Find all sets of three consecutive even integers whose sum is between 25 and 45

1st even integer is x,

2d consecutive even integer is x+2,

3d consecutive even integer is x+2+2 = x+4.

Sum is  x+ x+2 +x +4 = 3x + 6.

Sum is between 25 and 45, so we can write

25< 3x+6 < 45.

25 -6 < 3x < 45 -6

19 < 3x < 39

19/3 < x < 13

6 1/3 < x < 13

Between 6 1/2 and 13 there are even numbers 8,10,12 ,  so first even number can be 8, or 10, or 12.

1st set :     8, 10, 12

8+10+12 = 30         25<30<45

2d set:    10, 12, 14

10+12+14 =36    25<36<45

3d set :   12, 14, 16

12+14+16 = 42   25<42<45

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.

percentage - 25%

probability - 0.25

we know,

total amount of students in class = 20

total boys = 10

total girls = 10

no of girls who wear glasses = 10/2 = 5

probability of choosing a girl with glasses is =

number of girls wearing glasses/total number of students in the class = 5/20

thus, percentage of selecting a girl wearing glasses will be

= 5/20 × 100

= 5 × 5

25%

therefore,

probability will be 0.25

happy to

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