, how many pages
are there in the book?
In given word problem , number of total pages in the book is 168.
What is word problem?
Word problems in mathematics that concentrate on addition, subtraction, multiplication, and division, among other more precise operations A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.
Here Eden and Kember are reading the same book.
Here Eden reads 1/6 pages of the book. And Kimber reads,
=> 1/6(total pages)+32 which is 60.
=> 1/6(x)+32=60
=>1/6(x)=60-32=28
=> x = 28*6
=> x = 168.
Therefore total number of page in the book is 168.
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What does adding doubles mean?.
Adding doubles mean that the result will be obtained by adding 2 times of the numbers.
According to the question,
We have the following information:
We have to know what does it mean to add doubles.
Now, we know that doubles mean that the same number is added two times or in other words it has been multiplied by 2.
For example, the double of 3 is 6 and the double of 4 is 8 because we have multiplied both the numbers by 2.
Now, adding the doubles of 3 and 4 means that we will add 6 and 8 and the result in this case is 14.
Hence, adding doubles mean that the result will be obtained by adding 2 times of the numbers.
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a 16-ft. ladder is leaning against a house. the ladder angle of elevation is 470. how far above the ground is the top of the ladder?
a 16-ft. ladder is leaning against a house. the ladder angle of elevation is 470, the distance between the wall and the foot of the ladder is 10.991ft.
Given ,
Length of the ladder is 16ft
Angle of elevation is 47 degree
To calculate the distance between the wall and the foot of the ladder
Cos thete = BC/AC
Cos 47 deg = BC / 16
16*0.6819 = BC
BC = 10.911 ft
Therefore , the distance between the wall and the foot of the ladder is 10.991ft
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What is the length of BC?.
the length of BC is 10cm, in the given triangle.
What is are of the triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
Assuming that BR = 3 cm AR = 4 cm AC = 11 cm
Knowing that tangents to an exterior point are always equal,
BR = BP = 3 cm then.
4 cm when AR = AQ
QC= AC- AQ= 11 - 4 = 7 cm
Q = P = 7 cm
As a result, BC = BP+PC = 3 + 7 = 10 cm.
As a result, BC has a 10 cm length.
Hence the length of BC is 10cm.
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Python py 9.14 lab: triangle area comparison (classes) given class triangle, complete the program to read and set the base and height of triangle1 and triangle2, determine which triangle's area is larger, and output the larger triangle's info, making use of triangle's relevant methods. ex: if the input is: 3.0 4.0 4.0 5.0 where 3.0 is triangle1's base, 4.0 is triangle1's height, 4.0 is triangle2's base, and 5.0 is triangle2's height, the output is: triangle with larger area: base: 4.00 height: 5.00 area: 10.00 code---------------------------------------- class triangle: def __init__(self): self.base = 0 self.height = 0 def set_base(self, user_base): self.base = user_base def set_height(self, user_height): self.height = user_height def get_area(self): area = 0.5 * self.base * self.height return area def print_info(self): print('base: {:.2f}'.format(self.base)) print('height: {:.2f}'.format(self.height)) print('area: {:.2f}'.format(self.get_area())) if __name__ == "__main__": triangle1 = triangle() triangle2 = triangle()
The full Python code is included below as an image, and it sets the base and height of triangles 1 and 2, then calculates the bigger area.
What is Python code?The program sets the bases and heights of both triangle objects using the set base() and set height() methods.The triangle with the largest area is then identified and printed using an if statement. The results of calling both triangles' get area() methods are used to calculate the area information.The print info() method is used to print out details about the triangle with the larger area once the larger area has been obtained.The full Python code is included below as an image, and it sets the base and height of triangles 1 and 2, then calculates the bigger area.To learn more about Python code refer to:
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the continuous random variable n has a normal distribution with mean 7.5 and standard deviation 2.5. for which of the following is the probability equal to 0 ?
Using the normal distribution we find that P(X=8) equals zero.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome.According to our question-
Measures how many standard deviations a measurement is from its mean.
After finding the Z-score, look at the Z-score table to find the p-value (percentile of x) associated with that Z-score.
As with any continuous distribution, the probability of an exact value, P(X = x), is 0.
So t we know that P(X=8) equals zero.
Hence, Using the normal distribution we find that P(X=8) equals zero.
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