The center of mass for this collection of point masses on the real number line is approximately −3.067.
To find the center of mass for a collection of point masses on the real number line, you can use the formula:
Center of Mass=

where:
m_i represents the mass of the ith point mass.
x_i represents the position of the ith point mass.
For your given masses and positions:
m_1 =7 at x_1 =−3
m_2 =3 at x_2= -5
m_3 =5 at x_3 =−2
Let's plug these values into the formula:
Center of Mass= (7×(−3))+(3×(−5))+(5×(−2))/ 7+3+5
Calculating the numerator first:
(7×(−3))+(3×(−5))+(5×(−2))=(−21)+(−15)+(−10)=−46
Now, the denominator:
7+3+5=15
Finally, calculate the center of mass:
Center of Mass= −46/ 15 ≈−3.067
Therefore, the center of mass for this collection of point masses on the real number line is approximately −3.067.