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3 years ago

Minimize Q=x^2+2y^2, where x+y=3

1 answer:

Studentka2010 [4]3 years ago

6 0

<span>The first step you need to do is to rewrite
x+y=3
as y=3-x
</span><span>Now we can replace the y in the equation with our newfound value for y, which is
y=3-x.
So lets write it now like this
Q=x^2+2(3-y)^2
=x^2+18-12x+2x^2
=3x^2+18-12x
</span>Hope this helps

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(Y to the eighth power)(y to the second power) simpified

Lemur [1.5K]

Answer:

y^10

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3 years ago

7.34 in scientific notation

Allushta [10]

Answer:

7.34×10⁰

Unless you're missing something in your question then that'd be it I guess... There isn't really a reason to put 7.34 in scientific notation though, so I'm assuming something isn't loading for me (or the question was changed).

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3 years ago

For X a binomial random variable with n=5 and p=1/4, answer the following

mash [69]

Recall that for $X\sim\mathrm{Bin}(n,p)$ , i.e. a random variable $X$ following a binomial distribution over $n$ trials and with probability parameter $p$ ,

$\mathbb P(X=x)=f_X(x)=\begin{cases}\dbinom nx p^x(1-p)^{n-x}&\text{for }x\in\{0,1,\ldots,n\}\\\\0&\text{otherwise}\end{cases}$

So you have

$\mathbb P(X=2)=\dbinom52\left(\dfrac14\right)^2\left(1-\dfrac34\right)^{5-2}=\dfrac{135}{512}\approx0.26$

$\mathbb P(2\le X\le4)=\displaystyle\sum_{x=2}^4\mathbb P(X=x)$
$=\dbinom52\left(\dfrac14\right)^2\left(1-\dfrac14\right)^{5-2}+\dbinom52\left(\dfrac14\right)^3\left(1-\dfrac14\right)^{5-3}+\dbinom52\left(\dfrac14\right)^4\left(1-\dfrac14\right)^{5-4}$
$=\dfrac{375}{1024}\approx0.37$

The expected value of $X\sim\mathrm{Bin}(n,p)$ is simply $np$ , while the standard deviation is $\sqrt{np(1-p)}$ . In this case, they are $\dfrac54=1.25$ and $\sqrt{\dfrac{15}{16}}\approx0.97$ , respectively.

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3 years ago

For the function G defined by G(x)=5x+3, find G(r+5).

ycow [4]

Answer:

8x+5

Step-by-step explanation:

any letter will mean 1

4 0

3 years ago

Read 2 more answers

A line with a slope of –2 passes through the point (–4, 8). What is the equation of the slope-intercept form?

zloy xaker [14]

Answer:

y= -2x

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx+c, where m is the gradient and c is the y-intercept.

Given that the slope is -2, m= -2.

subst. m= -2 into the equation:

y= -2x +c

To find the value of c, substitute a coordinate.

When x= -4, y=8,

8= -2(-4) +c

8= 8 +c (expand)

c= 8-8 (-8 on both sides)

c=0 (simplify)

Thus, the equation of the line is y= -2x.

8 0

3 years ago