Adam, Brian, and Chris fire one shot each at a target. The probability that Adam will hit the target is \( 1 / 5 \). The probability that Brian will hit the target is \( 1 / 4 \). The probability that Chris will hit the target is 1/3. If they fire together, calculate the probability that i. All three shots hit the target, ii. Chris' shot only hits the target, iii. At least one shot hits the target, iv. Exactly two shots hit the target.

| Considere a equação do \( 2^{0} \) grau, em \( x \), dada por \[ 5 x^{2}+b x+c=0 \] Se as raízes dessa equação são \( \quad x_{1}=-1 \) e \( x_{2}=\frac{2}{5} \), determine o produto \( b \).c.

Assume that in a bakery each customer buys only one item at a time. There's a \( 70 \% \) chance a customer will buy a croissant and a \( 30 \% \) chance a customer will buy a muffin. There are only two muffins left and five people are still waiting in line. Compute the probability that these two muffins will be sufficient, i.e. no customer will want a muffin and find that there are none left, Thank you.

1.3. Find a power series representation for the following \[ h(x)=\frac{2 x^{2}}{1+x^{3}} \text {. } \] 1.4. Find a power series representation for the following function \[ g(x)=\frac{1}{(1-x)^{2}} \text {. } \] 1.5. Determine the first four terms of the Taylor series expansion for \( \ln x \) centred at \( a=1 \). Find the first four terms of the Maclaurin series for \( (1+x)^{m} \) where \( m \) is an

1. (i) \( \frac{x}{2}+\frac{2}{x} \)

how many answers does the equation \[ \frac{x^{2}-4}{x^{2}+1}+\frac{x^{2}+1}{x^{2}-4}=\frac{5}{2} \]