y is inversely proportional to a*3. when y=10, a=2. a is directly proportional to x. when x=4, a=20. find the formula of y in terms of x

The first statement should be;

y is inversely proportional to a³.

y = 0.64/x³

Step-by-step explanation:

y is inversely proportional to a³. This is;

y ∝ 1/a³

Thus, y = k(1/a³).

Where k is the constant of proportionality.

When y = 10, a = 2.

Thus; 10 = k(1/2³)

10 = k/8

k = 80.

Thus; y = 80(1/a³) - - -(1)

Also, a is directly proportional to x. Thus;

x ∝ a

So, x = ka

when x = 4, a = 20

Thus;

4 = 20k

k = 4/20

k = 1/5

Thus;

x = a/5

a = 5x

Put 5x for a in eq 1 to get;

y = 80(1/(5x)³)

y = (80/125) × 1/x³

y = 0.64/x³

hello,

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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