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rusak2 [61]
3 years ago
12

In a box of marbles, the ratio of red marbles to total marbles is 2:5. the ratio of green marbles to total marbles is 3:10. if t

he marbles that are neither red nor green are blue, how many blue marbles are in the box if there are 40 marbles in the box?
Mathematics
1 answer:
STALIN [3.7K]3 years ago
7 0
Ratio:

Red : Total 
  2   :    5
 (x2)    (x2)
  4   :   10

Green : Total
  3   :       10

Total of red and green marbles = 4 + 3 = 7

Blue marbles = 10 - 7 = 3

10 parts = 40 marbles
1 part = 40 ÷ 10 = 4
3 parts = 4 x 3 = 12

Answer: There are 12 blue marbles.
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find the angle between the vectors. (first find the exact expression and then approximate to the nearest degree. ) a=[1,2,-2]. B
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Answer:

\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately \theta \approx 48

Step-by-step explanation:

For this case first we need to calculate the dot product of the vectors, and after this if the dot product is not equal to 0 we can calculate the angle between the two vectors in order to see if there are parallel or not.

a=[1,2,-2], b=[4,0,-3,]

The dot product on this case is:

a b= (1)*(4) + (2)*(0)+ (-2)*(-3)=10

Since the dot product is not equal to zero then the two vectors are not orthogonal.

Now we can calculate the magnitude of each vector like this:

|a|= \sqrt{(1)^2 +(2)^2 +(-2)^2}=\sqrt{9} =3

|b| =\sqrt{(4)^2 +(0)^2 +(-3)^2}=\sqrt{25}= 5

And finally we can calculate the angle between the vectors like this:

cos \theta = \frac{ab}{|a| |b|}

And the angle is given by:

\theta = cos^{-1} (\frac{ab}{|a| |b|})

If we replace we got:

\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately \theta \approx 48

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Answer:

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Step-by-step explanation:

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