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3 years ago

10

Prove that y = -3x + 3 is linear.

1 answer:

shtirl [24]3 years ago

8 0

Graph it and you’ll see it’s a line

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A company orders supplies from M distributors and wishes to place n orders (n < M). Assume that the company places the orders

harkovskaia [24]

Answer:

a) 0.06048 b) 0.001344 c) 0.000294

Step-by-step explanation:

number of distributors = 10;

number of orders = 7

a)

There are 10 distributors for each order, so the no. of ways the 7 orders could be placed are = 10⁷ =10000000

no. of ways that orders goes to different distributors = ¹⁰C₇*7! = 604800

Probability = 604800/10000000 = 0.06048

b)

number of ways distributor 1 gets exactly 2 and distributor 2 gets exactly 3 orders = ⁷C₂*⁵C₃*8² = 13440

probability = 13440/10000000 = 0.001344

c)

number of ways distributor 1, 2,3 get exactly 2,3 and 1 order(s) = ⁷C₂*⁵C₃*²C₁*7¹ = 2940

probability = 2940/10000000 = 0.000294

3 0

4 years ago

Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer d

eduard

The Lagrangian is

$L(x_1,\ldots,x_n,\lambda_1,\ldots,\lambda_n)=x_1+\cdots+x_n+\lambda_1({x_1}^2+\cdots+{x_n}^2)+\cdots+\lambda_n({x_1}^2+\cdots+{x_n}^2)$

with partial derivatives (set equal to 0)

$\dfrac{\partial L}{\partial x_i}=1+2x_i(\lambda_1+\cdots+\lambda_n)=0$

$\dfrac{\partial L}{\partial\lambda_i}={x_1}^2+\cdots+{x_n}^2-36=0$

for each $1\le i\le n$ .

Let $\Lambda$ be the sum of all the multipliers $\lambda_i$ ,

$\Lambda=\displaystyle\sum_{k=1}^n\lambda_k=\lambda_1+\cdots+\lambda_n$

We notice that

$x_i\dfrac{\partial L}{\partial x_i}=x_i+2{x_i}^2\Lambda=0$

so that

$\displaystyle\sum_{i=1}^nx_i\dfrac{\partial L}{\partial x_i}=\sum_{i=1}^nx_i+2\Lambda\sum_{i=1}^n{x_i}^2=0$

We know that $\sum\limits_{i=1}^n{x_i}^2=36$ , so

$\displaystyle\sum_{i=1}^nx_i+2\Lambda\sum_{i=1}^n{x_i}^2=0\implies\sum_{i=1}^nx_i=-72\Lambda$

Solving the first $n$ equations for $x_i$ gives

$1+2\Lambda x_i=0\implies x_i=-\dfrac1{2\Lambda}$

and in particular

$\displaystyle\sum_{i=1}^nx_i=-\dfrac n{2\Lambda}$

It follows that

$-\dfrac n{2\Lambda}+72\Lambda=0\implies\Lambda^2=\dfrac n{144}\implies\Lambda=\pm\dfrac{\sqrt n}{12}$

which gives us

$x_i=-\dfrac1{2\left(\pm\frac{\sqrt n}{12}\right)}=\pm\dfrac6{\sqrt n}$

That is, we've found two critical points,

$\pm\left(\dfrac6{\sqrt n},\ldots,\dfrac6{\sqrt n}\right)$

At the critical point with positive signs, $f(x_1,\ldots,x_n)$ attains a maximum value of

$\displaystyle\sum_{i=1}^nx_i=\dfrac{6n}{\sqrt n}=6\sqrt n$

and at the other, a minimum value of

$\displaystyle\sum_{i=1}^nx_i=-\dfrac{6n}{\sqrt n}=-6\sqrt n$

4 0

4 years ago

The map shows the location of four places in a school. A coordinate plane is shown. There is a point at 5, 2 labeled Front offic

REY [17]

The library is in the 4th quadrant (+x,-y)

So the English class must have a positive x and a negative y

(4,-5) is the only point that fits

6 0

3 years ago

Read 2 more answers

In mr. Ochoas mathematics class, 1/2 of the students received as and 1/6 received bs. What fraction of the student received eith

Contact [7]

Answer:1/3

Step-by-step explanation:

6 0

3 years ago

Find the diameter of the circles having areas of 2464 cm square .

Katena32 [7]

Answer:

the diameter of a circle is 56 CM

4 0

3 years ago