a shop stocks six types of phone battery (b1, b2, b3, b4, b5, b6) and a total inventory of 60 phone batteries. assume that the store can get at least 60 of each type of battery. in how many ways can the inventory of 60 batteries be distributed over the six di? erent types if:
(a) there are no restrictions on the number of battery of any type?
(b) the shop must stock at least ? ve batteries of each type?
(c) the shop stocks either b1-type batteries or b2-type batteries, but not both (with no restriction on the type b3, b4, b5, b6 batteries)?

At the olympic games, many events have several rounds of competition. one of these events is the men's 100-meter backstroke. the upper dot plot shows the times (in seconds) of the top 8 finishers in the final round of the 2012 olympics. the lower dot plot shows the times of the same 8 swimmers, but in the semifinal round. which pieces of information can be gathered from these dot plots? (remember that lower swim times are faster.) choose all answers that apply: a: the swimmers had faster times on average in the final round. b: the times in the final round vary noticeably more than the times in the semifinal round. c: none of the above.

You are looking for your first credit card. you plan to use this credit card only for emergencies and to pay the credit card balance in full each month. which credit card feature is most important? a. no annual fee b. low apr c. generous rewards program d. no balance transfer fee select the best answer from the choices provided

A3cm×3cm\greend{3\,\text{cm} \times 3\,\text{cm}} 3cm×3cm start color greend, 3, space, c, m, times, 3, space, c, m, end color greend rectangle sits inside a circle with radius of 4cm\blued{4\,\text{cm}} 4cm start color blued, 4, space, c, m, end color blued . what is the area of the shaded region? round your final answer to the nearest hundredth.