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mathematics
contemporary mathematics
Contemporary Mathematics 1st Edition OpenStax - Solutions
Correctly apply the rules for the order of operations to accurately compute the following:\((10-3) \times 5^{3}\).
Correctly apply the rules for order of operations to accurately compute the following:\(4+2 \times\left(3^{2}-(2+5)^{2} \times 4\right) /(3+8)\).
Which of the following are perfect squares?1. 45 2. 144
Determine which of the following are rational numbers:1. \(\sqrt{73}\)2. 4.556 3. \(3 \frac{1}{5}\)4. \(\frac{41}{17}\)5. \(5 . \overline{64}\)
Determine if \(\frac{12}{30}\) and \(\frac{14}{35}\) are equivalent fractions.
Express the following rational numbers in lowest terms:1. \(\frac{36}{48}\)2. \(\frac{100}{250}\)3. \(\frac{51}{136}\)
Calculate \(\frac{23}{42}+\frac{9}{56}\) using Desmos.
Calculate \(\frac{13}{28}+\frac{7}{28}\).
Calculate \(\frac{45}{136}-\frac{17}{136}\).
Calculate \(\frac{11}{18}+\frac{2}{15}\).
Calculate \(\frac{14}{25}-\frac{9}{70}\).
Rewrite \(\frac{48}{13}\) as a mixed number.
Rewrite \(5 \frac{4}{9}\) as an improper fraction.
Round 5.67849 to three decimal digits.
Round 45.11475 to four decimal digits.
Convert \(\frac{47}{25}\) into decimal form.
Convert 3.2117 to fraction form.
Calculate \(\frac{12}{25} \times \frac{10}{21}\).
Calculate \(3.45 \div 2.341\) using a calculator. Round to three decimal places if necessary.
1. Calculate \(\frac{4}{21} \div \frac{6}{35}\).2. Calculate \(\frac{1}{8} \div \frac{5}{28}\).
Correctly apply the rules for the order of operations to accurately compute \(\left(\frac{5}{7}-\frac{2}{7}\right) \times 2^{3}\).
Correctly apply the rules for the order of operations to accurately compute \(4+\frac{2}{3} \div\left(\left(\frac{5}{9}\right)^{2}-\left(\frac{2}{3}+5\right)\right)^{2}\).
Demonstrate the density property of rational numbers by finding a rational number between \(\frac{4}{11}\) and \(\frac{7}{12}\).
James is mixing soil for a raised garden, in which he plans to grow a variety of vegetables. For the soil to be suitable, he determines that \(\frac{2}{5}\) of the soil can be topsoil, but \(\frac{2}{5}\) needs to be peat moss and \(\frac{1}{5}\) has to be compost. To fill the raised garden bed
At Bella's Pizza, one-third of the pizzas that are ordered are one of their specialty varieties. If there are 273 pizzas ordered, how many were specialty pizzas?
It is known that 1 liter (L) is 0.264172 gallons (gal). Use this to convert 14 liters into gallons.
It is known that 1 inch is 2.54 centimeters. Use this to convert 100 centimeters into inches.
Rewrite the following as fractions:1. \(31 \%\)2. \(93 \%\)
Rewrite the following percentages in decimal form:1. \(54 \%\)2. \(83 \%\)
1. Determine \(40 \%\) of 300 .2. Determine \(64 \%\) of 190 .
1. What is the total if \(28 \%\) of the total is 140 ?2. What is the total if \(6 \%\) of the total is 91 ?
Find the percentage in the following:1. Total is 300 , percentage of the total is 60 .2. Total is 440 , percentage of the total is 176.
A study revealed that \(70 \%\) of students suffer from sleep deprivation, defined to be sleeping less than 8 hours per night. If the survey had 400 participants, how many of those participants had less than 8 hours of sleep per night?
There are 126 million users who are U.S. Amazon Prime subscribers. If there are 328.2 million residents in the United States, what percentage of U.S. residents are Amazon Prime subscribers?
Evander plays on the basketball team at their university and \(73 \%\) of the athletes at their university receive some sort of scholarship for attending. If they know 219 of the student-athletes receive some sort of scholarship, how many studentathletes are at the university?
Determine which of the following are perfect squares.1. 45 2. 81 3. \(\frac{9}{28}\)4. \(\frac{144}{400}\)
Identify which of the following numbers are irrational.1. \(\sqrt{35}\)2. \(0 . \overline{15}\)3. \(\sqrt{121}\)4. \(4 \pi\)
Simplify the irrational number \(\sqrt{180}\) and express in lowest terms. Identify the rational and irrational parts.
Simplify the irrational number \(\sqrt{330}\) and express in lowest terms. Identify the rational and irrational parts.
