On January 1, Year 1, Mary Company (lessee) leased equipment, signing a five-year lease that requires annual lease payments of $20,000 at the end of each year, beginning on December 31, Year 1. The lease qualifies as a finance lease. In addition, Mary guarantees that the residual value will be $8,000 at the end of the lease term. The relevant interest rate is 12%.
The present value factors for five periods at 12% are as follows:
Present value of $1 0.567427
Present value of ordinary annuity of $1 3.604776
If the Mary Company uses the straight-line method of amortization for its assets, what is the amount of amortization expense for the leased equipment for the year ending December 31, Year 1?
A.$15,554.
B.$13,727.
C.$12,419.
D.$14,419.

Answers

Answer 1

The correct answer is option C: $12,419.

Explanation: To determine the annual payment for a lease, you have to use the following formula: Periodic payment = Present value of the annuity factor * lease payment In this case, the lease payment is $20,000 a year, the Present value of the annuity factor for 5 years at 12% is 3.604776.

Hence, the periodic payment = $20,000 * 3.604776 = $72,095.52. Now, to calculate the amount of amortization expense for the leased equipment for the year ending December 31, Year 1, we need to determine the interest portion and the principal portion of the periodic payment for the first year.

To do this, we will use the present value factor of $1 for one period at 12% which is 0.89384. Interest portion = Lease liability at the beginning of the year * interest rate Lease liability at the beginning of the year = Lease payment - Principal payment (for the first year) = $72,095.52 - ($72,095.52 - $8,000) / 5 = $14,419.10Principal payment (for the first year) = $72,095.52 - $14,419.10 = $57,676.42 Interest portion = $14,419.10 * 0.12 * 1 = $1,730.29Amortization expense = Principal portion + Interest portion = $57,676.42 + $1,730.29 = $12,419.71≈ $12,419

Therefore, the amount of amortization expense for the leased equipment for the year ending December 31, Year 1 is $12,419.

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Related Questions

Which of the following made the building of the first skyscrapers possible
A.Elevator
B.Light timber frame forms
C.Internal combustion engine
D. Rapid steel production

Answers

Answer:

choose all three

elevator

internal combustion engine

rapid steel production

Explanation:

Elevator, Internal combustion engine and Rapid steel production  made the building of the first skyscrapers possible. Hence, option A, C and D are correct.

What is Elevator?

An elevator, often called a lift, is a vehicle that goes in a vertical shaft to carry passengers or goods between floors of a multistory building. With the aid of a counterweight, the majority of modern elevators are propelled by electric motors through a system of cables and sheaves.

The four fundamental types of elevators are hydraulic, traction, machine-room-free, and vacuum. The fundamental distinction between these two words can be seen in the accents in which they are used; for instance, "lift" is used with a British accent whereas "elevator" is used in an American one.

Elevators or lifts carry people and cargo up and down, while escalators act as moving staircases from one story of a structure to another. Moving walkways transport people horizontally or at a slight slope.

Thus, option A, C and D are correct.

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Size is limited under a Sole Proprietorship.
True
False

Answers

Answer:

True

Explanation:

because 1 person can't control a huge company or business

How do any of these life decision problems

How do any of these life decision problems

Answers

Answer:

baseially you are putting in a person is affecting your life. you come up with a solution. write a postive way to solve it then right a negavitve way to solve it.  then write when you are going to solve  your problem. then the steps that are needed.

Which credit utilization rate would be preferable to a lender on a credit card application?

Answers

Your credit utilization ratio should be no higher than 30 percent, and the lower it is, the better for your credit score it will be.

What is the best credit card utilization rate?

30 percent Keeping your credit utilization below 30 percent is a good idea, especially if you want to keep your good credit score. This means that if you have $10,000 in credit available, your outstanding balances shouldn't be more than $3,000 at any given time.

Why is credit utilization recommended at 30%?

The normal exhortation is to continue to spin obligation beneath 30% of your accessible credit with the goal that your usage rate doesn't hurt your financial assessment. However, experts claim that your FICO score, which is used by the majority of lenders to make decisions, begins to decline well below that point.

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What does "Certeris Paribus" assume when
calculating how people spend money?
A. The person has held the same job with the same amount of
pay
B. The person has been promoted and makes more money than
before.
C. The person has lost their job and is unemployed at the
moment.
D. The person has taken a second job for additional income.

