Answer:
7.5(3(7) + 4)= 187.5
Step-by-step explanation:
Answer:
you would be dead
Step-by-step explanation:
Answer:
The range in which 90% of class will fall will be (40.2,89.67)
Step-by-step explanation:
Since the grades are normally distributed to obtain most possible range of grades obtained by the class we shall find the range of marks that give an area of 90% distributed equally about mean
These numbers shall correspond to
![Z_{1}=-1.6449\\\\Z_{2}=1.6449](https://tex.z-dn.net/?f=Z_%7B1%7D%3D-1.6449%5C%5C%5C%5CZ_%7B2%7D%3D1.6449)
![Z_{1}=\frac{X-\bar{X}}{\sigma }\\\\X_{1}=\sigma Z_{1}+\bar{X}\\\\\therefore X_{1}=-1.6449\times 15+65\\X_{1}=40.32\\Similarly\\\\X_{2}=\sigma Z_{2}+\bar{X}\\\\X_{2}=1.6449\times 15+65\\X_{2}=89.67](https://tex.z-dn.net/?f=Z_%7B1%7D%3D%5Cfrac%7BX-%5Cbar%7BX%7D%7D%7B%5Csigma%20%7D%5C%5C%5C%5CX_%7B1%7D%3D%5Csigma%20Z_%7B1%7D%2B%5Cbar%7BX%7D%5C%5C%5C%5C%5Ctherefore%20X_%7B1%7D%3D-1.6449%5Ctimes%2015%2B65%5C%5CX_%7B1%7D%3D40.32%5C%5CSimilarly%5C%5C%5C%5CX_%7B2%7D%3D%5Csigma%20Z_%7B2%7D%2B%5Cbar%7BX%7D%5C%5C%5C%5CX_%7B2%7D%3D1.6449%5Ctimes%2015%2B65%5C%5CX_%7B2%7D%3D89.67)
The simplified equation of 7y + 8 = 9 + 3y + 2y is 2y = 1
<h3>How to simplify an equation?</h3>
The equation can be simplified as follows:
7y + 8 = 9 + 3y + 2y
We have to combine like terms
Hence,
7y + 8 = 9 + 3y + 2y
7y + 8 = 9 + 5y
subtract 5y from both sides
7y - 5y + 8 = 9 + 5y - 5y
2y + 8 = 9
Let's subtract 8 from both sides
2y + 8 - 8 = 9 - 8
2y = 1
Therefore, the simplified equation of 7y + 8 = 9 + 3y + 2y is 2y = 1
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Hence, the numbers are 16 and 4
<u>Further Explanation:</u>
First of all we have to make the equations from the word problem.
Let x be the first number and y be the second number.
Then,
The sum of two numbers is 20 => x + y = 20 => Eqn 1
The difference between three times the first number and twice the second is 40 => 3x-2y = 40 => Eqn 2
![From\ Eqn\ 1\\x+y=20\\y = 20-x\\Putting\ y=20-x\ into\ Eqn\ 2\\3x - 2(20-x) = 40\\3x-40+2x = 40\\5x-40 = 40\\5x = 40+40\\5x = 80\\\frac{5x}{5} = \frac{80}{5} \\x = 16\\y = 20-x\\y=20-16\\y = 4](https://tex.z-dn.net/?f=From%5C%20Eqn%5C%201%5C%5Cx%2By%3D20%5C%5Cy%20%3D%2020-x%5C%5CPutting%5C%20y%3D20-x%5C%20into%5C%20Eqn%5C%202%5C%5C3x%20-%202%2820-x%29%20%3D%2040%5C%5C3x-40%2B2x%20%3D%2040%5C%5C5x-40%20%3D%2040%5C%5C5x%20%3D%2040%2B40%5C%5C5x%20%3D%2080%5C%5C%5Cfrac%7B5x%7D%7B5%7D%20%3D%20%5Cfrac%7B80%7D%7B5%7D%20%5C%5Cx%20%3D%2016%5C%5Cy%20%3D%2020-x%5C%5Cy%3D20-16%5C%5Cy%20%3D%204)
The numbers can be verified:
![x+y = 20\\16+4 =20\\20=20\\](https://tex.z-dn.net/?f=x%2By%20%3D%2020%5C%5C16%2B4%20%3D20%5C%5C20%3D20%5C%5C)
As the equation is verified by the values of x and y.
Hence, the numbers are 16 and 4
<u>Keywords:</u> Linear equations, Substitution method to solve equations
<u>Learn More at:</u>
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