Math 107

Make an order of magnitude estimate of the following quantity. Explain the assumption used in your estimation. The amount of water the average person drinks in a year

180​ gallons; assuming an average person drinks 4 pints per day

When I toss four​ coins, there are four different outcomes that all represent the event of four tails.

The statement does not make sense. There is only one way the event can occur.

Decide whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain your reasoning. The rate of return on our fund increased by​ 50%, to​ 15%.

The statement makes sense because if the rate of return on our fund increased by​ 50%, to​ 15%, then the previous rate is​ 10%, which makes sense.

The data in the following table shows the outcomes of guilty and​ not-guilty pleas in 1012 criminal court cases. Complete parts​ (a) and​ (b) below. Guilty plea ​Not-guilty plea Sent to prison 380 50 Not sent to prison 569 13 a. What is the probability that a randomly selected defendant either pled guilty or was sent to​ prison? What is the probability that a randomly selected defendent either pled not guilty or was not sent to​ prison?

a= 0.987 b= 0.625

Suppose that you arrive at a bus stop​ randomly, so all arrival times are equally likely. The bus arrives regularly every 80 minutes without delay. What is the expected value of your waiting​ time?

40

Suppose admission to a movie cost $ 8.50 in 2007. What was its price in 1976 ​dollars? Assume that all prices have risen at the same rate as the CPI.

$2.33

A leprechaun places a magic penny under a​ girl's pillow. The next night there are 2 magic pennies under her pillow. Each night the number of magic pennies doubles. How much money will the girl have after 22 ​nights?

How much money will the girl have after 22 ​nights? ​$41943.04

deductive

Identify the argument as inductive or deductive. Every coach must know his sport well. Marty Wright is a baseball​ coach, so Marty Wright knows baseball well.

Find the latitude and longitude of the location on Earth precisely opposite of a town located at latitude 42degrees S​, longitude 128degrees W.

latitude 42degrees N​, longitude 52degreesE

The doubling time of a population of flies is 8 hours. By what factor does the population increase in 31 ​hours? By what factor does the population increase in 2 weeks​?

31 hours= 2^3.875 . 2 weeks = 2^42

A line segment is divided in two​ segments, such that the ratio of the long segment to the short segment is equivalent to the golden ratio. If the length of the entire line segment is 15 inches​ long, what is the length of the longer piece of the divided​ segment? Use variant equals 1.618.

9.27 inches

In order to determine the opinions of people in the 18​- to 22​-year age group on regulating alcohol consumption comma nothing researchers survey a random sample of 1500 college students in this age group.

Selection bias only

A computer randomly selects 700 names from a list of all registered voters. Those selected are surveyed to predict who will win the election for Mayor.

Simple random sampling

If you toss a coin four​ times, it's much more likely to land in the order HTHT than HHHH.​ (H stands for heads and T for​ tails.)

The statement does not make sense because each outcome is equally likely since the probability of any single particular outcome is​ 1/2, so each set of outcomes have the same probability of 1/2^4= 1/16.

Decide whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain your reasoning. The probability that two people in a randomly selected group will have the same last name is much higher than the probability that someone in this group will have the same last name as you do.

The statement makes sense because the coincidence that two people in a randomly selected group will have the same last name is more likely than the coincidence that someone in this group will have the same last name as you do.

The interest rate on my student loan is only​ 7%, yet more than half of my payments are currently going toward interest rather than principal.

The statement makes sense. The portions of installment loan payments going towards principal and toward interest vary as the loan is paid down.

Brandon discovered that his daily routine of buying a slice of pizza and a soda at lunch was costing him more than ​$1700 per year.

This statement makes sense because this would mean that a slice of pizza and a soda costs him about ​$5 a day.

Because Social Security is​ off-budget, we could cut Social Security taxes with no impact on the rest of the federal government.

Does not make sense

We're both single with no children and we both have the same total​ (gross) income, so we must both pay the same amount in taxes.

The statement does not make sense because the two people may not have the same adjusted gross income or taxable income.

A report claims that the returns for the investment portfolios with a single stock have a standard deviation of 0.48​, while the returns for portfolios with 35 stocks have a standard deviation of 0.328. Explain how the standard deviation measures the risk in these two types of portfolios.

A lower standard deviation means more certainty in the return and less risk.A ​ Hence, the returns for portfolios with 35 stocks have less risk than the ones with a single stock.

Gained 800

A woman bought a dining table for ​$300 and then sold it for ​$800. She bought it back for ​$600 and then sold it again for ​$900. How much did she gain or lose on these​ transactions?

In a large resort​ city, the crime rate increased as the number of taxi cabs increased.

Positive correlation. This correlation is due to a common underlying cause because it is possible​ that, with an increase in​ tourism, both the crime rate and the number of cabs increase.

Starting at middle​ C, with a frequency of 260 ​cps, find the frequency of a note six ​half-steps above middle C.

The frequency six ​half-steps above 260 cps is 368 cps.

