Each cone of the hourglass has a height of 12 millimeters. The total height of the sand within the top portion of the hourglass is 47 millimeters. The radius of both the cylinder and cone is 4 millimeters. Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second. How many seconds will it take until all of the sand has dripped to the bottom of the hourglass? (4 points)

1. it's 4 points.

2. We have to calculate the height of a cylinder : h2 = ( 45 - 2 · 15 )/ 2 = 15 / 2 = 7.5 mm

Volume of the bottom of the hourglass:V = 1/3 r² π h1 + r² π h2 = = 1/3 · 6² · 3.14 · 15 + 6² · 3.14 · 7.5 = = 1/3 · 36 · 3.14 · 15 + 36 · 3.14 · 7.5 = = 565.2 + 847.8 = 1,413 mm³The rate is 10 π mm³/ sec = 31.4 mm³/secTime = 1,413 : 31.4 = 45 sec.

It will take 45 seconds.

answer: 25.4 units

step-by-step explanation: radius = 12.7 units

diameter = twice the radius

diameter = 12.7 x 2

= 25.4

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.