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#math #mistakes
When breaking up a square of the form \(41^2\) to make the squaring easier make sure that broken up form actually computes to the original number. For example \(40+1=41\) but \(40-1\neq1\)
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In Chapter 3 you’ll read about the anxious mind—the cognitive view of anxiety. Then, in Chapter 4, you will learn about how cognitive therapy works and what types of exercises you’ll be doing to address your anxiety using this book. In Chapter 5 you’ll create your own anxiety profile, which will be packed with information that you’ll use throughout the book’s exercises so that you really target your unique problems and identify your strengths. You should complete the exercises and worksheets as you read through Chapters 1–5 of the workbook.

In Chapters 6 and 7 you’ll learn the techniques that will help you lessen anxietyand its hold on you. We suggest you read those two chapters without doing the exercises and then follow the instructions in Chapter 8 for putting together the cognitive and behavioral techniques into an Anxiety Work Plan that you can use to systematically carry out your cognitive therapy program. Then start implementing the work plan by doing the exercises and worksheets you’ve selected from Chapters 6 and 7.
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An example of a goal for behavioral change might be to speak up and give your opinion more often at office meetings, a cognitive goal might be to stop assuming that every time your chest feels tight it could be a heart attack, and an emotional goal might be to feel less tense and agitated whenever you think about retirement.
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The idea that some people may decide to pay for producing and promoting a product (instead of buying it), and bear the risk associated with that decision, represents a further step in the evolution of consumers’ roles, that involves a mix of entrepreneurship and social network participation. The selection of the initiatives to be supported, the monetary investment from consumers, the outsourcing of entrepreneurial risk by the organization that sets up the crowdfunding activity, and the blurring boundaries between marketing and finance are only some of the new issues involved with crowdfunding initiatives.
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It is not surprising that the financing of early-stage creative projects and ventures is typically geographically localized since these types of funding decisions are usually predicated on personal relationships and due diligence requiring face-to-face interactions in response to high levels of risk, uncertainty, and information asymmetry. So, to economists, the recent rise of crowdfunding - raising capital from many people through an online platform - which offers little opportunity for careful due diligence and involves not only friends and family but also many strangers from near and far, is initially startling.
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After raising $375k (all amounts in USD) in seed funding from several high-profile Silicon Valley angel investors for an innovative e-paper display “Pebble” watch that enables users to interact with their Android or iOS device through a wrist interface, inventor-entrepreneur Eric Migicovsky required an additional $100k for tooling equipment to move from his pro- totype to a small production run. Despite having production experience with a previous watch he created for the Blackberry, experience raising seed capital, pedigree through his affiliation with a high-profile incubator (Y-Combinator), and being located in a region with a high concentration of angel investors, he could not find a willing backer. On April 11, 2012, he turned to crowdfunding, with the goal of raising capital in small amounts from many people through the Kickstarter online platform. He thus launched a campaign to raise $100k, promising contributors a watch for every $120 (approximately) they pledged. To his surprise, he raised the required capital in two hours. After 37 days, he closed his campaign, having raised more than $10M from 68,929 people and committed to producing 85,000 watches with expected delivery by September that year
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Around the same time, on April 5, 2012, President Obama signed into law the Jump- start Our Business Startups (JOBS) Act. In contrast to the already existing crowdfunding platforms that enable individuals to raise funds as donations or in return for rewards (sim- ilar to pre-sales of new products in some cases), a key provision of the JOBS Act legalizes crowdfunding for equity by relaxing various restrictions concerning the sale of securities. 1 However, the primary purpose of the Securities Act of 1933, which is the basis for most of the regulations in question, is to protect investors. Thus, relaxing these restrictions raises the concern that crowdfunding will expose investors to risk from fraud or incompetence
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In the case of the Pebble, for example, despite disappointed and vocal funders, the holiday season came and went without a single unit shipped or even produced. Although the well-intentioned inventor posted regular updates on his progress as he sourced components from vendors around the globe and set up a production facility in China, he was not able to fill all of his crowdfunded orders until May 2013. 2 Anticipating these types of problems (and worse), the JOBS Act stipulated that equity crowdfunding required rules be set by the Securities and Exchange Commission (SEC), which were anticipated for January 2013 but are still in progress as of this writing
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These two events in April 2012, the signing of the JOBS Act and the financing of the Pebble, legislated and demonstrated an innovation in the market for early-stage finance that could have significant economic consequences. Although the years of preamble leading to these events occurred primarily outside of mainstream attention, both events, particularly the former, raised general awareness of and interest in the potential of crowdfunding
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Funding is highly skewed - On the same platform, whereas 61% of all creators did not raise any money, 0.7% of them accounted for more than 73% of the funds raised between 2006 and 2009 (Agrawal, Catalini, and Goldfarb, 2011). Similarly, outcomes are highly skewed on Kickstarter, even conditioning the sample on successfully funded projects: 1% (10%) of projects account for 36% (63%) of funds (Agrawal, Catalini, and Goldfarb, 2013)
