In p_3 find the change of co-ordinate matrix from the basis b = {1, 1 + t, 1 + t + t^2, 1 + t + t^2 + t^3) to the standard basis. then write 2 + 4t + t^3 as a linear combination of the polynomials in b.

Recall that the owner of a local health food store recently started a new ad campaign to attract more business and wants to know if average daily sales have increased. historically average daily sales were approximately $2,700. the upper bound of the 95% range of likely sample means for this one-sided test is approximately $2,843.44. if the owner took a random sample of forty-five days and found that daily average sales were now $2,984, what can she conclude at the 95% confidence level?