A farmer who grows blackberries has found his harvest to be lower than usual. He suspects that some animals are eating the berries before he can pick them. The farmer thinks it may be either birds (landing on the bushes to feast on berries) or rodents (climbing the bushes from below to munch on berries). He decides to first test the hypothesis that birds are eating his berries, and consults with a local expert on how best to prevent the birds from eating berries. He has eight fields with 10 rows of berry bushes in each field. In one of his fields (depicted below, as viewed from above), he covers half of the rows with nets that will prevent birds from landing on the bushes, and he leaves the other half uncovered. Over the course of 8 weeks, he counts the berries harvested from each row of bushes in the test field. What are the independent and dependent variables in the farmer's experiment

A farmer who grows blackberries has found his harvest to be lower than usual. He suspects that some animals are eating the berries before he can pick them. The farmer thinks it may be either birds (landing on the bushes to feast on berries) or rodents (climbing the bushes from below to munch on berries). He decides to first test the hypothesis that birds are eating his berries, and consults with a local expert on how best to prevent the birds from eating berries. He has eight fields with 10 rows of berry bushes in each field. In one of his fields (depicted below, as viewed from above), he covers half of the rows with nets that will prevent birds from landing on the bushes, and he leaves the other half uncovered. Over the course of 8 weeks, he counts the berries harvested from each row of bushes in the test field.

What are the independent (treatment) and dependent (response) variables in the farmer's experiment?

a) The independent variable is number of rows and the dependent variable is number of berries harvested.

b) The independent variable is presence/absence of nets and the dependent variable is number of rows.

c) The independent variable is number of berries harvested and the dependent variable is presence/absence of nets.

d)The independent variable is presence/absence of nets and the dependent variable is number of berries harvested.

The independent variable is presence/absence of nets and the dependent variable is number of berries harvested.  (d)

Step-by-step explanation:

Independent variable: The independent variable is the vi=ariable in a scientific experiment that is under the complete manipulation by the experimenter. The independent variable can take on any value as predetermined by the experimenter. In this example, the farmer decides which row to fix a net or not, hence the presence or absence of nets is completely subject to the farmer, hence it is the independent variable

Dependent variable: The dependent variable is the variable whose values are dependent on the outcome of the independent variable. The dependent variable is the variable which the experimenter seeks to study in the experiment. In this example, the dependent variable is the number of berries harvested because this depends on whether the birds are able to access the berries covered by the nets or not, which in turn depends on the presence or absence of nets.

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

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