Hi

Solve by factoring 

    |Note use of ^ (uppercase 6 on Your keyboard)

   w^2 - 26x + 169 = 16

  w^2 -26x + 153

  (w-9)(w-17) = 0

  (w-9)= 0    w = 9

  (w-17)= 0   w = 17



CHECKING our Answer***

   w-13 = ± 4

    w = 13 ± 4 

Hi

Using the vertex form of a parabola,  where(h,k) is the vertex

f(x) = 3x^2-18x+11    |completing the square to put into vertex form

f(x) = 3(x^2-6)+11

f(x) = 3[(x-3)^2 - 9]+11

f(x) = 3(x-3)^2 - 16   Vertex is Pt(3,-16), minimum at this Pt ( a>)

 Line of symmetry is x = 3

Hi

Recommend re-posting with an example so as we as Tutors can best assist You.

Hi

Let x, 6x, 2x represent Jim's, Sues's and Ben's quarters respectively

Question states***CENTS makes sense

   25*9x = 900

Solving for x

       x = 4, number of quarters Jim had.  Sue 24 and Ben 8



CHECKING our Answer***

    25*(4+24+8) = 25*36 = 900 or $9.00

Hi

49 coins. The number of quarters is two more than twice the number of dimes

Let x , (2x+2), [49 -(3x+2)] represent the number of dimes, quarters and nickels

Question states***CENTS makes sense

  10x + 25(2x+2) + 5[49-(3x+2)] = 330

Solving for x

  10x + 50x+ 50 + 245 -15x - 10 = 330

        45x = 45

          x = 1, the number of dimes, 4 Quarters and 44 Nickels



CHECKING our Answer***

   10*1 + 25*4 + 5*44 =  110 + 220 = 330 or $3.30

Hi

60 coins

Let x and (60-x)represent the dimes and nickels respectively

Question states***CENTS makes sense

   10x + 5(60-x) = 445

Solving for x

         5x = 145

          x = 29, number of dimes.  31 Nickels  (60-29)



CHECKING our Answer***

   10*29 + 5*31 = 290 + 155 = 445 or $4.45

Hi

the larger number is 6 less than four times the smaller number

Let x and ( 4x-6) represent the smaller and larger number respectively

Question states***

   x + (4x-6) = 54

Solving for x

      5x = 60

       x = 12   The two numbers are 12 and 42  (48-6)



CHECKING our Answer***

     12 + 42 = 54

Hi

Let x represent the number

Question states***

  2x = 3x-10

Solving for x

  10 = x

CHECKING our Answer***

  20 = 30 - 10

Hi

divide 224 into two parts

Let x and (224-x) represent the smaller and larger part respectively

Question states***

  

Solving for x

    2(224-x) = 4x + x^2   |Multiplying thru by 2x

    x^2 +6x -448 = 0 







  x = 18.3776    | Tossing out negative solution

  CHECKING our Answer***

   205.6224/18.3776 = 11.1888 = 2 + (1/2)18.3776 = 2 + 9.1888

   

Hi

The measure of the first angle is 6* less than 4 times the second angle

Let x and (4x-6° )represent the second and first angle 

  x + (4x-6°) = 90°

     5x = 96°

      x = 19.2°   The first angle is 70.8°  (4*19.2° - 6°)

Hi

two consecutive even integers

Let x and (x+2)represent the smaller and larger respectively

Question states***

  5x = 4(x+2)

Solving for x

  x = 8    The two consecutive even integers are 8,10



CHECKING our Answer***

  5*8 = 4*10 = 40

Hi

   

      x = ± 6 

Hi

Shelly is 5 years older than Michele



Let x and (x+5) represent Michele's and Shelly's ages NOW respectively

Question states*** 4 yrs ago...

 (x-4) + [(x-4) +5] = 65

Solving for x

     2x = 68

      x = 34, Michele's age now.  Shelly is 39



CHECKING our Answer***

       35 + 30 = 65

Hi

solving by substitution

  x = -3y

 3y + x = -1

 3y + (-3y) = -1

      0 ≠ -1   there is NO solution

Hi

difference between the scores is 12

Let x and (x-12) represent the two scores

Question states***

 [x + (x-12]/2 = 80

Solving for x

  [x + (x-12] = 160

       2x = 172

        x = 86  the two scores 74 and 86

CHECKING our Answer***

 (74 + 86)/2 = 160/2 = 80





     

Hi

Find the area of a trapezoid with a height of 4 m and bases of 13 m and 22 m.

 Area (trapezoid) = 

  A = (35m/2)*4 = 70 m^2

Hi

Note: The probability of x successes in n trials is: 

P = nCx*  where p and q are the probabilities of success and failure respectively. 

