Help with this algebra 2 question

There are 20 players in a table tennis competition. each player must play exactly one match against every other player. how many

Flauer [41]

There are 10 matches in the competition if you count every other player you'll end up with 10

7 0

3 years ago

Find maclaurin series

Mumz [18]

Recall the Maclaurin expansion for cos(x), valid for all real x :

$\displaystyle \cos(x) = \sum_{n=0}^\infty (-1)^n \frac{x^{2n}}{(2n)!}$

Then replacing x with √5 x (I'm assuming you mean √5 times x, and not √(5x)) gives

$\displaystyle \cos\left(\sqrt 5\,x\right) = \sum_{n=0}^\infty (-1)^n \frac{\left(\sqrt5\,x\right)^{2n}}{(2n)!} = \sum_{n=0}^\infty (-5)^n \frac{x^{2n}}{(2n)!}$

The first 3 terms of the series are

$\cos\left(\sqrt5\,x\right) \approx 1 - \dfrac{5x^2}2 + \dfrac{25x^4}{24}$

and the general n-th term is as shown in the series.

In case you did mean cos(√(5x)), we would instead end up with

$\displaystyle \cos\left(\sqrt{5x}\right) = \sum_{n=0}^\infty (-1)^n \frac{\left(\sqrt{5x}\right)^{2n}}{(2n)!} = \sum_{n=0}^\infty (-5)^n \frac{x^n}{(2n)!}$

which amounts to replacing the x with √x in the expansion of cos(√5 x) :

$\cos\left(\sqrt{5x}\right) \approx 1 - \dfrac{5x}2 + \dfrac{25x^2}{24}$

7 0

2 years ago

In a certain community, 30% of the families own a dog, and 20% of the families that own a dog also own a cat. It is also known t

Komok [63]

Answer:

What is the probability that a randomly selected family owns a cat? 34%

What is the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat? 82.4%

Step-by-step explanation: We can use a Venn (attached) diagram to describe this situation:

Imagine a community of 100 families (we can assum a number, because in the end, it does not matter)

So, 30% of the families own a dog = .30*100 = 30

20% of the families that own a dog also own a cat = 0.2*30 = 6

34% of all the families own a cat = 0.34*100 = 34

Dogs and cats: 6

Only dogs: 30 - 6 = 24

Only cats: 34 - 6 = 28

Not cat and dogs: 24+6+28 = 58; 100 - 58 = 42

What is the probability that a randomly selected family owns a cat?

34/100 = 34%

What is the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat?

A = doesn't own a dog

B = owns a cat

P(A|B) = P(A∩B)/P(B) = 28/34 = 82.4%

5 0

3 years ago

Read 2 more answers

A Class 4 truck weighs between 14,000 and 16,000 pounds.

Nady [450]

Answer:

Class 4: This class of truck has a GVWR of 14,001–16,000 pounds or 6,351–7,257 kilograms. Class 5: This class of truck has a GVWR of 16,001–19,500 pounds or 7,258–8,845 kilograms.

Step-by-step explanation:

6 0

3 years ago

Depth of swimming pool

pashok25 [27]

29 ¼ inches [74.295 cm] and 31 inches [78.74 cm].

8 0

3 years ago