Simplify the irrational number \(\sqrt{2,548}\) and express in lowest terms. Identify the rational and irrational parts.
If possible, subtract the following irrational numbers without using a calculator. If this is not possible, state why.\(3 \sqrt{7}-8 \sqrt{7}\)
If possible, add the following irrational numbers without using a calculator. If this is not possible, state why.\(35 \pi+17 \pi\)
If possible, subtract the following irrational numbers without using a calculator. If this is not possible, state why.\(19 \sqrt{3}-5.6 \sqrt{7}\)
Perform the following operations without a calculator. Simplify if possible.1. \(3 \sqrt{15} \div(8 \sqrt{3})\)2. \(14.7 \sqrt{135} \div(3 \sqrt{5})\).
Perform the following operations without a calculator. Simplify if possible.1. \((19 \sqrt{3}) \times(5.6 \sqrt{12})\)2. \(13 \pi \times 8 \pi\)
Rationalize the denominator of the following:1. \(\frac{5}{\sqrt{7}}\)2. \(\frac{3 \sqrt{6}}{2 \sqrt{10}}\)
Rationalize the denominator of \(\frac{4}{6+\sqrt{10}}\).
Determine if each of the following are real numbers:1. \(\frac{4 \sqrt{3}}{7}\)2. 13.3381 3. \(17 \sqrt{-8}\)
Identify all subsets of the real numbers to which the following real numbers belong:1. 14 2. -14.223 3. \(\sqrt{17}\)
Place the following numbers correctly in the Venn diagram (Figure 3.33). -42-10 37 41 150 20 -18 4 N Z R Figure 3.33
In each of the following, identify which property of the real numbers is being applied.1. \(4+(8+13)=(4+8)+13\)2. \(34 \times\left(\frac{1}{34}\right)=1\)3. \(14+27=27+14\)
Use properties of the real numbers and mental math to calculate the following:1. \(2 \times 13 \times 50\)2. \(13+84+27\)3. \(9 \times 16 \times 11\)
Find the value of the following numbers modulo 12 :1. 34 2. 539 3. 156
If it's \(3: 00\), what time will it be in 89 hours?
If it is 4:00 now, what time was it 67 hours ago?
What is the product of 11 and 45 modulo 12 ?
Suppose it is 3:00, and you decide to check your email every 5 hours. What time will it be when you check your email the ninth time?
Your family has a cat, and no one wants to empty the litter box. However, it has to be done daily. The six of you agree to take turns, so everyone has to empty the litter box every 6 days. You empty the box on a Thursday. What day will you empty the box for the 10 th time?
If possible, use the product rule to simplify the following:1. \(21^{9} \times 21^{15}\)2. \(5^{9} \times 8^{4}\)
Use the product rule to simplify \(a^{4} \times a^{10}\).
Use the quotient rule to simplify \(\frac{5^{19}}{5^{11}}\).
Use the exponent distributive rule to expand \((6 \times 13)^{7}\).
Use the exponent distributive rule to expand \((c \times d)^{10}\).
Use the exponent distributive rule to expand the following:1. \(\left(\frac{4}{9}\right)^{6}\)2. \(\left(\frac{3}{b}\right)^{11}\)
Expand the following:1. \(\left(6^{7}\right)^{3}\)2. \(\left(b^{12}\right)^{4}\)
Convert the following to expressions with no negative exponent:1. \(3^{4} \times 5^{-8}\)2. \(a^{-9} \times b^{5}\)3. \(\frac{7}{c^{-2}}\)
Use negative exponents to rewrite the following expressions with no denominator:1. \(\frac{7^{3}}{13^{9}}\)2. \(\frac{c^{4}}{d^{8}}\)
Simplify the following:1. \(\left(\frac{4^{2} \times 7}{9^{3}}\right)^{5}\)2. \(\left(\frac{5 a^{4}}{b^{9}}\right)^{6}\)
Which of the following numbers are in scientific notation? If the number is not in scientific notation, explain why it is not.1. \(-9.67 \times 10^{20}\)2. \(145 \times 10^{-8}\)3. 1.45
Write the following numbers in scientific notation form:1. 428.9 2. -0.00000981 3. 8
Change \(456.142 \times 10^{5}\) by moving the decimal two places to the left.
Change \(12.3 \times 10^{2}\) by moving the decimal five places to the right.
