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3 years ago

15

A coin is biased such that it results in 2 heads in every 3 coin flips, on average. The sequence _____ is most probable for the

biased coin.

1 answer:

valentinak56 [21]3 years ago

3 0

I am relatively sure the answer you are looking for is;

H H H T T H T T H H H H

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What is the unit price of 3.40 and 12

Yanka [14]

Answer:

??

Step-by-step explanation:

what kind of math is this?

7 0

3 years ago

A committee consisting of 4 faculty members and 5 students is to be formed. Every committee position has the same duties and vot

Zina [86]

<u>Answer: </u>

The number of ways to form the committee is formed = 637065

<u>Solution: </u>

The number of combinations of n things such that m things taken together are given by:-

$C_{(\boldsymbol{n}, \boldsymbol{m})}=\frac{n !}{m !(\boldsymbol{n}-\boldsymbol{m}) !}$

Given Data:

A committee consisting of 4 faculty members and 5 students is to be formed. There are 12 faculty members and 13 students eligible to serve on the committee.

Then, the number of ways to form the committee is formed given by :-

$\begin{array}{l}{12 C_{4} \times 13 C_{5}} \\\\ {=\frac{12 !}{4 !(12-4) !} \times \frac{13 !}{5 !(13-5) !}} \\\\ {=\frac{12 !}{4 ! 8 !} \times \frac{13 !}{5 ! 8 !}} \\\\ {\frac{12 \times 11 \times 10 \times 9 \times 8 !}{27 \times 8 !} \times \frac{13 \times 12 \times 11 \times 10 \times 9 \times 8}{120 \times 8 !}} \\\\ {=637065}\end{array}$

Hence, the number of ways to form the committee is formed = 637065

7 0

3 years ago

During a sale a dress decreased in price from $60 to $48 what was the percent of decrease

Elza [17]

Answer:

The percent decrease was 20%

Step-by-step explanation:

In order to find this, use the percent change equation.

(New - Old)/(Old) * 100 = % Change

Now input 48 for the New price and 60 for the Old price.

(48 - 60)/(60) * 100 = % Change

12/60 * 100 = % Change

.2 * 100 = % Change

20 = % Change

3 0

3 years ago

The difference between eight times a number and six more than three times the number. Please help find the equation and simplify

Rainbow [258]

Answer: x>1.2

Step-by-step explanation:

Let a number is x.

Hence,

$8x-6 > 3x\\\\8x-6-3x > 3x-3x\\\\5x-6 > 0\\\\5x-6+6 > 0+6\\\\5x > 6\\$

Divide both parts of the equation by 5:

$x > 1.2$

8 0

2 years ago

P(x)= 3x^3-5x^2-14x-4

nexus9112 [7]

$\displaystyle\\
P(x)=3x^3-5x^2-14x-4\\\\
D_{-4}=\{-4;~-2;~\underline{\bf -1};~1;~2;~4\}\\\\
\text{We observe that } \frac{-1}{3} \text{ is a solution of the equation:}\\
3x^3-5x^2-14x-4=0\\\\
$

$\displaystyle\\
\text{Verification}\\\\
3x^3-5x^2-14x-4=\\\\
=3\times\Big(-\frac{1}{3}\Big)^3-5\times\Big(-\frac{1}{3}\Big)^2-14\times\Big(-\frac{1}{3}\Big)-4=\\\\
=-\frac{1}{9}-\frac{5}{9}+\frac{14}{3}-4=\\\\
=-\frac{6}{9}+\frac{14}{3}-4=\\\\
=-\frac{6}{9}+\frac{42}{9}- \frac{4\times 9}{9}=\\\\
 =-\frac{6}{9}+\frac{42}{9}- \frac{36}{9}= \frac{42-6-36}{9}=\frac{42-42}{9}=\frac{0}{9}=0\\\\
\Longrightarrow~~~P(x)~\vdots~\Big(x+ \frac{1}{3}\Big)\\\\
\Longrightarrow~~~P(x)~\vdots~(3x+1)$

$\displaystyle\\
3x^3-5x^2-14x-4=0\\
~~~~~-5x^2 = x^2 - 6x^2\\
~~~~~-14x =-2x-12x \\
3x^3+x^2 - 6x^2-2x-12x-4=0\\
x^2(3x+1)-2x(3x+1) -4(3x+1)=0\\
(3x+1)(x^2-2x -4)=0\\\\
\text{Solve: } x^2-2x -4=0\\\\
x_{12}= \frac{-b\pm \sqrt{b^2-4ac}}{2a}=\\\\=\frac{2\pm \sqrt{4+16}}{2}=\frac{2\pm \sqrt{20}}{2}=\frac{2\pm 2\sqrt{5}}{2}=1\pm\sqrt{5}\\\\
x_1 =1+\sqrt{5}\\
x_2 =1-\sqrt{5}\\
\Longrightarrow P(x)= 3x^3-5x^2-14x-4 =\boxed{(3x+1)(x-1-\sqrt{5})(x-1+\sqrt{5})}$

7 0

3 years ago