How many times greater is the intensity of sound from a concert speaker at a distance of 1 meter than the intensity at a distance of 14 ​meters?

The intensity of sound is 196 times as strong at 1 m as at 14 m.

Big circle steep, little circle hills inside steep, and X inside of hills. Argument valid but not sound.

​Premise: All hills are steep. ​Premise: El Mound is a hill. ​Conclusion: El Mound is steep.

Suppose you build an architectural model of a new concert hall using a scale factor of 25. How will the surface area of the actual concert hall compare to the surface area of the scale​ model?

625

The statement does not make sense because propositions are not questions.

Decide whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain your reasoning. My logical proposition is a question that you must answer.

The argument is deceptive because it assumes that many people readingTh ​ Shakespeare's plays is evidence that those people actually like Shakespeare. Appeal to Popularity

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

Fill in the blank. The retail cost of a TV is 40​% more than its wholesale cost.​ Therefore, the retail cost is​ ____ times the wholesale cost.

1.40

There are approximately 2.1 million deaths per year in country A. Express this quantity as deaths per minute.

4.0

How many permutations are there of the letters in the word ​'CHARGES​', if all the letters are used without​ repetition?

5040

Specify if there were 350 people on each jet or both jets combined.

Explain how the following quote is ambiguous. Two jumbo jets with more than 350 people aboard nearly collided during a landing attempt.

no

Half of the class consists of communication​ majors, and half of the class consists of men. Does it follow that one quarter of the class is male communication​ majors?

Discuss possible sources of error in the following measurements. Then state whether you think the measurement is​ believable, given the precision with which it is stated. In​ 2007, 5,253,350 domestic cars and​ 2,365,063 imported cars were sold in the country.

Inaccurate reportingIn ​ (by corrupt​ salesman), other human error, The recording of the sales data, The recording type of car sold​ (imported or​ domestic), The transfer of data. No

A toxic radioactive substance with a density of 7 milligrams per square centimeter is detected in the ventilating ducts of a nuclear processing building that was used 45 years ago. If the​ half- life of the substance is 20 ​years, what was the density of the substance when it was deposited 45 years​ ago?

The density of the radioactive substance when it was deposited 45 years ago was approximately 33.3 mg divided by cm squared.

A ​$400 washing machine in a laundromat is depreciated for tax purposes at a rate of $ 80 per year. Find a function for the depreciated value of the washing machine as it varies with time. When does the depreciated value reach​ $0?

The equation of the line in​ slope-intercept form is Vequals 400 minus 80 t. It takes 5 years for the machine to depreciate to ​$0.

I bought a fund advertised on the web that says it uses a secret investment strategy to get an annual return twice that of​ stocks, with no risk at all.

The statement does not make sense because investing in stocks is​ high-risk to get high​ returns, thus getting higher returns than stocks with this secret strategy must mean the fund advertised on the web is​ high-risk, not no risk.

Your life expectancy is the major factor in determining how long you live.

The statement does not make sense because life expectancy is based on the current state of medicine and technology. If you have healthy habits and exercise each​ day, then you are more likely to live​ longer, regardless of your life expectancy.

When we chart the price of milk in 1995 dollars we find that it has become slightly more​ expensive, but when we chart it in 1975 dollars we find that it has become cheaper.

The statement does not make sense because the same trend would be seen regardless of what kind of dollars are used.

I make only the minimum required payments on my credit card balance each​ month, because that way​ I'll have more of my own money to keep.

The statement does not make sense. It takes a very long time to pay off a credit card loan if only the minimum payments are made. This results in much more interest being paid.

Decide whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain your reasoning. Baggage screening machines are​ 98% accurate in identifying bags that contain banned materials.​ Therefore, if the screening shows a bag that contains banned​ materials, then it almost certainly does.

The statement does not make senseTh ​ because, depending on the proportion of true positives to total​ positives, the actual percentage of bags that show banned materials and actually have banned materials could be quite low.

My bank paid an annual interest rate​ (APR) of 3​.0% but at the end of the year my account balance had grown by 3​.1%.

This makes​ sense, because the annual interest rate​ (APR) does not always match the annual percentage yield​ (APY).

Two candidates for governor of a state differ in their accounts of the​ state's economy during the​ incumbent's term. The incumbent claims that during his​ four-year term the economy has​ improved, citing a rise in the median household income from $ 33 comma 000 to $ 34 comma 500. The challenger claims that the economy has​ declined, citing that the buying power of families in the state has declined during the four years. Which of the following best explains how both candidates can be​ right?

Though the median household incomeTh ​ increased, prices increased by a greater​ percent, meaning that in real terms the median income actually decreased.

There is no missing dollar.

Three guests checked into a hotel and paid ​$45 for their shared room. A while​ later, the desk clerk realized that the room should have cost only ​$40​, so she gave the bellhop​ $5 to return to the three guests. The bellhop realized that​ $5 couldn't be divided evenly among the three​ guests, so he kept​ $2 and gave​ $1 to each of the guests. It seems that each guest has spent ​$14 for the room​ (which makes ​$42​) and the bellhop has​ $2, for a total of ​$44. Where is the missing​ dollar?

