Math 1030 Quantitative Reasoning (EXAM 1)

Write the fraction in lowest terms 0.10

1/10

Divide 101 miles by 0.67 hours .

101 mi / 0.67 hr = 150 mi / hr

Convert the measurement to the units specified . 16 pounds to kilograms

16 pounds = 7.26 kg

Carry out the indicated operation and give your answer with the specified number of significant digits . 42x32.4 ; 3 significant digits

42x32.4 = 1360

Complete the following sentence with a power of ten greater than 1 . A cubic meter is times as large as a cubic centimeter

A cubic meter is 10^6 times as large as a cubic centimeter .

What is a fallacy ? Give examples of fallacies and describe how the argument is deceptive .

A fallacy is a deceptive argument. It is an argument in which the conclusion is not well supported by the premises . Society has an obligation to provide health insurance because health care is a right of citizenship . This argument is deceptive because the premise and conclusion essentially say the same thing . I placed the quartz crystal on my forehead , and in five minutes my headache was gone The crystal made my headache go away . This argument is deceptive because it claims that because one thing happened before another , the first event caused the second event , but it doesn't prove that there is any connection between two events . Company A makes the best pickup trucks in the world . More people drive Company A pickups fact that a large number of people buy Company A pickup trucks does not necessarily mean that they are the best trucks.

Complete the following sentence with a power of ten greater than 1 . A gigagram is times as large as a centigram .

A gigagram is 10^11 times as large as a centigram .

Complete the following sentence with a power of ten greater than 1 . A liter is times as large as a picoliter .

A liter is 10^12 times as large as a picoliter

career , approximately how much more does a man The table shows median annual earnings for women and men with various levels of education . Assuming the difference with a bachelor's degree earn than a man with a high school education ? in the table remains constant over a 40 - year

A man with a bachelor's degree earns $1030240 more than a man with a high school education over a 40 - year career .

Complete the following sentence with a power of ten greater than 1 . A square meter is times as large as a square nanometer .

A square meter is 10^18 times as large as a square nanometer .

How do we define argument ? What is the basic structure of an argument ?

An argument is a reasoned or thoughtful process . An argument consists of premises that are used to support a conclusion .

Paul denies that he opposes the plan to build a new dorm . Does Paul support building a new dorm ?

Choose the correct answer below . The first negation " opposes the plan " makes it seem that Paul would not support the new dorm . But the statement negates this negation , " Paul denies that he opposes the plan . " Therefore , it seems that Paul supports the plan for the new dorm .

Find a conversion factor between square feet and square miles . Write it in three forms .

Complete the conversion factor below. 27878400 square feet = 1 square mile Write the conversion factor in the form for converting square miles to square feet. 1 = 27878400 square feet / 1 square mile Write the conversion factor in the form for converting square feet to square miles. 1 = 1 square mile / 27878400 square feet

Use the table to the right to answer the following question . Energy Compare the energy released by fission of 1 kilogram kilogram of element B to that released by burning 1 kilogram of element A.

Fission of 1 kg of element B releases 3333 times as much energy as burning 1 kilogram of element A.

Use the data in the table below to determine how many average candy bars an adult would have to eat to supply the energy needed for seven hours of running .

I The adult would have to eat 27 average candy bars

The Alps are in North America or the Rockies are in South America .

Identify p. The Alps are in North America . Identify q. The Rockies are is in South America . What is the truth value of p? False What is the truth value of q? False Is the disjunction true or false? The disjunction is false because p is false and q is false

If 3x2 = 5 , then 3 + 2 = 5 .

Identify the hypothesis. 3x2 = 5 Identify the conclusion. 3 + 2 = 5 What is the truth value of the hypothesis? False What is the truth value of the conclusion? True Is the entire proposition true or false? The statement is true since the hypothesis is false and the conclusion is true.

My baby was vaccinated and later developed autism , which is why I believe that vaccines cause autism .

Identify the premise. My baby was vaccinated and later developed autism Identify the conclusion. I believe that vaccines cause autism . Explain why the argument is deceptive . The argument is deceptive because it attempts to create a link between vaccines and autism . The premise of the argument does not fully support the conclusion Which type of fallacy does the argument represent ? False Cause

Everyone loves Shakespeare , because his plays have been read for many centuries .

