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3 years ago

Find the area enclosed by the curve y^2=x^2-x^4

Mathematics

1 answer:

yulyashka [42]3 years ago

4 0

Answer: 4/3

Step-by-step explanation:

As you know this graph is a lemniscate

$4\int\limits^1_0 {x\sqrt{1-x^{2} } \, dx =\frac{4}{3} =1.33$$

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The night watchman in a factory cannot guard both the safe in back and the cash register in front. The safe contains $6000, whil

Zolol [24]

Answer:

The guard should be positioned at the safe

Step-by-step explanation:

The night watchmen should be positioned to guard whichever place gives the highest expected value to the thief.

The expected value of robbing the safe is:

$EV_{s} = \$ 6000*0.2\\EV_{s} = \$ 1200$

The expected value of robbing the cash register is:

$EV_{r} = \$ 1000*0.8\\EV_{r} = \$ 800$

Therefore, the guard should be positioned at the safe since it yields a higher expected value to the thief in case he tries to rob it.

7 0

3 years ago

Solve the system of equations below.

Ostrovityanka [42]

C - no solution
you take the second solution and times the entire equation by -1
then simply
and you get 0x + 0y = 20

5 0

3 years ago

Read 2 more answers

What is the probability of drawing a 9 of spades from a 52-card deck given the deck is properly shuffled?

avanturin [10]

1.923% (Roughly)

You can get this by dividing 1 by 52 to find the likelihood. <span />

4 0

3 years ago

Polly buys 14 cupcakes for a party. The bakery puts them into boxes that hold 4 cupcakes each.

Temka [501]

Answer:

Part a) The number of boxes needed will be 4

part b) The fraction of the box that is empty is $\frac{1}{2}$

Part c) Are needed 2 cupcakes to fill the last box

Step-by-step explanation:

Part a) How many boxes will be needed for Polly to bring all the cupcakes to the party?

To find out the number of boxes needed, divide the total number of cupcakes by 4 (maximum number of cupcakes that fit in each box).

$\frac{14}{4}=3.5\ box$

Round up

The number of boxes needed will be 4

Part b) If the bakery completely fills as many boxes as possible, what fraction of the last box is empty?

we know that

The maximum number of cupcakes per box is 4

The first three boxes have 4 cupcakes

The last box has

$14-3(4)=2\ cupcakes$

The fraction of the box that is empty is equal to the number of cupcakes missing to fill the box divided by the cupcake capacity of the box

$\frac{2}{4}=\frac{1}{2}$

Part c) How many more cupcakes are needed to fill this box

Subtract the number of cupcakes in the box from the cupcake capacity of the box

The last box has 2 cupcakes

The cupcake capacity of the box is 4

$4-2=2\ cupcakes$

therefore

Are needed 2 cupcakes to fill the last box

8 0

3 years ago

Customers arrat a service window according to a poisson process with an average of 0.2 per minute.

suter [353]

Answer:

Step-by-step explanation:

Given that customers arrat a service window according to a poisson process with an average of 0.2 per minute

= 12 per hour.

a) the probability that the time between two successive arrivals is less than 6 minutes

= For one hour more than 60/6 =10 customers arrive.

P(X>10) = 0.6528

b) Prob that there will be exactly three arrivals during a given 10-minute period

P(x=3) for average 2

= 0.1804

3 0

2 years ago