College Algebra
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Consider the set M = {-1028, -2050/5, -3/25, 0, 4/21, 1, √24, 11, 9π}. Identify which of its elements are irrational numbers.
Perform division in the given expression:
(37/6) / (-4/9)
State the property used in the given statement. (Note that the given variable belongs to the set of all real numbers, ℝ) 13(∛7) is a real number
(24/23) / (-3/8)
(-12/19) / (-27/25)
Solve the expression mentally by using the distributive property.
Solve the expression mentally by using the distributive property. 33∙78 +67∙78
State the property used in the given statement. (53 +132) +3 = 53 +(132 +3)
State the property used in the given statement. (Note that the given variable belongs to the set of all real numbers, ℝ)815∙(k +65) = (k +65)∙815
State the property used in the given statement. (Note that the given variable belongs to the set of all real numbers, ℝ)(x +133) +0 = x +133
State the property used in the given statement. (Note that the given variable belongs to the set of all real numbers, ℝ)(p - 73)(1/(p - 73)) = 1, if p -73 ≠ 0
State the property used in the given statement. 256∙13 + 256∙16 = 256(13 +16)
Consider the set M = {-1028, -2050/5, -3/25, 0, 4/21, 1, √24, 11, 9π}. Identify which of its elements are integers.
9/0
0/-8
Consider the set M = {-1028, -2050/5, -3/25, 0, 4/21, 1, √24, 11, 9π}. Identify which of its elements are natural numbers.
Given the following sets, find {x | x ∈ A or x ∈ C}, and indicate if A and C are disjoint sets:
U = {34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49}
A = {35, 37, 39, 41, 46, 48}
C = {39, 41, 43, 45, 47}
250/-50
-36/-6
-18/3
Given the following sets, find {x | x ∈ B and x ∈ D} or indicate if B and D are disjoint sets:
B = {35, 37, 39, 41, 46, 48, 49}
D = {39, 41, 43, 45, 47}
Given the following sets, find {x | x ∈ U, x ∉ B}:
Given the following sets, find {x | x ∈ U, x ∉ D}:
Given the following sets, find B ∪ (U ∩ ∅′). Also, indicate if there are disjoint sets:
B = {35, 37, 39, 41, 43}
Perform multiplication in the given expression:
-0.08(0.6)
-0.9(-0.7)
Given the following sets, find B ∩ (C ∪ D). Also, indicate if there are disjoint sets:
C = {34, 36, 38, 40, 42}
-4/9(-63/20)
Given the following sets, find (A ∪ D) ∩ C'. Also, indicate if there are disjoint sets:
A = {34, 36, 38, 40, 42}
C = {44, 45, 46, 47, 48}
D = {34, 38, 41, 44, 45}
-7/3(-27/42)
0(-7)
3(0)
9(-8)
Simplify the following expression such that the final answer has no exponents. (- 3)7
Simplify the following expression such that the final answer has no exponents. (- 6)3
-7(-6)
Simplify the following expression such that the final answer has no exponents. (- 3)8
Simplify the following expression such that the final answer has no exponents. (- 7)4
Simplify the following expression such that the final answer has no exponents. - 63
Simplify the following expression such that the final answer has no exponents. - 74
Given the following sets, find (A ∪ D) ∩ C. Also, indicate if there are disjoint sets:
Given the following sets, find (A ∩ B) ∪ C. Also, indicate if there are disjoint sets:
Given the following sets, find A ∪ ∅, and indicate if A and ∅ are disjoint sets:
A = {36, 38, 40, 42, 44}
Given the following sets, find Ø ∩ B, or indicate if Ø and B are disjoint sets:
B = {36, 37, 38, 39, 40}
Solve and express the answer as a real number.
