Answer:
3. 60 ÷ 5 = 12
12 × 3 = 36
7 3/5 hours = 7 hours and 36 minutes
7:36 - 30 = 7:06
7:06 - 42 = 6:24
6:24 ÷ 6 = 1:04
A. 1 1/15 hours
4. fractions are equivalent regardless of the negative sign placement
A. 4/-9 = -4/9
5. 3/2 = 12
4/2 = 16
12 × 16 = 192
C. 192 square feet
7. -2.9a + 6.8 + 4.4a - 7.3 (add -2.9a + 4.4a)
1.5a + 6.8 - 7.3 (subtract 6.8 - 7.3)
1.5a - 0.5
D. 1.5a - 0.5
8. 552.50 × 0.88 = 486.2
486.2 ÷ 7 = 69.457
B. m > 69.45
19. -1/6 + 2/3(9 - 3/4) - 1/2
2/3 × 9/1 = 18/3
2/3 × 3/4 = 6/12
-1/6 + 18/3 - 6/12 - 1/2
-1/6 + 36/6 - 6/12 - 1/2
35/6 - 6/12 - 1/2
70/12 - 6/12 - 1/2
64/12 - 1/2
64/12 - 6/12
B. 58/12
Answer:
Step-by-step explanation:
This is a differential equation problem most easily solved with an exponential decay equation of the form
. We know that the initial amount of salt in the tank is 28 pounds, so
C = 28. Now we just need to find k.
The concentration of salt changes as the pure water flows in and the salt water flows out. So the change in concentration, where y is the concentration of salt in the tank, is 
. Thus, the change in the concentration of salt is found in
inflow of salt - outflow of salt
Pure water, what is flowing into the tank, has no salt in it at all; and since we don't know how much salt is leaving (our unknown, basically), the outflow at 3 gal/min is 3 times the amount of salt leaving out of the 400 gallons of salt water at time t:
Therefore,
or just
and in terms of time,
Thus, our equation is
and filling in 16 for the number of minutes in t:
y = 24.834 pounds of salt
Start by doing the binomial expansion of (x+y)^6 where x represents success. This is
(x^6y^0) + 6(x^5y^1) +15(x^4y^2) +20(x^3y^3) +15(x^2y^4) +6(x^1y^5) +(x^0y^6)
We are interested in the x^3y^3 term which represents exactly 3 sucesses. Since the probalbility of sucess and failure are both .5 we should be able to figure this out just using the coefficients of the terms which is
20/64 = .3125 which is 31.25%
The anwer is 3. The volume of a cube is lwh. 3 x 3 x 3 = 27
