What is the decimals in tenth that less than 3.81 but greater than 3.0

Nine tiles are numbered $\color[rgb]{0.35,0.35,0.35}1, 2, 3, \ldots, 9$. Each of three players randomly selects and keeps three

Eduardwww [97]

The probability that all three players obtain an odd sum is 3/14.

<h3>What is probability?</h3>

The probability is the ratio of possible distributions to the total distributions.

I.e.,

Probability = (possible distributions)/(total distributions)

<h3>Calculation:</h3>

Given that,

There are nine tiles - 1, 2, 3,...9, respectively.

A player must have an odd number of odd tiles to get an odd sum. That means he can either have three odd tiles, or two even tiles and an odd tile.

In the given nine tiles the number of odd tiles = 5 and the number of even tiles = 4.

The only possibility is that one player gets 3 odd tiles and the other two players get 2 even tiles and 1 odd tile.

So,

One player can be selected in $^3C_1$ ways.

The 3 odd tiles out of 5 can be selected in $^5C_3$ ways.

The remaining 2 odd tiles can be selected and distributed in $^2C_1$ ways.

The remaining 4 even tiles can be equally distributed in $\frac{4 ! \cdot 2 !}{(2 !)^{2} \cdot 2 !}$ ways.

So, the possible distributions = $^3C_1$ × $^5C_3$ × $^2C_1$ × $\frac{4 ! \cdot 2 !}{(2 !)^{2} \cdot 2 !}$

⇒ 3 × 10 × 2 × 6 = 360

To find the total distributions,

The first player needs 3 tiles from the 9 tiles in $^9C3=84$ ways

The second player needs 3 tiles from the remaining 6 tiles in $^6C_3=20$ ways

The third player takes the remaining tiles in 1 way.

So, the total distributions = 84 × 20 × 1 = 1680

Therefore, the required probability = (possible distributions)/(total distributions)

⇒ Probability = 360/1680 = 3/14.

So, the required probability for the three players to obtain an odd sum is 3/14.

Learn more about the probability of distributions here:

brainly.com/question/2500166

#SPJ4

3 0

1 year ago

How much pure acid do you mix with 2L of 40% acid to get 70% acid

iris [78.8K]

(2*40%+x*10<span>0%)/(2+x) = 70%; calculate x !</span>

8 0

3 years ago

Read 2 more answers

Use the definition of the logarithmic function to find x. log4 0.25=x x=?

GREYUIT [131]

The answer is -1.

$log_4(0.25) =log_4( \frac{1}{4})= log_4(4^{-1} ) \\ \\ 
log(x^{a} ) = a*log(x) \\ \\ 
log_4(4^{-1} )= -1 *log_4(4) \\ \\ 
log_y(x) = \frac{log(x)}{log(y)} \\ \\ 
-1 *log_4(4) = -1* \frac{log(4)}{log(4)} = -1$

5 0

3 years ago

If the lines a and b in the diagram below are parallelm why do angles 2 and 6 measure 60 degree angles

Bas_tet [7]

Angles 2 and 6 are corresponding angles, which would explain why they are congruent if lines a and b are parallel, but there is nothing in the problem to explain that any of the angles equals 60 degrees since no measurements were given in the diagram.

8 0

3 years ago

A manufacturing company produces 3 different products A, B, and C. Three types of components, i.e., X, Y, and Z, are used in the

Murljashka [212]

Answer:

Step-by-step explanation:

Using the Excel Formula:

Decision Variable Constraint Constraint

A 65 65 100

B 80 80 80

C 90 90 90

14100 300 300

= (150 *B3)+(80*B4) +(65*B5)-(100-B3+80-B4+90-B5)*90

Now, we have:

Suppose A, B, C represent the number of units for production A, B, C which is being manufactured

A B C Unit price

Need of X 2 1 1 $20

Need of Y 2 3 2 $30

Need of Z 2 2 3 $25

Price of

manufac - $200 $240 $220

turing

Now, for manufacturing one unit of A, we require 2 units of X, 2 units of Y, 2 units of Z are required.

Thus, the cost or unit of manufacturing of A is:

$20 (2) + $30(2) + $25(2)

$(40 + 60 + 50)

= $150

Also, the market price of A = $200

So, profit = $200 - $150 = $50/ unit of A

Again;

For manufacturing one unit of B, we require 1 unit of X, 3 units of Y, and 2 units of Z are needed and they are purchased at $20, $30, and 425 each.

So, total cost of manufacturing a unit of B is:

= $20(1) + $30(3) + $25(2)

= $(20 + 90+50)

= $160

And the market price of B = $240

Thus, profit = $240- $160

profit = $80

For manufacturing one unit of C, we have to use 1 unit of X, 2 unit of Y, 3 units of Z are required:

SO, the total cost of manufacturing a unit of C is:

= $20 (1) + $30(2) + $25(3)

= $20 + $60 + $25

= $155

This, the profit = $220 - $155 = $65

However; In manufacturing A units of product A, B unit of product B & C units of product C.

Profit --> 50A + 80B + 65C

This should be provided there is no penalty for under supply of there is under supply penalty for A, B, C is $40

The current demand is:

100 - A

80 - B

90 - C respectively

So, the total penalty

${(100 - A) + (80 - B) +(90 - C) } + \$40$

This should be subtracted from profit.

So, we have to maximize the profit

$Z = 50A + 80B + 65C = {(100 -A) + (80 - B) + (90 - C)};$

Subject to constraints;

we have the total units of X purchased can only be less than or equal to 300 due to supplies capacity

Then;

$2A + B +C \le 300$ due to 2A, B, C units of X are used in manufacturing A, B, C units of products A, B, C respectively.

Next; demand for A, B, C will not exceed 100, 80, 90 units.

Hence;

$A \le 100$

$B \le 80$

$C \le 90$

and $A, B, C \ge 0$ because they are positive quantities

The objective is:

$\mathbf{Z = 50A + 80B + 65 C - (100 - A + 80 - B + 90 - C) * 40}$

A, B, C $\to$ Decision Varaibles;

Constraint are:

$A \le 100 \\ \\ B \le 100 \\ \\ C \le 90 \\ \\2A + B + C \le 300 \\ \\ A,B,C \ge 0$

6 0

3 years ago