Out of 136 students in a school, 60 take french, 100 take chemistry and 48 take physics. if 28 take french and chemistry, 44 take chemistry and physics and 20 take french and physics, how many take all three subjects?

20

Step-by-step explanation:

Let us see the formula to find intersection of 3 sets.

n(A∪B∪C)=n(A)+n(B)+n(C)-n(A∩B)-n(B∩C)-n(C∩A)+n(A∩B∩C)

Here we are given three sets as the number of students in class of French , physics and Chemistry . Let these sets be denoted by F,C, P. Hence the formula for them will be

n(F∪C∪P)=n(F)+n(C)+n(P)-n(F∩C)-n(C∩P)-n(P∩F)+n(F∩C∩P)

Also we are given that

n(F∪C∪P)=136

n(F)=60

n(C)=100

n(P)=48

n(F∩C)=28

n(C∩P)=44

n(P∩F)=20

n(F∩C∩P)=x

Hence put these values in the above equation and solve for x

136=60+100+48-28-44-20+x

136=208-92+x

136=116+x

20=x

Hence , there are 20 students who took all the three subjects.

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752