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3 years ago

7) What is the solution to the system of equations?

Mathematics

1 answer:

DiKsa [7]3 years ago

3 0

Answer:

Step-by-step explanation:

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In a particular game, a fair die is tossed. If the number of spots showing is either four or five, you win $1. If the number of

TiliK225 [7]

Answer:

The probability that you win at least $1 both times is 0.25 = 25%.

Step-by-step explanation:

For each game, there are only two possible outcomes. Either you win at least $1, or you do not. Games are independent. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Probability of winning at least $1 on a single game:

The die has 6 sides.

If it lands on 4, 5 or 6(either of the three sides), you win at least $1. So

$p = \frac{1}{2} = 0.5$

You are going to play the game twice.

This means that $n = 2$

The probability that you win at least $1 both times is

This is P(X = 2).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{2,2}.(0.5)^{2}.(0.5)^{2} = 0.25$

The probability that you win at least $1 both times is 0.25 = 25%.

4 0

3 years ago

The resquest of the y'+6y=e^4t, y(0)=2

kotegsom [21]

This is a linear differential equation of first order. Solve this by integrating the coefficient of the y term and then raising e to the integrated coefficient to find the integrating factor, i.e. the integrating factor for this problem is e^(6x).
Multiplying both sides of the equation by the integrating factor: 

(y')e^(6x) + 6ye^(6x) = e^(12x) 

The left side is the derivative of ye^(6x), hence 

d/dx[ye^(6x)] = e^(12x) 

Integrating 

ye^(6x) = (1/12)e^(12x) + c where c is a constant 

y = (1/12)e^(6x) + ce^(-6x) 

Use the initial condition y(0)=-8 to find c: 

-8 = (1/12) + c 
c=-97/12 

Hence 

y = (1/12)e^(6x) - (97/12)e^(-6x)

7 0

3 years ago