Identify the premise. Shakespeare's plays have been read for many centuries . Identify the conclusion. Everyone loves Shakespeare . Explain why the agreement is deceptive. The argument is deceptive because it assumes that many people reading Shakespeare's plays is evidence that those people actually like Shakespeare. Which type of fallacy does the argument represent? Appeal to Popularity

I will eat lunch at restaurant A or restaurant B.

In the given proposition , is or inclusive or exclusive? Exclusive

Given my work schedule , I would be glad to be off Sunday or the holiday .

In the given proposition , is or inclusive or exclusive? Inclusive

Why did you do it ?

Is the given statement a proposition ? No , because the statement does not make a claim ; it is a question .

It snows more at the Grand Canyon than it does in Minneapolis , Minnesota .

Is the given statement a proposition ? Yes , because the given statement can be either true or false , and it is a complete sentence .

What is logic ? Briefly explain how logic can be useful .

Logic is the study of the methods and principles of reasoning. It can be useful in providing strong support for conclusions , and to help identify errors in reasoning , or fallacies.

My new music player has a capacity of 390 gigabytes . ( Recall that giga means billion . )

My new music player has a capacity of 3.9 x 10^11 bytes .

Sid needs 0.5 meters of canvas material to make a carry - all bag for his wheelchair . If canvas is $ 9.25 per meter , how much will Sid spend ? ( Note that $ 9.25 per meter is the same as $ 9.25 for one meter . )

Sid must spend $ 4.63.

What is meant by standardized units and why are they useful ?

Standardized units are units that have the same meaning for everyone who uses them . When using standardized units , people can communicate measurements and know that they mean the same thing to both people .

If airplanes can fly , then airplanes have wings .

State the hypothesis and conclusion , and give their truth values. The hypothesis is airplanes can fly , which is true . The conclusion is airplanes have wings , which is true. Is the entire proposition true or false? True

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The 2015 population of a certain state was approximately 36.6 million . The 2011 population was approximately 30.7 million .

The 2015 population of the state was 119.2 % of the 2011 population .

You return from a trip with 270 Canadian dollars . How much are your Canadian dollars worth in U.S. dollars ? Use the exchange rate shown below .

The 270 Canadian dollars are equivalent to about $ 218.54

Decide which of the two given prices is the better deal and explain why . You can buy shampoo in a 5 - ounce bottle for $ 2.79 or in a 15 - ounce bottle for $ 11.29 .

The 5 - ounce bottle is the better deal because the cost per ounce is $ 0.56 per ounce while the 15 - ounce bottle is $ 0.75 per ounce .

The average sale of a house decreased from $ 306,000 in February 2008 to $ 155,000 in February 2013 .

The absolute change is - 151000 The relative change is -49.3 %.

Find the absolute change and the relative change in the following case . The number of daily newspapers in a country decreased from 2628 in 1900 to 1341 in 2010 .

The absolute change is -1287 . The relative change is -49 % .

You deposit $ 3700 in an account with an annual interest of 5.4 % for 10 years .

The amount of money you'll have at the end of 10 years is $5698

You invest $ 1000 in an account that pays simple interest of 3 % for 30 years .

The amount of money you'll have at the end of 30 years is $1900

Which is greater , the time the average student spends in a year studying or the time the average student spends in a year sleeping .

The amount of time a student spends sleeping in a year is greater.

A $200 deposit in an account with an APR of 2.7%

The balance in the account after 1 year is approximately $205.47 The balance in the account after 5 years is approximately $228.91 The balance in the account after 20 years is approximately $343.20 The APY for the account is approximately 2.74%

A $ 6000 deposit in an account with an APR of 4.5 %

The balance in the account after 1 year is approximately $6276.17 The balance in the account after 5 years is approximately $7513.94 The balance in the account after 20 years is approximately $14757.62 The APY for the account is approximately 4.60%

$ 9,000 is invested for 19 years with an APR of 3.27 % and monthly compounding .

The balance in the account after 19 years is $16737.97

$ 25,000 is invested for 4 years with an APR of 5.4 % and daily compounding .

The balance in the account after 4 years is $31027.06

$ 15,000 is invested for 5 years with an APR of 6 % and quarterly compounding

The balance in the account after 5 years is $20202.83

What are the basic metric units of length , mass , time , and volume ? How are the metric prefixes used ?

The basic metric units of length , mass , time , and volume are the meter ( m ) for length , the kilogram ( kg ) for mass , the second ( s ) for time , and the liter ( L ) for volume . These basic units can be combined with a prefix that indicates multiplication by a power of 10 .

