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Mathematics

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Luda [366]2 years ago

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A circle has a radius of 7.5 centimeters and a central angle AOB that measures 90 degrees. What is the length of the intercepted

Julli [10]

Since there are $360^{\circ}$ in a circle, and central $\angle AOB = 90^{\circ}$ , you can see that the part "sliced out" by the central angle is $\frac{90^{\circ}}{360^{\circ}} = \frac{1}{4}$ of the whole circle.

This means that the length of the intercepted arc $\stackrel{\frown}{AB}$ is $\frac{1}{4}$ of the circumference of the circle. So,

$\stackrel{\frown}{AB} = \frac{1}{4}(2 \pi r) = \frac{1}{4}(2 \pi (7.5 cm)) = \bf \frac{15 \pi}{4} cm$

6 0

3 years ago

Consider an urn containing 8 white balls, 7 red balls and 5 black balls.

weqwewe [10]

Answer + Step-by-step explanation:

1) The probability of getting 2 white balls is equal to:

$=\frac{8}{20} \times \frac{7}{19}\\\\= 0.147368421053$

2) the probability of getting 2 white balls is equal to:

$=C^{2}_{5}\times (\frac{8}{20} \times \frac{7}{19}) \times (\frac{12}{18} \times \frac{11}{17} \times \frac{10}{16})\\=0.397316821465$

3) The probability of getting at least 72 white balls is:

$=C^{72}_{150}\times \left( \frac{8}{20} \right)^{72} \times \left( \frac{7}{20} \right)^{78} +C^{73}_{150}\times \left( \frac{8}{20} \right)^{73} \times \left( \frac{7}{20} \right)^{77} + \cdots +C^{149}_{150}\times \left( \frac{8}{20} \right)^{149} \times \left( \frac{7}{20} \right)^{1} +\left( \frac{8}{20} \right)^{150}$