A sector of a circle has an area of 12π and a central angle of 2pi/3 radians. The radius of the circle is how many units long?

There are 7 acts in a talent show.

lara31 [8.8K]

Answer:

Event A: 1/35

Event B: 1/840

Explanation:

Event A

For the event A, the order of the first 4 acts does not matter.

The number of different four acts taken from a set of seven acts, when the order does not matter, is calculated using the concept of combinations.

Thus, the number of ways that the first four acts can be scheduled is:

$C(m,n)=\dfrac{m!}{n!(m-n)!}$

$C(7,4)=\dfrac{7!}{4!(7-4)!}=\dfrac{7!}{4!(3)!}=35$

And the number of ways that four acts is the singer, the juggler, the guitarist, and the violinist, in any order, is 1: C(4,4).

Therefore the probability of Event A is:

$P(A)=1/35$

Event B

Now the order matters. The difference between combinations and permutations is ordering. When the order matters you need to use permutations.

The number of ways in which four acts can be scheculed when the order matters is:

$P(m,n)=\dfrac{m!}{(m-n)!}$

$P(m,n)=\dfrac{7!}{(7-4)!}=P(m,n)=\dfrac{7!}{4!}=840$

The number of ways the comedian is first, the guitarist is second, the dancer is third, and the juggler is fourth is 1: P(4,4)

Therefore, the probability of Event B is:

$P(B)=1/840$

7 0

3 years ago

Together Ron and Tori have 35 trading cards. Ron has 9 more than Tori. How many cards does Ron have?

Anit [1.1K]

Ron has 22 cards
number one tip in math, try to create equation!
set number of cards Ron has as x (always set x as what you are looking for)
set number of cards Tori has as (x-9) because if Ron has 9 more cards than Tori that's same thing as saying Tori has 9 cards less than Ron
Number of cards Tori and Ron has need to equal 35
Therefore,
x + (x-9) = 35
Solve:
2x-9=35
bring over 9 to other side
2x=44
divide both sides by 2
x=22
So number of cards Ron has is 22

3 0

3 years ago

A large aquarium should contain 10,000 liters of water when it is filled correctly. It will overflow if it gets up to 12,000 lit

never [62]

Answer:

The water level is rising because it is filling 10 more liters than it is draining

16.7 hours

Step-by-step explanation:

4 0

2 years ago

Andrew

PilotLPTM [1.2K]

Let's say Bailey takes "b" days to paint it.

and Andrew takes "a" days to paint the same house.

now, Andrew is 6 times faster than Bailey, therefore, if Andrew takes "a" days to do it, Bailey takes then "6a" days, or b = 6a.

now, the year they worked together, they finished it in 7 days.

so, after 1 day then, they have only done 1/7 of the whole work.

and Andrew for one day, has done 1/a of the house, whilst Bailey has done 1/b of the house or 1/(6a).

$\bf \stackrel{\textit{Andrew's rate}}{\cfrac{1}{a}}+\stackrel{\textit{Bailey's rate}}{\cfrac{1}{b}}=\stackrel{\textit{1 day of work}}{\cfrac{1}{7}}
\\\\\\
\cfrac{1}{a}+\cfrac{1}{6a}=\cfrac{1}{7}\impliedby 
\begin{array}{llll}
\textit{let's multiply all by }\stackrel{LCD}{42a}\textit{ to toss the}\\
denominators
\end{array}$

$\bf 42a\left( \cfrac{1}{a}+\cfrac{1}{6a} \right)=42a\left( \cfrac{1}{7} \right)\implies 42+7=6a\implies \cfrac{49}{6}=a
\\\\\\
\stackrel{days}{8\frac{1}{6}}=a
\\\\\\
\textit{how many days will it take Bailey then?}\quad b=6a
\\\\\\
b=6\cdot \cfrac{49}{6}\implies b=\stackrel{days}{49}$

6 0

3 years ago

The number(s) that appear(s) most often in a set of data

Maslowich

what is the answer the answer is what

7 0

2 years ago