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Funding propensity increases with accumulated capital and may lead to herding - The propensity of individual funders to invest in a project increases rapidly with accumulated capital. On Sellaband, in a given week, funders were more than twice as likely to invest in creators who reached 80% of their funding goal, relative to those who had raised only 20% of it (Agrawal, Catalini, and Goldfarb, 2011). The acceleration is particularly strong towards the end of the fundraising campaign, similar to online lending platforms (Zhang and Liu, 2012), and raises concerns of herding behavior. At the same time, projects that are eventually successful might slow down in the middle of the process because of a bystander effect - a reduction in the propensity to fund by new individuals because of the perception that the target will be reached regardless (Kuppuswamy and Bayus, 2013).
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Funding follows existing agglomeration - Despite the decoupling of funding and location, funds from crowdfunding disproportionately flow to the same regions as tra- ditional sources of finance (Agrawal, Catalini, and Goldfarb, 2013), perhaps due to the location of human capital, complementary assets, and access to capital for follow-on financing
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In the technology and design categories on Kickstarter, estimates suggest that more than 50% of products are de- livered late (Mollick, 2013)
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Why was crowdfunding for early-stage creative projects not a meaningful method of finance before the commercialization of the internet? First, matching funders with creators is now more efficient and effective due to lower search costs online. Second, risk exposure is reduced because funding in small increments is economically fea- sible online. Finally, low communication costs facilitate better (though far from perfect) information gathering and progress monitoring for distant funders and also better enable funders to participate in the development of the idea
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Unlike non-equity crowdfunders who make funding decisions based on their own interest in the offering, an equity funder must also assess the expected demand from others.
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To the extent that creators are able to raise capital and demonstrate demand through non-equity crowdfunding (e.g., “pre-sales”), thus avoiding dilution, and then raise later-stage capital from established investors with status, reputa- tion, a valuable network, and an ability to engage in follow-on financing rounds, creators with high-quality inventions may have little incentive to employ equity crowdfunding.
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traditional equity investors may be able to offer capital at a lower price than equity crowdfunding because they are able to conduct face-to-face due diligence and thus are better able to assess risk and return. Indeed, after demonstrating customer demand in a non-equity crowdfunding setting, the creator of the Pebble chose to raise his next round of $15m from traditional equity investors through conventional channels.
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In general, the most critical differences between equity and non-equity crowdfunding will arise due to the amplification of information asymmetries. Whereas the asymmetry problem currently concerns the feasibility of and the creator’s ability to deliver the product, in the equity setting the asymmetry problem includes the above as well as the creator’s ability to generate equity value by building a company rather than just delivering a product. In the absence of strict governance, reporting, accounting, and other requirements common in publicly traded securities markets, crowdfunders are subject to an unusually high degree of risk.
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“Fred Wilson, a prominent venture capitalist, calculates that if Americans used just 1% of their investable assets to crowdfund business they would release a $300 billion surge of capital.” - The Economist 6
http://www.economist.com/node/21556973
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“Crowdfunding has the potential to revolutionize the financing of small business, transforming millions of users of social media such as Facebook into overnight venture capitalists, and giving life to valuable business ideas that might otherwise go unfunded.” - The Wall Street Journal 7
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“...crowdfunding could become an efficient, online means for defrauding the in- vesting public.” - Wired 10
http://www.wired.com/business/2011/12/crowdfunding-big-thing-fraud/
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The honeymoon period that we are experiencing around crowdfunding is begin- ning to come to a close, said Wil Schroter, co-founder and chief executive of FundablePeople realize there is real risk involved in investing in anything early- stage, whether it’s an idea, a charity or a product, and they’re starting to under- stand they aren’t buying off of Amazon.” - The New York Times 11
http://www.nytimes.com/2012/09/18/technology/success-of-crowdfunding-puts-pressure-on-
entrepreneurs.html
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In 2012, the US government recognized crowdfunding as a key to economic growth because it allows more individuals to engage as producers and consumers in the economy without the backing of high net-worth individuals
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Compared with all Internet users, crowdfunding platforms tend to appeal to childless college graduates under the age of 35 who browse from work and have incomes over $30,000 [33].
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Not only are creators motivated to raise funds, but they are motivated to raise funds in a democratic way. A respondent noted: “…it feels…you know, democratic, and people are able to contribute if they want and not to contribute if they don’t want.
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Funders are motivated to raise funds in a way that is consistent with their values. This is consistent with identity- based motivation in which people are motivated to give in ways that are consistent with their identity [27]. This is also consistent with identity-based motivations for joining online communities [13].
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committed long-term interactions allow creators to collaborate directly with funders, blurring the role between producer and consumer. An informant noted: “[Participating in Kickstarter] made me realize that I don’t want my projects to be like only mine. Like, I want others to share in my projects. So, I think all of my projects moving forward, they would all have some type of either interactive, interactivity to them? Or some means of crowd- based engagement.”
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Creators: Establish Relationships

