The bottle is completely full at 11: 40 a. m. which statements explain this result? check all that apply. the bottle was 1/2 full at 11: 35 a. m. and doubled again after 5 minutes. the bottle was 1/4 full at 11: 30 a. m. and doubled twice after 10 minutes. the bottle was 1/2 full at 11: 35 a. m. and more bacteria were added to fill the bottle. exponential growth involves a constant multiplicative rate of change. exponential growth involves a constant additive rate of change.

Step-by-step explanation:

Given that bottle was half full at 11.35 a.m. and full at 11.40 a.m.

This implies it takes 5 minutes for the liquid to double.

This is confirmed by the statement that before 5 minutes i.e. at 11.30 the bottle was only 1/4 full.

Hence true statements would be:

1) The bottle was 1/2 full at 11:35 a.m. and doubled again after 5 minutes.

2)  The bottle was 1/4 full at 11:30 a.m. and doubled twice after 10 minutes. The bottle was 1/2 full at 11:35 a.m.

3) Exponential growth involves a constant multiplicative rate of change.

(The rate cannot be additional as we get 2 times every 5 minutes)

The correct statements can be determine by doing arithmetic operations in mind and by carefully read the given information and the correct statements are A), B), and D).

Given :

The bottle is completely full at 11:40 a.m.

Check each statement to determine which statement is correct:

A). The bottle was 1/2 full at 11:35 a.m. and doubled again after 5 minutes means that at 11:40 a.m. the bottle is completely full. Therefore, this statement is correct.

B). The bottle was 1/4 full at 11:30 a.m. and doubled twice after 10 minutes means that at 11:40 a.m. the bottle is completely full. Therefore, this statement is correct.

C). The bottle was 1/2 full at 11:35 a.m. and more bacteria were added to fill the bottle means that the bottle is completely full but with bacteria present in it. Therefore, this statement is incorrect.

D). Exponential growth involves a constant multiplicative rate of change means that bottle level rises with a constant multiplicative rate of change. Therefore, this statement is correct.

E). Exponential growth involves a constant additive rate of change means that bottle level rises with a constant additive rate of change. Therefore, this statement is incorrect.

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answer: 15

step-by-step explanation:

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12