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2 years ago

342 employees prefer a bonus over extra vacation days from a survey of 450 employees what is the population proportion

Mathematics

1 answer:

salantis [7]2 years ago

8 0

Answer:

Step-by-step explanation:

450/100 = 4.5

342/4.5 = 76

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You place a 16 foot ladder against a building. The angle that the ladder forms with

gulaghasi [49]

Answer:The base of the ladder should be placed so that it is one foot away from the building for every four feet of hight to where the ladder rests against the building. This is known as the 4 to 1 rule.

Step-by-step explanation:

7 0

3 years ago

Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:

ryzh [129]

First find the critical points of f :

$f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7$

$\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1$

$\dfrac{\partial f}{\partial y}=6y=0\implies y=0$

so the point (1, 0) is the only critical point, at which we have

$f(1,0)=-7$

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

$f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t$

Find the critical points of g :

$\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0$

$\implies\sin t=0\text{ OR }1+5\cos t=0$

$\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi$

where n is any integer. We get 4 critical points in the interval [0, 2π) at

$t=0\implies f(10,0)=155$

$t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299$

$t=\pi\implies f(-10,0)=235$

$t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299$

So f has a minimum of -7 and a maximum of 299.

4 0

3 years ago

If f(x)= x^-2, and g(x)=3x-1 whats the domain of f(g(x))?

andrey2020 [161]

4 and 7 and 8 and 9 and10

5 0

3 years ago

Write <, >, or = to make the statement true : .293 ___ .29

JulsSmile [24]

If you add a zero to the end of .29 it becomes .290
So, the answer is .293 > .29

7 0

3 years ago

It is given that y=ax²-3. Express a in terms of x and y.

Elena-2011 [213]

A=(3+y)/x^2
Hope this helps

7 0

3 years ago