Let y be the difference of two numbers such that one number varies directly as x while the other number varies inversely as x. if y = –7 when x = –2, and y = 5 when x = 1, express y in terms of x. show your work.

Step-by-step explanation:

If y is directly proportional to x, then

where, a is constant of proportionality.

If y is inversely proportional to x, then

where, b is constant of proportionality.

It is given that y be the difference of two numbers such that one number varies directly as x while the other number varies inversely as x.

           ..... (1)

We have y=-7 at x=-2.

Multiply both sides by 2.

                 .... (2)

We have y=5 at x=1.

                .... (3)

Add equation (2) and (3).

Divide both sides by -3.

The value of a is 3.

Substitute a=3 in equation (3).

The value of b is -2.

Substitute a=3 and b=-2 in equation (1).

Therefore the required equation is .

160

step-by-step explanation:

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b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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