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3 years ago

Could I solve this inequality by completing the square? How would I do so?

Mathematics

1 answer:

sammy [17]3 years ago

8 0

Answer:

$\large\boxed{x>-2+\sqrt{14}\ \vee\ x$

Step-by-step explanation:

$x^2+4x>10\\\\x^2+2(x)(2)>10\qquad\text{add}\ 2^2=4\ \text{to both sides}\\\\x^2+2(x)(2)+2^2>10+4\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+2)^2>14\Rightarrow x+2>\sqrt{14}\ \vee\ x+2-2+\sqrt{14}\ \vee\ x$

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A 5-card hand is dealt from a perfectly shuffled deck. Define the events: A: the hand is a four of a kind (all four cards of one

TiliK225 [7]

In a hand of 5 cards, you want 4 of them to be of the same rank, and the fifth can be any of the remaining 48 cards. So if the rank of the 4-of-a-kind is fixed, there are $\binom44\binom{48}1=48$ possible hands. To account for any choice of rank, we choose 1 of the 13 possible ranks and multiply this count by $\binom{13}1=13$ . So there are 624 possible hands containing a 4-of-a-kind. Hence A occurs with probability

$\dfrac{\binom{13}1\binom44\binom{48}1}{\binom{52}5}=\dfrac{624}{2,598,960}\approx0.00024$

There are 4 aces in the deck. If exactly 1 occurs in the hand, the remaining 4 cards can be any of the remaining 48 non-ace cards, contributing $\binom41\binom{48}4=778,320$ possible hands. Exactly 2 aces are drawn in $\binom42\binom{48}3=103,776$ hands. And so on. This gives a total of

$\displaystyle\sum_{a=1}^4\binom4a\binom{48}{5-a}=886,656$

possible hands containing at least 1 ace, and hence B occurs with probability

$\dfrac{\sum\limits_{a=1}^4\binom4a\binom{48}{5-a}}{\binom{52}5}=\dfrac{18,472}{54,145}\approx0.3412$

The product of these probability is approximately 0.000082.

A and B are independent if the probability of both events occurring simultaneously is the same as the above probability, i.e. $P(A\cap B)=P(A)P(B)$ . This happens if

the hand has 4 aces and 1 non-ace, or
the hand has a non-ace 4-of-a-kind and 1 ace

The above "sub-events" are mutually exclusive and share no overlap. There are 48 possible non-aces to choose from, so the first sub-event consists of 48 possible hands. There are 12 non-ace 4-of-a-kinds and 4 choices of ace for the fifth card, so the second sub-event has a total of 12*4 = 48 possible hands. So $A\cap B$ consists of 96 possible hands, which occurs with probability

$\dfrac{96}{\binom{52}5}\approx0.0000369$

and so the events A and B are NOT independent.

4 0

3 years ago

Which is greater 8 1/2 or 9 1/2 and how do you put it as a expression using > < and =

aivan3 [116]

Answer: 8 1/2 is less than 9 1/2, 8 1/2< 9 1/2

7 0

3 years ago

Read 2 more answers

Can someone please help me

Salsk061 [2.6K]

Answer:

Step-by-step explanation:

Area of pool = l × b

l = 6x and b = 3x - 5

Area = 6x(3x - 5)

Area = 18x² - 30x

4 0

3 years ago

Hi I need this asap if you also explain the work on how you got answers plz and thank you

weeeeeb [17]

Answer:

Q/ Draw a line ; Ans; 

$\frac{9}{5} —>1 \frac{4}{5}$

*explain ; We put the 5 in the denominator and 5 multiply 1 + 4 so equal 9 so the choice 9/5 .

Ans; 7/3—> 2 1/3

*explain ; We put the 3 in the denominator and 3 multiply 2 + 1 so equal 7 so the choice 7/3 .

Ans; 12/10 —> 1 1/5

*explain; simple (12 and 10) ÷ 2 so equal 6/5

We put the 5 in the denominator and 5 multiply 1 + 1 so equal 6 so the choice 6/5 =12/10 .

$\frac{12 \div 2}{10 \div 2} = \frac{6}{5} = 1 \frac{1}{5}$

Q/ Compare the fractions;Ans;

$\frac{2}{3} < \frac{14}{6}$

* explain; 2/3 = 0.66 and 14/6=2.33 so 2.33 greater from 0.66 so 14/6 greater from 2/3 .

$\frac{3}{8} < \frac{8}{3}$

* explain; 3/8 = 0.375 and 8/3=2.666 so 2.666 greater from 0.375 so 8/3 greater from 3/8 .

$2 \frac{1}{6} > \frac{5}{9}$

* explain; 2 1/6 —> We put the 6 in the denominator and 6 multiply 2 + 1 so equal 13 so equal 13/6

13/6 = 2.16 and 5/9=0.55 so 2.16 greater from 0.55 so 13/6 = 2 1/6 greater from 5/9 .

Q/Add; Ans;

$\frac{7}{8} + \frac{5}{8} = \frac{7 + 5}{8} = \frac{12}{8} = \frac{3}{2}$

$\frac{1}{9} + \frac{2}{3} \\ \\ \frac{1}{9} + \frac{6}{9} = \frac{ 1+6 }{9} = \frac{7}{9}$

Q/Subtract; Ans;

$\frac{6}{7} - \frac{4}{7} = \frac{6 - 4}{7} = \frac{2}{7}$

$\frac{7}{3} - \frac{2}{9} \\ \\ \frac{21}{9} - \frac{2}{9} = \frac{21 - 2}{9} = \frac{19}{9}$

Q/ Multiply;Ans;

$\frac{1}{5} \times \frac{1}{2} = \frac{1}{10}$

$\frac{2}{3} \times \frac{3}{8} = \frac{6}{24} = \frac{1}{4}$

Q/Divide;Ans;

$\frac{3}{4} \div \frac{2}{5} \\ \\ \frac{3}{4} \times \frac{5}{2} = \frac{15}{8}$

$\frac{8}{9} \div \frac{1}{3} \\ \\ \frac{8}{9} \times \frac{3}{1} = \frac{24}{9} = \frac{8}{3}$

I hope I helped you^_^

5 0

3 years ago

Can somebody HELP me as soon as possible.

Butoxors [25]

Answer:

A: Linear

B: Nonlinear

C: Linear

4 0

3 years ago

Read 2 more answers