Decide which of the two given prices is the better deal and explain why . You can fill a 15 - gallon tank of gas for $ 49.68 or buy gas for $ 3.10 / gallon .

The better deal is to buy gas for $ 3.10 / gallon because the price to fill a 15 - gallon tank of gas for $ 49.68 is $ 3.31 per gallon

The diameter of a certain bacterium is about 0.0000009 meters .

The diameter of a certain bacterium is about 9x 10^-7 meters .

Your weight is 49.92 kilograms . A scale at a health clinic that gives weight measurements to the nearest Kilogram gives your weight as 50 kilograms . A digital scale the gym that gives readings to the nearest 0.02 kilogram gives your weight as 49.98 kilograms .

The digital scale is both more accurate and more precise.

In the following statement , express the first number as a percentage of the second number . The full - time year - round median salary for U.S. men in 2010 was $ 42,400 , and the full - time year - round salary for U.S. women in 2010 was $ 35,700 .

The full - time year round median salary for U.S. men in 2010 was 118.8 % of the full - time year - round median salary for U.S. women in 2010 .

Your true height is 60.90 inches . A tape measure that can read to the nearest 1/2 inch gives your height as 60 1/2 inches . A new laser device at the doctor's office that gives readings to the nearest 0.02 inch gives your height as 60.74 inches .

The laser device is both more accurate and more precise .

Lan pays a semiannual premium of $ 700 for automobile insurance , a monthly premium of $ 145 for health insurance , and an annual premium of $ 400 for life insurance .

The monthly expense is $295 .

In filing his income tax , Raul reported annual contributions of $ 350 to a public radio station , $ 190 to a public TV station , $ 150 to a local food bank , and $ 305 to other charitable organizations .

The monthly expense is $82.92 .

You maintain an average balance of $ 600 on your credit card , which carries a 15 % annual interest rate .

The monthly interest payment is $7.50.

State the number of significant digits and the implied precision of the given number . 1.68987 mi

The number 1.68987 has 6 significant digit ( s ). What is the implied precision of 1.68987 mi? The number is precise to the nearest hundred - thousandth of a mile.

State the number of significant digits and the implied precision of the given number . 210

The number 210 has 2 significant digit What is the implied precision of 210? The number is precise to the tens place .

In the following statement , express the first number as a percentage of the second number . A certain candidate won 345 electoral votes in an election , out of a total of 415 .

The number of electoral votes won by the candidate is 83.1 % of the total votes .

Alcohol use by high school seniors in a certain state decreased from 53.3 % in 2000 to 37.9 % in 2015. Describe this change as an absolute change in terms of percentage points and as a relative change in terms of a percentage

The percentage of high school seniors using alcohol decreased by 15.4 percentage points . The percentage of high school seniors using alcohol decreased by 28.9 % .

Responding to Democrats who support doubling the federal minimum wage , a Republican says , " The Democrats think that everyone should have the same income . "

The premise is some Democrats support doubling the federal minimum wage. The conclusion is Democrats think everyone should have the same income. Why is the argument deceptive ? The argument is based on a distortion of someone's beliefs . This is an example of a Straw Man argument.

How much will a person pay for 6.8 pounds of bananas at a price of $ 1.89 per pound ?

The price the person will pay is 12.85 dollars.

Sara pays $ 4400 for tuition and fees for each of the two semesters , plus additional $ 370 for textbooks each semester .

The prorated monthly cost for tuition and fees and textbooks is $795 .

The total ( after - tax ) cost of a laptop computer is $ 1624.66 . The local sales tax rate is 6.5 % . What is the retail ( pre - tax ) price ?

The retail ( pre - tax ) price of the computer is $ 1525.50 .

1 mm ( map ) = 5 m ( actual )

The scale ratio is 1 to 5000

1 inch on the map represents 13 miles

The scale ratio is 823680 to 1 .

" The unemployment rate has risen more than a percentage point to 8.7 % in February from 7.2 % last November . " What is the relative change in the unemployment rate expressed as a percentage ?

The unemployment rate has risen 20.8 % .

When I figured out my monthly budget , I included only my rent and my spending on gasoline , because nothing else could possibly add up to much

This statement does not make sense because everything she buys during the month will affect her monthly costs and overall cash flow.

