The circular base of the cone below has center C and another circle, with center B, as shown on the diagram at right. The circle is the base of a smaller cone with height AB. The measurements in the diagram are giving in inches. Triangle ABD is similar to triangle ACE. The smaller cone is removed to create a new object, as shown below.

What is the volume of this new object? Use 3.14 for π. Round your answer to the nearest tenth. Enter your answer and your work or explanation in the space provided.

What is the explicit rule for the sequence in simplified form? −1,−4,−7,−10,−13… an=4−5n an=−4−3n an=2−3n an=−6−5n

Sally deposited money into a savings account paying 4% simple interest per year. the first year, she earned $75 in interest. how much interest will she earn during the following year? show your work and explain your reasoning in the space provided below.

In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. consider the data set 14, 6, 8, 15, 15. (a) use the defining formula, the computation formula, or a calculator to compute s. (round your answer to one decimal place.) s = 4.28 (b) multiply each data value by 3 to obtain the new data set 42, 18, 24, 45, 45. compute s. (round your answer to one decimal place.) s = 12.83 (c) compare the results of parts (a) and (b). in general, how does the standard deviation change if each data value is multiplied by a constant c? multiplying each data value by the same constant c results in the standard deviation remaining the same. multiplying each data value by the same constant c results in the standard deviation being |c| times as large. multiplying each data value by the same constant c results in the standard deviation increasing by c units. multiplying each data value by the same constant c results in the standard deviation being |c| times smaller. (d) you recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 3.8 miles. your friend wants to know the standard deviation in kilometers. do you need to redo all the calculations? yes no given 1 mile ≠1.6 kilometers, what is the standard deviation in kilometers? (enter your answer to two decimal places.)