Concentric circles have radil of 4 cm and 8 cm. What is the probability that a
grain of rice dropped onto the circles at random lands outside the circle with the
4-cm radius and inside the circle with a radius of 8 cm?

The probability that a  grain of rice dropped onto the circles at random lands outside the circle with the  4-cm radius and inside the circle with a radius of 8 cm is or 75%.

Step-by-step explanation:

Step 1:

First, we need to calculate the areas of both circles.

The area of a circle where r is the radius of the circle.

The inner-circle has a radius of 4 cm.

The area of the inner circle

The outer circle has an inner radius of 4 cm and an outer radius of 8 cm.

So its area is where R is the outer radius and r is the inner radius.

The area of the outer circle

So the inner circle has an area of 50.264 square cm and the outer circle has an area of 150.792 square cm.

Step 2:

To find the probability of an event we divide the number of favorable outcomes by the total number of outcomes.

The total number of outcomes is the area of the entire circle

square cm.

The number of favorable outcomes is the area of the outer circle i.e. 150.792 square cm.

The probability of the rice falling in the outer circle .

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.

there is no question content here, but you for the free points! : d