What does "Certeris Paribus" assume whencalculating how people spend money?A. The person has held the

Answers

ceteris paribus assumes things like confidence and income remain the same, so that we may study simply the interaction between interest rates and the demand for loans and ignore how all the other variables might affect the outcome.

What is an optical cue?

Answers

answer well they  provide depth information when viewing a scene with both eyes.

i don't know how else to explain it

why did God call abraham​

Answers

Answer: god chose Abraham and said i will make you a great nation and i will bless you.

Explanation: god commanded  Abram to move to another country . This is why god planned to make of Abram a new nation from which the prophets of god and the savior of the world would arise.

How much tim e will be needed for 525,000 to grow to $28.162.31 if deposited at
6% compounded quarterty?

Answers

It will take approximately 30.63 years for $525,000 to grow to $28,162.31 if deposited at a 6% interest rate compounded quarterly.

To calculate the time required for the initial amount to grow to the desired amount, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount ($28,162.31)

P = Principal amount ($525,000)

r = Annual interest rate (6% or 0.06)

n = Number of times interest is compounded per year (quarterly, so 4)

t = Time in years (unknown)

Rearranging the formula to solve for t, we have:

t = (log(A/P))/(n * log(1 + r/n))

Plugging in the values, we get:

t = (log(28,162.31/525,000))/(4 * log(1 + 0.06/4))

t ≈ 30.63 years

Therefore, it will take approximately 30.63 years for the initial deposit of $525,000 to grow to $28,162.31 at a 6% interest rate compounded quarterly.

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A deed conveyed the NE 1/4 of Section 18 and the NW 1/4 of Section 20, Are these parcels contiguous? How many acres were conveyed?

Answers

The parcels in question are the NE 1/4 of Section 18 and the NW 1/4 of Section 20. To determine if these parcels are contiguous, we need to consider their location within the grid system.

Parcels are considered contiguous if they share a common boundary or corner. In this case, the NE 1/4 of Section 18 is located directly south of the NW 1/4 of Section 20. Since they share a common boundary along their north-south edges, these parcels are contiguous. As for the number of acres conveyed, each section in the grid system contains 640 acres, and since both parcels are 1/4 sections, each parcel contains 640 acres * 1/4 = 160 acres. Therefore, the total number of acres conveyed in the deed is 160 acres (NE 1/4 of Section 18) + 160 acres (NW 1/4 of Section 20) = 320 acres.

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please be my dad? yes or yes?

Answers

Answer:

or

Explanation:

Answer:

yes i'm you new father figure

Explanation:

Ace electronics had sales of $1,000,000 in 2021 and sales of $1,040,000 in 2022. the percentage increase in sales was:_________

Answers

Ace electronics had sales of $1,000,000 in 2021 and sales of $1,040,000 in 2022. the percentage increase in sales was: 4%

Percentage increase =

($1,040,000 - 1,000,000)/$1,000,000) x 100 = 4%

How is sales growth determined?

To start, subtract the net sales of the prior period from those of the current period. Next, divide the outcome by the prior period's net sales. To get the % sales growth, multiply the figure by 100.

(Net sales this period – net sales prior period) / net sales prior period * 100

It is important to calculate sales growth

This formula can produce either a positive or a negative integer as the outcome. If the figure is positive, your sales revenue is increasing. For obvious reasons, this is ideal, but it's also crucial to consider the percentage itself; the greater the number, the better your organization is performing.

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Damerly Company (a Utah employer) wants to give a holiday bonus check of $350 to each employee. Since it wants the check amount to be $350, it will need to gross-up the amount of the bonus. Calculate the withholding taxes and the gross amount of the bonus to be made to John Rolen if his cumulative earnings for the year are $46,910. Besides being subject to social security taxes and federal income tax (supplemental rate), a 5% Utah income tax must be withheld on supplemental payments.