In addition to raising funds, initial evidence finds that creators are motivated to engage in crowdfunding for the direct connection to the funders through a long term interaction that extends beyond the moment of the financial transaction. An informant noted: “[The funding process] creates a longer-term connection to people that you know. Weeks later, months later, you’re still interacting, and they are expecting to get something….I

think potentially you can build relationships with people, you know, over the course of time.”

Such committed long-term interactions allow creators to collaborate directly with funders, blurring the role between
producer and consumer. An informant noted:

“[Participating in Kickstarter] made me realize that I don’t
want my projects to be like only mine. Like, I want others to
share in my projects. So, I think all of my projects moving
forward, they would all have some type of either
interactive, interactivity to them? Or some means of crowd-
based engagement.”

The long term relationship stands in contrast to the short
term relationship that occurs in many online financial
transactions, however it is consistent with many online
communities that are not focused on financial transactions,
such as online discussion communities [13].
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Creators: Receive Validation

Initial evidence suggests that a creator’s online validation increases perceptions of ability. People’s beliefs in their ability increase when they have successful experiences and receive public recognition of their success [36]. An informant who sought funds for a youth photography workshop documenting neighborhood improvements commented on the effect of crowdfunding on his confidence to complete the project:

“I feel much more confident about my ability to do it [his project]”

An informant describes her experience before launching her project and how her confidence increased through online conversation.

“You sort of wonder if people are going to like you and like your research, and so I definitely got more confident once people were clearly interested in it and clearly engaging in the dialogue and supporting me financially.”

A founder of RocketHub describes how validation occurs. Funders seek funds from a community of people who care not just about the project, but about the individual’s success. The founder explains:

“You are embedding yourself in an active community…you are being validated…Friends and families become evangelists for you…these are completely normal people [creators] and they are working way outside their comfort zone…With crowdfunding, you are allowing people to do something…You have people saying, I believe in you.”

