Jorge needs to ship a thin metal rod to a metalworking shop. the only boxes available for shipping are 7-inch cubes. to the nearest inch, what is the length of the longest metal rod that can be sent?
11 inches
12 inches
13 inches
14 inches

The length of the longest metal rod that can be sent is 12 inches.

As given, the only boxes available for shipping are 7-inch cubes. As Jorge needs to ship a thin metal rod to a metalworking shop, he will put the rods diagonally or space diagonally in the box.

The space diagonal of a cube can be found by the formula :

=

Here, x is 7 inches.

So, Diagonal is =

= inches.

Rounding this to nearest whole number we get 12.

So, the length of the longest metal rod that can be sent is 12 inches.

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.