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Lelu [443]
3 years ago
15

A game spinner has 8 sections, 3 red, 1 blue, 2 yellow, and 2 green. What is the probability of not spinning a green?

Mathematics
1 answer:
jekas [21]3 years ago
4 0

Answer:

3/4

Step-by-step explanation:

green takes up 1/4 so the rest that arnt green is the answer

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1. Write the following numbers in the expanded form:<br>(i) 20.03 <br>(ii) 200.03 <br>(iii) 2.034​
PSYCHO15rus [73]

Answer:

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Whats 19 divided by 5 in long division
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Move the decimal 1 place to the left.
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Show that the line integral is independent of path by finding a function f such that ?f = f. c 2xe?ydx (2y ? x2e?ydy, c is any p
Juli2301 [7.4K]
I'm reading this as

\displaystyle\int_C2xe^{-y}\,\mathrm dx+(2y-x^2e^{-y})\,\mathrm dy

with \nabla f=(2xe^{-y},2y-x^2e^{-y}).

The value of the integral will be independent of the path if we can find a function f(x,y) that satisfies the gradient equation above.

You have

\begin{cases}\dfrac{\partial f}{\partial x}=2xe^{-y}\\\\\dfrac{\partial f}{\partial y}=2y-x^2e^{-y}\end{cases}

Integrate \dfrac{\partial f}{\partial x} with respect to x. You get

\displaystyle\int\dfrac{\partial f}{\partial x}\,\mathrm dx=\int2xe^{-y}\,\mathrm dx
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Differentiate with respect to y. You get

\dfrac{\partial f}{\partial y}=\dfrac{\partial}{\partial y}[x^2e^{-y}+g(y)]
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Integrate both sides with respect to y to arrive at

\displaystyle\int2y\,\mathrm dy=\int g'(y)\,\mathrm dy
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So you have

f(x,y)=x^2e^{-y}+y^2+C

The gradient is continuous for all x,y, so the fundamental theorem of calculus applies, and so the value of the integral, regardless of the path taken, is

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