Hi,

the sum of two  integers and is 4 times the smaller. 

Question states***

 x + y = 4x   Or 

Question also states***

the positive difference of their squares is 8 times the larger

 y^2 - x^2 = 8y

 (3x)^2 - x^2 = 8(3x)

  9x^2 - x^2 = 24x

  8x^2 - 24x = 0

 8x(x - 3) = 0

 8x = 0 ,  x = 0   Toss out this solution (0 is not a positive integer)

0r 

(x - 3) = 0 , x = 3  and  y = 9

and...  

Product of the two integers is 27

 

 

Hi,

if four times the smaller of two consecutive integers  and 

is subtracted from six times the larger, the result is 156. 

Question states***

 6(x+1)-4x = 156    || Solve for x

 

Hi,

If the largest of three consecutive even integers 

   10

  12

  14

is multiplied by three, the product is  2 less than twice the sum of the first two integers

Question states***

 3(x+4) = 2[x +(x+2)] - 2

 3x + 12 = 2(2x+2) - 2

 3x + 12 = 4x + 4 - 2

      10 = x

and...

 

Hi,

Three consecutive odd integers

 





are such that the sum of the first and the third is  70. 

Question states***

 x + (x+4) = 70    ||Solve for x and name ALL Three consecutive odd integers above

 

Hi,



   s = (2x-3y)

 

Hi,

 

Hi,

find three consecutive numbers

 





such that the sum of the first and three times the second is forty-four less than five times the third

Question states***

 x + 3(x+1) = 5(x+2) - 45    ||Solve for x and list ALL three of the consecutive numbers above

 

Hi,

the sum of twice a number and 8 

is equal to the sum of the number and 9

Question states***

 2x + 8 = x + 9

    x = 1

and...

 

Hi,

if marvin adds his current age to the age that he will be next year on this date, 

the sum is 79 years

Question states***

 x + (x+1) = 79

    2x = 78

     x = 39

How old will marvin be 11 years from today? 

 

Hi,

 

Hi,

27,000 people at a ball game. 

How many people paid $14.00 for reserved seats and 

how many people paid $6.00 for general admission? 

Question states***The day's receipts were $210,000.

 $14x + $6(27000-x) = $210000

 

Hi,

2x - 3y = 6 

if the x is: 0  ⇒  y = -2   (x,y) Ordered Pair Pt(0,-2) on this Line

if the y is: 0  ⇒  x = 3      (x,y) Ordered Pair Pt(3,0) on this Line

Plotting points,connecting them and graphing Line 2x - 3y = 6 

 

Hi,

Two angles form a linear pair. (their sum = 180° )

THe measure of one angle is 5 times bigger of the other 

  x + 5x = 180°

    6x = 180°

     x = 30°

 

Hi,

A side of a square is 10 meters longer than the side of an equilateral triangle. 

If the perimeter of the triangle is 9 meters, find the perimeter of the square.

Question states***perimeter of the triangle is 9 meters

  3x = 9m

   x = 3m  

s = 3m + 10m = 13m

 

Hi,

Keisha is 3 years older than Ana. Jermain is twice as old as Keisha's age . 

Monica is 5 years older than Jermain.

Keisha's age: x

Ana's age: x - 3

Jermain's age: 2x

Monica's age: 2x+ 5

Question states*** sum of the ages is 56 

 x + (x-3) + 2x + (2x+5) = 56 || Solve for x

                  6x = 54

                   x = 9 yr, Keisha's age

and...

 

 

 

Hi,

"I have to graph this but cannot make a graph."

1. need two points to connect to draw a graph of a Line...

3x-y=0   This line has (x,y) ordered pairs: (0,0)when x = 0     and (1,3)when x= 1

2x-y=-1  This line has (x,y) ordered pairs: (0,1)when x = 0     and (-1/2,0)when y =0

2 . Plotting these (x,y) ordered pairs and connecting with their respective Lines

3.  We find the lines intersect at (x,y) ordered pair (1,3)

4. Ordered Pair (1,3) is the solution for this system of EQs

 

 

Hi,

Yes! y = 5 ia an horizontal line

Line perpendicular to that would need to be a vertical Line.