My vacation travel cost a total of $ 1920 , which I entered into my monthly budget as $ 80 per month .

This statement does not make sense because the value entered into the monthly budget should be $160

Brandon discovered that his daily routine of buying a slice of pizza and a soda at lunch was costing him more than $ 2100 per year .

This statement makes sense because this would mean that a slice of pizza and a soda costs him about $6 a day.

Distinguish between random errors and systematic errors . How can we minimize the effects of random errors ? How can we account for the effect of a systematic error ?

To minimize the effects of random errors , make many measurements and average them . To account for the effect of a systematic error , adjust all measurements accordingly.

Explain why a unit conversion involves just multiplying by 1. Find the two forms of 1 that are equivalent to the conversion 1 lb = 16 oz .

Unit conversion always involves multiplying by the appropriate form of 1 so that the meaning of the original expression does not change . Find the two forms of 1 that are equivalent to the conversion 1 lb = 16 oz The two forms of 1 that are equivalent to the conversion 1 lb = 16 oz are 16 oz / 1 lb or 1 lb / 16 oz

What are significant digits ? How can you tell whether zeros are significant ?

What are significant digits? Significant digits are the digits in a number that represent actual measurements and therefore have meaning. How can you tell whether zeros are significant ? The position of zeros in a number with respect to the position of the nonzero numbers in a number is what determines the significance of zeros.

Your average speed on a long walk , found by dividing distance traveled in meters by time elapsed in minutes .

What are the units mathematically? m/min What are the units in words? meters per minute

Carry out the indicated operation and give your answer with 2 significant digits . 274.23 + 0.087

What is 274.23 +0.087 with two significant digits ? 3200

Vic bought a new plasma TV for $ 2400 He made a down payment of $ 200 and then financed the balance through the store . Unfortunately , he was unable to make the first monthly payment and now pays 7 % interest per month on the balance ( while he watches his TV ) .

What is Vic's monthly interest payment ? $154

What is a budget ? What is cash flow ? Describe the four - step process of figuring out your monthly budget .

What is a budget? A budget keeps track of how much money one has coming in and how much one has going out and helps to determine what adjustments need to be made. What is cash flow? The difference between expenses and income Describe the four - step process of figuring out your monthly budget. First, list all monthly income. Next, list all monthly expenses. Then subtract total expenses from total income to determine net monthly cash flow. Finally, make adjustments as needed.

3 + 2 = 5 and 4 x 8 = 32 .

What is the first proposition? 3 + 2 = 5 What is the second proposition? 4x8 = 32 Is the first proposition true or false ? True Is the second proposition true or false? True Is the statement, 3+2=5 and 4x8=32, true or false? The statement is true because the first proposition and the second proposition is true

Express the given decimal as a percentage and a reduced fraction . 0.70

What is the percentage form of 0.70 ? 70 % What is the reduced fraction form of 0.70 ? 7 /10

Express the given percentage as a reduced fraction and a decimal . 425 %

What is the reduced fraction form of 425 % ? 17/4 What is the decimal form of 425 % ? 4.25

Express the given percentage as a reduced fraction and as a decimal . 50 %

What is the reduced fraction form of 50 % ? 1/2 Simplify What is the decimal form of 50 % ? .5

How much does a typical water bed weigh ? Note that 1 cubic foot of water weighs 64.2 pounds and a typical water bed holds 28 cubic feet of water .

What is the unknown in this problem? the weight of the water bed What is the weight of the water bed? The weight of the water bed is 1797.6 pounds. Explain why the weight of the water bed makes sense. The weight of the water bed can be calculated by the equation x= 28 ft3 x 64.2 lb / 1 ft3

How fast does Earth rotate ? Note that in one full rotation of Earth , a point on the equator travels about 25,000 miles in 24 hours .

What is the unknown in this problem? The speed What is the speed of the Earth? The speed of the Earth is 1041.7 miles per hour. Explain why the speed of the Earth makes sense. Speed = distance/time = 25,000 miles/24 hours

Why is it so important to understand your personal finances ? What types of problems are more common among people who do not have their finances under control ?

Why is it so important to understand your personal finances? It is important to understand your personal finances because you need to know how much money you have and how much money you spend in order to find a way to live within your means . What types of problems are more common among people who do not have their finances under control? People who do not have their finances under control suffer from financial stress , higher divorce rates , and other difficulties in personal relationships . They also suffer from higher rates of depression among a variety of other ailments.

