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LUCKY_DIMON [66]
3 years ago
12

In the game of roulette a metal ball is dropped into a spinning wheel having 38 compartments, 18 of which are red, 18 are black,

two are green. suppose we spin the wheel ten consecutive times and let a random variable x be the number of times the metal ball will land on a red color.
Suppose you always bet $5 on red. If red shows up you win $5 otherwise you lose your bet. What is the probability of
A. Making a $30 profit if you bet on ten consecutive spins of the wheel?
B. Breaking even if you bet on 10 consecutive spins
C. Being $5 in deficit if you bet on 10 consecutive spins
Mathematics
1 answer:
leonid [27]3 years ago
8 0
I think its A but i dont sure sorry
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A swimming pool whose volume is 10 comma 000 gal contains water that is 0.03​% chlorine. Starting at tequals​0, city water conta
Katarina [22]

Answer:

C(60) = 2.7*10⁻⁴

t = 1870.72 s

Step-by-step explanation:

Let x(t) be the amount of chlorine in the pool at time t. Then the concentration of chlorine is  

C(t) = 3*10⁻⁴*x(t).

The input rate is 6*(0.001/100) = 6*10⁻⁵.

The output rate is 6*C(t) = 6*(3*10⁻⁴*x(t)) = 18*10⁻⁴*x(t)

The initial condition is x(0) = C(0)*10⁴/3 = (0.03/100)*10⁴/3 = 1.

The problem is to find C(60) in percents and to find t such that 3*10⁻⁴*x(t) = 0.002/100.  

Remember, 1 h = 60 minutes. The initial value problem is  

dx/dt= 6*10⁻⁵ - 18*10⁻⁴x =  - 6* 10⁻⁴*(3x - 10⁻¹)               x(0) = 1.

The equation is separable. It can be rewritten as dx/(3x - 10⁻¹) = -6*10⁻⁴dt.

The integration of both sides gives us  

Ln |3x - 0.1| / 3 = -6*10⁻⁴*t + C    or    |3x - 0.1| = e∧(3C)*e∧(-18*10⁻⁴t).  

Therefore, 3x - 0.1 = C₁*e∧(-18*10⁻⁴t).

Plug in the initial condition t = 0, x = 1 to obtain C₁ = 2.9.

Thus the solution to the IVP is

x(t) = (1/3)(2.9*e∧(-18*10⁻⁴t)+0.1)

then  

C(t) = 3*10⁻⁴*(1/3)(2.9*e∧(-18*10⁻⁴t)+0.1) = 10⁻⁴*(2.9*e∧(-18*10⁻⁴t)+0.1)

If  t = 60

We have

C(60) = 10⁻⁴*(2.9*e∧(-18*10⁻⁴*60)+0.1) = 2.7*10⁻⁴

Now, we obtain t such that 3*10⁻⁴*x(t) = 2*10⁻⁵

3*10⁻⁴*(1/3)(2.9*e∧(-18*10⁻⁴t)+0.1) = 2*10⁻⁵

t = 1870.72 s

7 0
3 years ago
If ABC forms a linear pair with CBD, use the Linear Pair Postulate to determine the value of x
arsen [322]
There you go any questions?

7 0
3 years ago
Solve the system of linear equations below 2x-y=0 3x-2y=-3
Lynna [10]
2x - y = 0
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3x - 2(2x) = -3
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2(3) = y
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3 0
3 years ago
Could someone pls send me an example of using the substitution method in algebra?
Elden [556K]

Answer:

in this method a variable is expressed in terms of another variable from one equation and it is substituted in remaining equation.

Step-by-step explanation:

solve:x+2y=9 and 3x-y=13.

x+ 2y=9…be the first equation

3x-y=13…be the second equation

from first equation

x=9-2y…be the third equation substituting value of x from third equation in second equation, we get

3(9-2y)-y=13

or, 27-6y-y=13

or, y=2

now,

substituting value of y in third equation, we get,

x=9-2×2

=9-4

=5

the required value of x and y are 5&2

8 0
3 years ago
Rena spent 6 days reading her book completing the same fraction of the book each day, she read a total of 8/9 of her book what f
seraphim [82]

Answer:

The answer would be A. 1 1/5

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1 8/40 Simplify to 1 1/5

Hope this helps!

Step-by-step explanation:

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6 0
3 years ago
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