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yuradex [85]
3 years ago
10

Here’s my dilemma, I can accept a $1000 bill or play a game ten times. For each roll of the single die, I win $500 for rolling 1

or 2, I win $400 for rolling 3; and I lose $300 for rolling 4,5,or 6. Based on the expected value, I should accept the $1000 bill.
Mathematics
1 answer:
Aloiza [94]3 years ago
5 0

Answer:

you should accept the $1,000 bill

Step-by-step explanation:

Given the information:

  • $500 for rolling 1 or 2
  • $400 for rolling 3
  • lose $300 for rolling 4,5,6

P (rolling 1 or 2) = 1/6 + 1/6 = 2/6 = 1/3

P (rolling a 3) = 1/6

P (rolling 4 or 5 or 6) = 3/6 = 1/2

Hence, the expected value for 1 time is:

E = (1/3)*500 + (1/6)*400 - (1/2)*300

E = $166 + $66 - $150

E = $82

Expected value is linear so if you roll the die 10 times, expected value is: 10*82 = $820

The expected value is $82, meaning you should accept the $1,000 bill

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The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula below:
Anni [7]

Given y_1=e^{2x} is a fundamental solution, we posit a second solution of the form y_2=y_1v=e^{2x}v, with derivatives

{y_2}'=e^{2x}v'+2e^{2x}v=e^{2x}(v'+2v)

{y_2}''=e^{2x}v''+4e^{2x}v'+4e^{2x}v=e^{2x}(v''+4v'+4v)

Substitute these into the ODE:

e^{2x}(v''+4v'+4v)-4e^{2x}(v'+2v)+4e^{2x}v=0\implies v''=0

Integrate both sides twice to get

v''=0\implies v'=C_1\implies v=C_1x+C_2

Then the second fundamental solution is

y_2=xe^{2x}+e^{2x}

but y_1 already cover e^{2x}, so y_2=xe^{2x}.

6 0
3 years ago
$675 borrowed for six years at an interest rate of 10% how much is interest
IrinaK [193]

Answer:$405

Step-by-step explanation:

Simple interest = Principal x Rate x Time

Given that Principal =$675

Rate= 10% = 10/100 = 0.1

Time = 6years

Slot the values into the formula, then multiply:

I= 675 x 0.1 x 6

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Interest of $405 will be paid.

I hope this helps.

8 0
3 years ago
Help me on dis please
riadik2000 [5.3K]

Answer:

16?

Step-by-step explanation:

Im not sure sorry if its wrong

6 0
3 years ago
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A right triangle has one angle that measures 55°. What is the measure of the other acute angle?
Gemiola [76]

Answer:

35 degrees.

Step-by-step explanation:

In order to find an angle in a triangle we need to know the other two angles, because the angles in a triangle all add up to 180 degrees. So, knowing two will get us the other one. In this case, we know two angles. One of them is 55, and the other, since it is a right triangle, is 90. So the two angles we know are 55 and 90. Using that all angles in a triangle add up to 180, we can use

55 + 90 + x = 180

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x = 35

7 0
3 years ago
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Vinil7 [7]

ac = ab + bc

11x  + 2  = 3 + 2x + 5

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bc = 6 1/3


    

6 0
3 years ago
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