1.) A sheet of paper is cut into 6 same-size parts. Each of the parts is...

1.) A sheet of paper is cut into 6 same-size parts. Each of the parts is then cut into 6 same-size parts and so on.

a. After the 8th cut, how many of the smallest pieces of paper are there?

b. After the nth cut, how many of the smallest pieces of paper are there?

2.) Find the sum of the sequence 5+15+25+35+...65

3.)How many terms are there in each of the following sequences?

a. 1,2,2²,2³,...2²⁹⁹

b.9,13,17,21,...329

c.32,33,34,35,...432

Expert Solution

Colby Messinger answered 1 year ago

Suppose that you have cut circles of different diameters from the same uniform sheet of paper.You...

Suppose that you have cut circles of different diameters from the same uniform sheet of paper.You measure the diameter and mass of each circle and collect the following data: Mass of Circles as a Function of DiameterD (cm) (m) (g)10.0 0.624 12.0 0.886 14.0 1.148 16.0 1.429 18.0 1.859 20.0 2.307 As an exercise you will now make a graph of vs. in Excel. Note that when you are asked to make a graph in the form " vs ",...

Prepare a vertical analysis or same size income statement and balance sheet for Pepsi and Coca...

Prepare a vertical analysis or same size income statement and balance sheet for Pepsi and Coca Cola for 2016 and 2017. Write a paragraph highlighting what you learn from the percentages of sales or total assets calculated from the financial statements. Write also about the comparison between 2016 and 2017 and between Coke and Pepsi.

1.Why is the equilibrium cluster size not same as the efficient cluster size? Explain with a...

1.Why is the equilibrium cluster size not same as the efficient cluster size? Explain with a graph. 2.The production of wooden ships is a weight-losing activity (as shown by the large piles of sawdust and wood-scraps) and yet most of the shipyards are located far from a forest. Shipyards locate far from a forest because...Illustrate.

Below is the balance sheet information on two companies. Prepare a common-size balance sheet for each...

Below is the balance sheet information on two companies. Prepare a common-size balance sheet for each company. Review each company's percentage of total assets. Are these companies operating with similar philosophies or in similar industries? What appears to be the major difference in financing for these two companies? Account Balance Sheet Company 1 Balance. Sheet Company 2 Current Assets Cash $5,377 $299 Investments $4,146 $354 Accts. Rec. $8,100 $221 Inventory $5,372 $494 Total Current $22,995 $1,368 Long Inv. $84 $307...

Prove that the number of partitions of n into parts of size 1 and 2 is...

Prove that the number of partitions of n into parts of size 1 and 2 is equal to the number of partitions of n + 3 into exactly two distinct parts

Two stacks are the same if they have the same size and their elements at the...

Two stacks are the same if they have the same size and their elements at the corresponding positions are the same. Add the method equalStack to class ArrayStack that takes as a parameter ArrayStack object otherStack, and returns true if this stack is the same as otherStack. Use the following signature for your method: public boolean equalStack(ArrayStack otherStack) { ... }

In the manufacture of paper, logs are cut into small chips, which are stirred into an...

In the manufacture of paper, logs are cut into small chips, which are stirred into an alkaline solution that dissolves several of the chemical constituents of wood but not cellulose. The slurry of undissolved chips in solution is further processed to recover most of the original solution constituents and dried wood pulp. In one such process, wood chips with a specific gravity of 0.64 containing 45 wt% water and 47 wt% (dry basis) cellulose are treated to produce 1400 tons/day...

This problem has 6 parts. This is part 1 of 6. A 2018 study by the...

This problem has 6 parts. This is part 1 of 6. A 2018 study by the USDA found that less than 20% of people do not wash their hands for at least 20 seconds, which is the CDC recommended amount of time. A healthcare professional believes that the COVID-19 outbreak has led to people being more diligent about handwashing, and that now this proportion has increased to greater than 20%. She designs a study and finds that 82 out of...

Two parallel electrical conducturs each leads a current of the same size. The distance between the...

Two parallel electrical conducturs each leads a current of the same size. The distance between the center of the conductors can be varied from 100 mm to 1000 mm. The currents are going in the same directions in both of the conductors and have a value of I=19 A. Calculate the force per meter (F/l) between the conductors in their plane and plot F/l against the distance between them (100 mm to 1000 mm) in a graph. Do not take...

1. Explain how it is that cells in different parts of the body have the same...

1. Explain how it is that cells in different parts of the body have the same DNA yet express different genes. Explain using molecular components of gene regulation.

Question