Answers

Answer:

$350

Explanation:

Calculation for the withholding taxes and the gross amount of the bonus to be made to John Rolen if his cumulative

Social Security rate 6.20%

Medicare rate 1.45%

Federal Income tax 22.00%

State income tax 5.00%

Total tax percentage 34.65%

Calculation for the Required gross bonus

Required gross bonus =$350/(1-34.65%)

Required gross bonus=$350/1-0.3465

Required gross bonus=$350/0.6535

Required gross bonus=$535.57

Gross bonus amount $535.57

Federal Income tax withheld (117.82) ($535.57*22%)

OASDI tax withheld (33.20)

($535.57*6.2%)

HI tax withheld (7.76)

($535.57*1.45%)

Utah Income tax withheld (26.77)

($535.57*5%)

Take home bonus check $350.00

Therefore the withholding taxes and the gross amount of the bonus to be made to John Rolen if his cumulative will be $350.00

information in data warehouses and data marts generally are ____, which means they are organized by business dimensions, which are subjects such as product, geographic area, and time period.
a. time variant
b. integrated
c. nonvolatile
d. multidimensional

Answers

Information in data warehouses and data marts generally are multidimensional, which means they are organized by business dimensions, which are subjects such as product, geographic area, and time period. The Option D is correct.

What is data warehouses and data mart?

A data warehouse is a large collection of historical data that supports decision making in an organization. A data mart is a smaller subset of a data warehouse that focuses on a specific topic or department.

A multidimensional data model allows users to view and analyze data from different perspectives and levels of detail. For example, a user can query the sales data by product, region, and month, or drill down to see the sales data by product, city, and day.

A multidimensional data model is often represented by a cube or a hypercube, where each dimension is a side or an axis of the cube. Each dimension can have multiple attributes or levels of hierarchy. For example, the product dimension can have attributes such as category, subcategory, and name. The data values are stored in the cells of the cube, which can be aggregated or disaggregated along the dimensions.

Some benefits of a multidimensional data model are:

It is intuitive and easy to understand for business users, as it reflects the way they think and talk about their data.It supports complex and ad hoc queries, as it allows users to slice and dice the data along any dimension or combination of dimensions.It improves query performance, as it precomputes and stores the summary data for each possible combination of dimensions, reducing the need to scan large tables.

Some examples of multidimensional data models are:

Star schema: A star schema consists of a fact table and multiple dimension tables. The fact table contains the measures or metrics of the business process, such as sales amount or quantity. The dimension tables contain the descriptive attributes of the dimensions, such as product name or region name. The fact table and the dimension tables are linked by foreign keys, forming a star-like structure.Snowflake schema: A snowflake schema is a variation of the star schema, where some of the dimension tables are normalized into multiple tables. This reduces data redundancy and storage space, but increases the complexity and number of joins in the queries.OLAP cube: An OLAP (online analytical processing) cube is a data structure that stores the precomputed summary data for a multidimensional data model. An OLAP cube can be created from a star or snowflake schema, or from other sources of data. An OLAP cube allows users to perform fast and interactive analysis on the data, using operations such as roll-up, drill-down, slice, dice, and pivot."

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A person who works as a sales representative for a manufacturer or wholesaler and gets paid a commission on any sales is classified a(n):

Answers

A person who works as a sales representative for a manufacturer or wholesaler and gets paid a commission on any sales is classified an agent.

Who is an agent?

This is a person that is signed on to work on behalf of another person. This may be someone who helps to make decisions on behalf of the person that they represent.

Also a person that does business on behalf of another for the sake of commissions is an agent.

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Which of the following is true of using qualitative research for measuring brand equity?
A)It helps in identifying the sources of brand equity.
B)It involves the use of brand recognition.

Answers

It helps in identifying the sources of brand equity is true of using qualitative research for measuring brand equity.

Qualitative research is a type of research that involves gathering data through open-ended questions and discussions to understand consumer behavior and perceptions. When it comes to measuring brand equity, qualitative research can be very useful in identifying the sources of brand equity, such as the emotions and values associated with a brand, the perception of quality, and the brand's personality.

Qualitative research can provide insights into how consumers interact with a brand and their motivations for doing so. By understanding the sources of brand equity, companies can develop strategies to enhance and maintain it. Qualitative research can also help companies understand how their brand is perceived in the market, which can help inform branding and marketing strategies. In conclusion, using qualitative research for measuring brand equity is an effective way to gain insights into the sources of brand equity and consumer perceptions of a brand.

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a 7.15 percent coupon bond with 27 years left to maturity can be called in eight years. the call premium is one year of coupon payments. it is offered for sale at $1,096.85. what is the yield to call of the bond? (assume interest payments are semiannual.) (round your answer to 2 decimal places.)

