Sets & Venn Diagrams
Let A be a set. Simplify:
(a) A\cap\emptyset
(b) A\cup\emptyset
(a)
A\cap\emptyset =\emptyset
(b)
A\cup\emptyset =A
98765+(-98765)
98765+(-98765)=0
Solve:
\abs{x}=7.3
x\in{-7.3,7.3}
Simplify.
-(-x+1.2)
-(-x+1.2)
=(-1)(-x+1.2)
= x-1.2
Evaluate.
5^{-4}
5^{-4}
=\frac{1}{5^4}
=\frac{1}{625
Fill in the blanks with always, sometimes, or never:
(a) If A is a set, it is ______ true that \emptyset \subset A .
(a) If A is a set, it is ______ true that \emptyset \in A .
always, sometimes
Compare using >,<,= :
(a) -9^3 and (-9)^3
(b) -5^4 and (-5)^4
-9^3=(-9)^3
-5^4<(-5)^4
Solve.
-\abs{y}=-\abs{-y}
all real numbers, i.e.
y\in (-\infty, \infty)
Simplify.
(0.3x^3)^2
(0.3x^3)^2
=0.3^2\cdot (x^3)^2
=0.09x^6
Express in scientific notation:
2.1\times 10^{-43}\times 7.5\times 10^-3
1.575\times 10^{-47}
Let A, B be sets with A\subset B . Find:
(a) A \cup B
(b) A \cap B
(a) A \cup B=B
(b) A\cap B=A
Evaluate.
-1.13-(-9.831+0.13)
8.571
Evaluate when a=-9.25, b=-0.042 :
\abs{a-2b}-\abs{-a}
-0.084
Simplify.
13-3(0.5m+3)(0.2)+0.8
-0.3m+12
Express 64 as a power of -\frac{1}{2} .
64=(-\frac{1}{2})^{-6}
A group of 75 students visited Washington D.C. last spring. 40 students visited the Washington Monument, 35 went to the White House, 15 visited the Kennedy Center, 10 visited the White House and the Kennedy Center, 8 went to the White House and the Washington Monument, 6 went to the Kennedy Center and the Washington Monument, and 4 visited all three sites. How many students visited none of the three sites?
5 students
Evaluate.
0.9\times 9.13-9.13(-1.1)
18.26
(Use the distributive property!)
Solve. Express your answer in interval notation!
\abs{-x}\geq \abs{-6.12}-(-\abs{-6.12})
x\in(\infty , -12.24]\cup [12.24,\infty)
Simplify.
(-2c^3d)^2+(4cd^2)(-3c^5)
-8c^6d^2
Simplify:
\frac{-18x^5y^{-7}}{-27x^{-10}y^2}
\frac{2x^15}{3y^9
Two-thirds of the dogs at a certain shelter are labs. Half of the dogs at the shelter are female, and three-quarters of the male dogs at the shelter are labs. If there are 14 female labs at the shelter, how many dogs are there total?
48
Evaluate for x=-0.45, y=-7 :
(-x^2-(-3y))\div 50
-0.42405
Solve.
2\abs{r+8}-7=11
r\in{-17,1}
Simplify.
(3xy^3)^3(\frac{6x}{y})^{-4}+\frac{y^13}{x}
\frac{49y^13}{48x}
Simplify:
(-\frac{15a^{-5}b^3}{25b^{-8}a^10})^{-2
\frac{25a^30}{9b^22}