Will is 29 % taller than Wanda , so Will's height is % of Wanda's height .

Will's height is 129 % of Wanda's height .

Asia is in the northern hemisphere .

Write the negation of the proposition. Asia is not in the northern hemisphere. The truth value of the original proposition is true. The truth value of the negation is false.

Could an average person lift the weight of $ 100 in dimes? (A single dime weighs approximately 2.27 grams.)

Yes because the weight of 1000 dimes is about 5 pounds .

Do the following operations without a calculator . Be sure to express answers in scientific notation . You may round your answers to one decimal place ( as in 3.2 x 105 ) . a . ( 3x102 ) x ( 2x10⁹ ) b . ( 6 × 104 ) + ( 3x10³ ) c . ( 10x10¹1 ) + ( 2x108 )

a . ( 3x10^2 ) x ( 2x10⁹ ) = 6 × 10^11 b . ( 6x10^4 ) + ( 3x10³ ) = 6.3 × 10^4 c . ( 10x10^11 ) + ( 2x10^8 ) = 5x10³

Write each of the following numbers in scientific notation . a . 37,000 b . 0.0587 c . 5914.1

a . 37,000 = 3.7 x 10^4 b . 0.0587 = 5.87 x 10^-2 c . 5914.1 = 5.9141 × 10^3

Convert each of the following numbers from scientific to ordinary notation , and write its name . a . 4 x 105 b . 2.4x107 c . 7x10-3 d . 7.8 x 10-6

a . 4 × 10^5 = 400000 = four hundred thousand b . 2.4x 10^7 = 24000000 = twenty - four million c . 7x10^-3 = 0.007 = seven thousandths d . 7.8 x 10^-6 = 0.0000078 = seventy - eight ten - millionths

He refused to testify by invoking his Fifth Amendment rights , so he must be guilty .

a . Identify the premise and conclusion of the argument . Premise : He refused to testify by invoking his Fifth Amendment rights . Conclusion : He must be guilty . b . Briefly describe how the stated fallacy occurs in the argument . The conclusion is stated as if it were the only possible conclusion .

Compare A and B in three ways , where A = 51,672 is the number of deaths due to a deadly disease in the United States in 2005 and B = 17,803 is the number of deaths due to the same disease in the United States in 2009 . a . Find the ratio of A to B. b . Find the ratio of B to A. c . Complete the sentence : A is percent of B.

a . The ratio of A to B is 2.9 b . The ratio of B to A is .34 c . A is 290 percent of B

The mayor wants to raise taxes to fund social programs , so she must not believe in the value of hard work .

a . What is the premise ? The mayor wants to raise taxes to fund social programs . What is the conclusion ? She must not believe in the value of hard work . b. Briefly explain how straw man occurs in the argument. The mayor is characterized (perhaps wrongly) by one quality, on which the conclusion is based.

Convert the following fractions to decimal form. a) 4/5 b) 4/9

a) 0.8 b) 0.444

Evaluate the following expressions. a) 6/7 x 1/9 b) 3/4 + 5/8

a) 2/21 b) 11/8

Evaluate the following expressions. a) 1/2 + 2/3 + 2/9 b) 1/2 x 14/3 x 9/7

a) 25/18 b) 3

Round the following numbers to the nearest tenth and nearest ten . a . 448.75 b . 479.084 c . 662.2 d . - 55.834

a) 448.75 rounded to the nearest tenth is 448.8 and rounded to the nearest ten is 450 . b) 479.084 rounded to the nearest tenth is 479.1 and rounded to the nearest ten is 480 . c) 662.2 rounded to the nearest tenth is 662.2 and rounded to the nearest ten is 660 . d) - 55.834 rounded to the nearest tenth is -55.8 and rounded to the nearest ten is -60 .

Convert the following temperatures from Fahrenheit to Celsius or vice versa . a . 90 ° F b . 85 ° C . -20 ° C

a) 90 ° F = 32.2 ° C b) 85 ° C = 185 ° F . c) -20 °C = -4 ° F

Round the following numbers to the nearest integer . a . 4.16 b . 298.836 c . 7646.8 d . - 10.3499

a). The number 4.16 rounded to the nearest integer is 4 b) The number 298.836 rounded to the nearest integer is 299 c) The number 7646.8 rounded to the nearest integer is 7647 d) The number - 10.3499 rounded to the nearest integer is -10