5,120........................................
Answer:

Step-by-step explanation:
<u>Fundamental Theorem of Calculus</u>

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a <u>constant of integration</u>.

Increase the power by 1, then divide by the new power.
Given <u>indefinite integral</u>:

To integrate the given integral, use Integration by Parts:



Therefore:

Learn more about integration here:
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Answer:
the probability that two 18 year old boys chosen at random will have heights greater than 185cm is 0.403
Step-by-step explanation:
P( x > 193) = 0.15
= 1- p(x less than or equal 193)
= 1 -p( z < (x- u) /sigma)
= 1- p( z< (193 - 187)/ sigma)
= 1- p( z< 6/ sigma)
P(z< 6/sigma) = 1 - 0.15
P(z < 6/sigma)= 0.85
6/sigma =1.036
Sigma= 6/1.036
Sigma= 5.79
P( x> 185) = 1- p( x< 185)
= 1- p (z < (185- 187)/5.79)
= 1- p( z< -0.345)
= 1- 0.365
= 0.635
P (x> 185) = 0.635 × 0.635
=0.403
Answer:
C= 82.1116
k=-0.0007192
Step-by-step explanation:

Applying logarithmic properties yields in the following linear system:

Solving for k:

Solving for C:

C= 82.1116
k=-0.0007192
Eighths and their multiples are common fractions which I recommend memorizing, but to actually solve this, you use the literal meaning of a fraction and divide 5 by 8. See the long-division below (it was surprisingly difficult to type, so I hope it helps!).
To round 0.625 to the nearest hundredth, we go to the second decimal place, which is 5, so we round up to 0.63.