A number increased by fifteen is nineteen. A number increased by fifteen is nineteen.

Consider the functionf:R→Rdefined viaf(x) =|x|.(a) Give a functiongwith domainRsuch thatg◦fis one-to-one, or describe why it is

yaroslaw [1]

Answer:

(a) Is not possible

(b) It is possible

(c) It is possible

(d) Is NOT possible.

Step-by-step explanation:

(a)

Is not possible, notice that for any function $g$ such that

$g : \mathbb{R} \rightarrow \mathbb{R}$

you would have that

$(g\circ f)(x) = g(f(x)) = g(|x|)$

And for, lets say -3,3 you have that

$g(|-3|) = g(|3|) = g(3)$ therefore is not possible to find a function that is one to one.

(b)

It is possible. Take the following function

$g(x) = x\sin(x)$ since $\sin$ is periodic it will take positive and negative numbers and if you multiply by $x$ each period will become bigger and bigger.

(c)

It is possible. Take the function

$g(x) = \sqrt{x}$

Then

$(f \circ g )(x) = | \sqrt{x} | = \sqrt{x}$ and $\sqrt{x}$ is one to one.

(d)

It is NOT possible because $(f\circ g)(x) = f(g(x)) = |g(x)|$ and that will always be positive.

7 0

4 years ago

Solve the equation. 3x^2+4x+5=0

Daniel [21]

Use the Quadratic Formula

x = -4 + 2 √11i/6, -4 - 2√11i/6

Simplify solutions

x = - 2 - √11i/3, - 2 + √11i/3

5 0

3 years ago

. The admission fee for a basketball game is $5 for students and $7 for adults. At one of the girl’s home games, 150 people atte

exis [7]

Answer:

Adults =58, Students=92

Step-by-step explanation:

7 0

3 years ago

Plz help plzzzz. !!!

abruzzese [7]

For each of these problems, all you need to do is isolate the variable. I’ll do the first few to help you out :)

32) 7 = -12 + e
Add 12 to both sides to isolate e.
19 = e

35) (r + 4) + 2 = 1
Subtract 2 from both sides.
r + 4 = -1
Subtract 4 from both sides to isolate r.
r = -5

38) -2 + (1 + p) = 5
Add 2 to both sides.
1 + p = 7
Subtract 1 from both sides to isolate p.
p = 6.

So essentially, all you need to do is add and subtract from each side to isolate the variable given in each problem. :)

Extra tip: In order to get rid of a number on one side (to isolate a variable), you must perform the opposite operation. For example, -2 + x = 1. In order to isolate x, add 2 to the left side to get rid of it, as well as adding it onto the right side so that it is not erased completely to get x=3)

3 0

3 years ago

Read 2 more answers

with the salary cap in the NFL, it is said that on "any given Sunday" any team could beat any other team. If we assume every wee

prohojiy [21]

Answer:

$P(X \geq 1) = 1-P(X$

And we can find the individual probability like this:

$P(X=0) = 16C0 (0.5)^0 (1-0.5)^{16-0} = 0.0000153$

And replacing we got:

$P(X \geq 1) = 1-P(X$

Step-by-step explanation:

Assuming the following question: With the salary cap in the NFL, it is said that on any given Sunday any team could beat any other team. If we assume every week of the 16 week season a team has a 50% chance of winning, what is the probability that a team will have at least 1 win?

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".

Solution to the problem

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

$X \sim Binom(n=16, p=0.5)$