Answer: z=4
Step-by-step explanation:
4z+12=28
-12 on both sides
28-12=16
4z=16
divide 4 on both sides
z=4
Answer:AB = 30 in and BC = 50 in.
We use Pythagorean theorem to solve this. Since AN is an altitude, this means that it is perpendicular to BC. This means BN and AN are the legs of one right triangle, with AB being the hypotenuse:
18²+24² = AB²
324 + 576 = AB²
900 = AB²
Take the square root of both sides:
√900 = √AB²
30 = AB
NC and AN form the legs of the other right triangle, with AC being the hypotenuse:
24²+NC² = 40²
576 + NC² = 1600
Subtract 576 from both sides:
576 + NC² - 576 = 1600 - 576
NC² = 1024
Take the square root of both sides:
√NC² = √1024
NC = 32
BC = BN + NC = 18 + 32 = 50
Step-by-step explanation:
Answer:
set them equal to each other and solve for x. both those angles should be the same
Step-by-step explanation:
Answer:
The minimum score required for admission is 558.75.
Step-by-step explanation:
When the distribution is normal, we use 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.
Suppose SAT Critical Reading scores are normally distributed with a mean of 501 and a standard deviation of 110.
This means that 
A university plans to admit students whose scores are in the top 30%. What is the minimum score required for admission
This is the 100 - 30 = 70th percentile, which is X when Z has a pvalue of 0.7. So X when Z = 0.525. So




The minimum score required for admission is 558.75.