In a group of 270 college students, it is found that 64 like brussels sprouts, 94 like broccoli, 58 like cauliflower , 26 like both brussels sprouts and broccoli, 28 like both brusselssprouts and cauliflower , 22 like both broccoli and cauliflower , and 14 like all three vegetables.
how many of the 270 students do not like any of these vegetables?

116 students

Step-by-step explanation:

we let

U=[Total number of students ]

This implies that,

n(U)=270

B.S=[Those who like brussels sprouts ]

This implies that,

n(B.S)=64

B=[Those who like broccoli]

This implies that,

n(B)=94

C=[Those who like cauliflower]

This implies that,

n(C)=58

Using the formula :

n(U)=n(B.S)+n(B)+n(C)-n(B.S n B)-n(B.S n C)-n(B n C)+n(B.S n C n B)+n(no set)

By substitution we get,

270=64+94+58-26-28-22+14+n(no set)

270=154+n(no set)

270-154=n(no set)

n(no set)=116

Hence number of students who do not like any of the three vegetables is 116

given : the shape of his satellite can be modeled by   where x and y are modeled in inches.

now,the given equation   is a equation of parabola.

here, coefficient of x is positive, hence the parabola opens rightwards.

on comparing this equation with standard equation , we get

in standard equation, coordinates of focus=(0,m)

thus for given equation coordinates of focus=(0,1.5)

step-by-step explanation:

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)