Examine a closed book. a. How many dimensions are needed to describe the​ book? Explain. b. How many dimensions describe the surface​ (cover) of the​ book? Explain. c. How many dimensions describe an edge of the​ book? Explain d. Describe some aspect of the book that represents zero dimensions.

a= Three dimensions are needed because the book has the form of a rectangular prism​ (box), and three coordinates are needed to locate a point in a rectangular prism​ (box). b= Two dimensions are needed because the surfaceTw ​ (cover) of the book is a plane​ object, and two coordinates are needed to locate a point in a plane object. c= One dimension is needed because an edge of a book is a lineOn ​ segment, which is a​ one-dimensional object requiring only one coordinate to locate a point on a line. d= A corner of a page A corner of the surface​ (cover)

Decide whether the following statement makes sense or does not make sense. My share of the federal​ government's debt is greater than the cost of a new car.

makes sense

a. Create an exponential function of the form Upper Q equals Upper Q 0 times left parenthesis 1 plus r right parenthesis Superscript t​, ​(where rgreater than0 for growth and rless than0 for​ decay) to model the situation described.

a.= Q= 69,000 times ​(1 + 0.055​)^t

The lengths of pregnancy terms for a particular species of mammal are nearly normally distributed about a mean pregnancy length with a standard deviation of 16 days. About what percentage of births would be expected to occur within 16 days of the mean pregnancy​ length?

68%

Find the margin of error and​ 95% confidence interval for the survey result described. According to a poll of 1284 ​people, about​ one-third ​(32​%) of Americans keep a dog for protection.

Margin of error equals 3​% ​(Round to the nearest whole number as​ needed.) Confidence interval is from 29​% to 35​%.

Randomly selecting a​ four-person committee consisting entirely of women from a pool of 10 men and 15 women

The event of selecting a woman and the event of selecting a woman the next time are dependent. The probability of randomly selecting a​ four-person committee consisting entirely of women from a pool of 10 men and 15 women is 0.1079.

I estimate that the probability of my getting married in the next 3 years is 0.7.

The statement makes sense. The statement is an example of subjective probability.

I was unable to make a bar​ chart, because the data categories were qualitative rather than quantitative.

The statement does not make sense because bar graphs are commonly used to show data when the categories are qualitative.Th

Identify all of the symmetries in the following figure. (circle)

There are exactly two lines across which it can be reflected. It can be rotated through 180degrees.

The price of a computer component is decreasing at a rate of 9​% per year. State whether this decrease is linear or exponential. If the component costs ​$60 ​today, what will it cost in three​ years?

exponential What will the component cost in three​ years?$45.21

Consider the graph to the right that relates a​ person's height to their shoe size. a. In​ words, describe the function shown on the graph. b.Find the slope of the graph and express it as a rate of change. c. Briefly discuss the conditions under which a linear function is a realistic model for the given situation.

According to the​ function, shoe size increases by 2 every 30 inches. rate of change = 0.0667 size per inch This model is a rough approximation at best.

A​ double-blind drug versus placebo study of 113 patients suffering from tinnitus​ (the perception of ringing in the​ ears) demonstrated the effectiveness of ginkgo biloba extract. The ginkgo treatment improved the condition of all the tinnitus patients.

​​Experiment; the treatment group is patients that received the drug and the control group is patients that received the​ placebo; double blind

Suppose that you currently own a clothes dryer that costs ​$20 per month to operate. A new efficient dryer costs ​$690 and has an estimated operating cost of ​$10 per month. How long will it take for the new dryer to pay for​ itself?

69 months.

The table shows the numbers of cell phone subscriptions. Display the data using an ordinary vertical scale and an exponential vertical scale. Which graph is more​ useful? Why?

The graph in part a gives a better picture of the true nature of the rate of change. The graph in part b makes it easier to see the changes in the early years.

Wilma used a yard stick to measure the length of her kitchen to the nearest micrometer.

The statement does not make sense because a yard stick measures length in yards not micrometers.​ Therefore, the measurement will not be precise to the nearest micrometer.

If I double the amount of water in the​ cup, I'll also double the pH of the water in the cup.

The statement does not make sense because acidity is related to the concentration of positively charged hydrogen ions and not to the amount of liquid.

I'm putting all my savings into stocks because stocks always outperform other types of investments over the long term.

The statement does not make sense because although stocks historically outperform bonds and cash over the longTh ​ term, investing in stocks is​ high-risk and there is no guarantee that the investment will yield a high return.

The histogram to the right shows the times between eruptions of a geyser for a sample of 300 eruptions​ (which means 299 times between​ eruptions). Over the​ histogram, draw a smooth curve that captures its general features. Then classify the distribution according to its number of peaks and its symmetry or skewness.

one peak, right skewed, moderate variation