Solve and express the answer as a real number. (- 6/7 - 2/3) - [- 9/14 - (- 5/6)]
Solve and express the answer as a real number. (8 - 43)(√1600 - 34)
Solve and express the answer as a real number. (90 - 34)(- 18 + √49)
Solve and express the answer as a real number. 5 × 16 - 39 ÷ 3
Solve and express the answer as a real number. - 7 × 24
Solve and express the answer as a real number. - |- 157|
Solve and express the answer as a real number. - |- 71|
Solve and express the answer as a real number. - |81/4|
Solve and express the answer as a real number. - |12/19|
Solve and express the answer as a real number. |- 327|
Solve and express the answer as a real number. |- 90|
Solve and express the answer as a real number. |- 9|
Solve and express the answer as a real number. 3 × 11 - 108 ÷ 27
Solve and express the answer as a real number. 107
Solve and express the answer as a real number. 0/131
Perform subtraction in the given expression:
19 - |-11|
-6 - |-7|
|-5 - 9|
7/6 - (-4/5)
Given the following sets, find B ∩ C', or indicate if B and C' are disjoint sets:
C = {37, 39, 41, 43, 45, 47, 49}
-13.42 - (4.12)
Given the following sets, find A' ∩ C, or indicate if A' and C are disjoint sets:
Given the following sets, find B':
2 - (-17)
Given the following sets, find A':
Given the following sets, find C ∪ D, and indicate if C and D are disjoint sets:
C = {37, 39, 41, 43, 45, 47}
D = {34, 35, 36, 37, 38}
-7 - 3
Given the following sets, find A ∩ C, or indicate if A and C are disjoint sets:
Given the following sets, find A ∪ B, and indicate if A and B are disjoint sets:
5 - 8
Perform addition in the given expression:
-3.7 + 7.6
-13/8 + 5/8
17 + (-12)
Given the following sets, find A ∩ B, or indicate if A and B are disjoint sets:
-21 + 7
-9 + (-19)
For the statement given below, write if it is true or false.
|-48|/|6| = |-48/6|
|-7| × |9| = |-7 × 9|
|21| × |-8| = |-168|
|13 - 18| = |13| - |18|
|9 + (-21)| = |9| + |-21|
|37| = |-37|
In the given statement, fill ∈ or ∉ to make the final statement true.
∅____ ∅
{0} ____ ∅
{1} _____ {1, 6, 11, 16}
In the given statement, fill ∈ or ∉ to make the final statement true. {783} _____
{783, 784, 785, 786}
106 _____ {12, 82, 106, 123}
3 _____ {3, 10, 28, 82}
18 _____ {11, 17, 19, 26}
76 _____ {78, 79, 80, 81}
32 _____ {30, 31, 32, 33}
Enumerate all the elements of the set using the set notation.
{x | x is a natural number not greater than 10}
{x | x is an integer between 96 and 105}
{27, 23, 19, ...., 3}
{312, 318, 324,..., 354}
{1, 1/6, 1/36, ...., 1/7776}
{101, 102, 103,....,110}
Find out whether the given set is finite or infinite, and also check if 15 belongs to the set.
{x | x is a fraction between 13 and 14}
Find out whether the given set is finite or infinite, and also check if 95 belongs to the set.
{x | x is greater than 100 and less than 126 and multiple of 5}
Find out whether the given set is finite or infinite, and also check if 6 belongs to the set.
{1, 1/6, 1/36, 1/216,...}
Find out whether the given set is finite or infinite, and also check if 33 belongs to the set.
{27, 28, 29,.....,40}
Work out {2, 512, 1024, 2048} ∪ {512, 1024, 3072}.
Work out {2, 512, 1024, 2048} ∩ {512, 1024, 3072}.
For the given set U = {24, 33, 42, 51, 60} and A = {24, 60}, Find out the complement of A.
For the following elements of the set described, express in set notation: {x | x is an integer greater than 137 and less than 141}.
Which of the following is true for the given set: {96, 98, 100, 102....}
∅ ∪ ∅ = ∅
∅ ∩ ∅ = ∅
{11, 21, 41} ∪ {11, 21, 41} = {11, 21, 41}
Consider the following expression. 918
Identify whether 9 and 18 is the base, the exponent, or the coefficient.
{8, 16, 21, 29} ∪ ∅ = {8, 16, 21, 29}
{5, 9, 14, 23} ∩ ∅ = {5, 9, 14, 23}
{4, 7, 12, 18} ∪ {7, 18, 21} = {7, 18}
{3, 6, 8, 13} ∩ {6, 8, 14, 17} = {6, 8}
Determine whether adding ⊆ or ⊄ in between the sets would make the following set statement true. ∅ ___ ∅
Determine whether adding ⊆ or ⊄ in between the sets would make the following set statement true. ∅ ___ {33, 67, 98, 109}
Determine whether adding ⊆ or ⊄ in between the sets would make the following set statement true. {1024, 2048, 4096} ___ {128, 256, 512, 1024, 2048}
Check whether the set statement given below is true or false.
∅ ⊆ ∅
Determine whether adding ⊆ or ⊄ in between the sets would make the following set statement true. {0, 128, 256} ___ {128, 256, 512, 1024, 2048}
Determine whether adding ⊆ or ⊄ in between the sets would make the following set statement true. {11, 29} ___ {0, 11, 17, 23, 29}
Determine whether adding ⊆ or ⊄ in between the sets would make the following set statement true. {13, 17, 19} ___ {11, 13, 17, 19, 23}
A set is given below.
