A cylinder has a volume of 200 mm3 and a height of 17 mm.

Response:

When combining two fractions that each exceeds 1/2, their sum will invariably exceed 1.

Detailed breakdown: 1/2 + 1/2 = 1    

Since both fractions exceed this amount, it is evident that the sum must as well.

Examples: 2/3+3/4= 1 5/12        4/6+6/9= 1 1/3

Hope this adds clarity

Answer:

Here’s the response provided

Step-by-step explanation:

Referring to the flask diagram, the diameter of the cylinder measures 1 inch and its height (h) is 3 inches. Thus, the radius of the cylinder (r) = diameter / 2 = 1/2 = 0.5 inch

The volume of the cylinder can be calculated as πr²h = π(0.5)² × 3 = 2.36 in³

As for the sphere, its diameter is 4.5 in. Hence, the radius of the sphere R = diameter / 2 = 4.5/2 = 2.25 in

The volume of the sphere is calculated as 4/3 (πR³) = 4/3 × π × 2.25³ = 47.71 in³

The total volume of the flask = Volume of the cylinder  + Volume of the sphere = 2.36 + 47.71 = 50.07 in³

<pWhen the cylinder and the sphere are expanded by a scale factor of 2, the height (h') of the cylinder becomes 3/2 = 1.5 inches and the radius (r') becomes 0.5/2 = 0.025 inches.

The new volume for the cylinder = πr'²h' = π(0.25)² × 1.5 = 0.29 in³

For the sphere, the new radius is R' = 2.25 / 2 = 1.125 in.

The new volume of the sphere = 4/3 (πR'³) = 4/3 × π × 1.125³ = 5.96 in³

Thus, the new volume of the flask = The new volume of the cylinder  + The new volume of the sphere = 0.29 + 5.96 = 6.25 in³

<pThe ratio of the new volume to the original volume = New Volume of the flask / Volume of the flask = 6.25 / 50.07 = 1/8 = 0.125<pThe resulting volume will thus be 0.125 times the original volume

9

5400000, since the 7 rounds the 8 up to 4.

When there is one table (t=1), you can place 6 chairs (c=6) around it: 2 along the length of each side and 1 at each end.
With t=2, where the tables are positioned end to end (joined at the width), c=10, that means 4 chairs along each side of the joined tables and 1 chair at each end. Each additional table increases the number of chairs by 4, thus we can express this as c=4t+2, with the constant 2 representing the individual chair at each end. If the tables are spread apart, then c=6t.