How many solutions does the equation 6y - 3y -7 = -2 +3 have?

Mathematics

1 answer:

kenny6666 [7]3 years ago

8 0

Answer:

6y - 3y - 7 = -2 +3

Simplify both sides:

3y -7 = 1

Add 7 to both sides:

3y = 8

Divide both sides by 3:

y = 8/3 = 2 2/3

There is only one solution.

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In an Algebra II class with 135 students, the final exam scores have a mean of 72.3 and standard deviation 6.5. The exams on the

gregori [183]

Population = 135 students
Mean score = 72.3
Standard deviation of the scores = 6.5

Part (a): Students from 2SD and 3SD above the mean
2SD below and above the mean includes 95% of the population while 3SD includes 99.7% of the population.
95% of population = 0.95*135 ≈ 129 students
99.7% of population = 0.997*135 ≈ 135 students

Therefore, number of students from 2SD to 3SD above and below the bean = 135 - 129 = 6 students.
In this regard, Students between 2SD and 3SD above the mean = 6/2 = 3 students

Part (b): Students who scored between 65.8 and 72.3
The first step is to calculate Z values
That is,
Z = (mean-X)/SD
Z at 65.8 = (72.3-65.8)/6.5 = 1
Z at 72.3 = (72.3-72.3)/6.5 = 0
Second step is to find the percentages at the Z values from Z table.
That is,
Percentage of population at Z(65.8) = 0.8413 = 84.13%
Percentage of population at (Z(72.3) = 0.5 = 50%
Third step is to calculate number of students at each percentage.
That is,
At 84.13%, number of students = 0.8413*135 ≈ 114
At 50%, number of students = 0.5*135 ≈ 68

Therefore, students who scored between 65.8 and 72.3 = 114-68 = 46 students

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