How many cubic blocks of side length 1/6 inch would take to fill a rectangular prism with a length, width, and height of 1/2 cm, 1/6 cm, and 1/2 cm respectively ?

9 blocks

Step-by-step:  

One way in which to do this problem is to find the volume of the rectangular prism and then divide that by the volume of one  cubic block of side length 1/6 inch.

V = (length)(width)(height) = (1/2 cm)(1/6 cm)(1/2 cm) = 1/24 cm³.

Volume of one cubic block of side length 1/6 cm is (1/6 cm)³ = 1/216 cm³.

Dividing 1/24 cm³ by 1/216 cm³ yields 216/24 blocks, or 9 blocks.

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

there would only be 50 odd numbers between 1 and 100 so therefor there would be 50 even so that would only be 50 odd numbers.