mat 143 3 A, B, and E
The United States has seen the federal debt grow considerably and the total debt now is over $17 trillion dollars. On a single day in October of 2013, the debt grew by a record amount in a single day when the federal government borrowed $328 billion dollars to fund measures from the past five months. The previous record was set two years ago when $238 billion dollars was added to the national debt.
1.7 *10^13
Fill in the blank. Will is 24% taller than Wanda, so Will's height is ____% of Wanda's height.
100+24=124% height
Between 2007 and 2020, the number of twin births in a certain country decreased by 15%, to approximately 101,575. About how many twin births were there in 2007?
119500 in 2007 100-15= 0.85 101575/0.85= 119500
A certain candidate won 248 electoral votes in an election, out of a total of 405.
248/405= 0.612 0.612*100= 61.2%
Rewrite the following statement using a number in scientific notation. The number of different eight-character passwords that can be made with 26 capital letters and 26 lowercase letters is approximately 53 trillion.
5.3 *10^13
Rewrite the following statement using a number in scientific notation. The diameter of a certain atom is about 0.56 nanometers (Recall that nano- means "billionth.")
5.6* 10^-10
Rewrite the following statement using a number in scientific notation. A large power plant generates 8.4 gigawatts of electrical power. (Recall that giga- means "billion.")
8.4 *10^9
The number 90,000,000 is the same as _________.
9*10^7 To convert a number to scientificnotation, the decimal point is moved to come after the first nonzero digit. The power of 10 is the number of places that the decimal point moved. In thiscase, the power is 7.
There are approximately 3.4 million deaths per year in country A. Express this quantity as deaths per minute.
In country A, there are 6.5 3,400,000/ 365*24*60 = 6.5 deaths/min.
rewrite the following statement using a number in scientific notation. My new music player has a capacity of 380 gigabytes (.Recall that Giga means billion.)
My new music player has a capacity of 3.80×10^11 bytes.
Clint's salary increased from $23,000 to $36,800 over a three-year period. Helen's salary increased from $29,000 to $46,400 over the same period. Whose salary increased more in absolute terms? In relative terms? Explain
Part 1 Whose salary increased more in absolute terms? Select the correct choice below and fill in the answer box(es) to complete your choice. Helen's salary increased more because her salary increased by $17400. 46400-29000= 17400 This is more than $13800 36800-23000 the amount that Clint's salary increased. part2 36800-23000/23000= 0.6 0.6*100=60% 46400-29000/29000= 0.6 0.6*100=60%
Find the absolute change and the relative change in the following case. The per person consumption of meat in a certain country decreased from 70.8 pounds in 2000 to 43.8 pounds in 2020.
The absolute change is negative −27 pounds per person. 43.8- 70.8 = -27 Part 2 The relative change is negative −38.1%. -27/70.8= -.381 0.381*100= -38.1%
You are looking at a map with a scale of 1- inch 40 miles. If two towns are separated on the map by inches, what is the actual distance between them? Explain your reasoning.
The actual distance between them is 320 miles. Since 1 inch=40 miles, 8 inches equals 8•40 miles, or 320 miles.
At the end of a year, the gross debt of a country stood at about $17 trillion. Express this amount in dollars per person, assuming that the population of the country is about 313 million.
The gross debt is about $54300 1.7*10^13 / 3.13 *10^8 1.7/3.13 *10^13-8 0.543 *10^5 = 54300 per person.
Suppose the value of a home changed by −31% over the past five years. Which of the following is true?
The house decreased in value over the past five years because the relative change is negative.
The price of a movie ticket increased from $25 to $30. What does this mean about the new price?
The new price is 120% of the old price because the price increases by 20% which is added to 100%
Fill in the blank. The retail cost of a TV is 15% more than its wholesale cost. Therefore, the retail cost is ____ times the wholesale cost.
The retail cost is 1.15 times the wholesale cost. 100+15= 115 115/100=1.15
The total (after-tax) cost of a laptop computer is $1613.62. The local sales tax rate is 5.4%. What is the retail (pre-tax) price?
