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Nice, Bosco !!!!

41409 / 9  =  4601

Factorization of 4601 = 43 * 107

sum = AB + CDE =   43 + 107  =   150

Rhombus ABCD has perimeter 148, and one of its diagonals has length 28. what is the area of ABCD?     

The Parallelogram Law states that the sum of the squares of     

the diagonals equals the sum of the squares of the four sides.     

All a rhombus is, is a parallelogram with the four sides equal.     

d₁² + d₂²  =  4 s²     

d₁² + 28²  = 4 • 37²     

          d₁²  =  (4 • 1369) – 784     

          d₁²  =  5476 – 784     

          d₁²  =  4692     

          d₁¹  =  sqrt(4692)     

          d₁¹  =  68.5     

_.     

If a and b are nonzero real number such that $|a| \neq |b|$,     

compute the value of the expression (a + b)(b - a)/(a^2 - b^2).     

   (a+b)(b–a)         (a+b)(b–a)                             (b–a)           –1(a–b)     

  –––––––––   =   –––––––––   cancel (a+b) =  ––––––   =   ––––––   cancel (a–b)  =  – 1     

     a² – b²            (a+b)(a–b)                              (a–b)               (a–b)     

_.     

A number is chosen at random from among all 9-digit numbers that use each of the digits 1 through 9 exactly once.     

What is the probability that this number is a multiple of 2?     

How many are a multiple of 2       4     

How many might be chosen         9     

Probability of getting one of      

the four even numbers                  4 / 9  =  44.44%     

_.     

A boy scout troop is selling Christmas trees at a local tree lot.     

In the morning, they sold 4 Douglas Fir trees and 15 Noble Fir trees, earning a total of $862.     

In the afternoon, they sold 4 Douglas Fir trees and 23 Noble Fir trees, earning a total of $1,262.     

How much does each type of tree cost?      

                                 4D + 23N  =  1,262     

                                 4D + 15N  =     862     

subtract                               8N  =     400     

                                              N  =       50   —>  price of 1 Noble Fir     

                                 4D + 23N  =  1,262     

                                 4D + (23)(50)  =  1,262     

                                 4D                   =  1,262 – 1,150     

                                 4D                   =  112     

                                   D                   =    28   —>  price of 1 Douglas Fir     

check answer     

                    Does       (4)(28) + (15)(50)  =  862 ?     

                                     112     +     750     =  862 ?     

                                                       862     =  862  True     

_.     

  How much it's 2.13604289e-9     

  it's 0.00000000213604289     

  In scientific notation, e –9 means move     

  the decimal point nine places to the left.     

_.     

Tell whether the triangle with each set of side lengths is a right triangle.     

(1.)  0.9, 1.2, 1.5       (2.) 3.1, 5.7, 7.1       (3.)1, 2.4, 2.6      

(1)  Does (0.9)² + (1.2)²  =  (1.5)² ?     

                 0.81  +  1.44   =   2.25  ?   Yes     

(2)  Does (3.1)² + (5.7)²  =  (7.1)²  ?     

                9.61  +  32.49  =  50.41  ?   No     

(3)  Does (1.0)² + (2.4)²  =  (2.6)²  ?     

                 1.00  +  5.76   =  6.76    ?   Yes     

_.     

Translate the difference of five squared and n into symbols.     

A. 5^2 ÷ n     

B. 5^2x n     

C. 5^2- n     

D. 5^2+ n     

The answer is C. 5² – n     

^.     

E = (10, 10sqrt 3)  F = (10sqrt 3, 10)

The area is compsed of a  square whose  area = EF^2  = [ 2(10 - 10sqrt3)]^2  =  400 (2 -sqrt 3) =

800 - 400sqrt 3

And  4  equal sectors  =  4 [ pi /6 * 20^2  - (1/2) (20^2) sqrt (3) /2)]  = 4 (200pi/3 - 100) =

(800/3)pi  - 400

Total area =  400 - 400sqrt 3 + (800/3)pi =    400 [ 1 - sqrt 3 + 2 pi / 3 ]

Here's what I get

1,2,3,4,5,5,5,5,5,5,5,5,6,7,8,9

Mean = 5

Median = 5

Mode = 5

Largest value  =  9

the question was: 58,511 / 21 = 2,786 R? the calculator's answer was: 2.786238095238052 I have no idea if that's correct or nonsense     

Did you notice that 58,511 / 21 is   2786.238095238052     

and what you saw was                   2.786238095238052     

which are the same thing, just with the decimal point in a different place.     

Did you see something on the right of the display that looked like E3 or similar?     

That's scientific notation.  The "E3" means move the decimal point three places to the right.     

_.     

All the sides of a triangle have integer length.  One of the sides has length $28$.  What is the smallest possible perimeter of the triangle?     

By the Triangle Inequality Theorem,     

the smallest sum of the other two sides has to be more than 28.  But the sum cannot be 29     

because then they wouldn't be integers.  So the smallest sum of the other sides must be 30.     

So that makes 28 + 30 = 58 the smallest possible perimeter of the triangle.     

_.     

What is the cubic yard of 27,000sq ft?     

Assuming you meant 27,000 cubic feet . . .     

There are 27 cubic feet in 1 cubic yard,     

so 1,000 cu yd comprises 27,000 cu ft.     

_.     

surface area =  2 (LW + LH + WH)  =  24    ⇒    LW + LH + WH  =  12

sum of  edge lengths = 4 [ L + W + H)  = 24   ⇒  L + W + H =   6

Using a little logic and assuming integer values for  each dimensinon, each edge measures 2

Proof

L + W + H = 6                 LW + LH + WH  =12

2 + 2 + 2  =  6                 2*2 + 2*2 + 2*2 =  12

The volume =  LWH =  2*2*2  =   8 cubic units

          P

     5           8

Q         M           R

     5.5       5.5

Law of Cosines  (twice)

[QP^2 - QR^2 - PR^2] /[-2* QR * PR] =  cos PRQ

[ 25 - 121 - 64] / [-2 * 11 *8 ] = cos PRQ  = 10/11

PM^2 = MR^2 + PR^2  - 2 (MR * PR) *cos (PRQ)

PM^2  = 30.25 + 64 - 2[5.5 * 8]* (10/11)

PM ^2  =14.25

PM =sqrt [14.25] ≈ 3.77

At 60 mph, it takes him 20 minutes to drive 20 miles

After 15 min , he has traveled 15 miles

The time it akes the taxi to arrive is irrelevant

So....he has 85  miles left to travel at 50mph

The total time in the taxi is    85 m / 50 m/h =  1.7 hrs 

2

11

Two primes

Either  the segment connecting these two points is an edge or it is the  diagonal of a square

If it  is an edge  the  area =  (12 + 98)^2 + (56 -34)^2  = 12584 units^2

If it is a diagonal the area =  (diagonal length) /sqrt (2) ) ^2   =  [ sqrt [ 12584] / sqrt 2]^2  = 6292 units^2

Sum of all possible area values =  12584 + 6292 = 18,876 units^2