Hi

In how many ways can the first 4 places be filled by 10 horses in a race

 (assuming there are no ties)

Order Important

  10P4 = 10!/6! = 5040 ways

 

Hi, Note use of ^ (uppercase 6)



(2r+1)(12r^2 +5r-3)=0   |completing the factoring

(2r+1)(4r +3)(3r -1) = 0

(2r+1) = 0

   r = -1/2

(4r +3)= 0

  r = -3/4

(3r -1)= 0

  r = 1/3 

 

Hi

shade the portion of the number line between the respective numbers...

putting an open circle on the numbers as they are not included.

3 < x < 6  and 9 < x < 12

 

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.

   y= -2x+7

    slope m = -2

y intercept is Pt(0,7)

 

Hi

In both cases shade the portion of the number line between the numbers.

Recommend putting an open circle on the numbers as they are not included.

3 < x < 9  





6 < x < 12

 

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.  

x-intercept=4, m=2

  y = 2x + b   |Pt(4,0) on the line: use ordered pair to solve for b

  0 = 8 + b

 -8 = b

  y = 2x - 8

 

Hi



   F	First terms (3x+1)

   O	Outside terms 2

   I	Inside terms  2

   L	Last terms    4

   

                 3x + 5 + 4

 

Hi

the pentagon building in washington D.C is shaped like a 'regular' pentagon

(all five sides of equal length)

If the length of one side of the pentagon is represented by n+2

  Perimeter = 5(n+2) = 5n+10

 

Hi, Previously listed

 Standard Form of an Equation of an Ellipse is 

where Pt(h,k) is the center and a and b  are the respective vertices distances from center.

endpoints of the major axis: (1,-5), (1,11)

   C(1,3)

foci are along the major axis: need to determine that major axis

foci are (1,1), (1,5)  F = 2  = 2

  

 

Hi

 Standard Form of an Equation of an Ellipse is 

where Pt(h,k) is the center and a and b  are the respective vertices distances from center.

endpoints of the major axis: (1,-5), (1,11)

   C(1,3)

foci are along the major axis: need to determine that major axis

foci are (1,1), (1,5)  F = 2  = 2

  

 

Hi

 Standard Form of an Equation of an Ellipse is 

where Pt(h,k) is the center and a and b  are the respective vertices distances from center.



 C(1,-6)  Yes!

  F = 

foci are along the major axis: need to determine that major axis

foci are (1,0) and (1,-12)

 

Hi

1M tickets are sold for a lottery in which a single prize will be awarded

a) If you purchase a ticket, determine your odds against winning.

   999,999:1

b) If you purchase 10 tickets, determine your odds against winning.

   P(10/1,000,000)= 1/100,000  99,999:1

 

Hi

how many cases can be filled with 9900 cans if each case holds 48 cans 

  9900/48 = 206.25 cases

 

Hi

contrator one(2x) is twice as likely to win as contractor 3 (x)

contractor two(3x) is three times as likely to win as contractor three(x)

what are the probabilities of winning for each 

P(contractor one) = 2/6 = 1/3

P(contractor two) = 3/6 = 1/2

P(contractor three) = 1/6



Note: 2/6 + 3/6 + 1/6 = 1

 

Hi

data set has a mean of 104 and a standard deviation of 5.

Find the z score for a data value of 107:  z = (107-104)/5 = 3/5

 

Hi

how many different 3-members teams can be selected from a group of 7 students? 

      7C3 = 35 different 3-member teams

 

Hi

A deli has 5 types of meat,2 types of cheese,and 3 types of bread.

different sandwiches,consisting of one type of meat,one type of cheese,

and one type of bread ,does the deli serve = 5*2*3 = 30 different sandwiches

 

Hi

how many different 4-letter arrangements can be formed 

using the letters of the word JUMP if each letter is used only once?

 4! = 24 different 4-letter arrangements can be formed 

 

Hi

Area(trapezoid) = 

trapezoid has an area of 120in^ and h = 8" 

  = 15" or  = 30"

  12" and 18" would be  possible lengths for the bases of the trapezoid

 

Hi

Solve the system of equations then classify the system.

y = -x-11

3x -2y = -18

3x -2(-x-11) = -18

3x + 2x+22 = -18

      5x = -40

       x = -8 and y = -3 (y = -(-8) - 11 = -3)

  Ordered pair(-8,-3) the solution for this Independent system

CHECKING our Answer***

3x -2y = -18

3*-8 + 2*3 = -18



A consistent system has at least one solution.

An inconsistent system has no solutions.

An independent system has exactly one solution.

A dependent system has infinitely many solutions.

 

Hi





log_8(x^6/x^(2/3)) = log_8(x^(16/3))     |Note: x^(18/3-2/3)= x^(16/3)



become familiar with the Properties

 

Hi

In reply: yes, that x was not shown. See below had it been.







log_8(x^6/x^(2/3)) = log_8(x^(16/3))     |Note: x^(18/3-2/3)= x^(16/3)



become familiar with the Properties

 

Hi





  5^2 = (x+3)/x

 25x = x+3

 24x = 3

   x = 1/8

 

Hi

Rectangular lake: L=75' and W=30'

two poles at opposite ends of a lake

applying the Pythagorean Theorem: answer to the nearest foot

D(between poles) =  = 81'

 

Hi

line j is perpendicular to line k

slope of line j = 5/2

slope of line k = -2/5

Note: slopes of perpendicular lines are negative reciprocals of one another

that is: 5/2*-2/5 = -1

 

Hi

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

y= .5x^2 -5  

1) Parabola 

2)Parabola with vertex Pt(0,-5)

3)  y-axis the line of symmetry

4) Parabola Opens Upward a = .5 >0

5) x-intercepts(when y = 0) are x =  ± 

 

Hi

Re: reply  4X^2+4Y^2=16 

 x^2 + y^2 = 4    | II.  circle: C(0,0) radius 2 

x^2/16+ y^2/4=1  Ellipse

Need to be familiar with various standard forms:

I.The standard form of a Parbola is  

II.Standard Form of an Equation of a Circle is 

III. Standard Form of an Equation of an Ellipse is 

IV.Standard Form of an Equation of an Hyperbola is 

  OR    

 

Hi, unable to do Venn diagrams here: Chart may be useful to guide You.

 sample of 125 people

      Total          one /both/neither

		

LLIME	  80      -42       38

COLA    68      -42       26

BOTH                      42 

Neither                   19

Total                    125        

c) How many liked either one or the other or both? 106

d) How many did not like either flavor?  19

 

Hi

two supplementary angles are in the ratio 7 to 2.

Let x and (180°-x)represent the smaller and larger of these supplementary angles.

     |Cross Multiplying 

    7x = 2(180°-x)

     9x = 360°

      x = 40°, the smaller angle

 

Hi

2sin^2(x) + 3sin(x) +1 = 0 

factoring

(2sinx +1)(sinx + 1) =0

(2sinx +1)= 0

   sinx = -1/2

(sinx + 1) =0

  sinx = -1

See following (cosx,sinx) summary for the corresponding solutions for the above

 

Hi

 11 candies (6 cherry, 3 orange, 2 lemon)

You reach in and take 2 pieces of candy at random.

 P (2 lemon) = 2/11*1/10 = 2/110 = 1/55