All categories

3 years ago

Y=5x^2-8x-12 linear , exponential , or quadratic and why

Mathematics

1 answer:

Assoli18 [71]3 years ago

4 0

Answer:

Quadratic

Step-by-step explanation:

This is a quadratic equation because it's in the form of y=ax^2+bx+c

If it were linear, the graph would be a straight line and wouldn't contain a second degree term

If it were exponential there would be a growth or decay factor

You might be interested in

An oak tree in Jake's yard is 13 times taller than a model tree that he's making for a performance set.Together,the oak tree and

gladu [14]

The answer would be 8.6 to check multiply 8.6*13

7 0

3 years ago

Read 2 more answers

2) X and Y are jointly continuous with joint pdf

Nady [450]

From what I gather from your latest comments, the PDF is given to be

$f_{X,Y}(x,y)=\begin{cases}cxy&\text{for }0\le x,y \le1\\0&\text{otherwise}\end{cases}$

and in particular, f(x, y) = cxy over the unit square [0, 1]², meaning for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. (As opposed to the unbounded domain, x ≤ 0 *and* y ≤ 1.)

(a) Find c such that f is a proper density function. This would require

$\displaystyle\int_0^1\int_0^1 cxy\,\mathrm dx\,\mathrm dy=c\left(\int_0^1x\,\mathrm dx\right)\left(\int_0^1y\,\mathrm dy\right)=\frac c{2^2}=1\implies \boxed{c=4}$

(b) Get the marginal density of X by integrating the joint density with respect to y :

$f_X(x)=\displaystyle\int_0^1 4xy\,\mathrm dy=(2xy^2)\bigg|_{y=0}^{y=1}=\begin{cases}2x&\text{for }0\le x\le 1\\0&\text{otherwise}\end{cases}$

$f_Y(y)=\displaystyle\int_0^14xy\,\mathrm dx=\begin{cases}2y&\text{for }0\le y\le1\\0&\text{otherwise}\end{cases}$

(d) The conditional distribution of X given Y can obtained by dividing the joint density by the marginal density of Y (which follows directly from the definition of conditional probability):

$f_{X\mid Y}(x\mid y)=\dfrac{f_{X,Y}(x,y)}{f_Y(y)}=\begin{cases}2x&\text{for }0\le x\le 1\\0&\text{otherwise}\end{cases}$

(e) From the definition of expectation:

$E[X]=\displaystyle\int_0^1\int_0^1 x\,f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=4\left(\int_0^1x^2\,\mathrm dx\right)\left(\int_0^1y\,\mathrm dy\right)=\boxed{\frac23}$

$E[Y]=\displaystyle\int_0^1\int_0^1 y\,f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=4\left(\int_0^1x\,\mathrm dx\right)\left(\int_0^1y^2\,\mathrm dy\right)=\boxed{\frac23}$

$E[XY]=\displaystyle\int_0^1\int_0^1xy\,f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=4\left(\int_0^1x^2\,\mathrm dx\right)\left(\int_0^1y^2\,\mathrm dy\right)=\boxed{\frac49}$

(f) Note that the density of X | Y in part (d) identical to the marginal density of X found in (b), so yes, X and Y are indeed independent.

The result in (e) agrees with this conclusion, since E[XY] = E[X] E[Y] (but keep in mind that this is a property of independent random variables; equality alone does not imply independence.)

8 0

3 years ago

using the distance formula d=√(x2- x1)^2 +(y2-y^1, what is the distance between point (-3,1) and point (-2,4) rounded to the nea

defon

Answer:

$d = \sqrt{(x2 - x1) + (y2 - y1)} \\ d = \sqrt{ (- 3 + 2) + (1 + - 4)} \\ d = \sqrt{ - 1 + - 3 } \\ d = \sqrt{ - 4 } \\ d = - 2$

Step-by-step explanation:

<h2>hope it helps you<3</h2>

4 0

2 years ago

A bottle holds 64 fluid ounces of lemonade. How much is this in pints?

myrzilka [38]

Answer:

there are 4 pints

Step-by-step explanation:

64 / 16 = 4

4 0

2 years ago

The phone lines to an airline reservation system are occupied 45% of the time. Assume that the events that the lines are occupie

dimaraw [331]

Answer:

0.1569 = 15.69%

Step-by-step explanation:

If eight calls were placed, and we need to know the probability of exactly two calls were occupied, we need to calculate a combination of 8 choose 2 (all the combinations of 2 occupied calls in the 8 total calls), and multiply by the probability of each case in the 8 calls (2 cases occupied and 6 cases not occupied):

P(8,2) = C(8,2) * p(occupied)^2 * p(not_occupied)^6

P(8,2) = (8*7/2) * (0.45)^2 * (0.55)^6

P(8,2) = 28 * 0.2025 * 0.02768 = 0.1569 = 15.69%

7 0

2 years ago