Answer:
The minimum score required for the scholarship is 644.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:

What is the minimum score required for the scholarship?
Top 8%, which means that the minimum score is the 100-8 = 92th percentile, which is X when Z has a pvalue of 0.92. So it is X when Z = 1.405.




The minimum score required for the scholarship is 644.
The formula for an average of three numbers is (x+y+z)/3. So if V equals the average, then we find the formula
V = (x+y+z)/3
We are now looking for x. We can divide each of the variables in the parentheses by 3, making the formula
V = x/3 + y/3 + z/3
So now bring the unwanted variables to the same side as V.
V - y/3 - z/3 = x/3
Now multiply both sides by 3 to find x.
3V - y - z = x
x = 3V - y - z
Answer:
Second option
Step-by-step explanation:
Math
Answer:
653
Step-by-step explanation:
The surface area of the larger cube is
2(10 x 7) + 2(12x7) + 2(10x12) = 140 + 168 + 240 = 548
The surface area of the smaller cube (minus the surface that is covered by the other figure)
4(8x3) + 1(3x3) = 96 + 9 = 105
105 + 548 = 653