Bosco

Find the coefficient of y^4 in the expansion of (2y - 5 + y^2)^6.     

The coefficient of y⁴ is –14625     

_.     

Amaretta's birthday is July 27, and her brother Enzo's birthday is September 3. Every year, Amaretta and Enzo celebrate by eating cake every day from Amaretta's birthday through Enzo's birthday (including both birthdays). If they did this for the first time in 2003, how many cake-eating days will they have observed by the end of 2020?     

39 ^days/_year  x  28 years  =  1,092 days to eat cake     

July 27 through September 3 inclusive is   39 days     

2003 through 2020 inclusive is                   28 years     

_.     

Lana collects 20-cent and 50-cent coins. The total value of her coins is currently $9.70. If Lana has 4 more 50-cent coins than 20-cent coins, how many of each type does she have?     

Let F stand for the number of 50¢ coins     

Let T stand for the number of 20¢ coins     

50F + 20T  =  970         (equation 1)     

F  =  T + 4                     (equation 2)     

substitute (T+4) in place of F in eq 1     

50(T+4) + 20T  =  970     

50T + 200 + 20T  =  970     

                    70T  =  770     

                        T  =  11     

                        F  =  T + 4     

                        F  =  15     

check answer     

50F + 20T  =  970     

(50)(15) + (20)(11)  =?  970     

   750     +     220    =?  970     

                     970    =    970     true     

_.     

Laura got 33/35 points on an exam. Mathew got 97% correct on the same exam. What percentage lower or higher, did Mathew get correct on their exam than Laura? Round your answer to the nearest hundredth.     

Matthew got                               97.000%     

Laura got 33/35 which equals   94.286%     

Matthew's score was                   2.714%  higher, rounds to  2.71%     

_.     

¿how can I divide 10 by 3 without get decimal?     

A couple of ways to avoid a decimal.     

Use a fraction:       ¹⁰/₃  =   3 ¹/₃     

Use a remainder:   ¹⁰/₃  =  3 R 1     

_.     

Consider two positive even integers less than 19 (not necessarily distinct). When the sum of these two numbers is added to their product, how many different possible values may result?     

Between 1 to 19 are nine even integers, namely 2, 4, 6, 8, 10, 12, 14, 16, 18.     

We will use two of those integers.  How many pairs of integers could there be.     

It's ₉C₂ = 36.  But wait, the combination process calculates different numbers.     

We have to add another 9, to take doubles into account, for example 4 and 4.     

So, adding 36 and 9, we get 45 possibilities, if my reasoning is correct.     

_.     

-7x^2-23x+10=0     

          –7x² – 23x + 10 = 0     

            7x² + 23x – 10 = 0     

             –23 + sqrt(23² –  (4 • 7 • –10))     

     x  =  ––––––––––––––––––––––––     

                             2 • 7     

             –23 + sqrt(809)     

     x  =  –––––––––––––     

                      14     

             –23 + 28.44293     

     x  =  –––––––––––––     

                      14     

     x = +0.38878    

     x = –3.67449     

_.     

The marks family has two orchards. The orchard by the river is 6 acres in size. The orchard on the hill is 9 acres in size . If 2/3 of the river orchard has apple trees &1/3 of the hill orchard has apple trees, how many total acres are plated with apple trees?     

2/3 of 6 acres  =  4 acres     

1/3 of 9 acres  =  3 acres     

total                 =  7 acres     

_.     

Alex spent $300 of his money on an oven and 2/5 of the remainder on a cupboard. He had 1/2 of his money left in the end.  

(a) What fraction of the Alex's money was spent on the cupboard?     

(b) How much money did Alex have at first?      

     Call "x" the original amount.     2/5 = 0.40  1/2 = 0.50     

     (x – 300) – (0.40)(x – 300)  =  (0.50)(x)     If he had half his money left, that means     

                                                                        the amount he spent was the other half.     

     x – 300 – 0.40x  + 120  =  0.50x     

     x – 0.40x – 0.50x  =  300 – 120     

     0.10x  =  180     

            x  =  1800     

     check answer     

     Alex spent 300, so 1800 – 300  =  1500       He spent 300     

     Alex spent (2/5)(1500)               =    600       He spent 600     

                                                                 total spent was 900     

     Is 900 half of 1800?  True     

_.     

A kite’s string is 155 meters long and is flying 90 meters in the air. What is the measure of the angle that kite string makes with the ground?     

sine = opposite over hypotenuse     

sine(α)  =  90 / 155     

sine(α)  =  0.5806     

arcsin(0.5806)  =  35.5^o     

_.     

     Area  =  Circumference x Height     

     Area  =  π d h     

     Area  =  3.1416 • 8 in • 7.5 in     

     Area  =  188.496 in²     

_.     

     [ (–3) x (5) ]  + (15)  +  (–9)  =  –9     

     (–3)  +  (5)  +  (15)  +  (–9)  =  +8     

     [ (–3) x (5) ]  +  (15)  – (–9)  =  +9     

     (5)  +  (15)  –  [ (–3) x (–9) ]  =  –7     

_.     

what is 30% of 45     

     30% of 45  =  0.30 • 45  =  13.5     

_.     

8y-2(y+4) simplify     

     8y – 2(y + 4)     

     8y – 2y – 8     

     6y – 8     

_.