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The number of squares crossed by an ant crawling diagonally across an

l*w rectangle formula is

l+w−gcd(l,w)

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The rectangle dimensions are

4*4 so l=4, w=4

4+4-gcd(4,4)=8-4=4

f(x)=12(x+2)/(x+1) grafic

At which integer-x is f(x) a integer?

There, f(x)=b.

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No, that's not helpful. It would be helpful if you explained your solution to us.

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factors of 1,000,000,000,000     

The prime factors of a trillion are 2 and 5.     

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In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color, and at lest three of the squares are red.  How many ways are there to color the five squares?     

In order not to have two reds next to each other,     

the three reds must occupy squares 1, 3, and 5.     

That way, there's another color in between them.     

That leaves squares 2 and 4 to fill, and two colors     

to do it with. There are only four ways.    

Blue Blue     Yellow Yellow     Blue Yellow     Yellow Blue      

So, the answer is four ways.     

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The solution was actually -2.

How many ways can you arrange 2 boys and 3 girls in a line, if the 2 boys must stand next to each other?     

Strap the boys together and consider the pair as a single unit.  With the 3 girs, there are 4 units.     

The possible arrangements of 4 units is ₄P₄  =  24 ... but wait, we're not through yet.     

Now, have the two boys swap places and there are another 24 arrangements.   

So, altogether, there are 48 possible arrangements.     

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      what is 9% of 25000       

      0.09 x 25,000  =  2250     

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A spherical tank has a radius of 6 yards. It is filled with a liquid that costs $7.15 per cubic yard. What is the total value of the liquid in the tank? Use 3.14 for π . Enter your answer in the box to the nearest cent.     

     V_sphere  =  (⁴/₃) π r³     

     V  =  (⁴/₃) • 3.14 • (6 yd)³     

     V  =  (⁴/₃) • 3.14 • 216 yd³     

     V  =  904.32 yd³     

     Cost  =  (904.32 cuyd) •  (7.15 ^dollars/_cuyd)     

     Cost  =  6465.89 dollars     

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A cylinder has a height of 13 feet and a radius of 8 feet. What is its volume? Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.     

          V_cyl  =  π r² h    where r is the radius of the circular base and h is the height     

          V  =  (3.14)(8²)(13)     

          V  =  3.14 • 64 • 13     

          V  =  2612.48 ft³     

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A standard six-sided die is rolled twice. What is the probability that the product of the rolls is 3 or 12?     

How to get   3  .......     1, 3    3, 1                           2  ways     

How to get 12  .......     2, 6    6, 2    3, 4    4, 3       4  ways     

                                                                 total        6  ways     

Number of total possible combinations  6 x 6  =   36  ways     

                              So the probability is  6 / 36  =  1 / 6     

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Find the number of ordered pairs (a,b).

\(\dfrac{{\color{blue}a} + 2}{a + 1} = \dfrac{\color{blue}b}{12}\\ \)

\(\dfrac{{\color{blue}1}+2}{1+1}=\dfrac{\color{blue}18}{12}\\ \dfrac{{\color{blue}3}+2}{3+1}=\dfrac{\color{blue}15}{12}\\ \dfrac{{\color{blue}5}+2}{5+1}=\dfrac{\color{blue}14}{12}\\ \)

\( \dfrac{{\color{blue}11}+2}{11+1}=\dfrac{\color{blue}13}{12}\)

\(\color{blue}(a,b)\in\{(1,18)\ ; (3,15)\ ; (5,14)\ ; (11,13)\}\)

The number of solutions is 4.

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One ordered pair (a,b) satisfies the two equations ab^4 = 384 and ab^5 = 4608. What is the value of a in this ordered pair?     

                                                        ab⁵  =  4608     (equation 1)     

                                                        ab⁴  =    384     (equation 2)     

Divide both sides of eq 1 by  

both sides of eq 2 respectively            b  =  12     

sub 12 into equation 2                a • 12⁴  =  384     

                                                  20736a  =  384     

                                                            a  =  384 / 20736     

                                                            a  =  1 / 54     

check answer     

sub values into eq 1                        ab⁵  =    4608     

                                      (1/54)(248832)  =?  4608     

                                                      4608  =    4608     

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Find the coefficient of y^4 in the expansion of (2y - 7)^5.     

   32y⁵ – 560y⁴ + 3920y³ – 13720y² + 24010y – 16807     

             – 560     

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Louise earned $529 dollars in a two-week period.  She had $85 deducted for health insurance, but got a $300 bonus.  Not considering any other deductions, how much did she receive?     

                    $529  –  $85  +  $300  =  $744     

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A list of ten distinct, positive integers has a median of 5.5.  What is the smallest possible average of the ten positive integers?  Explain your ansswer in complete sentences.     

For the median to be 5.5, the list can have 5 and 6 in the middle.     

It could have 3 and 8 there, but then it wouldn't be the smallest.     

The list would look like this:                            5  6                             

You have to fill in the blanks with the smallest integers possible, and     

every integer has to be positive and every integer has to be different.     

This is the smallest possible:    1   2   3   4   5   6   7   8   9   10     

The average of that list is:    55 / 10  =  5.5     

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Andre and elena are each saving money. Andre starts with $100 in his savings account and adds $5 per week. Elena starts with $10 in her savings account and adds $20 each week? After 4 weeks, who has more money in their savings account?     

End of Which Week     Andre's Balance     Elena's Balance     

end of 1st week                   105                             30     

end of 2nd week                  110                             50     

end of 3rd week                   115                             70     

end of 4th week                   120                             90     

The Andre account has more money than the Elena account.     

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