Write the fraction 28/21 in its simplest
1 answer:
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I'll do a similar problem, and I challenge you to do this on your own using similar methods!
x+5y+2z=23
8x+4y+3z=12
9x-3y-7z=-10
Multiplying the first equation by -8 and adding it to the second one (to get rid of the x) and also multiplying the first equation by -9 and adding the third one to get rid of the x there too, we end up with
-36y-13z=-92
and
-48y-25z=-217
Multiplying both equations by -1, we get
36y+13z=-92
48y+25z=217
Multiplying the (new) first equation by -4/3 and adding it to the second (to get rid of the y), we get
(7+2/3)z=94+1/3
Dividing both sides by (7+2/3) to separate the z, we get
z=
Plugging that into
48y+25z=217, we can subtract 25z from both sides and divide by 48 to get
Lastly, we plug this into x+5y+2z=23 to get
x=23-5y-2z by subtracting 5y+2z from both sides to get
Good luck, and feel free to ask with any questions!
x+5y+2z=23
8x+4y+3z=12
9x-3y-7z=-10
Multiplying the first equation by -8 and adding it to the second one (to get rid of the x) and also multiplying the first equation by -9 and adding the third one to get rid of the x there too, we end up with
-36y-13z=-92
and
-48y-25z=-217
Multiplying both equations by -1, we get
36y+13z=-92
48y+25z=217
Multiplying the (new) first equation by -4/3 and adding it to the second (to get rid of the y), we get
(7+2/3)z=94+1/3
Dividing both sides by (7+2/3) to separate the z, we get
z=
Plugging that into
48y+25z=217, we can subtract 25z from both sides and divide by 48 to get
Lastly, we plug this into x+5y+2z=23 to get
x=23-5y-2z by subtracting 5y+2z from both sides to get
Good luck, and feel free to ask with any questions!
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Answer:
A- Triangle 2: {8, 15, 17}
Step-by-step explanation:
You may recognize that the triple of choice A is a Pythagorean triple, so can be the side lengths of a right triangle.
Checking the numbers can be done nicely by a graphing calculator or spreadsheet to help avoid the tedium of doing it "by hand".
The basic idea is that the triangle will be a right triangle if the sum of the squares of the shorter sides is the square of the longer side.
Complete Question
The mean finish time for a yearly amateur auto race was 186.94 minutes with a standard deviation of 0.305 minute. The winning car, driven by Roger, finished in 185.85 minutes. The previous year's race had a mean finishing time of 110.7 with a standard deviation of 0.115 minute. The winning car that year, driven by Karen, finished in 110.48 minutes.
Find their respective z-scores.
Who had the more convincing victory?
A. Roger had a more convincing victory because of a higher z-score.
B. Karen a more convincing victory because of a higher z-score.
C. Roger had a more convincing victory, because of a lower z-score.
D. Karen a more convincing victory because of a lower z-score.
Answer:
The correct option is D
Step-by-step explanation:
From the question we are told that
The mean of the current year is
The standard deviation is
The time taken by the winning car for the current year is
The mean of the previous year is
The standard deviation the previous year is
The time taken by the winning car for the previous year is
Generally the z-score for current year is mathematically evaluated as
=>
=>
Generally the z-score for previous year is mathematically evaluated as
=>
=>
From the value obtained we see that , Hence Karen had a more convincing victory because of the lower z -score.