D = {1, 9}
{0, 1} ⊆ D
Two sets are given below.
A = {1, 3, 5, 7, 9, 11} and C = {3, 7, 11}
A ⊆ C
B = {1, 3, 7, 9} and C = {3, 7, 11}
B ⊆ C
A = {1, 3, 5, 7, 9, 11} and D = {1, 9}
D ⊆ A
C = {3, 7, 11} and U = {1, 3, 5, 7, 9, 11, 13}
C ⊆ U
A = {1, 3, 5, 7, 9, 11} and U = {1, 3, 5, 7, 9, 11, 13}
A ⊆ U
For the following set statement, write if it is true or false. {y | y is a negative integer more than - 10} = {- 9, - 8, - 7, ..., - 1}
For the following set statement, write if it is true or false. {33, 11, 17} = {0, 33, 11, 7}
Write the fraction given below in its percentage equivalent.
14/5
13/4
2/3
For the following set statement, write if it is true or false. {10, 21, 34, 47, 58} = {21, 58, 47, 10, 34}
For the following set statement, write if it is true or false. {1, 16, 82, 96} = {96, 1, 16, 82}
For the following set statement, write if it is true or false. 8 ∉ {35, 24, 13, 9, 6}
For the following set statement, write if it is true or false. 6 ∈ {35, 24, 13, 9, 6}
For the following set statement, write if it is true or false. 20 ∈ {1, 7, 15, 25}
For the following set statement, write if it is true or false. 5 ∈ {1, 7, 15, 25}
17/33
7/16
9/25
7/10
3/4
For the given fraction, convert it to its equivalent decimal expression. Have two final answers, one using bar notation and the other one rounded to the nearest hundredths place value.
5/6
7/9
Perform division as indicated in the given expression: 15.24/12
Perform multiplication in the given expression: 0.09 ✖ 0.008
Perform multiplication in the given expression: 36.72 ✖ 57
Perform multiplication in the given expression: 87.01 ✖ 0.36
Perform multiplication in the given expression: 52.1 ✖ 5.8
Perform subtraction in the given expression: 59 - 5.256
Perform addition in the given expression: 46.9 + 578.12 +6.978
Rewrite the given fraction in its equivalent decimal notation. Round the answer to the nearest hundredths place value.
Perform addition in the given expression: 24.12 + 78.628 + 2.9
Perform addition in the given expression: 8.19 +56 + 6.2
Perform subtraction in the given expression: 812.6 - 29.79
Perform subtraction in the given expression: 97.25 - 63.13
Perform subtraction in the given expression: 88.88 - 8.76
Perform addition in the given expression: 93.84 + 718.6 + 1.874
Consider the given decimal number and show it as a fraction without writing in the lowest terms: 0.0018
Consider the given decimal number and show it as a fraction without writing in the lowest terms: 0.035
Rewrite the given fraction in its equivalent decimal notation. Round the answer to the nearest thousandths place value.
17/8
Consider the given decimal number and show it as a fraction without writing in the lowest terms: 0.781
For the following number written in percentage notation, rewrite in its fraction equivalent and reduce to the lowest terms possible. 1.25%
Consider the given decimal number and show it as a fraction without writing in the lowest terms: 0.91
Consider the given decimal number and show it as a fraction without writing in the lowest terms: 0.2
For the following number written in percentage notation, rewrite in its fraction equivalent and reduce to the lowest terms possible. 8.75%
Consider the given decimal number and show it as a fraction without writing in the lowest terms: 0.9
For the following number written in percentage notation, rewrite in its fraction equivalent and reduce to the lowest terms possible. 340%
For the following number written in percentage notation, rewrite in its fraction equivalent and reduce to the lowest terms possible. 260%
For the following number written in percentage notation, rewrite in its fraction equivalent and reduce to the lowest terms possible. 6%
For the following number written in percentage notation, rewrite in its fraction equivalent and reduce to the lowest terms possible. 4%
For the following number written in percentage notation, rewrite in its fraction equivalent and reduce to the lowest terms possible. 85%
For the following number written in percentage notation, rewrite in its fraction equivalent and reduce to the lowest terms possible. 45%
For the following number written in percentage notation, rewrite in its fraction equivalent and reduce to the lowest terms possible. 39%
For the following number written in percentage notation, rewrite in its fraction equivalent and reduce to the lowest terms possible. 61%
Write the decimal and percentage notation for the value given in fraction notation.