Vertical line passing thru (-2,2) would be x = -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, Yes!  p = .20 & q = .80

P(15 correct out of 20 questions)= 20C15 (.20)^15 (.80)^5 = 15,504(.20)^15 (.80)^5= .00000017

Probability so...small, UNLIKELY

 

Hi,

300 patients found that of 100 alcoholic patients, 87 had elevated cholesterol levels,  

and of 200 nonalcoholic patients, 43 had elevated cholesterol levels. 

P(A & elevated cholesterol levels) = 

P(not A) = 2/3 = %

P(not A & non-elevated cholestrol levels) = 

 

Hi,



width of the soccer field is the reciprocal of the length

 P = 2L + 2W = 20/3

0r    L + W = 10/3

Question states***

      |Multiplying thru by 3x so as all denominators = 1

    3x^2 + 3 = 10x

   3x^2 - 10x + 3 = 0

factoring

  (3x - 1)(x - 3) = 0

  x = 1/3 m  0r  x = 3m

Dimensions are:  1/3 m  by 3m

 

Hi,

Exterior Angles of this hexagon: (Note:  Their Sum is 360° )

(6x-1)

(10x+2)

(8x+2) 

(9x-3)

(5x+4)

(12x+3)

  |Solve for x

then find each of the six exterior angles above

 

Hi

A swimming pool can be filled in 24 hours by 5 equal pumps.

how many such pumps are required to fill the pool in 6 hours?



   

        20 = x, number of pumps needed to fill the pool in 6hrs

 

Hi,

 4x^3-104x^2+640x=1152

 x^3-26x^2+160x - 288 = 0    | x = 4, one solution

Using synthetic Divsion

4	1	-26	160	-288

 	 	  4	-88	 288

 	1	 -22	 72	  0

Results in:

        x^2 - 22 + 72 = 0

factoring

       (x-4)(x-18)= 0

Roots:  4,4,18

 

Hi,

Elimination:

4x+5y=13

4x+3y=9   | Subtracting 2nd from the 1st EQ to eliminate x

   2y = 4

    y = 2  and x = 3/4   



substitution

 4x+5y=13   0r  4x = -5y +13

 4x+3y=9    0r  4x = -3y + 9

 -3y +9 = -5y + 13

  2y = 4

   y = 2   and x = 3/4

 

Hi,

How many different 20 persons committee can be formed each containing at least 2 professors and atleast 3 associate professors 

from a set of 10 professors and 42 associate professors.  professors in all

   

 

 

Hi,

   |Multiplying thru by 12 so as all denominators = 1

   8y - 9 = 5

 

Hi,

Using the standard slope-intercept form for an equation of a line y = mx + b

  where m is the slope and b the y-intercept.

1) y-intercept of -2.1,x-intercept of 3.5   ||Points:  (0,-2.1) and (3.5,0)

  y = mx + (-2.1)

  y = mx - 2.1

finding the slope m

(0,-2.1) and 

(3.5,0) m = -2.1/-3.5 = .6

  y = .6x - 2.1



2)through(1.2,5.1),

x-intercept of 3.7  Pt(3.7,0)

(3.7,0)

(1.2,5.1)  m = -5.1/2.5 = - 2.04

 y = -2.04x + b   || Using Pt(3.7,0) to solve for b

 0 = 

7.548 = b

  y = -2.04x + 7.548

 

Hi,

A = 3y

B = 2A   

B = 

Angles supplementary: 

  A + B =  180°

 3y + 6y = 180°

     9y = 180°

      y = 20°

 

Hi,

RE TY, Yes, NORMSDIST(-2.8) is .00256  and NORMSDIST(1.4) is .91924

 .91924

-.00256  is  .91668  Or = .9167   Or 91.67%

(Ans Correct, as listed, rounded to 4 decimal points, calculation  Using 5)

As to: .9192 - .0026 (Using 4 decimal points for calculation...)= 91.66% 



t = (190-200)/(25/√49)= -10/3.57= -2.80 Yes

t =  (205-200)/(25//√49)= 5/3.57= 1.4   Yes

P(180< x    <205) = P( -2.80  ≤ t  ≤ 1.4) = .91924 - .00256 = .9167

 

Hi,

/

 

Hi,