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2 years ago

What is the greatest integer k such that 2k is a factor of 67!?

Mathematics

2 answers:

Artist 52 [7]2 years ago

8 0

Answer:

k=64

Step-by-step explanation:

To find out the greatest integer such that 2^{k}is a factor if 67!

We divide the quotients by 2 and then finally add all the quotients.

67/2 = 33.5 --------> 33

33/2 = 16.5 ---------> 16

16/2 = 8 --------> 8

8/2= 4 ---------> 4

4/2 = 2--------> 2

2/2 = 1 ----------> 1

k= 33+16+8+4+2+1

= 64

Hence, 64 is the greatest integer such that 2^{k} is a factor of 67!.

almond37 [142]2 years ago

7 0

67!/2 = k = 18 235 555 459 094 342 644 124 929 548 302 732 213 583 817 657 024 762 296 850 814 250 133 981 218 471 936 000 000 000 000 000

about 1.82×10⁹⁴

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Which table contains only corresponding x-values and y-values where the value of y is one more than the product of x and 2?

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Answer:

Option (C)

Step-by-step explanation:

Value of y is more than the product of x and 2.

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x 0 1 2 3 4

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Solve for x: 3(5x + 10) + 10 = 6x - (x + 10)

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Answer:

x= -5

Step-by-step explanation:

3(5x+10)+10=6x-(x+10)

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2 years ago

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A company manufactures aluminum mailboxes in the shape of a box with a half-cylinder top. The company will make 1863 mailboxes t

worty [1.4K]

Answer:

3433 m²

Step-by-step explanation:

From the image, we have a rectangular box without cover and half a cylinder on top.

Formula for surface area of rectangular box with top is;

S = 2(lh + wh + lw)

From the image,

l = 0.6 m

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h = 0.55 m

Thus;

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S = 1.58 m²

Now, since the top is not included for this figure, then;

Surface area of this rectangular box is;

S1 = 1.58 - (lw) = 1.58 - (0.4 × 0.6) = 1.34 m²

Surface area of a cylinder is;

S = 2πr² + 2πrh

r is radius and in this case = 0.4/2 = 0.2 m

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Since it is half cylinder, then we have;

S2 = 1.005/2

S2 = 0.5025 m²

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S_t = 1.34 + 0.5025

S_t = 1.8425 m²

This is the surface area of one mail box.

Thus, for 1863 mailboxes, total surface area is;

S = 1863 × 1.8425 = 3432.5775 m²

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2 years ago

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Explanation:

1) Data:

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2) Formula

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