Answers

The return an investor will receive if they retain the bond until the call date is known as yield to call, or YTC (not maturity date). Typically, a call date comes before a maturity date. Only when a bond is callable does YTC happen.

Yield to Call (Semi-annual Bond) Callable in years 8

Number of semi-annual periods                            16           NPER

Default Par value of the Bond                              $1,000

Annual Coupoun rate                                            7.15%

Semi-annual Coupon Rate                                    3.58%

Semi-annual Coupon Payment                           $35.75           PMT

Call premium (One year coupon payment)        $71.50

Callable Price = Par value + Call premium          $1,071.50       FV

Current Market Price                                            $1.096.85           PV

Semi-annual yield                                                  3.15%                   RATE

Yield to Call (YTC)                                                  6.29%

Therefore, the yield to call is 6.29%

The return on the bond, if purchased today and held until the call date, is shown by this number. Note: The bond will be called at the earliest opportunity according to the yield to call calculation. Use the Yield to Maturity (YTM) Calculator if the bond under consideration is not callable.

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Hello pls help
3.08 free trade and barriers
Economic class

Hello pls help 3.08 free trade and barriers Economic class

Answers

To get this visual item, you can choose a cartoon that shows a fat cook who says that to make nice food, you have to break some tins. The topic of this cartoon is that economic success requires breaking some barriers.

This cartoon and protectionism

This cartoon is against the idea of protectionism because it advocates measures that would break the barriers of nations to attain success.

You might add that you agree on this topic about free trade because no nation can exist successfully by itself. To attain success, they need to liaise with other nations through trade.

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Which one is not a Function in MS Excel?

MAX
ARG
MIN
SUM

Answers

ARG is not a function I’m familiar with in Excel, however I’m familiar with MAX, MIN, and SUM in Excel.

There for the answer is ARG.

Ramirez Company installs a computerized manufacturing machine in its factory at the beginning of the year at a cost of $84,200. The machine's useful life is estimated at 20 years, or 391,000 units of product, with a $6,000 salvage value. During its second year, the machine produces 33,100 units of product.

Answers

The depreciation expense for the second year is $6,620.

To calculate the depreciation expense for the second year using the units-of-production method, we need to determine the depreciation cost per unit produced. Depreciation cost per unit = (Cost - Salvage value) / Total units of production

Cost = $84,200

Salvage value = $6,000

Total units of production = 391,000 units

Depreciation cost per unit = ($84,200 - $6,000) / 391,000 units

Depreciation cost per unit = $78,200 / 391,000 units

Depreciation cost per unit ≈ $0.20 per unit

Next, we can calculate the depreciation expense for the second year by multiplying the depreciation cost per unit by the units produced in the second year.

Depreciation expense for the second year = Depreciation cost per unit × Units produced in the second year

Depreciation expense for the second year = $0.20 per unit × 33,100 units

Depreciation expense for the second year = $6,620

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Which of the following should be considered last when searching for financing?
Question 18 options:

Family members

Banks

Commercial finance companies

Credit cards

Answers

When looking for funding, credit cards should be the last thing to consider. A credit card can be described as a small rectangular-shaped plastic card that is issued to consumers by a financial institution and normally enables them to make purchases on credit so that the money will be paid back later with a predetermined interest rate.

When looking for funding, credit cards should be the last thing to consider. Family, banks, businesses, and finance corporations are the main sources of funding. Using the idea of making a purchase now and paying for it later, a credit card is a type of payment card. OPTION C

A credit card enables the cardholder to make purchases without using cash anywhere that accepts credit cards. Based on your credit score, the card issuer decides what the credit limit will be.

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What type of credit is a monthly telephone bill? a) single -payment credit b) installment credit c) revolving credit.

Answers

A monthly telephone bill is an example of revolving credit i.e. option C. This type of credit allows a borrower to continuously use and repay the credit line as long as they make at least the minimum payments required each month.

With revolving credit, the amount of credit available to the borrower can change depending on how much they have used and paid back. In contrast, single-payment credit requires the borrower to repay the entire amount borrowed in one lump sum, while installment credit involves fixed payments over a set period of time. Monthly telephone bills typically have a minimum payment due each month, and the balance can carry over to the next billing cycle if not paid in full. Therefore, it falls under the category of revolving credit.

Thus, the right option is C.

