The element europium (EU) exists in nature as two isotopes: (151 EU)with a mass of 150.9196 amu & (153 EU) with a mass of 152.9209 amu. The average mass of EU is 151.96 How do you calculate the relative abundance of the two EU isotopes? X% times 150.9196 (plus) Y% times 152.9209 equals = 151.96. what are the X and Y percentages? And what is the formula to identify the unknowns X and Y?

X = 48.014%

Y = 51.986%

Step-by-step explanation:

Given

151 EU has a mass of 150.9196 amu

153 EU has a mass of 152.9209 amu

Calculating the relative abundance of the two EU isotopes.

First condition that must be satisfied is

X + Y = 100%;

X + Y = 1. Equation 1

Second Condition is;

150.9196X + 152.9209Y = 151.96 Equation 2

In Equation 1; make Y the subject of formula.

So, Y = 1 - X.

Substitute (1 - X) for Y in Equation 2

150.9196X + 152.9209(1 - X) = 151.96 Open bracket

150.9196X + 152.9209 - 152.9209X = 151.96 Collect Like Terms

150.9196X - 152.9209X = 151.96 - 152.9209

−2.0013X = -0.9609

X = -0.9609/-2.0013

X = 0.480137910358267

X = 48.014% Approximated

Y = 1 - X

Y = 1 - 48.014%

Y = 0.51986

Y = 51.986% Approximated

54

step-by-step explanation:

6x9

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".