The retail (pre-tax) price of the computer is $1530.95 100+5.4= 105.4 1613.62/105.4= 1530.95
State whether the following statement is true or false, and explain why. If the statement is false, state the true change. The cost of tuition at a college falls 12% then later rises by 12%. After the two changes in tuition, the cost is unchanged.
The statement is false because the reference values for the increase and decrease in the cost of tuition are not the same. The true change in the cost is -1.44%. 100+12=112 100-12=88 1.12*.88*1000= 985.6 1000-985.6= 14.4 14.4/1000=0.0144 0.0144*100 = 1.44
At a particular college, 95% of the undergraduates are female. If 5130 women attend the college, and how many total undergraduates attend the college?
The total number of undergraduates is 5400 5130/0.95= 5400
Fill in the blank in the following statement. The wholesale price of a TV is 60% less than retail price. Therefore, the wholesale price is _____ times the retail price.
The wholesale price is .4 times the retail price 100-60= 40 40/ 100= .4
Restate the following fact as indicated. Approximately 104.5 million passengers passed through a certain airport in 2019. Because of the coronavirus pandemic, only 44.2 million passengers passed through the same airport in 2020. Express these quantities in passengers per hour.
There were 11929 104.5 *10^7 aka 6 104500000/ 365*24 104500000/8760 = 11929 passengers per hour passing through the airport in 2019. There were 5046 44.2 *10^7 442000000/8760= 5046 passengers per hour passing through the airport in 2020.
In the following statement, express the first number as a percentage of the second number. The full-time year-round median salary for workers in a certain country was $32,758 in 2000, compared to $52,860 in 2020.
The full-time year-round median salary in 2000 was 32758/52860= 0.620 0.620*100= 62.0 62.0% of the full-time year-round median salary in 2020.
You are running for mayor this year in a city with 260,000 households. You decide to campaign by going door to door and spending a few minutes talking with members of every household in the town. What can you conclude about this plan?
This plan will be impossible to carry out. Assuming you spend about 3 minutes talking at each household, it will take longer than a year to reach every household.
Assume that 30% of city employees in City A ride the bus to work. Consider the following two statements: The percentage of city employees who ride the bus to work is 10% higher in City B than in City A. The percentage of city employees who ride the bus to work is 10 percentage points higher in City B than in City A. For each case, state the percentage of city employees in City B who ride the bus to work. Briefly explain why the two statements have different meanings.
When the percentage of city employees who ride the bus to work is 10% higher in City B than in City A, what percentage of city employees in City B ride the bus to work? 33% When the percentage of city employees who ride the bus to work is 10 percentage points higher in City B than in City A, what percentage of city employees in City B ride the bus to work? 40 30+10 Percentage points describe an absolute change or difference, and percent (or %) describes a relative change or difference.
Write each of the following numbers in scientific notation. a. 670,000 b. 0.0000464 c. 0.00028166
a- 6.7*10^5 b- 4.64 *10^-5 c- 2.8166 *10^-4
The percentage of people accessing the Internet in a given area increased from 66% in 2005 to 89% in 2020. Complete parts (a) and (b) below.
a. Describe the change as an absolute change in terms of percentage points. 89-66=23 b. Describe the change as a relative change in terms of a percentage. 89-66/66= .348 .348*100=34.8%
Fill in the blank in the following statement. The population of city A is 26% less than the population of city B, so city A's population is _____% of city B's.
city A population is 74% of city B 100-26= 74%
Absolute change and Relative change
if the new value is 50 and the reference value is 20, then relative change = 50-20/ 20 * 100%= 150%
Make an order of magnitude estimate of the following quantity. Explain the assumption used in your estimation. The number of times the average person's heart beats in a day
86,400; assuming an average person's heart beats once a second
State whether the following statement is true or false, and explain why. If the statement is false, state the true change. If the sales in your pizza restaurant increase by 5% in one year and decrease by 3% the following year, your sales are up by 2% over two years.
False; if the sales in your pizza restaurant increase by 5% one year and decrease by 3% the following year, your sales are up by 1.85 100+5=105 100-3=.97 .97*1.05=1.0185 1.0185*1000= 1018.5 1018.5-1000= 18.5 18.5/1000=0.0185 0.0185*100= 1.85 over two years.