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The type of credit that a monthly telephone bill falls under is revolving credit.

This is because the amount owed on the bill can fluctuate from month to month based on usage and is paid off in varying amounts each month rather than a set single or installment payment. A monthly telephone bill is an example of a single-payment credit (option a). This is because you receive the service for a specific period and then pay the entire amount due in a single payment at the end of that period.

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in the ________ phase of the strategic marketing planning process, the tone of decision-making questions is centered on the notion of "should we?"

Answers

In the planning phase of the strategic marketing planning process, the tone of decision-making questions is centered on the notion of "Should we?".

The most important as it analyzes internal strengths and weaknesses, external competition, changes in technology, and industry culture shifts and provides an overall picture of the state of the organization is known as the planning phase. It involves the identification and assessment of goals, merits, shortcomings, assets, and liabilities and lays down the groundwork for the subsequent phases.

The strategic marketing planning process typically consists of several phases. These phases generally include the following:

Planning PhaseAnalysis PhaseDevelopment Phase

The different marketing strategies that companies can use to reach their target audience and achieve their marketing goals include:

Paid advertisingCause marketingRelationship marketingUndercover marketingWord of mouthInternet MarketingTransactional marketingDiversity marketing

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How do perception, learning and attitudes affect consumer decision making and how marketer influence these processes

Answers

Perception means how a person is thinking, learning refers to acquiring new knowledge and attitudes means feeling towers the product or service. Consumer decision-making is significantly influenced by perception, learning, and attitudes.


Perception, learning, and attitudes are all important factors that affect consumer decision making. Perception influences how a consumer interprets and evaluates stimuli in the marketplace. Learning affects how a consumer learns from past experiences and develops buying habits. Attitudes influence a consumer's predisposition towards a product or service. Marketers can influence these processes by designing their campaigns to appeal to the target audience's senses, past experiences, and biases.

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the belief that personal qualities, such as intelligence, can be developed through effort and practice is indicative of a person who has a(n) ________ mindset.

Answers

The belief that personal qualities, such as intelligence, can be developed through effort and practice is indicative of a person who has a growth mindset.

A person who believes that personal qualities, including intelligence, can be developed through effort and practice is indicative of having a growth mindset.

The concept of a growth mindset was introduced by psychologist Carol Dweck. It refers to the belief that one's abilities, skills, and intelligence are not fixed traits but can be cultivated and improved over time with dedication, hard work, and learning from mistakes.

In contrast, a fixed mindset is the belief that personal qualities are static and cannot be changed significantly. Individuals with a fixed mindset tend to believe that intelligence and abilities are innate and predetermined, leading them to avoid challenges and view failure as a reflection of their inherent limitations.

On the other hand, individuals with a growth mindset embrace challenges, persist in the face of obstacles, and see setbacks as opportunities for learning and growth. They understand that effort, practice, and learning strategies can lead to improvement and the development of their abilities.

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does minimum wage automatically increase as inflation or prices of goods increase?

Answers

Answer:

nope. prices have been going up alot in even just the past decade, and yet minimum wage is still $7.25

is it ethical or unethical to cheat on your taxes? Explain why or why not

Answers

Answer:

it would be unethical to do that because you are breaking the law

Answer:

It would be unethical.

Explanation:

coconutoil2217 is correct, it would be unethical to cheat on your taxes.

a firm whose operations are human-capital intensive would most likely use which of the following entry modes? a. licensing b. a cross-border acquisition c. exporting d. a greenfield venture

Answers

A greenfield venture would most likely be the chosen entry strategy for a company whose operations depend heavily on human capital, such as those in the technology, education, or consulting sectors. The Correct option is D

Building a new subsidiary from the ground up in a foreign market is known as a "greenfield venture," and it enables the parent firm to fully control and transfer its human capital, knowledge, and expertise to the new organization. The parent firm can tailor its products and services to match the particular needs of the local market thanks to the entry mode's maximum operational flexibility and control.

Licensing does not include the transfer of human resources; instead, it involves giving a foreign firm permission to exploit the parent company's intellectual property. Exporting entails selling goods or services directly to customers overseas without first establishing a physical presence there. Because it could be challenging to combine the cultures and experience of the two organizations, cross-border acquisitions might not be as appropriate for human-capital intensive businesses.

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What is The Humane Society of North Central Florida's mission? *

Answers

Answer:

Our mission is to build an ecologically sustainable and humane world for all animals.

