Mathematics, 10.04.2020 21:14, burners

How many anagrams are there to the word FRIDAY? In how many of these do the letters 'DAY' appear consecutively? (Disregard whether the word actually exists in the dictionary or can even be pronounced)

Answers: 3

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Answers

There are 720 total different combinations, and 24 of those will have the letters DAY consecutively within all those combinations.

Explanation:

FRIDAY is a six letter word.

To form all combinations of letters, we would have six choices of letters to fill the first spot. Whatever letter you choose for the first spot, you then have five choices of letters to fill the second spot. Four choices of letters to fill the third spot. And so on.

So, the total number of different combinations of the six letters would be 6!

6! = 6 X 5 X 4 X 3 X 2 X 1

= 720

DAY could appear consecutively starting in 4 different spots: the 1st, 2nd, 3rd, and 4th spots of all combinations. DAY will appear consecutively 6 times in each of those 4 starting spots.

6 X 4 = 24.

So, there are 720 total different combinations, and 24 of those will have the letters DAY consecutively within all those combinations.

answered: Guest

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

answered: Guest

Answerthe simplified expression is $2x + 28$ explanationthe given expression is, $2(10) + 2(x - - 4)$ let us deal with the bracket first.the two negatives in the parenthesis will become positive.the expression now becomes, $2(10) + 2(x + 4)$ we now expand the parenthesis to get, $20 + 2x + 8$ we group like terms to obtain, $2x + 8 + 20$ this simplifies to, $2x + 28$

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How many anagrams are there to the word FRIDAY? In how many of these do the letters 'DAY' appear con...