Bosco

Ayana has 2.35 in nickels and dimes. If she has 33 coins total, find the number of nickels and dimes.    

5N + 10D  =  235         (eq 1)    

  N +     D  =    33         multiply both sides of this by 5    

5N +   5D  =  165         (eq 2)    

subtract (eq 2) from (eq 1)     5N + 10D  =  235    

                                               5N +   5D  =  165    

                                                          5D  =    70    

                                                            D  =    14 dimes    

substitute into original        N + D    =  33    

                                           N + 14  =  33    

                                           N          =  33 – 14    

                                           N          =  19 nickels    

check answer  (5)(19) + (10)(14)  =?  235     

                              95  +  140        =    235 ... luciendo bien    

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I have 2 standard, 6-sided dice; one is brown, and the other is black. I roll them both. What is the probability that the sum of the numbers that I roll is less than 3?    

The only possible sum less than 3 is 2.    

That is, you have to roll a 1 on each die.    

The chance of rolling two 1's is (1 / 6) • (1 / 6)  =  1 / 36    

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How many ways can Amir, Bin, Charles, and Daria stand in a line if Amir and Bin want to stand next to each other?    

Consider Amir & Bin as a unit.  Then, how many ways can you arrange 3 items.    

The answer to that is 3 • 2 = 6    

Now have A & B swap places.  You can arrange this configuration 6 ways as well.    

Total of ways to arrange them, add both configurations:   6 + 6  =  12    

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The teacher asked Jenny's class to solve the equation 5x - 6 = 4x + 9. Jenny copied the coefficient of  on the left-hand side incorrectly and wrote down a different equation. Jenny correctly determined that her equation had no solutions. What was the coefficient of x on the left-hand side of Jenny's equation?    

4 would do it.  That would create 4x – 6 = 4x + 9    

working problem out                                   4x – 6  =  4x + 9    

next, subtract 4x from both sides and get        – 6  =  + 9      which cannot be    

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Two circles have the same center (Circles which have the same center are called concentric.) The larger circle has radius 10 and the smaller circle has radius 5. Determine the area of the ring between these two circles.    

π r² (larger)  –  π r² (smaller)  =  area of ring    

π • 10² – π • 5²  =  π • 100 – π • 25  =  π • 75    

π • 75 equals approx  235.6    

The area of the ring is the area of the larger circle minus the area of the smaller cirlle.    

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What is the maximum value of 4(x + 7)(2 + x) , over all real numbers x?    

4(x + 7)(2 + x) multiplies out to 4x² + 36x + 56    

The +4x² identifies the expression as a parabola opening upward.     

As such, there is no maximum value of x, it goes on forever.    

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Three candidates were running for office. One of them got half of the vote. Another got two fifths of the vote. What fraction did the third candidate get?    

1 / 2  =  5 / 10    

2 / 5  =  4 / 10     add those two fractions   

             9 / 10     is the total of the first two candidates    

So the third candidate got the other 1 / 10 of the votes    

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A bag contains 6 red marbles, 5 blue marbles and 8 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 10th of a percent, that all three marbles drawn will be green?    

The probability of the 1st marble being green is 8 / 19    

If the 1st marble was green, that leaves 7 in the bag    

The probability of the 2nd marble being green is 7 / 18    

If the 2nd marble was green, that leaves 6 in the bag    

The probability of the 3rd marble being green is 6 / 17    

The probability of all three occurring is (8 / 19) x (7 x 18) x (6 / 17)  =  336 / 5814    

336 / 5814  =  0.05779  which is 5.779%  which rounds to 5.8%    

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Real numbers x and y satisfy    

x + xy = 250y    

x - xy = -240y    

Enter all possible values of x, separated by commas.     

First thing to do is just add them together.    

  x + xy  =    250y    

  x – xy  =  –240y    

2x          =     10y          ——>>     x = 5y    

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Three red and two blue balls are placed in a hat. A ball is chosen at random and not replaced. A second ball is chosen at random. What is the probability that both balls chosen will be blue.    

The 1st ball probability is 2 / 5   

If the first ball is blue, there's only one blue ball in the hat, so ...    

The 2nd ball probability is 1 / 4    

Probability of both happening is (2 / 5) x (1 / 4)  =  2 / 20  =  1 / 10    

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