Explanation:

I hope it help u

An example of a cost is _____.


revenues

principal and interest on loans

tornadoes

profits

Answers

An example of a cost is profits.

What is a benefit of getting college credit in high school?
A) Graduating early
B) Spending more time on homework
C) Showing friends how smart I am
D) Spending too much money on tuition

Answers

a bc when u do college credits u are doung collehe in highsvool and so ubhet to graduate early ceom college
A, getting college credits can not only help with your tuition and save money. it also can provide a possible early graduation.
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780 people wanted cranberry blast 220 wanted melon splash. In the taste test % of the people wanted cranberry blast. In aqueous solution the Al+3 ion forms a complex with six fluoride anions.Write the formation constant expression for the equilibrium between the hydrated metal ion and the aqueous complex. Under that, write the balanced chemical equation for the last step in the formation of the complex. Double Mass but Half Speed ? 2 2M Before Collision Two blocks on a horizontal frictionless track head toward each other as shown. One block has twice the mass and half the velocity of the other. toward the left. toward the right. 2V. 1) The velocity of the center of mass of this system before the collision is zero. Submit M Your submissions: Submitted: Sunday, July 3 at 5:27 AM Feedback: Feedback will be available after 10:00 AM on Monday, July 4 Submit (Survey Question) 2) Briefly explain your answer to the previous question. C 3) Suppose the blocks collide elastically. Picking the positive direction to the right, what is the velocity of the bigger block after the collision takes place? +2V +V zero. -V. -2V. Submit Your submissions: B? Submitted: Sunday, July 3 at 5:29 AM Feedback: Feedback will be available after 10:00 AM on Monday, July 4 (Survey Question) 4) Briefly explain your answer to the previous question. population studies across the globe suggest that diets high in _____ promote the risk of colon cancer. a. processed meat b. boiled foods c. avocados d. leafy vegetables e. whole grains Governments used what during the war as a way to influence public opinion and rally support Are my answers correct> please show work.The formula for the illegal drug cocaine is C17H21NO4. What is the mass percentage of oxygen in the compound? (Answer: 22.12%)What is the mass of silver metal produced from 6.35 g of copper? Answer: 21.6gCu(s) + 2AgNO3(aq) Cu(NO3)2(aq) + 2Ag(s)What is the mass of copper metal that yields 0.500 g of silver? 0.147g CuCu(s) + 2AgNO3(aq) Cu(NO3)2(aq) + 2Ag(s)What is the volume of oxygen gas at STP from the decomposition of 1.70 g of NaNO3 (MM = 85.00 g/mol)? Answer: 0.0224L2NaNO3 (s) ---(spark) 2NaNO2 (s) + O2(g) in the sherbert case, the supreme court ruled that denying unemployment benefits to someone who was fired for refusing to work on saturdays for religious reasons was quizletg HELPPP We know Anne Frank from her diary. Imagine that you are hiding with Anne and her family.Write a diary entry for one day hiding in the annex. For example, you might describe theday that you go into hiding, an ordinary day during the two years of hiding, or the day ofdiscovery. Write at least three paragraphs in your diary entry. PLEASE ANSWER!!!!!!!!!! please answer i will answer any question and mark you as brain lest it gives you 50 points answer both for 100 What is investigative journalism Only number 3 and thats it ! And please help Ill mark u brainly Which is the standard form for this number? What are 5 facts about prohibition? Which of the following best describes how to measure the spread of the data? The IQR is a better measure of spread for movies than it is for basketball games. The standard deviation is a better measure of spread for movies than it is for basketball games. The IQR is the best measurement of spread for games and movies. The standard deviation is the best measurement of spread for games and movies. On your way to work about two hours after sunrise, you notice the moon setting. What phase is it in? what is the definition of one map unit? group of answer choices 1 nanometer of distance between two genes the recombination frequency between two genes assorting independently the physical distance between two linked genes a 1% frequency of recombination between two genes the joint pow/mia accounting command central identification laboratory (jpac-cil) is known for: boeing engineers were encouraged to conduct increased safety testing to certify the max even when this would increase requirements for pilot training and therefore costs. consider the initial value problem system of two equations: ( x (t) = w w (t) = sin(x) with initial values x(t0) = x0 and w(t0) = w0.