The universal set is the set of whole numbers less than 14.U = {0,1,2,3,4,5,6,7 ,8 ,9 ,10 ,11 ,12 ,13}

Set J is the set that represents the numbers that Janet thinks are lucky.
J={3,7}

Set K is the set that represents the numbers that Kyle thinks are awesome!
K={2,4,6,8}

Set L is the set that represents the numbers that Lauren thinks she should write on the wall of her bedroom (with her parent’s permission, of course)!
L={0,3,5,6,7,8,9}

What is the set defined by ~(J ∪K) ?

Answers

Answer 1

Answer: ~(J ∪K) = not J union K = not {2, 3, 4, 6, 7, 8} = {0, 1, 5, 9, 10, 11, 12, 13}

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Lucy has a hemisphere shaped goldfish pond in her backyard. The pond has a circumference of 11.9 feet . The pond has a population density of 3.6 cubic feet of water for each goldfish. How many goldfish are in Lucy's pond ?

Answers

40.38 my answer is 40.38 or 40 goldfish

Around 40.38 - 40 goldfish is your answer.

√48a^4 b^5 c^3 d simplify and keep it in radical form

Answers

I will assume the square root extends all the way across.

$√(48a^4b^5c^3)$

$√(2^4\cdot3\cdot a^4b^5c^3)$

$√((2^2)^2\cdot3\cdot(a^2)^2\cdot(b^2)^2\cdot b\cdot c^2\cdot c)$

$√((4)^2\cdot3\cdot(a^2)^2\cdot(b^2)^2\cdot b\cdot c^2\cdot c)$

$√((4\cdot a^2 \cdot b^2 \cdot c)^2\cdot3\cdot b\cdot c)$

$4\cdot a^2\cdot b^2\cdot c√(3\cdot b\cdot c)$

$\boxed{4a^2b^2c√(3bc)}$

Solve the logarithm. show steps.

Answers

$log_82+log_84x^2=1;\ D:x^2 > 0\Rightarrow x\neq0\n\nlog_8(2\cdot4x^2)=log_88^1\n\nlog_88x^2=log_88\iff8x^2=8\ \ \ |both\ sides\ /:8\n\nx^2=1\iff x=-1\ or\ x=1.\n\nSolutions:x=-1\ \vee\ x=1.$