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Find the value of x so that (x,-4) is on the line given by -2x + 3y = 6.

lord [1]

Answer:

Step-by-step explanation:

-2x + 3y = 6.....(x, -4)...so y = -4

-2x + 3(-4) = 6

-2x - 12 = 6

-2x = 6 + 12

-2x = 18

x = -18/2

x = -9

so the value of x is -9.....(-9,-4)

6 0

3 years ago

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

4 0

3 years ago

Solve the following system of equations for a and for b:

viktelen [127]

Answer:

$a=3\\b=1$

Step-by-step explanation:

$9a+3b=30\\8a+4b=28$

Let's solve the second equation for a to later on replace it in the first equation.

$8a+4b=28\\8a=28-4b\\a=\frac{28-4b}{8}$

Now plug this into the first equation.

$9a+3b=30\\9(\frac{28-4b}{8})+3b=30$

Distribute the 9

$(\frac{252-36b}{8}) +3b=30$

Break down the fraction.

$\frac{252}{8}-\frac{36b}{8}+3b=30$

Simplify.

$\frac{63}{2}-\frac{9}{2}b+3b=30$

Subtract $\frac{63}{2}$

$-\frac{9}{2}b+3b=30-\frac{63}{2}$

Combine like terms.

$\frac{-9+2*3}{2}b=\frac{30*2-63}{2}$

$\frac{-9+6}{2}b=\frac{60-63}{2}$

$\frac{-3}{2}b=\frac{-3}{2}$

Muliply by the reciprocal or inverted fraction next to b.

$(-\frac{2}{3})(-\frac{3}{2}) b=-\frac{3}{2}(-\frac{2}{3})$

$b=1$

Now plug this value into any of the equations to find the value of a.

$8a+4b=28\\8a+4(1)=28\\8a+4=28\\8a=28-4\\8a=24\\a=\frac{24}{8}\\ a=3$

5 0

4 years ago

Complete the statement using always, sometimes, or never. A rectangle is __________________ a rhombus.

Lesechka [4]

Hi!

A rectangle can sometimes be a rhombus if it has sides of all equal lengths. If a rectangle was a rhombus, it would also be a square. Furthermore, a square is always a rhombus.

Hope this helps! :)

7 0

3 years ago

The constant of ________ is the value that relates two variables that are directly proportional or inversely proportional.

krok68 [10]

The constant of proportion is the value that relates two variables that are directly proportional or inversely proportional.

Option B is correct!!~

6 0

2 years ago