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3 years ago

What is the slope in the equation y=4x+3

Mathematics

2 answers:

cestrela7 [59]3 years ago

7 0

4 is the slope, hope this helps

Liula [17]3 years ago

6 0

Answer:

Step-by-step explanation:

y= mx+b

b is the y intercept

m is the slope

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Suppose n people, n ≥ 3, play "odd person out" to decide who will buy the next round of refreshments. The n people each flip a f

blondinia [14]

Answer:

Assume that all the coins involved here are fair coins.

a) Probability of finding the "odd" person in one round: $\displaystyle n \cdot \left(\frac{1}{2}\right)^{n - 1}$ .

b) Probability of finding the "odd" person in the $k$ th round: $\displaystyle n \cdot \left(\frac{1}{2}\right)^{n - 1} \cdot \left( 1 - n \cdot \left(\frac{1}{2}\right)^{n - 1}\right)^{k - 1}$ .

c) Expected number of rounds: $\displaystyle \frac{2^{n - 1}}{n}$ .

Step-by-step explanation:

To decide the "odd" person, either of the following must happen:

There are $(n - 1)$ heads and $1$ tail, or
There are $1$ head and $(n - 1)$ tails.

Assume that the coins here all are all fair. In other words, each has a $50\,\%$ chance of landing on the head and a

The binomial distribution can model the outcome of $n$ coin-tosses. The chance of getting $x$ heads out of

The chance of getting $(n - 1)$ heads (and consequently, $1$ tail) would be $\displaystyle {n \choose n - 1}\cdot \left(\frac{1}{2}\right)^{n - 1} \cdot \left(\frac{1}{2}\right)^{n - (n - 1)} = n\cdot \left(\frac{1}{2}\right)^n$ .
The chance of getting $1$ heads (and consequently, $(n - 1)$ tails) would be $\displaystyle {n \choose 1}\cdot \left(\frac{1}{2}\right)^{1} \cdot \left(\frac{1}{2}\right)^{n - 1} = n\cdot \left(\frac{1}{2}\right)^n$ .

These two events are mutually-exclusive. $\displaystyle n\cdot \left(\frac{1}{2}\right)^n + n\cdot \left(\frac{1}{2}\right)^n = 2\,n \cdot \left(\frac{1}{2}\right)^n = n \cdot \left(\frac{1}{2}\right)^{n - 1}$ would be the chance that either of them will occur. That's the same as the chance of determining the "odd" person in one round.

Since the coins here are all fair, the chance of determining the "odd" person would be $\displaystyle n \cdot \left(\frac{1}{2}\right)^{n - 1}$ in all rounds.

When the chance $p$ of getting a success in each round is the same, the geometric distribution would give the probability of getting the first success (that is, to find the "odd" person) in the $k$ th round: $(1 - p)^{k - 1} \cdot p$ . That's the same as the probability of getting one success after $(k - 1)$ unsuccessful attempts.

In this case, $\displaystyle p = n \cdot \left(\frac{1}{2}\right)^{n - 1}$ . Therefore, the probability of succeeding on round $k$ round would be

$\displaystyle \underbrace{\left(1 - n \cdot \left(\frac{1}{2}\right)^{n - 1}\right)^{k - 1}}_{(1 - p)^{k - 1}} \cdot \underbrace{n \cdot \left(\frac{1}{2}\right)^{n - 1}}_{p}$ .

Let $p$ is the chance of success on each round in a geometric distribution. The expected value of that distribution would be $\displaystyle \frac{1}{p}$ .

In this case, since $\displaystyle p = n \cdot \left(\frac{1}{2}\right)^{n - 1}$ , the expected value would be $\displaystyle \frac{1}{p} = \frac{1}{\displaystyle n \cdot \left(\frac{1}{2}\right)^{n - 1}}= \frac{2^{n - 1}}{n}$ .

7 0

3 years ago

Happy kids charge $19.00 plus $1.50 per hour to keep a kid during the day. Fun city charges $14.00 plus $2.75 per hour. Write an

MatroZZZ [7]

Answer: y = 1.50x + 19 and y = 2.75x + 14
y = 25
x = 4
Both services will charge an equal cost of $25 for 4 hours.

6 0

2 years ago

Read 2 more answers

TV studio has brought in 9 boy kittens and 6 girl kittens for a cat food commercial. The director is going to choose 9 of these

Amanda [17]

Answer:

probability = 0.2517

Step-by-step explanation:

given data

boy kittens = 9

girl kittens = 6

choose kittens at random = 9

solution

total kitten are = 9 + 6 = 15

first we get here total no of probability that is

n(s) = 15 C 9

n(s) = $\frac{15!}{9!(15-9)!}$

n(s) =5005

and

total way to chose 5 boy kittens is = 9 C 3

n(3) = $\frac{9!}{3!(9-3)!}$

n(3) = 84

and

total way to chose 4 girl kittens is = 6 C 4

n(4) = $\frac{6!}{4!(6-4)!}$

n(4) = 15

total way to chose 5 boy kittens and 4 girl kittens is

total way = 84 ×15 = 1260

so probability that the director chooses 5 boy kittens and 4 girl kittens is

probability = $\frac{1260}{5005}$

probability = 0.2517

6 0

4 years ago

Will the following measurements create a triangle? 25 25 130

WINSTONCH [101]

Answer:

if those measurements are degrees, then yes. If those measurements are the side lengths, then no.

Step-by-step explanation:

all angles on a triangle must had up to 180 degrees.

the two smaller sides of the triangle must add up to be larger than the largest side.

7 0

3 years ago

The band at charles high school had a concert for charity. They raised $15,000. Adult tickets were $5 each and student tickets w

Vika [28.1K]

Answer:

Adults =1500 and student= 2500

Step-by-step explanation:

Step one:

GIven data

let Adults be x and student be y in numbers

5x+3y=15000------------1

x+y=4000---------------------2

from 1

x=4000-y, put this in 2, we have

5(4000-y)+3y=15000

20000-5y+3y=15000

-2y=15000-20000

-2y= -5000

2y=5000

divide both sides by 2

y= 2500

put y= 2500 in 2

x+2500= 4000

x= 4000-2500

x=1500

3 0

3 years ago