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natima [27]
2 years ago
15

Evaluate | -65 | = ?

Mathematics
1 answer:
il63 [147K]2 years ago
6 0

Answer:

65

Step-by-step explanation:

It's the absolute value of -65

Hope this helped, Have a Wonderful Day!!

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A bag contains a number of marbles of which 35 are blue, 10 are red and the rest are
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Answer:

Y = 45*p(y) / (1 - p(y))    if I knew what p(y) is, we can find how many yellow marbles there are.   p(y) = probability of choosing yellow.

Step-by-step explanation:

Total marbles =  35 + 10 + yellow

If probability of choosing yellow =p(y) = yellow/Total

p(y) =  Y/(35 + 10 + Y)

Solve for Y,

p(y)*(35 + 10 + Y) = Y

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You have 100 cm of string which can be cut in one place (or not cut at all) and then formed into a circle and a square (or just
Ne4ueva [31]

Answer:

44cm for minimum area and 0 for maximum area (circle)

Step-by-step explanation:

Let's C be the circumference of the circle and S be the circumference of the square. If we cut the string into 2 pieces the total circumferences would be the string length 100cm.

S + C  = 100 or S = 100 - C

The side of square is S/4 and radius of the circle is \frac{C}{2\pi}

So the area of the square is

A_S = \frac{S^2}{4^2} = \frac{S^2}{16}

A_C = \pi\frac{C^2}{(2\pi)^2} = \frac{C^2}{4\pi}

Therefore the total area is

A = A_S + A_C = \frac{S^2}{16} + \frac{C^2}{4\pi}

We can substitute 100 - C for S

A = \frac{(100 - C)^2}{16} + \frac{C^2}{4\pi}

A = \frac{100^2 - 200C + C^2}{16} + \frac{C^2}{4\pi}

A = 625 -12.5C + \frac{C^2}{16} + \frac{C^2}{4\pi}

A = 625 -12.5C + C^2(\frac{1}{16} + \frac{1}{4\pi})

To find the maximum and minimum of this, we can take the first derivative and set that to 0

A^{'} = -12.5 + 2C(\frac{1}{16} + \frac{1}{4\pi}) = 0

C(\frac{1}{8} + \frac{1}{2\pi}) = 12.5

C \approx 44 cm

If we take the 2nd derivative:

A^{''} = \frac{1}{8} + \frac{1}{2\pi} > 0

We can see that this is positive, so our cut at 44 cm would yield the minimum area.

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if C = 100 then A_C = \frac{C^2}{4\pi} = \frac{100^2}{4\pi} = 795.77 cm^2

if S = 100 then A_S = \frac{S^2}{16} = \frac{100^2}{16} = 625 cm^2

So to yield maximum area, you should not cut at all and use the whole string to form a circle

4 0
3 years ago
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