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Answer:
The probability that no more than 70% would prefer to start their own business is 0.1423.
Step-by-step explanation:
We are given that a Gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than work for someone else.
Let = <u><em>sample proportion of people who prefer to start their own business</em></u>
The z-score probability distribution for the sample proportion is given by;
Z = ~ N(0,1)
where, p = population proportion who would prefer to start their own business = 72%
n = sample of 18-29 year-olds = 600
Now, the probability that no more than 70% would prefer to start their own business is given by = P(
70%)
P(
70%) = P(
) = P(Z
-1.07) = 1 - P(Z < 1.07)
= 1 - 0.8577 = <u>0.1423</u>
The above probability is calculated by looking at the value of x = 1.07 in the z table which has an area of 0.8577.
We need a system of equations to solve this. "Difference" is to subtract, and we are taking this difference of the 2 squared unknowns to be 20. That equation is 
. Our "first number is x^2, so 3 times that is 3x^2. "Increased by" is adding to that first number. What we are adding is the second number. The second equation is 
. Let's solve the first equation for x^2: 
and sub that value for x^2 into the second equation. 
and 
. Subtract 60 from both sides and combine the y^2 terms to get 
. Divide both sides by 4 to get y^2 = 16 and y = 4. Let's go back now and solve for x. We will use the fact that y^2 = 16 to solve for x^2 and then take the square root of it. 
, x^2 = 4, so x = 2. Your solutions are x = 2 and y = 4. There you go!