Some values of the exponential function f (x ) are shown in the table, where m and n are real numbers.

Please help ASAP I’ll mark you as brainlister

zavuch27 [327]

Answer:

So Sorry Omg Wait I'll will come back

8 0

3 years ago

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A company wishes to manufacture some boxes out of card. The boxes will have 6 sides (i.e. they covered at the top). They wish th

Serhud [2]

Answer:

The dimensions are, base $b=\sqrt[3]{200}$ , depth $d=\sqrt[3]{200}$ and height $h=\sqrt[3]{200}$ .

Step-by-step explanation:

First we have to understand the problem, we have a box of unknown dimensions (base $b$ , depth $d$ and height $h$ ), and we want to optimize the used material in the box. We know the volume $V$ we want, how we want to optimize the card used in the box we need to minimize the Area $A$ of the box.

The equations are then, for Volume

$V=200cm^3 = b.h.d$

For Area

$A=2.b.h+2.d.h+2.b.d$

From the Volume equation we clear the variable $b$ to get,

$b=\frac{200}{d.h}$

And we replace this value into the Area equation to get,

$A=2.(\frac{200}{d.h} ).h+2.d.h+2.(\frac{200}{d.h} ).d$

$A=2.(\frac{200}{d} )+2.d.h+2.(\frac{200}{h} )$

So, we have our function $f(x,y)=A(d,h)$ , which we have to minimize. We apply the first partial derivative and equalize to zero to know the optimum point of the function, getting

$\frac{\partial A}{\partial d} =-\frac{400}{d^2}+2h=0$

$\frac{\partial A}{\partial h} =-\frac{400}{h^2}+2d=0$

After solving the system of equations, we get that the optimum point value is $d=\sqrt[3]{200}$ and $h=\sqrt[3]{200}$ , replacing this values into the equation of variable $b$ we get $b=\sqrt[3]{200}$ .

Now, we have to check with the hessian matrix if the value is a minimum,

The hessian matrix is defined as,

$H=\left[\begin{array}{ccc}\frac{\partial^2 A}{\partial d^2} &\frac{\partial^2 A}{\partial d \partial h}\\\frac{\partial^2 A}{\partial h \partial d}&\frac{\partial^2 A}{\partial p^2}\end{array}\right]$

we know that,

$\frac{\partial^2 A}{\partial d^2}=\frac{\partial}{\partial d}(-\frac{400}{d^2}+2h )=\frac{800}{d^3}$

$\frac{\partial^2 A}{\partial h^2}=\frac{\partial}{\partial h}(-\frac{400}{h^2}+2d )=\frac{800}{h^3}$

$\frac{\partial^2 A}{\partial d \partial h}=\frac{\partial^2 A}{\partial h \partial d}=\frac{\partial}{\partial h}(-\frac{400}{d^2}+2h )=2$

Then, our matrix is

$H=\left[\begin{array}{ccc}4&2\\2&4\end{array}\right]$

Now, we found the eigenvalues of the matrix as follow

$det(H-\lambda I)=det(\left[\begin{array}{ccc}4-\lambda&2\\2&4-\lambda\end{array}\right] )=(4-\lambda)^2-4=0$

Solving for $\lambda$ , we get that the eigenvalues are: $\lambda_1=2$ and $\lambda_2=6$ , how both are positive the Hessian matrix is positive definite which means that the function $A(d,h)$ is minimum at that point.

4 0

3 years ago

An experimenter is randomly sampling 4 objects in order from among 43 objects. What is the total number of samples in the sample

Ivenika [448]

Answer:

10.75

Step-by-step explanation:

First you see how many times 4 can go into 4 in the tens place which is 1 .You multiply 4 times 1and you get 4 .Then you minus 4 from 4 and get

Then you bring down the 3 and see how many times 4 can go into 3 which is 0 .So you put a decimal point and bring down a 0.

See how many times 4 can go into 30,which will be 7 times.After , you multiply 7 times 4 and you get 28.Subtract 29 from 30 and you get 20.You bring down the 0 .

See how many times 4 can go into 20 which is 5.Mutiply 5 times 4 and get 20 then subtract 20 from 20.

Get a final quotient of 10.75.

4 0

3 years ago

About 10% of the human population is left-handed. Suppose a researcher speculates that artists are more likely to be left-handed

nevsk [136]

Answer:

Given the information in the question;

a) The parameter of interest is the population of artists who are left-handed and its is 10% = (10/1000 = 0.10

b) The Null hypothesis and alternative hypothesis are;

<em>H₀ : p </em>= 0.10

<em>H₁ : p</em> > 0.10

c) The sample proportion is calculated as:

p = number of left handed artist / sample size

p = 26 / 200

p = 0.13

d) To find the p-value, The researcher should calculate the probability that the sample proportion would be 0.13 or larger for a sample of size 200 if the population proportion is actually 0.10.

4 0

3 years ago

Please help, multiple choice

leonid [27]

Answer:

H=25√3

Step-by-step explanation:

So you would use the 30°,60°,90° Triangle theorem to solve this problem

Since we are trying to find out the 60°, because the x is across from 60° we can assume that we are just going to plug in x√3.

Hopefully you understand, didn't really explain it that well...

6 0

3 years ago

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