Online validation supports perceptions of ability and pushes people to expand capability. This finding is consistent with social cognitive theory, which suggests that people build beliefs in their ability through social interactions [36]. This finding is supported by prior research in online communities, which finds that people engage in these communities to build self-esteem [22].
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Creators: Replicate Successful Experience of Others

Initial findings suggest that people participate in crowdfunding because they want to replicate the success of others [37]. An informant describes how her project success helped encourage another creator to pursue crowdfunding:

“There’s a fellow archeologist that I’ve never met, but she just started a new Rockethub project, and so she’s in the process of funding, and she claimed to be inspired by me.”

Another informant spreads out his successful Kickstarter experience to people he knows after he launched a project, and several people got motivated and started to follow along and participate in crowdfunding as a creator:

"After I did this Kickstarter fundraising, and it was successful…a number of people I know started their own Kickstarter projects. I think, I kind of, you know motivate some people to try it themselves."

Successful experiences can be replicated among people through social proof. Beyond establishing general relationships within the online community, creators not only generate more interest among people but also show them how to become a creator recognized by the larger online community through doing. Seeing other creators succeed in launching a project online provides social proof for anyone who wants to get started and become a creator on crowdfunding platforms.
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Creators: Expands Awareness of Work through Social Media Initial findings suggest that creators were motivated to participate in crowdfunding because it expanded their awareness through social media. An anthropologist who used RocketHub to fund her research on ancient Roman skeletons, described being motivated to not only share her work publically but engage in a dialogue about her work. “I’ve gotten dozens of emails from people around the world who are really interested in the project, and who want to help on the scientific end or telling their friends and family. A documentary TV producer contacted me… these are things that don’t normally happen if you just have a grant proposal, or you have an article in the journal, you know, that maybe nobody reads. And so putting it out to the public um has been really, really great for me…[My project] was picked up on Twitter by a British science journalist, and so he pitched it to CNN, and then CNN covered it and Forbes covered it and then everything just went crazy after that... I really didn’t expect this… I’m really excited that people are just so, so excited about this project that they're willing to give me $20 or $50 or $1000.”

In addition to the online communication about her work, the monetary gifts confirms that awareness of her work is spreading.

Participation also influenced her online profile. She commented:

“I’ve been communicating with people through Twitter, I’ve gained a bunch of new Twitter followers, a bunch of new G+ followers…I put up a website with a blog, and people can comment on the blog…I wanted to engage the public in a little more of a dialogue.”
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Funders: Seek Rewards

While creators seek funds, funders seek rewards, often in the form of tangible products and/or services. A funder who funded an iPad accessory noted: “I like to buy things that I can play with.” Funders refer to the transaction as “buying,” “getting,” “giving.” A funder who contributed funds to a project that employed local women in a Chilean community commented: “I like that I get something sent to me. I know it’s small, but like, I enjoyed getting a postcard and a CD…I’m looking forward to getting a DVD if the project actually comes to fruition.”
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Funders consistently reported being motivated to give to get the product first or get a limited edition of the work. A funder who supported a film commented: “I want to see [the film] right when it’s out. So, instead of giving $10, I gave $25.”
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Initial evidence suggests that funders are aware of the exchange of value. Further, they are disappointed when funds are not used to produce rewards directly related to the project. A funder who contributed funds to a weather prediction app noted: “Don’t spend that money on making t-shirts, spend it on building software…I want to see, like, I know that my money is being used well.”
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another funder noted the sense of security she felt by giving money through Kickstarter, which has an all or nothing funding model. “There’s a security to knowing that if the goal isn’t met, my money doesn’t just get wasted.”
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The first two chapters contain a brief introduction to cognitive therapy and an invitation to take another look at your own anxiety.
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The first two chapters contain a brief introduction to cognitive therapy and an invitation to take another look at your own anxiety. In Chapter 3 you’ll read about the anxious mind—the cognitive view of anxiety. Then, in Chapter 4, you will learn about how cognitive therapy works and what types of exercises you’ll be

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#math #mistakes
Remember that the Distributive Property of Multiplication applies to both sums and subtractions so it's \(a(b\pm c)\) not just \(a(b+c)\).
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