All categories

3 years ago

Which function grows at the fastest rate for increasing values of x?

Mathematics

2 answers:

Stels [109]3 years ago

8 0

<h2>Answer:</h2>

The function which has the fastest rate for increasing values of x are:

$p(x)=5x^3+3$

<h2>Step-by-step explanation:</h2>

We are given four polynomial functions as:

$p(x)=5x^3+3\\\\\\ f(x)=8x^2-3x\\\\\\h(x)=2x\\\\\\g(x)=19x$

Now as we know that if the degree of the polynomial increases the function becomes more extreme i.e. it increases very quickly with the increasing value of x.

Hence, among the given options the function which has the fastest rate of increase is:

$p(x)=5x^3+3$

( Since, it's degree is 3 which is highest as compared to the other polynomials (one of degree 2 and 2 of degree 1) )

Komok [63]3 years ago

7 0

Calculate the derivative of each function
And btw answer is p(x)

You might be interested in

In a particular faculty 60% of students are men and 40% are women. In a random sample of 50 students what is the probability tha

zimovet [89]

Answer:

a) The expected value is given by:

$E(X) = np = 50*0.4 = 20$

and the variance is given by:

$Var(X) =np(1-p) = 50*0.4*(1-0.4) = 12$

b) $P(X>25)= 1-P(X\leq 25)$

And we can find this probability with the following Excel code:

=1-BINOM.DIST(25,50,0.4,TRUE)

And we got:

$P(X>25)= 1-P(X\leq 25)=0.0573$

c) 1) Random sample (assumed)

2) np= 50*0.4= 20 >10

n(1-p) =50*0.6= 30>10

3) Independence (assumed)

Since the 3 conditions are satisfied we can use the normal approximation:

$X \sim N(\mu = 20 , \sigma= 3.464)$

d) $P(X>25) = 1-P(Z< \frac{25-20}{3.464}) = 1-P(z$

e) $P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)$

$P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)= 1-P(Z$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=50, p=0.4)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Part a

The expected value is given by:

$E(X) = np = 50*0.4 = 20$

and the variance is given by:

$Var(X) =np(1-p) = 50*0.4*(1-0.4) = 12$

Part b

For this case we want to find this probability:

$P(X>25)= 1-P(X\leq 25)$

And we can find this probability with the following Excel code:

=1-BINOM.DIST(25,50,0.4,TRUE)

And we got:

$P(X>25)= 1-P(X\leq 25)=0.0573$

Part c

1) Random sample (assumed)

2) np= 50*0.4= 20 >10

n(1-p) =50*0.6= 30>10

3) Independence (assumed)

Since the 3 conditions are satisfied we can use the normal approximation:

$X \sim N(\mu = 20 , \sigma= 3.464)$

Part d

We want this probability:

$P(X>25) = 1-P(Z< \frac{25-20}{3.464}) = 1-P(z$

Part e

For this case we use the continuity correction and we have this:

$P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)$

$P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)= 1-P(Z$

4 0

3 years ago

the sum of two numbers is 44. the smaller number is five-sixths of the larger number. what are the numbers?

Sindrei [870]

X+y=44
x=5/6y

x+y=44
5/6y+y=44
11/6y=44
11y=264
y=24
x=5/6y=(5/6)*24=20
Answers: numbers are 20, 24

7 0

3 years ago

The student council made a profit of $3,000 on a car wash. If they invest the money at 5% interest

zzz [600]

Answer:

560000

Step-by-step explanation:

As the profit is 3000 on car wash

And there is 5 percent interest

As the 5ser of 3000 is 559995

So the 4 years add to 559995

Equals 560000

HOPE THIS HELPED

YOUR WELCOME

LOVE KITTY 

CAT

5 0

3 years ago

How to show the ratio 3:8 is equal to 12:32

Agata [3.3K]

12:32 is simply 3:8 but divided by 4 to both sides.

3 0

3 years ago

Read 2 more answers

How do I do this 7:13 21:39

GarryVolchara [31]

That is a ratio. 7 x 3 = 21 and 13 x 3 = 39.

5 0

3 years ago