Answer:
![x + 9 = 15](https://tex.z-dn.net/?f=x%20%2B%209%20%3D%2015)
<h2>Algebraic (Maybe) </h2>
Step-by-step explanation:
Hope it helps..
Answer:
5 seats
Step-by-step explanation:
if I'm getting the right idea, the seats are NOT enough
since the number of arrangement of 10 people in a row is
10! = 3628800 which is a lot larger than 30240.
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Let number of seats be
10PX = 30240
= 30240
(10-X)! = ![\frac{10!}{30240}](https://tex.z-dn.net/?f=%5Cfrac%7B10%21%7D%7B30240%7D)
(10-X)! = 120
(10-X)! = 5!
10-X = 5
X = 5
Variance = square of standard deviation
Variance = (2.5)^2 = 6.25 = 6.3 to the nearest tenth.
Answer:
27.63 mph
Step-by-step explanation:
First we find the distance, p between the Car and the house using Pythagoras theorem.
![p^2=x^2+y^2\\p^2=7^2+9^2\\p^2=49+81=130\\p=\sqrt{130} miles](https://tex.z-dn.net/?f=p%5E2%3Dx%5E2%2By%5E2%5C%5Cp%5E2%3D7%5E2%2B9%5E2%5C%5Cp%5E2%3D49%2B81%3D130%5C%5Cp%3D%5Csqrt%7B130%7D%20miles)
Taking derivatives of:
![p^2=x^2+y^2\\2p \frac{dp}{dt} =2x \frac{dx}{dt} + 2y \frac{dy}{dt}](https://tex.z-dn.net/?f=p%5E2%3Dx%5E2%2By%5E2%5C%5C2p%20%5Cfrac%7Bdp%7D%7Bdt%7D%20%3D2x%20%5Cfrac%7Bdx%7D%7Bdt%7D%20%2B%202y%20%5Cfrac%7Bdy%7D%7Bdt%7D)
Since the farmhouse does not move, its speed ![\frac{dy}{dt}=0](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%3D0)
Therefore:
![2*\sqrt{130} *\frac{dp}{dt} =2*7*45 + 2y*0\\2*\sqrt{130} *\frac{dp}{dt}=630\\\frac{dp}{dt}=\frac{630}{2\sqrt{130}}\\\frac{dp}{dt}=27.63 mph](https://tex.z-dn.net/?f=2%2A%5Csqrt%7B130%7D%20%2A%5Cfrac%7Bdp%7D%7Bdt%7D%20%3D2%2A7%2A45%20%2B%202y%2A0%5C%5C2%2A%5Csqrt%7B130%7D%20%2A%5Cfrac%7Bdp%7D%7Bdt%7D%3D630%5C%5C%5Cfrac%7Bdp%7D%7Bdt%7D%3D%5Cfrac%7B630%7D%7B2%5Csqrt%7B130%7D%7D%5C%5C%5Cfrac%7Bdp%7D%7Bdt%7D%3D27.63%20mph)
The distance between the automobile and the farmhouse is increasing at a rate of 27.63mph.