Amandatory competency test for high school sophomores has a normal distribution with a mean of 400 and a standard deviation of 100. if the top 3% of students receive $500, find the minimum score you would need to receive this award.

To solve for the minimum score required, we find for the z score value at P = 0.97 (top 3%). The z score is:

z = 1.88

Then we use the formula to find for X:

z = (X – u) / s

1.88 = (X – 400) / 100

X = 588

You have to score at least 588.

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step-by-step explanation:

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places