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2 years ago

[50 points]

Mathematics

1 answer:

Marina86 [1]2 years ago

4 0

Answer:

$\sf \dfrac{1}{10}$

Step-by-step explanation:

From the table:

Total number of Sophomores = 10
Total number of students = 37
Total number of Boys who are Sophomores = 1

$\sf Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ possible \ outcomes}$

$\sf \implies P(Sophomore)=\dfrac{10}{37}$

$\sf \implies P(Boy \cap Sophomore)=\dfrac{1}{37}$

$\begin{aligned}\sf P(Boy | Sophomore) & = \sf\dfrac{P(Boy \cap Sophomore)}{P(Sophomore)}\\\\ & = \sf \dfrac{1}{37} \div \dfrac{10}{37}\\\\ & = \sf\dfrac{1}{37} \times\dfrac{37}{10}\\\\ & = \sf\dfrac{1}{10}\end{aligned}$

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Walk fifty meters at 30o north or east from the old oak tree. (2) Turn 45o to your left (you should now be facing 75o north of e

saw5 [17]

Answer:

A straight line of approximately 75 meters, 1.4º north

Step-by-step explanation:

Hi, let's make it step by step to make it clearer

1) If we walk 50 meters in 30º angle Northeast, assuming the Old Oak tree is the point 0,0 and we're dealing with vectors in $R^{2}$ . To say 30º Northeast is 30º clockwise (or 60º counter clockwise).

2) Then there was a the turning point to the left. If I turn to the left, on my compass 45º , I'll face 75º northeast.

3) Finally, the last vector leads to the treasure from the Old Oak Tree, i.e. the resultant.

So, let's calculate the norm which is the length of the each vector.

1) Graphing them we can find the points, then the components and then calculate the norm, the length of each vector.

Since the Oak Tree is on (0,0). The turning point (50,86.61) and the Rock (R=(1.4,74,85) we can write the following vectors:

$\vec{u}=\left \langle 50,86.61 \right \rangle\\\vec{v}=\left \langle -48.6,-11.76\right \rangle\\\vec{w}=\left \langle 1.4,74.85 \right \rangle$

Now, let's calculate each vector length by calculating the norm.

$\left \| \vec{u} \right \|=\sqrt{50^{2}+86.6^2}=100\\\left \| \vec{v} \right \|=\sqrt{(-48.6)^2+(-11.76)^2}=50\\\left \| \vec{u} \right \|=\sqrt{(1.4)^2+(74.85)^2}=74.86$

The path is almost 75 meters. And since it is less than 15º degrees to the left of the North (or to the right) its direction is still north of the Old Oak Tree.

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Is the following statement a good definition? Why? An obtuse angle is an angle whose measure is greater than 90°.

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180° measures more than 90°, so according to the given statement, a plane angle is also an obtuse angle, and that is incorrect. From that, we conclude that the statement is not a good definition.

<h3>Is the following statement a good definition? </h3>

The given statement is:

"An obtuse angle is an angle whose measure is greater than 90°."

This is the common, but incorrect, definition for obtuse angles.

We know that an angle that measures 180° is called a plane angle and by definition, a plane angle is not an obtuse angle.

And the angles larger than 180° (and smaller than 360°) are the reflex angles.

Now, 180° measures more than 90°, so according to the given statement, a plane angle is also an obtuse angle, and that is incorrect. From that, we conclude that the statement is not a good definition.

If you want to learn more about obtuse angles:

brainly.com/question/5023725

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Step-by-step explanation:

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