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3 years ago

A jar contains blue, red, yellow, and green marbles.P(blue) = 1/4. What type of probability is illustrated and why?

1 answer:

8 0

Do you have the pic or did it not come with one and the answer is 1/4 is every color theres 4 colors and 1/4 of blue so 1/4 of red 1/4 of yellow 1/4 green hope this helps

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Problems 2.21, 2.22, 2.23

RoseWind [281]

Statements can be proved by contrapositive, contradiction or by induction.

2.21 and 2.23 are proved by contrapositive
2.22 is proved by induction

2.21: If $n^3$ is even, then n is even (By contrapositive)

The contrapositive of the above statement is that:

If n is odd, then $n^3$ is odd

Represent the value of n as:

$n = 2k + 1$ , where $k \ge 0$

Take the cube of both sides

$n^3 = (2k + 1)^3$

Expand

$n^3 = 8k^3 + 6k^2 + 6k + 1$

Group

$n^3 =[ 8k^3 + 6k^2 + 6k] + 1$

Factor out 2

$n^3 =2[4k^3 + 3k^2 + 3k] + 1$

Assume w is an integer; where:

$w =4k^3 + 3k^2 + 3k$

So, we have:

$n^3 =2w + 1$

The constant term (i.e. 1) means that $n^3$ is odd.

Hence, the statement has been proved by contrapositive.

i.e. If n is odd, then $n^3$ is odd

2.22 $3n + 4$ is even, if and only if n is even

We have: $3n + 4$

Assume that: $n = 2k + 2$ for $k \ge 0$

So, we have:

$3n + 4 = 3(2k + 2) + 4$

Open bracket

$3n + 4 = 6k + 6 + 4$

$3n + 4 = 6k + 10$

Factorize

$3n + 4 = 2(3k + 5)$

The factor of 2 means that $3n + 4$ is even.

Hence, $3n + 4$ is even, if and only if n is even

2.22: $s \ne -1$ and $t \ne -1$ , then $s + t + st \ne -1$

To do this, we prove by contrapositive.

The contrapositive of the above statement is:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$

We have:

$s + t + st = -1$

Substitute the values of s and t in: $s + t + st = -1$

$-1 -1 -1 \times -1 = -1$

$-1 -1 + 1 = -1$

$-1 = -1$

Hence, by contrapositive:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$

Read more about proofs at:

brainly.com/question/19643658

7 0

3 years ago

Migration is

omeli [17]

Answer:

Migration is D, the seasonal movement of organisms between locations!

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3 years ago

What is f(g(x)) if f(x)= 4x²+3x-4 and g(x)=2x

S_A_V [24]

Answer:

f(g(x))=16x^2+6x-4

Step-by-step explanation:

f(g(x))=4(2x)^2 +3(2x)-4

f(g(x))=16x^2+6x-4

8 0

3 years ago

I don’t get it please help : /

katrin2010 [14]

Answer:

Step-by-step explanation:

20 x 10 = 200 so 20 students sleep for 9 hours

that leaves 10

since 10 is half of 20, half of 2 is 1 so that last 10 = 1 student,

making 21 students

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3 years ago

How do you find the bearing and speed of a ship?

Usimov [2.4K]

Finding the Bearing of a Ship
Example : A ship leaves the port of Miami with a bearing of S80◦E and a speed of. 15 knots. After 1 hour, the ship turns 90◦ toward the south.

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3 years ago