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OlgaM077 [116]
3 years ago
11

mary selects a piece of candy at random form a jar that contains four peopermint, five cherry, three butterscotch, and two lemon

candies. what is the probability that the candy she selects is not lemon?
Mathematics
1 answer:
Vadim26 [7]3 years ago
3 0

Answer:

6/7 or 85.7 percent

Step-by-step explanation:

First, you will want to add all of the candies together and find the sum

Then you will want to take away the Lemon candies as you are looking for the probability of NOT choosing those,

so at this point, you should have 12 take that 12, and put it over the total number, so 12/14 then either simplify, or switch to a percentage, or both, and there is your answer.

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Find the area of the triangle with the given vertices. Use the fact that the area of the triangle having u and v as adjacent sid
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Answer:

The area of the triangle is A=\sqrt{\frac{4027}{2}}

Step-by-step explanation:

Using the fact that the area of the triangle having u and v as adjacent sides is given by

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According with the graph we can build the vectors:

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{\bf AC}=(-4-3,0-5,2-9)=(-7,-5,-7)

Next we need to find the cross product of this vectors.

{\bf AB} \times {\bf AC}=\begin{pmatrix}2&0&-9\end{pmatrix}\times \begin{pmatrix}-7&-5&-7\end{pmatrix}

This is the definition of cross product of two vectors in space:

Let {\bf u} = u_1{\bf i}+u_2{\bf j}+u_3{\bf k} and {\bf v} = v_1{\bf i}+v_2{\bf j}+v_3{\bf k} be vectors in space. The cross product of {\bf u} and {\bf v} is the vector

{\bf u} \times {\bf v}=(u_2v_3-u_3v_2){\bf i}-(u_1v_3-u_3v_1){\bf j}+(u_1v_2-u_2v_1){\bf k}

Applying this definition we get

{\bf AB} \times {\bf AC}=\begin{pmatrix}2&0&-9\end{pmatrix}\times \begin{pmatrix}-7&-5&-7\end{pmatrix}

\begin{pmatrix}0\cdot \left(-7\right)-\left(-9\left(-5\right)\right)&-9\left(-7\right)-2\left(-7\right)&2\left(-5\right)-0\cdot \left(-7\right)\end{pmatrix}\\\\\begin{pmatrix}-45&77&-10\end{pmatrix}

||{\bf AB} \times {\bf AC}||=\sqrt{(-45)^2+(77)^2+(-10)^2} \\\\||{\bf AB} \times {\bf AC}||=\sqrt{2025+5929+100}\\\\||{\bf AB} \times {\bf AC}||=\sqrt{8054}

The area of the triangle is

A=\frac{1}{2}||{\bf AB} \times {\bf AC} ||=\frac{1}{2}\sqrt{8054}=\sqrt{\frac{4027}{2}}

7 0
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