Three times a number is greater than -15 and less than 12.

To avoid detection at customs, a traveler has placed 6 narcotic tablets in an Urn containing 9 vitamin pills that are similar in

Alexus [3.1K]

Answer:

$\frac{4}{91}$

Step-by-step explanation:

We are told that to avoid detection at customs, a traveler has placed 6 narcotic tablets in an Urn containing 9 vitamin pills that are similar in appearance.

To find the probability that the traveler will be arrested for illegal possession of narcotics we will use theoretical probability formula.

$\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}$

Favorable outcomes will be $_{3}^{6}\textrm{C}$ .

$\text{Favorable outcomes}=_{3}^{6}\textrm{C}=\frac{6!}{(6-3)!3!}$

$\text{Favorable outcomes}=\frac{6!}{3!3!}$

$\text{Favorable outcomes}=\frac{6\cdot 5\cdot 4\cdot3!}{3\cdot 2\cdot 1\cdot3!}$

$\text{Favorable outcomes}=\frac{6\cdot 5\cdot 4}{3\cdot 2}$

$\text{Favorable outcomes}=5\cdot 4=20$

Now let us find number of possible outcomes.

$\text{Number of possible outcomes}=_{3}^{15}\textrm{C}=\frac{15!}{(15-3)!3!}$

$\text{Number of possible outcomes}=\frac{15!}{12!3!}$

$\text{Number of possible outcomes}=\frac{15\cdot 14\cdot 13\cdot 12!}{12!\cdot 3\cdot 2\cdot 1}$

$\text{Number of possible outcomes}=\frac{15\cdot 14\cdot 13}{ 3\cdot 2\cdot 1}$

$\text{Number of possible outcomes}=5\cdot 7\cdot 13=455$

Upon substituting our values in probability formula we will get,

$\text{Probability that the traveler will be arrested for illegal possession of narcotics}=\frac{20}{455}$

Upon dividing numerator and denominator by 5 we will get,

$\text{Probability that the traveler will be arrested for illegal possession of narcotics}=\frac{4}{91}$

Therefore, the probability that the traveler will be arrested for illegal possession of narcotics is $\frac{4}{91}$ .

6 0

3 years ago

Solve 2/3 plus 5/6 and put answer in simplest form. a9/6 b 2/3 c 7/6 d 11/2

Kamila [148]

$\frac{2}{3} + \frac{5}{6}$ = $\frac{3}{2}$

4 0

3 years ago

Read 2 more answers

Use the given conditions to write an equation for the line in point-slope form and general form. Passing through (8 comma negat

miskamm [114]

Answer:

The answer to your question is y = -5x + 32 point-slope form

5x + y - 32 = 0 general form

Step-by-step explanation:

Data

(8, -8)

⊥ x - 5y - 6 = 0

Process

1.- Get the slope of the line given

x - 5y - 6 = 0

-5y = -x + 6

y = -x/-5 + 6/-5

y = x/5 - 6/5

slope = 1/5

slope of the new line -5, because the lines are perpendicular

2.- Get the equation of the new line

y - y1 = m(x - x1)

y + 8 = -5(x - 8)

y + 8 = -5x + 40

y = -5x + 40 - 8

y = -5x + 32 point-slope form

Equal to zero to find the general form

5x + y - 32 = 0 general form

5 0

3 years ago

Which Expression is Equivalent to the given expression? (4m^2n)^2/2m^5n

Daniel [21]

Answer:

D. $8 {m}^{ - 1} n$

Step-by-step explanation:

$\huge \frac{(4 {m}^{2} n)^{2} }{2 {m}^{5}n } \\ \\ \huge= \frac{16 {m}^{4} {n}^{2} }{2 {m}^{5}n } \\ \\ \huge = 8 {m}^{4 - 5} {n}^{2 - 1} \\ \\ \huge \purple{ \boxed{= 8 {m}^{ - 1} n}}$

7 0

3 years ago

Asa saves dimes and quarters so that he will have exact change for he bus. He dabs and then dumps the container that he has been

koban [17]

Asa has 15 dimes and 32 quarters.

Step-by-step explanation:

Given,

Total coins = 47

Worth of coins = $9.50 = 9.50*100 = 950 cents

1 dime = 10 cents

1 quarter = 25 cents

Let,

Number of dimes = x

Number of quarters = y

According to given statement;

x+y=47 Eqn 1

10x+25y=950 Eqn 2

Multiplying Eqn 1 by 10

$10(x+y=47)\\10x+10y=470\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(10x+25y)-(10x+10y)=950-470\\10x+25y-10x-10y=480\\15y=480$

Dividing both sides by 15

$\frac{15y}{15}=\frac{480}{15}\\y=32$

Putting y=32 in Eqn 1

$x+32=47\\x=47-32\\x=15$

Asa has 15 dimes and 32 quarters.

Keywords: linear equation, elimination method

Learn more about elimination method at:

#LearnwithBrainly

7 0

3 years ago