Best Answer
x means everything in algebra. It is a variable, which means that its meaning changes based on context. For example, x could be time, but it could also be cars. x is what all Mathematicians chase after and it is also the greatest tool at their disposal. x is generally called an independent variable because its value determines the output of a function. y, on the other hand, is the result of fooling around with x. It's a dependent variable, which means that y changes when x changes.
Answer:
x = 1, y = 6
or
x = 5, y = 2.
Step-by-step explanation:
y=x2−7x+12
y=−x+7
Substitute for y in the first equation:
- x + 7 = x^2 - 7x + 12
x^2 - 7x + x + 12 - 7 = 0
x^2 - 6x + 5 = 0
(x - 1)(x - 5) = 0
x = 1, 5.
When x = 1, y = -1 + 7 = 6.
when x = 5, y = -5+7 = 2.
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
Answer:
6
Step-by-step explanation:
Total number of subsets is given as
But the subset of a set consists of the proper subsets, an empty set and the set itself.
Total number of subsets are 64
Therefore,
Comparing both sides
Answer:
see below
Step-by-step explanation:
3x^2 + 17x +10 =0
(3x+ ) ( x+ ) =0
We need to factor 10 = 2*5 or 1*10
They are positive since we have all positive terms
3*5 = 15+2 = 17
The 5 needs to multiply the 3 so it goes on the outside
(3x+ ) ( x+ 5 ) =0
That leaves the 2 on the inside
(3x+ 2 ) ( x+ 5 ) =0
Using the zero product property
3x+2 =0 x+5=0
3x = -2 x=-5
x = -2/3 x = -5
