Maya makes trail mix by combining 1/3 cup of mixed nuts,1/4 cup of dried fruit, and 1/6 cup of chocolate morsels. What is the total amount of ingredients in her trail mix?

3/4 cups is the total amount of ingredients in her trail mix.

Step-by-step explanation:

1/3 + 1/4 + 1/6 = total

Convert all fractions to have a common denominator:

Between all three denominators (3, 4, and 6), the least common factor is 12.

1/3 × 4/4 = 4/12

1/4 × 3/3 = 3/12

1/6 × 2/2 = 2/12

Substitute these numbers into the equation:

4/12 + 3/12 + 2/12 = 9/12

Simplify:

9/12 ÷ 3/3 = 3/4

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3