Convert the following into standard form:1. \(2.78 \times 10^{9}\)2. \(9.04 \times 10^{-8}\)
Calculate the following:1. \(3.8 \times 10^{-3}+1.006 \times 10^{-3}\)2. \(9.61 \times 10^{8}-3.85 \times 10^{8}\)
Calculate the following:1. \(7.03 \times 10^{13}+8.5 \times 10^{13}\)2. \(4.3 \times 10^{21}-4.613 \times 10^{21}\)
Calculate the following:\(6.1 \times 10^{4}+4.8 \times 10^{5}\)
Calculate the following:\(7.9 \times 10^{-15}-6.8 \times 10^{-13}\)
Calculate the following:1. \(\left(4.3 \times 10^{3}\right) \times\left(1.8 \times 10^{7}\right)\)2. \(\left(5 \times 10^{-13}\right) \times\left(7.3 \times 10^{6}\right)\)
Calculate the following:1. \(\left(8.4 \times 10^{31}\right) /\left(2.1 \times 10^{7}\right)\)2. \(\left(4.14 \times 10^{-13}\right) /\left(8.28 \times 10^{9}\right)\)
How much farther from the sun is Earth compared to Venus if Venus is \(6.7667 \times 10^{7}\) miles from the sun and Earth is \(9.1692 \times 10^{7}\) miles from the sun?
The probability of winning the Mega Millions lottery is published as \(3.304693 \times 10^{-9}\). The probability of being hit by lightning is approximated to be \(2 \times 10^{-6}\). How many times more likely are you to be hit by lightning than win the Mega Millions?
Sometimes it is entertaining to determine the time it takes for something to happen. Fingernails grow about \(8.032 \times 10^{-11} \mathrm{~km}\) per minute. How many kilometers long would fingernails be after \(6 \times 10^{4}\) minutes?
As mentioned in the opening to this section, it is estimated that we're producing 2.5 quintillion bytes of data per day. A good estimate is that there are 7.674 billion people on the planet. Convert both of those numbers to scientific notation, and then determine how much data is being generated
Determine if the following sequences are arithmetic sequences. Explain your reasoning.1. \(\{4,7,10,13,16,19,22,25, \ldots\}\)2. \(\{20,40,80,160,320,640\}\)3. \(\{7,1,-5,-11,-17,-23,-29,-34,-40\}\)
Identify \(a_{1}\) and \(d\) for the following arithmetic sequence. Use this information to determine the 60 th term.\[ \{18,31,44,57,70,83, \ldots\} \]
A sequence is known to be arithmetic. Two of its terms are \(a_{7}=56\) and \(a_{19}=104\). Use that information to find the constant difference, the first term, and then the 50 th term of the sequence.
What is the sum of the first 60 terms of an arithmetic sequence with \(a_{1}=4.5\) and \(d=2.5\) ?
Jordan has just watched The Queen's Gambit and decided to hone their skills in chess. To really improve at the game, Jordan decides to practice for 3 hours the first week, and increase their time spent practicing by 30 minutes each week. How many hours will Jordan practice chess in week 20 ?
Let's check back in on Jordan. Recall, Jordan had just watched The Queen's Gambit and decided to hone their skills, practicing for 3 hours the first week, and increasing the time spent practicing by 30 minutes each week. How many hours total will Jordan have practiced chess after 30 weeks of
For each sequence, determine if the sequence is a geometric sequence. If so, identify the common ratio.1. \(\{5,20,80,320,1,280,5,120,20,480, \ldots\}\)2. \(\{-3,6,-12,24,11,33\}\)3. \(\left\{4,2,1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \ldots\right\}\)
In the following geometric sequences, determine the indicated term of the geometric sequence with a given first term and common ratio.1. Determine the 9 th term of the geometric sequence with \(a_{1} \times 6\) and \(r=3\).2. Determine the 11 th term of the geometric sequence with \(a_{1}=2\) and
1. What is the sum of the first 13 terms of the geometric sequence with first term \(a_{1}=5\) and common ratio \(r=3\) ?2. What is the sum of the first 7 terms of the geometric sequence with first term \(a_{1}=16\) and common ratio \(r=\frac{1}{8}\) ?
Daryl deposits \(\$ 1,000\) in an account earning \(4 \%\) interest compounded yearly. How much money is in the account after 25 years?
When Escherichia coli (E. coli) is in a broth culture at \(37^{\circ} \mathrm{C}\), the population of \(E\). coli doubles in number with 30 organisms, how many \(E\). coli bacteria are present in the culture after 16 hours?
A player places one grain of rice on the first square of a chess board. On the second square, the player places 2 grains of rice. On the third square, the player places 4 grains of rice. On each successive square of the board, the player doubles the number of grains of rice placed on the chess
\(1+2-3=0\)Determine whether each of the following sentence represent a logical statement. If it is a logical statement, determine whether it is true or false.
All mammals lay eggs.Determine whether each of the following sentence represent a logical statement. If it is a logical statement, determine whether it is true or false.
Some monkeys do not have tails.Write the negation of each statement below.
\(p \wedge \sim q\)Write the negation of each statement below.
If the plumber does not remove the clog, then the homeowner will not pay the plumber.Write the negation of each statement below.
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