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3 years ago

I NEED HELP - HOMEWORK

Mathematics

1 answer:

postnew [5]3 years ago

6 0

Bag 1: 2R, 1B

Bag 2: 1R, 1B, 2Y

Draw 1 from each bag

a) P(same color)

We have 2/3 chance of drawing R from bag 1 and a 1/4 chance of drawing R from bag 2

P(both R) = (2/3)(1/4) = 1/6

We have a 1/3 chance of drawing B from bag 1 and 1/4 chance of B from bag 2

P(both B) = (1/3)(1/4) = 1/12

P(same color) =1/6 + 1/12 = 3/12 = 1/4

Answer: a) 1/4

b) P(exactly one R)

Same story except we look at the complement in bag 2

We have 2/3 chance of drawing R from bag 1 and a 1/4 chance of drawing R from bag 2, so a 3/4 chance of NOT drawing R.

P(1st red, second not red) = (2/3)(3/4) = 1/2

We have 1/3 chance of drawing B from bag 1, so 1/3 chance of drawing NOT red from bag 1. We have a 1/4 chance of drawing R from bag 2, so

P(1st blue, second not blue) = (1/3)(1/4) = 1/12

P = 1/2 + 1/12 = 6/12 + 1/12 = 7/12

Answer: 7/12

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9. A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

SSSSS [86.1K]

Answer:

Part 4) $r=84\ units$

Part 9) $sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) $sin(\theta)=-\frac{9\sqrt{202}}{202}$

Step-by-step explanation:

Part 4) A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

we know that

The circumference of a circle subtends a central angle of 360 degrees

The circumference is equal to

$C=2\pi r$

using proportion

$\frac{2\pi r}{360^o}=\frac{56\pi}{120^o}$

simplify

$\frac{r}{180^o}=\frac{56}{120^o}$

solve for r

$r=\frac{56}{120^o}(180^o)$

$r=84\ units$

Part 9) Given cos(∅)=-2/3 and ∅ lies in Quadrant III. Find the exact value of sin(∅) in simplified form

Remember the trigonometric identity

$cos^2(\theta)+sin^2(\theta)=1$

we have

$cos(\theta)=-\frac{2}{3}$

substitute the given value

$(-\frac{2}{3})^2+sin^2(\theta)=1$

$\frac{4}{9}+sin^2(\theta)=1$

$sin^2(\theta)=1-\frac{4}{9}$

$sin^2(\theta)=\frac{5}{9}$

square root both sides

$sin(\theta)=\pm\frac{\sqrt{5}}{3}$

we know that

If ∅ lies in Quadrant III

then

The value of sin(∅) is negative

$sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) The terminal side of ∅ passes through the point (11,-9). What is the exact value of sin(∅) in simplified form?

see the attached figure to better understand the problem

In the right triangle ABC of the figure

$sin(\theta)=\frac{BC}{AC}$

Find the length side AC applying the Pythagorean Theorem

$AC^2=AB^2+BC^2$

substitute the given values

$AC^2=11^2+9^2$

$AC^2=202$

$AC=\sqrt{202}\ units$

$sin(\theta)=\frac{9}{\sqrt{202}}$

simplify

$sin(\theta)=\frac{9\sqrt{202}}{202}$

Remember that

The point (11,-9) lies in Quadrant IV

then

The value of sin(∅) is negative

therefore

$sin(\theta)=-\frac{9\sqrt{202}}{202}$

5 0

3 years ago

How many cubes are in rectangular prism

Svet_ta [14]

Answer:

Finding Volume of Prisms Using Unit Cubes

These cubes make up a rectangular prism. The cubes represent the volume of the prism. This prism is five cubes by two cubes by one cube. In other words, it is five cubes long, by two cubes high by one cube wide.

Step-by-step explanation:

hope this helps

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3 years ago

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