1/9
For the following number written in decimal notation, rewrite in its percentage equivalent. 0.9
For the following number written in decimal notation, rewrite in its percentage equivalent. 0.7
Write the fraction (in lowest terms) and decimal notation for the value given in percentage notation.
90%
For the following number written in decimal notation, rewrite in its percentage equivalent. 0.009
For the following number written in decimal notation, rewrite in its percentage equivalent. 0.002
For the following number written in decimal notation, rewrite in its percentage equivalent. 0.09
40%
For the following number written in decimal notation, rewrite in its percentage equivalent. 0.04
For the following number written in decimal notation, rewrite in its percentage equivalent. 0.81
1/100
Write the fraction notation (in lowest terms or whole number) for the values given in decimal and percentage notation.
Decimal: 0.08
Percentage: 8%
Write the decimal notation for the values given in fraction and percentage notation.
Fraction: 1/25
Percentage: 4%
For the following number written in percentage notation, rewrite in its decimal equivalent.
Write the percentage notation for the values given in decimal and fraction notation.
Fraction (Whole number): 2
Decimal: 2.0
For the following number written in percentage notation, rewrite in its decimal equivalent. 4.2%
Fraction: 1/1000
Decimal: 0.001
For the following number written in percentage notation, rewrite in its decimal equivalent. 289%
For the following number written in percentage notation, rewrite in its decimal equivalent. 2%
For the following number written in percentage notation, rewrite in its decimal equivalent. 9%
For the following number written in percentage notation, rewrite in its decimal equivalent. 31%
For the following number written in percentage notation, rewrite in its decimal equivalent. 77%
Evaluate the following and reduce the final answer to the lowest terms possible.
Perform division in the given fraction:
76.36/1000
Evaluate the following and reduce the final answer to the lowest terms possible. 17/24 - 1/6
367.58/100
Evaluate the following and reduce the final answer to the lowest terms possible. 13/36 - 1/9
3.87/10
Evaluate the following and reduce the final answer to the lowest terms possible. 16/21 - 9/21
Evaluate the following and reduce the final answer to the lowest terms possible. 8/13 - 3/13
0.025 × 1000
645.345 × 100
567.24 × 10
18.2903/3.71
71.531/2.33
Consider the given decimal number and round it to the nearest hundredth: 0.1367
Consider the given decimal number and round it to the nearest hundredth: 0.5629
Consider the given decimal number and round it to the nearest hundredth:
24.82/14.6
Round the following decimal number 2461.23783 to the nearest thousands place.
Round the following decimal number 2461.2378 to the nearest hundreds place.
Round the following decimal number, 2461.2378, to the nearest ten thousandth place.
Round the following decimal number, 2461.2378, to the nearest thousandths place.
Choose the decimal number from the following options that fulfills all of the given conditions:
(a) 7 in the hundreds place (b) 2 in the tens place (c) 6 in the tenths place
Write down the digit that has the tenths place value in the decimal number 1347.25892.
Write down the digit that has the thousands place value in the decimal number 1347.25892.
Write down the digit that has the ten thousandths place value in the decimal number 1347.25892.
Write down the digit that has the hundredths place value in the decimal number 1347.25892.
Write down the digit that has the hundreds place value in the decimal number 1347.25892.
Evaluate the following and reduce the final answer to the lowest terms possible. 11/51 + 6/51
Evaluate the following and reduce the final answer to the lowest terms possible. 11/29 + 13/29
Write the equivalent improper fraction for the given mixed number.
Write the equivalent mixed number form for the given improper fraction.
110/17
34/7
72/13
Evaluate the following and reduce the final answer to the lowest terms possible. 3 ÷ (1/5)
Evaluate the following and reduce the final answer to the lowest terms possible. (3/8) ÷ 32
Evaluate the following and reduce the final answer to the lowest terms possible. (2/7) ÷ 14
Evaluate the following and reduce the final answer to the lowest terms possible. (56/9) ÷ (8/63)
Convert the fraction given below into simplified terms possible.
36/108
Evaluate the following and reduce the final answer to the lowest terms possible. (5/3) ÷ (7/12)
8/120
200/340
Evaluate the following and reduce the final answer to the lowest terms possible. (8/13) ÷ (7/2)
60/140
25/30
7/14
6/24
Evaluate the following and reduce the final answer to the lowest terms possible. (27/26) × (13/9)
Evaluate the following and reduce the final answer to the lowest terms possible. (2/9) × (15/11)
Evaluate the following and reduce the final answer to the lowest terms possible. (6/28) × (7/18)
Evaluate the following and reduce the final answer to the lowest terms possible. (1/8) × (3/5)
Evaluate the following and reduce the final answer to the lowest terms possible. (7/8) × (5/6)
Write the fraction which is not equivalent to 7/8.
