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Brrunno [24]
2 years ago
4

A woman is traveling with a​ wolf, a​ goose, and a mouse. She must cross a river in a boat that will only hold herself and one o

ther animal. If left to​ themselves, the wolf will eat the goose and the goose will eat the mouse. How many crossings are required to get all four creatures across the river​ alive
Mathematics
1 answer:
marysya [2.9K]2 years ago
8 0

W - wolf, G - goose, M - mouth

1. Woman takes G and crosses the river.

1st bank | 2nd bank

W, M      | G

2. She leaves G on the opposite  second bank and turns back.

1st bank | 2nd bank

W, M      | G

3. She takes W and goes with him to the bank where G already is.

1st bank | 2nd bank

M           | G, W and woman

4. She takes G back to the first bank and leaves W on the second bank.

1st bank | 2nd bank

G, M      | W

5. Woman leaves G on the first and takes M to the second bank.

1st bank | 2nd bank

G            | W, M

6. She leaves M on the second bank and returns to the first bank.

7. Takes G and delivers it to the second bank.

1st bank | 2nd bank

              | G, W, M and woman

Answer: 7 crossings.

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Patterns can be used to determine products of a number of a power of 10 by following it to obtain easily the answer. When you multiply a number by the power of 10 you just have to write the number then add the number of corresponding number of 0s to the end which will be the same number as the power used. 

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a

Step-by-step explanation:

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While exercising, Carly burns 450 calories per hour biking and 620 calories per hour playing racquetball. Sarah burns 560 calori
Katyanochek1 [597]

Answer:

A

Step-by-step explanation:

30 minutes = half an hour

Carly:

450/2 = 225

620/2= 310

225 + 310 = 535

Carly burned 535 calories total

Sarah:

560/2 = 280

510/2 = 225

280 + 225 = 505

Sarah burned 505 calories total

Carly burned more calories than Sarah

4 0
2 years ago
Find the absolute maximum and absolute minimum of the function f(x,y)=2x2−4x+y2−4y+1 on the closed triangular plate bounded by t
marusya05 [52]

First check for the critical points of <em>f</em> by checking where the first-order derivatives vanish.

\dfrac{\partial f}{\partial x}=4x-4=0\implies x=1

\dfrac{\partial f}{\partial y}=2y-4=0\implies y=2

Notice how the point (1, 2) lies on the line <em>y</em> = 2<em>x</em> ; at this point, we get a value of <em>f</em>(1, 2) = -5 (MIN).

Next, check the points where the boundary lines intersect, which occurs at the points (0, 0), (0, 2), and (1, 2). We already checked the last one. We find <em>f</em>(0, 0) = 1 (MAX) and <em>f</em>(0, 2) = -3.

Now check on the boundary lines themselves. If <em>x</em> = 0, then

f(0,y)=y^2-4y+1=(y-2)^2-3

which has a maximum value of -3 when <em>y</em> = 2 (so we get the same critical point as before).

If <em>y</em> = 2, then

f(x, 2)=2x^2-4x-3=2(x-1)^2-5

with a maximum of -5 when <em>x</em> = 1.

If <em>y</em> = 2<em>x</em>, then

f(x,2x)=6x^2-12x+1=6(x-1)^2-5

with the same maximum of -5 when <em>x</em> = 1.

6 0
2 years ago
The following histogram shows the relative frequencies of the heights, recorded to the nearest inch, of a population of women. T
Airida [17]

Answer:

The following histogram shows the relative frequencies of the height recorded to the nearest inch of population of women the mean of the population is 64.97 inches and the standard deviation is 2.66 inches

(a) Based on the histogram, what is the probability that the selected woman will have a height of at least 67 inches? Show your work

Answer:

0.22268

Step-by-step explanation:

z-score is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

(a) Based on the histogram, what is the probability that the selected woman will have a height of at least 67 inches? Show your work

At least means equal to or greater than 67 inches

z = 67 - 64.97/2.66

z = 0.76316

P-value from Z-Table:

P(x<67) = 0.77732

P(x>67) = 1 - P(x<67) = 0.22268

The probability that the selected woman will have a height of at least 67 inches is 0.22268

Step-by-step explanation:

6 0
2 years ago
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