How do you know if an number composite or not

Mathematics

1 answer:

cestrela7 [59]3 years ago

3 0

Answer:

A prime number has only two factors: 1 and itself. A composite number has more than two factors

Step-by-step explanation:

Can i have a thanks?

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Express the following rate as a rate.

mixas84 [53]

So u do 63/3 so that is 21

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4 years ago

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Ruby and her friends are going into a restaurant. How much would it cost to buy 3

Gnoma [55]

Answer:

Step-by-step explanation:

3x2.25=6.75

4x4=16

16+6.75=22.75

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3 years ago

Find the minimum and maximum of f(x,y,z)=x^2+y^2+z^2 subject to two constraints, x+2y+z=4 and x-y=8.

Alika [10]

The Lagrangian for this function and the given constraints is

$L(x,y,z,\lambda_1,\lambda_2)=x^2+y^2+z^2+\lambda_1(x+2y+z-4)+\lambda_2(x-y-8)$

which has partial derivatives (set equal to 0) satisfying

$\begin{cases}L_x=2x+\lambda_1+\lambda_2=0\\L_y=2y+2\lambda_1-\lambda_2=0\\L_z=2z+\lambda_1=0\\L_{\lambda_1}=x+2y+z-4=0\\L_{\lambda_2}=x-y-8=0\end{cases}$

This is a fairly standard linear system. Solving yields Lagrange multipliers of $\lambda_1=-\dfrac{32}{11}$ and $\lambda_2=-\dfrac{104}{11}$ , and at the same time we find only one critical point at $(x,y,z)=\left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right)$ .

Check the Hessian for $f(x,y,z)$ , given by

$\mathbf H(x,y,z)=\begin{bmatrix}f_{xx}&f_{xy}&f_{xz}\\f_{yx}&f_{yy}&f_{yz}\\f_{zx}&f_{zy}&f_{zz}\end{bmatrix}=\begin{bmatrix}=\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}$

$\mathbf H$ is positive definite, since $\mathbf v^\top\mathbf{Hv}>0$ for any vector $\mathbf v=\begin{bmatrix}x&y&z\end{bmatrix}^\top$ , which means $f(x,y,z)=x^2+y^2+z^2$ attains a minimum value of $\dfrac{480}{11}$ at $\left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right)$ . There is no maximum over the given constraints.

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4 years ago

Solve y=.80x+100 based on bread machine costs 100. Ingredients for one loaf is .80 and what is the cost to make 50 loaves of bre

Ugo [173]

Substitute 50 loaves into the given equation

y= cost to make 50 loaves

y= 0.80x + 100
y= 0.80(50) + 100
multiply first, then add
y= 40 + 100
y= $140 cost to make 50 loaves

Hope this helps!

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3 years ago

When designing a study to determine this population proportion, what is the minimum number of drivers you would need to survey t

Vlada [557]

Answer: 601

Step-by-step explanation:

The formula to find the minimum sample size(n) , if the prior population proportion is unknown:

$n=0.25(\dfrac{z^c}{E})^2$ , where E = margin of error , $z^c$ = critical z-value for confidence level c.