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Elden [556K]
2 years ago
5

Calvin throws 12 sheets of paper up in the air and randomly catches one of the sheets as they float down. Of the 12 sheets of pa

per, 9 are white and 3 are red. The probability that Calvin caught a white sheet is . It is that this event occurs. The probability that Calvin caught a red sheet is . It is that this event occurs.
Mathematics
1 answer:
Leokris [45]2 years ago
7 0

Total number of sheets are 12.

Total number of white sheets= 9

Total number of red sheets = 3

Probability = Number of favorable outcomes/ total number of outcomes.

Hence

When Calvin throws the sheets in the air, the probability that he gets a white sheet is

\frac{9}{12}

which equals to \frac{3}{4}

that becomes 0.75

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Bulan rows on a crew team. Her team rows their boat at a split (rate) of 2 min/500 m.
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Answer:

250

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8 0
2 years ago
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Describe the first step when factoring any polynomial. Why is this the first step? Explain.
seropon [69]
Step 1: If there is a common factor, factor out the GCF. Step 2<span>: Identify the number of terms: (i) If polynomial has two terms, convert polynomial into difference of two squares or sum of two cubes or difference of two cubes.</span>
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Two forces, F1 and F2, are represented by vectors with initial points that are at the origin. The first force has a magnitude of
Strike441 [17]

Answer:

Step-by-step explanation:

The two force F1 and F2  are represented by vectors with initial points that are at the origin.

the terminal point of the vector is point P(1, 1, 0)

Therefore, the direction of the vector force is

v_1=(1-0)\hat i+(1-0)\hat j +(0-0)\hat k\\\\=1\hat i+1\hat j+0\hat k\\\\=\hat i + \hat j

The unit vector in the direction of force will be

\frac{v_1}{|v_1|} =\frac{\hat i+ \hat j}{\sqrt{1^2+1^2+0^2} } \\\\=\frac{1}{\sqrt{2} (\hat i +\hat j)}

The magnitude of the force is 40lb, so the force will be

F_1=40\times \frac{1}{\sqrt{2} } (\hat i+\hat j)\\\\=20\sqrt{2} (\hat i+\hat j)

The terminal point of its vector is point Q(0, 1, 1)

Therefore, the direction of the vector force is

v_2=(0-0)\hat i+(1-0)\hat j +(1-0)\hat k\\\\=0\hat i+1\hat j+1\hat k\\\\=\hat j + \hat k

\frac{v_2}{|v_2|} =\frac{\hat j+ \hat k}{\sqrt{0^2+1^2+1^2} } \\\\=\frac{1}{\sqrt{2} (\hat j +\hat k)}

The magnitude of the force is 60lb, so the force will be

F_2=60\times \frac{1}{\sqrt{2} } (\hat j+\hat k)\\\\=30\sqrt{2} (\hat j+\hat k)

The resultant of the two forces is

F=F_1+F_2\\\\=[20\sqrt{2} (\hat i+\hat j)]+[30\sqrt{2} (\hat j +\hat k)]\\\\=20\sqrt{2} \hat i+20\sqrt{2} \hat j +30\sqrt{2} \hat j+30\sqrt{2} \hat k\\\\=20\sqrt{2} \hat i+50\sqrt{2} \hat j+30\sqrt{2} \hat k

The magnitude force will be

|F|=\sqrt{(20\sqrt{2} )^2+(50\sqrt{2} )^2+(30\sqrt{2} )^2} \\\\=\sqrt{800+5000+1800} \\\\=\sqrt{3100} \\\\=55.68

to (1 decimal place)=55.7lb

b) The direction angle of force F

The angle formed by F and x axis

\alpha=\cos^{-1}(\frac{20\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.5080)\\\\=59.469

The angle formed by F and y axis

\alpha=\cos^{-1}(\frac{50\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(1.270)\\\\=

The angle formed by F and z axis

\alpha=\cos^{-1}(\frac{30\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.7620)\\\\=40.359

8 0
2 years ago
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pishuonlain [190]

<u><em>a=1/100pt is the correct answer.</em></u> First you had to multiply by t from both sides of equation, and it gave us, ⇒ pt=100a. And then you had to flip an equation, and it gave us, ⇒100a=pt. You can also divide by one-hundred (100) from both sides of equation, and it gave us, \frac{100a}{100}=\frac{pt}{100}. And finally, and it gave us the answer is a=1/100pt is the final answer. Hope this helps! And thank you for posting your question at here on brainly, and have a great day. -Charlie

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I need help with this quick
ziro4ka [17]

The best answer for this question is A.

Best of luck.

8 0
2 years ago
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