Write the given fraction into its lowest form.
36/63
Write the reciprocal of the given fraction.
9/4
27/4
Identify the numerator and denominator in the given fraction.
34/19
When 9.4 is multiplied by 105, what does this operation do to the decimal point in 9.4?
Perform the indicated operation and express the answer in scientific notation:
Perform the indicated operation and express the answer in scientific notation: 384,000,000/0.0000192
Perform the indicated operation and express the answer in scientific notation: (5.6 x 105)(2.1 x 109)
Perform the indicated operation and express the answer in scientific notation: (2.3 x 10-6)(3 x 10-8)
The number 0.000037 is written in decimal notation. Express it in scientific notation.
Express the following scientific notation as decimal notation: -3.0005 x 108
Express the following scientific notation as decimal notation: 5.8 x 104
Identify the property shown by the following equation:
Identify the property shown by the following equation: 1 + (14 + 9) = (1 + 14) + 9
Consider the integers -17 and 9. Determine the distance between them by using and evaluating absolute value expression.
Consider the integers 5 and 28. Determine the distance between them by using and evaluating absolute value expression.
The given expression includes absolute value bars. Evaluate the expression considering a = 1 and b = -7:
|a| - |b|
The given expression includes absolute value bars. Evaluate the expression considering x = 6 and y = -2:
6|x + y|
An expression shown is enclosed in absolute value bars. Rewrite it without the absolute value bars: ||-8|-|-14||
An expression shown has its denominator enclosed in absolute value bars. Rewrite the entire expression without the absolute value bars: -17/|-17|
An expression shown is enclosed in absolute value bars. Rewrite it without the absolute value bars: |22 - π|
An expression shown is enclosed in absolute value bars. Rewrite it without the absolute value bars: |125|
Identify whether the given inequality statement is true or false: 0 ≥ -12
Identify whether the given inequality statement is true or false: -4π ≤ -4π
Identify whether the given inequality statement is true or false: -35 ≤ -11
Classify which of the following numbers are real numbers, irrational numbers, rational numbers, integers, whole numbers, and natural numbers: {-2/5, 0, 0.3, √7, π, √25}
Classify which of the following numbers are real numbers, irrational numbers, rational numbers, integers, whole numbers, and natural numbers: {-5, -1/3, 0, 0.75, √11, 10.2, √81}
Find the union of the following sets: {d, r, e, a, m} ∪ ∅
Find the intersection of the following sets: {x, r, p, q} ∩ ∅
Find the intersection of the following sets. {4, 8, 12, 15} ∩ {3, 11, 12, 25, 15}
A rocket was launched vertically upward from a platform at a height of 8 feet. The initial speed of the rocket is 135 feet per second. Its height (in ft), relative to the ground, is defined by the equation h = 8 + 135t - 16t2, t seconds after it was launched. Calculate the rocket's height 4 seconds after it was launched.
The equation F = (9/5)C + 32 allows the conversion between Celsius temperature and Fahrenheit temperature. Use this equation to convert 20 °C to its equivalent temperature in Fahrenheit scale.
Let D = {x, y, z}, E = {w, x, z, 4}.
Find D ∪ E.
Find D ∩ E.
Use the properties of exponents to simplify: (6y4/5)(3y9/2)
Simplify the following expression: 363/2
Simplify the following expression: 343-1/3
Simplify the following expression: 25(1/2)
Simplify this expression: √81/√16
Use the product rule to simplify the following expression. √81x2. Note that x ≥ 0.
Evaluate by performing the indicated operation, and write the final answer in decimal notation. (2 × 104)(7.2 × 103)
Express 91 980 000 in scientific notation.
Express 1.29*10-7 in decimal notation.
For the following exponential expression, simplify. (-12a4b7)(-4a-7b-3)
Perform the indicated operation. (254)/(58)
For the exponential expression, simplify. (-4z4y8)2
Evaluate and simplify. 11-4 • 11
Evaluate and simplify. 3-2 - 2-3
Evaluate and simplify. (-7)2(-6)3
Identify the mathematical property being observed in the equation: (1 • 11) + (2 • 11) = (2 • 11) + (1 • 11)
Identify the mathematical property being observed in the equation: 11 • (1 • 7) = (1 • 7) • 11
Identify the mathematical property being observed in the equation: 12 + 21 = 21 + 12