Answer:
5 miles
Step-by-step explanation:
The two legs of Deborah's hike form the right-angle legs of a right triangle. The shortest distance is then the hypotenuse of that triangle, found using the Pythagorean theorem.
d^2 = 3^2 + 4^2 = 9 +16 = 25
d = √25 = 5
Deborah ends 5 miles from her start.
Answer:
Grade A: 
Grade B: 
Grade C: 
Grade D: 
Step-by-step explanation:
Problems of normally distributed samples can be solved using the Z score table.
The Z score of a measure represents how many standard deviations it is above or below the mean of all the measures.
Each Z score has a pvalue. This represents the percentile of the measure.
In this problem, we have that:
The upper 16% of the class get A grades. The upper 16% has a pvalue of at least 100% = 16% = 84% = 0.84. This is
.
The middle 34% of the class get B grades. The middle 34% has a pvalue of at least 84%-35% = 50% = 0.5 and at most 0.84. This is
.
Those between a pvalue of 0.5-0.34 = 0.16 and 0.5 get get grade C.
has a pvalue of 0.16. So a grade C is in the interval
.
Those with Z lesser than -1 get grades D and F
My best interpretation of the math here is that you're talking about the line integral,

I won't bother trying to decipher what look like multiple choice solutions.
By Green's theorem, the line integral above is equivalent to

where D is the set

Compute the double integral:

Answer:
8 in
Step-by-step explanation:
? = a
a² + b² = c²
a² + 15² = 17²
a² + 225 = 289
a² = 289 - 225
a² = 64

a = 8