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4 years ago

What is the maximum value of the objective function, P, with the given constraints?

Mathematics

1 answer:

Gala2k [10]4 years ago

7 0

Answer:

C. 450

Step-by-step explanation:

Plot the solution area for the system of four inequalities

$\left\{\begin{array}{l}4x+y\le 16\\x+y\le 10\\x\ge 0\\y\ge 0\end{array}\right.$

You'll get the quadrilateral with vertices at points (0,0), (0,10), (2,8) and (4,0).

The maximum value of the function can be at vertices, so

$P=25x+45y\\ \\P(0,0)=25\cdot0+45\cdot 0\\ \\P(0,10)=25\cdot 0+45\cdot 10=450\\ \\P(2,8)=25\cdot 2+45\cdot 8=50+360=410\\ \\P(4,0)=25\cdot 4+45\cdot 0=100$

The maximum value of the function is 450 at point (0,10)

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In the 30-60-90 triangle below, side s has a length of _ and side q has a length of _.

gregori [183]

Answer: F

Step-by-step explanation:

For a 30-60-90 triangle, we know that the hypotenuse is 2x. Since we know the hypotenuse is 10, we can solve for x.

2x=10

x=5

Now that we know x is 5, we can use this to solve for s and q. The side across from 30° is just x. Since we know x, s is 5.

The side across from 60° is x√3. Since we know what x is, we can just plug in. q is 5√3.

4 0

3 years ago

Which of the following are true

Eva8 [605]

I cannot see the question

6 0

3 years ago

A pen company averages 1.2 defective pens per carton produced (200 pens). The number of defects per carton is Poisson distribute

nlexa [21]

Answer:

a. P(x = 0 | λ = 1.2) = 0.301

b. P(x ≥ 8 | λ = 1.2) = 0.000

c. P(x > 5 | λ = 1.2) = 0.002

Step-by-step explanation:

If the number of defects per carton is Poisson distributed, with parameter 1.2 pens/carton, we can model the probability of k defects as:

$P(k)=\frac{\lambda^{k}e^{-\lambda}}{k!}= \frac{1.2^{k}\cdot e^{-1.2}}{k!}$

a. What is the probability of selecting a carton and finding no defective pens?

This happens for k=0, so the probability is:

$P(0)=\frac{1.2^{0}\cdot e^{-1.2}}{0!}=e^{-1.2}=0.301$

b. What is the probability of finding eight or more defective pens in a carton?

This can be calculated as one minus the probablity of having 7 or less defective pens.

$P(k\geq8)=1-P(k$

$P(0)=1.2^{0} \cdot e^{-1.2}/0!=1*0.3012/1=0.301\\\\P(1)=1.2^{1} \cdot e^{-1.2}/1!=1*0.3012/1=0.361\\\\P(2)=1.2^{2} \cdot e^{-1.2}/2!=1*0.3012/2=0.217\\\\P(3)=1.2^{3} \cdot e^{-1.2}/3!=2*0.3012/6=0.087\\\\P(4)=1.2^{4} \cdot e^{-1.2}/4!=2*0.3012/24=0.026\\\\P(5)=1.2^{5} \cdot e^{-1.2}/5!=2*0.3012/120=0.006\\\\P(6)=1.2^{6} \cdot e^{-1.2}/6!=3*0.3012/720=0.001\\\\P(7)=1.2^{7} \cdot e^{-1.2}/7!=4*0.3012/5040=0\\\\$

$P(k$

c. Suppose a purchaser of these pens will quit buying from the company if a carton contains more than five defective pens. What is the probability that a carton contains more than five defective pens?

We can calculate this as we did the previous question, but for k=5.

$P(k>5)=1-P(k\leq5)=1-\sum_{k=0}^5P(k)\\\\P(k>5)=1-(0.301+0.361+0.217+0.087+0.026+0.006)\\\\P(k>5)=1-0.998=0.002$

5 0

3 years ago

Find the unknown side length, x. Write your answer in simplest radical form.

Mama L [17]

<span>The correct answer between all the choices given is the second choice or letter B. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.</span>

4 0

3 years ago

Complete the square to rewrite x^2+y^2+2x+6y-6=0 in graphing form

Ksivusya [100]

Answer:

(x + 1)² + (y + 3)² = 16

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² + 2x + 6y - 6 = 0

Collect the x and y terms together and add 6 to both sides

x² + 2x + y² + 6y = 6

To complete the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(1)x + 1 + y² + 2(3)y + 9 = 6 + 1 + 9

(x + 1)² + (y + 3)² = 16

with centre = (- 1, - 3) and r = $\sqrt{16}$ = 4

4 0

3 years ago