Solve the questions in order

A jar contains 6 yellow marbles, 4 black marbles, and 2 purple marbles. Two marbles are picked at random, without replacement. W

ludmilkaskok [199]

Answer:

The probability of selecting both yellow is 5/22.

Step-by-step explanation:

Given the number of yellow marbles = 6

Black marbles = 4

Purple marble = 2

Now find the total number of marbles in the jar.

Thus total marbles = Yellow marbles + Black marbles + Purples marble

Now insert the values in the above formula.

Total marbles = 6 + 4 + 2

Total marbles = 12

The probability of 2 yellow marble:

$= \frac{6}{12} \times \frac{5}{11} \\= \frac{5}{22}$

Thus, the probability of selecting both yellow is 5/22.

3 0

3 years ago

Eight people attend the theater "together and sit in a row with exactly eight seats. Suppose the eight people consist of three m

Nata [24]

Answer:

They can be seated in 120 differents ways.

Step-by-step explanation:

Taking into account that there are 3 couples and every couple has an specific way to sit, for simplify the exercise, every couple is going to act like 1 option and it's going to occupy 1 Place. If this happens we just need to organize 5 options (3 couples and 2 singles) in 5 Places (3 for a couple and 2 for the singles)

It means that now there are just 5 Places in the row and 5 options to organized. So the number of ways can be calculated using a rule of multiplication as:

5 * 4 * 3 * 2 * 1 = 120

1st place 2nd Place 3rd place 4th Place 5th Place

Because we have 5 options for the 1st Place, the three couples and the 2 singles. Then, 4 options for the second Place, 3 options for the third place, 2 for the fourth place and 1 option for the 5th place.

Finally, they can be seated in 120 differents ways.

8 0

3 years ago

If a bottle rotates through 250 degrees in 50 min,how many degress will it rotate in 5 min

sp2606 [1]

There is more than one way to solve this.
250° : 50min.
You can divide each side by ten for 5 minutes.
50/10 = 5 minutes
250/10 = 25°

3 0

3 years ago

Simplify the expression. Write your answer using only positive exponents. Evaluate any numerical powers.

gtnhenbr [62]

Answer:

9x⁵

Step-by-step explanation:

Use properties of exponents:

$a^{b} a^{c} = a^{b+c}$ , $(a^{b} ^)^{c} = a^{bc}$ , $1/a^{-b} = a^{b}$

Simplify the given expression:

3⁴⋅x⋅(3/x²)⁻² =
3⁴·x·(3x⁻²)⁻² =
3⁴·x·(3⁻²)(x⁻²ˣ⁻²) =
3⁴⁻²·x¹⁺4 =
3²·x⁵ =
9x⁵

5 0

2 years ago

Is (1, 2) a solution to the inequality 6x - y> 3?

Lostsunrise [7]

Answer:

Yes.

Step-by-step explanation:

To find the answer we will put it into the equation, since x = 1 and y = 2 we will write it like this, 6(1) - 2 > 3. Since 6 x 1 = 6, we will now subtract 6 from 2 which equals 4. Therefore, the equation is correct because 4 is bigger than 3.

5 0

3 years ago