In this case p =.3 and q = .7

nCx = 

P(that the pet store gets exactly one blue parakeet) = 1-P(none) = 1 - (.7)^3

Hi

is having One pair of consecutive angles are congruent 

enough information to prove a quadrilateral is a parallelogram?

  NO, one of the following conditions must be shown to be true.

1) If a quadrilateral has one pair of sides that are both parallel and congruent, 

then the quadrilateral is a parallelogram. 

2) If the opposite sides of a quadrilateral are congruent, 

then then quadrilateral is a parallelogram. 

3) Opposites sides are parallel. 

4) 'Opposite angles are congruent' 

5) Diagonals bisect each other. 

Hi

 y = (-1/4)x  negative correlation

 y = (-1/4)*4 = -1

 y = (-1/4)x is a function representative of a line

 Slope of this line is = (-1/4) and is < 0 or negative

Hi

Start 25 22 20 21 20 15 17 22 19 16 19 18

Mean[S]= 18.5833

 SD[S] = 3.8720

End 25 23 23 22 22 20 19 20 18 18 21 23

mean[E] = 21.1667  

SD[E} = 2.2088



t =  

 t = -2.0075

P(t<-2.0075) = .02 (one-tailed)  .04 (two-tailed)

At the .05  level ofsignificance: .04 <.05 

there is reason to believe there is a dfference in the reading readiness of the

 pupils at the start and at the end of the school year, however at a lower

confidence interval there would not.

Hi

Recommend posting a particular example so as we as Tutors

can best be of assistance to You.

Hi

           true/false multiple choice  total

correctly      6           14           20

incorrectly    4            1            5

  total       10           15           25

 Of questons answered correctly (20)what % were T/F questions

          6/20 = .30  or 30%

Hi

a card is chosen at random from a pack of 52 playing cards.

P( king 'or' a red card)= P(king) + P(red) - P(both) = 4/52 + 26/52 - 2/52

Hi

What is the probability that three tails come up on a throw of three dimes?

P(tails) = 1/2

P(3 tails on 3 throws) = (1/2)^3 = 1/8

Hi

          No Help  Help  Total

Drug:       22     47    69

Placebo:    31     20    51

Total       53     67    120

What is the probability that: 

a) the participants perceived that their “medication”

helped if they received the drug?  47/69

b) the participants perceived that their “medication”

helped if they received the placebo? 20/51

c) the participants perceived that their “medication”

helped?  67/120

Hi

Note: The probability of x successes in n trials is: 

P = nCx*  where p and q are the probabilities of success and failure respectively. 

In this case p = .5 and q = .5 

nCx = 

Assume sales calls are independent and the employee is doing 2 sales calls

P(at least one of the two sales calls is successful) = 1-P(none)= 1 - (.5)^2

P(at least one of the two sales calls is successful) = .75

Hi

 Total of 52 cards of which 13 are spades

 P(no spade) = 1 - P(spade) = 1 - 13/52 = 39/52 = 3/4

Hi

 P(getting a 2 'or' 12 on two dice ) =  1/36 + 1/36 = 2/36 = 1/18

___1_2_3__4__5__6

1|_2_3_4__5__6__7

2|_3_4_5__6__7__8

3|_4_5_6__7__8__9

4|_5_6_7__8__9_10

5|_6_7_8__9_10_11

6|_7_8_9_10_11_12

Hi

 P(getting a 9) =  4/36 = 1/9

___1_2_3__4__5__6

1|_2_3_4__5__6__7

2|_3_4_5__6__7__8

3|_4_5_6__7__8__9

4|_5_6_7__8__9_10

5|_6_7_8__9_10_11

6|_7_8_9_10_11_12

Hi

 P(not getting a 9) = 1 -  P(9) = 1 - 4/36 = 32/36 = 8/9

___1_2_3__4__5__6

1|_2_3_4__5__6__7

2|_3_4_5__6__7__8

3|_4_5_6__7__8__9

4|_5_6_7__8__9_10

5|_6_7_8__9_10_11

6|_7_8_9_10_11_12

Hi

perimeters in the ratio of 5 to 3

floor that is 20 x 15: P =70

Let x represent the P of the rug

         |Cross Multiplying to solve for x

   5x = 210

    x = 42, the perimeter of the rug. (OR 21 the sum of its length and width)

The rug and the floor are similar rectangles

    |Cross Multiplying to solve for x

   20x = 15*(21-x)

   35x = 15*21

     x = 15*21/35

     x = 9   the rug is 12 x 9.  It's area is 108 

CHECKING our Answer***

 20/15 = 12/9 = 4/3