Tertiary alcohols with two identical alkyl groups attached to the alcohol carbon can be made either from an ester and two moles of a Grignard reagent, or from a ketone and one mole of a Grignard reagent. Use retrosynthetic analysis to suggest one path of each type to synthesize 3‑methyl‑3‑pentanol (or 3‑methylpentan‑3‑ol).

Allie and sarah decided that they want to purchase renters insurance for the apartment they share. they made a list of all of the items to be covered by the insurance policy, along with their estimated values. if the items to be covered total more than $3000, the insurance company charges an annual premium of 23% of the total value of the items. if the items to be covered total $3000 or less, the insurance company charges an annual premium of 20% of the total value of the items.

Sye chase started and operated a small family architectural firm in 2016. the firm was affected by two events: (1) chase provided $25,000 of services on account, and (2) he purchased $2,800 of supplies on account. there were $250 of supplies on hand as of december 31, 2016. record the two transactions in the accounts. record the required year-end adjusting entry to reflect the use of supplies and the required closing entries. post the entries in the t-accounts and prepare a post-closing trial balance.

Suppose that two firms produce differentiated products and compete in prices. as in class, the two firms are located at two ends of a line one mile apart. consumers are evenly distributed along the line. the firms have identical marginal cost, $60. firm b produces a product with value $110 to consumers. firm a (located at 0 on the unit line) produces a higher quality product with value $120 to consumers. the cost of travel are directly related to the distance a consumer travels to purchase a good. if a consumerhas to travel a mile to purchase a good, the incur a cost of $20. if they have to travel x fraction of a mile, they incur a cost of $20x. (a) write down the expressions for how much a consumer at location d would value the products sold by firms a and b, if they set prices p_{a} and p_{b} ? (b) based on your expressions in (a), how much will be demanded from each firm if prices p_{a} and p_{b} are set? (c) what are the nash equilibrium prices?