Answer:
Number of marbles with Williams at the starting = 192
Step-by-step explanation:
Let total number of marbles with Williams = m
He lost marbles = 25% of the total number
= 
= 
Remaining marbles with Williams = m - 
= 
He gave marbles to his brother =
th of the remaining marbles
= 
= 
Remaining marbles after giving marbles to his brother = 120
Therefore, 


m = 
m = 192
Number of marbles with Williams at the starting = 192
(a)

Substitute <em>x</em> = 3 tan(<em>t</em> ) and d<em>x</em> = 3 sec²(<em>t </em>) d<em>t</em> :


(b) The series

converges by comparison to the convergent <em>p</em>-series,

(c) The series

converges absolutely, since

That is, ∑ (-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ converges absolutely because ∑ |(-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ| = ∑ (<em>n</em> ² + 9)/<em>e</em>ⁿ in turn converges by comparison to a geometric series.
Domain is [-10,∞)
2 is included , only at x=2 new function begins
Range is the values of y , so range is [-7]∪[-4,6
I think, it should be like this.
Answer:
rate boat = 15 mph
rate current = 5 mph
explanation:
d = r * t
t = d/r
240 / (r_boat + current) = 12 Multiply both sides by r_boat + r_current.
240 = 12(r_boat + current)
240/ (r_boat - current) = 24 Multiply both sides by r_boat - r_current
240 = 24*(r_boat - current)
Since the distances are the same in both equations, you can equate the right side of each.
12 (r_boat + current) = 24(r_boat - current) Divide by 12
r_boat + current = 2 (r_boat - current) Remove the brackets.
r_boat + current = 2*r_boat - 2* current add 2 currents to both sides
r_boat + 3currents = 2*r_boat Subtract r_boat both sides
3 currents = r_boat.
240 = 12*(r_boat + current. Divide by 12
20 = r_boat + current Put 3 currents in for r_boat
20 = 3currents + 1 current Combine
20 = 4 currents Divide by 4
5 = current
The rate of the current = 5 miles / hour
3 currents = r_boat
3*5 = rate_boat
15 = rate of the boat
Answer:
x=-8
Step-by-step explanation:
I always change the decimals into whole numbers by multiplying them by 10. If you do this, it is much easier to solve. All you do is multiply every term by 10.
the equation changes to
-5(x+3)-2x=41
-5x-15-2x=41
combine like terms
-7x-15=41
bring the 15 over to the 41
-7x=56
divide everything by 7
-x=8
change x to a positive
x=-8