8x-10y=-23
9x+10y=-16
(8x+9x)+(10y-10y)=(-23+(-16))
17x+0y=-39
x=-39/17
8(-39/17)-10y=-23
-312/17-10y=-23
-10y=-23+312/17
-10y=-79/17
y=79/170
13. The words are telling you
.. HT +TS = HM +MS +2
.. (2x +1) +(x) = (x +1) +(x +2) +2
.. 3x +1 = 2x +5 . . . . . . . . . . . . . . collect terms
.. x = 4 . . . . . . . . . . . . . . . . . . . . . add -2x-1
HT +TS = 3x +1 = 3*4 +1 = 13 miles
The route via the theater is 13 miles.
Via the mall, the route is 11 miles.
14. Solve this the way you would any 2-step linear equation. Subtract terms that don't have h, and divide by the coefficient of h.
S = 2πr^2 +2πrh
S -2πr^2 = 2πrh
(S -2πr^2)/(2πr) = h
If you like, you can rearrange this to
.. h = (S/(2πr)) -r
Answer: This would be expressed as: " (x + 2) / 8 " .
The cistern is losing approximately 3.963 gallons of water per hour.
<u><em>Explanation</em></u>
A cistern is leaking 0.25 liters of water per minute.
<u>We know, 1 gallon = 3.785 liters</u>
So, 0.25 liters =
gallons
That means, the cistern is losing 0.06605....gallons of water per minute.
So, the amount of water losing in 1 hour or 60 minutes
<em>(Approximately)</em>
(a) The probability that an individual is within 1 standard deviation of the mean is
0.1585(b) The probablity that the mean of a sample of 12 is within 1 standard deviation of the population mean is
0.5116