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Zarrin [17]
1 year ago
8

A biased die has a probability of 1/4 of showing a 5, while the probability of any of 1, 2, 3, 4, or 6 turning up is the same .

If three such dice are rolled, what is the probability of getting a sum of at least 14 without getting a 6 on any die ?
Option 1 : 5/24
Option 2 : 9/160
Option 3 : 1/30
Option 4 : 7/160
Mathematics
1 answer:
just olya [345]1 year ago
7 0
Possibilities of outcomes:
5, 5, 5
5, 5, 4

P(sum at least 14) = P(5,5,4) + P(5,5,5)
= 1/4 x 1/4 x 3/20 + 1/4 x 1/4 x 1/4
1/40

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2 years ago
A car tire with a radius of 16inches is turning at a rate of 120 revolutions per minute. Find the exact linear speed of the tire
anygoal [31]

Answer:

The speed of the tyre of the car is 1002.24 feet per minute .

Step-by-step explanation:

Given as :

The radius of the car wheel = r = 16 inches

Since 12 inches = 1 feet

So,  16 inches = \frac{1}{12}×16 = 1.33 feet

The number of revolution of the wheel = 120 revolution per minute

Let The speed of the wheel = s feet per minute

The circumference of wheel = 2 × \pi × radius

where  \pi  = 3.14

or, circumference =  2 × 3.14 × 1.33

Or, Circumference = 8.352 feet

Now , Speed =  circumference of wheel × number of revolution

or, Speed = 8.352 feet × 120 revolution per minute

∴ Speed = 1002.24 feet per minute

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4 0
2 years ago
If cos(t) = 2/7 and t is in the 4th quadrant, find sin(t).
Yuliya22 [10]
We can use the Pythagorean Trigonometric Identity which says:
sin^2(t)+cos^2(t)=1

Since we need to find sin(t), we have to solve for it:
sin(t)= \sqrt{1-cos^2(t)}

Let's plug in the given cos(t) value:
sin(t) = \sqrt{1-cos^2( \frac{2}{7})}

And solve sin(t):
sin(t) = \sqrt{1- \frac{4}{49} } = \frac{x}{y} \sqrt{ \frac{49}{49}- \frac{4}{49} }

Simplify further:
sin(t) = \sqrt{ \frac{45}{49} } = \frac{ \sqrt{45} }{7} = \frac{ \sqrt{9*5} }{7}

And it all simplifies down to:
sin(t) = \frac{3 \sqrt{5} }{7}

Since it's in the 4th quadrant, the sin(t) value is going to be negative. So, your final answer is: 
sin(t) = - \frac{ 3\sqrt{5} }{7}

Hope this helps!
7 0
2 years ago
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