Find the length of the arc intercepted on the unit circle by the following central angle. 0=5π

A sock drawer contains eight navy blue socks and five black socks with no other socks. If you reach in the drawer and take two s

Rzqust [24]

Answer:

a. the probability of picking a navy sock and a black sock = P (A & B)

= (8/13 ) * (5/12) = 40/156 = 0.256

b. the probability of picking two navy or two black is

= 56/156 + 20/156 = 76/156 = 0.487

c. the probability of either 2 navy socks is picked or one black & one navy socks.

= 40/156 + 56/156 = 96/156 = 0.615

Step-by-step explanation:

A sock drawer contains 8 navy blue socks and 5 black socks with no other socks.

If you reach in the drawer and take two socks without looking and without replacement, what is the probability that:

Solution:

total socks = N = 8 + 5 + 0 = 13

a) you will pick a navy sock and a black sock?

Let A be the probability of picking a navy socks first.

Then P (A) = 8/13

without replacing the navy sock, will pick the black sock, total number of socks left is 12.

Let B be the probability of picking a black sock again.

P (B) = 5/12.

Then, the probability of picking a navy sock and a black sock = P (A & B)

= (8/13 ) * (5/12) = 40/156 = 0.256

b) the colors of the two socks will match?

Let A be the probability of picking a navy socks first.

Then P (A) = 8/13

without replacing the navy sock, will pick another navy sock, total number of socks left is 12.

Let B be the probability of another navy sock again.

P (B) = 7/12.

Then, the probability of picking 2 navy sock = P (A & B)

= (8/13 ) * (7/12) = 56/156 = 0.359

Let D be the probability of picking a black socks first.

Then P (D) = 5/13

without replacing the black sock, will pick another black sock, total number of socks left is 12.

Let E be the probability of another black sock again.

P (E) = 4/12.

Then, the probability of picking 2 black sock = P (D & E)

= (5/13 ) * (4/12) = 5/39 = 0.128

Now, the probability of picking two navy or two black is

= 56/156 + 20/156 = 76/156 = 0.487

c) at least one navy sock will be selected?

this means, is either you pick one navy sock and one black or two navy socks.

so, if you will pick a navy sock and a black sock, the probability of picking a navy sock and a black sock = P (A & B)

= (8/13 ) * (5/12) = 40/156 = 0.256

also, if you will pick 2 navy sock, Then, the probability of picking 2 navy sock = P (A & B)

= (8/13 ) * (7/12) = 56/156 = 0.359

now either 2 navy socks is picked or one black one navy socks.

= 40/156 + 56/156 = 96/156 = 0.615

4 0

3 years ago

To prepare for a bicycling event, you warm up each day at a moderate pace then you ride hard for a number of miles. one day you

vovangra [49]

Answer:

The total distance covered is 15.6 miles.

Step-by-step explanation:

One day you warm up for 15 minutes at a pace of 0.1 miles per 25 seconds.

The rule of three or is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them. If the relationship between the magnitudes is direct, like in this case, the direct rule of three can be applied as follow:

a ⇒ b

c ⇒ x

Then $x=\frac{c*b}{a}$

First, the simple rule of three can be applied in the following way: if 1 minute equals 60 seconds, 15 minutes equals how many seconds?

$seconds=\frac{15 minutes*60 seconds}{1 minute}$

seconds= 900

So now you can apply the following rule of three: if in 25 seconds you travel 0.1 miles, in 900 seconds how many miles do you travel?

$distance=\frac{900 seconds*0.1 miles }{25 seconds}$

distance= 3.6 miles

If you then ride hard for 12 miles, the total distance traveled will be the sum of both:

3.6 miles + 12 miles = 15.6 miles

The total distance covered is 15.6 miles.

6 0

3 years ago

Matthew wants to estimate the mean height of students attending his college. He records the heights of 100 randomly selected stu

Mnenie [13.5K]

The correct option that shows the population of the research carried out by Matthew is;

Option D; all the students attending the college

We are told that Matthew wants to estimate the mean height of students attending his college.

Now, let us say the total number of students in his college is x. If he decides to select 100 students randomly to record their height, it means this 100 students is a sample out of the total number of students which is x that is the population.

In conclusion, we can say that the population of this research by Matthew is the total number of students that attend the college.

Read more at; brainly.com/question/6028584

6 0

2 years ago

What is the range for this set of data? 7, 15, 12 A. 3 B. 5 C. 8 D. 12

UNO [17]

Answer:

8 is your answer

Step-by-step explanation:

Hope this helps sorry if I'm wrong

7 0

2 years ago

Read 2 more answers

HELP PLEASE Simplify.

maksim [4K]

Simplifying
2x + -3(3 * 0.6x + 2.7)

Multiply 3 * 0.6
2x + -3(1.8x + 2.7)

Reorder the terms:
2x + -3(2.7 + 1.8x)
2x + (2.7 * -3 + 1.8x * -3)
2x + (-8.1 + -5.4x)

Reorder the terms:
-8.1 + 2x + -5.4x

Combine like terms: 2x + -5.4x = -3.4x
-8.1 + -3.4x

7 0

3 years ago