Hi, 

      f(x)=|x|   Note: f(x) ≥  0

 

Hi, 

Find the sum of the first four terms of the geometric sequence that starts with 3 and has r = 8.

   = 3(-4095/-7) = 1755



Find the sum of the following infinite geometric series, if it exists.

4 + 3 + 2.25 + 1.6875 +…

 =  =  = 16

 

Hi, 

Let x and y represnt the ten and unit digits of the original number.

Note: .625 = 5/8

When the digits of a two-digit number are reversed, the result is 

another two-digit number that is 62.5% smaller than the original number

62.5% smaller or 3/8 of original number

 10y + x = (3/8)(10x+y)

  80y + 8x = 30x + 3y

     77y = 22x

       7/2 = x/y

Original number is 



 27 = 3/8(72)

     

 

Hi, 

Note: 



***

  218 - 154 = 2d

         32 = d

   ***     154 = 2a[1] + 96

         29 = a[1]



   218 = 58 + 160 

 

Hi, 

R(x) = 55x - 2x^2 

C(x) = 21x + 98

P(x) = 55x - 2x^2 -(21x + 98)

P(x) = -2x^2 + 34x - 98

  x = 8.5 makes max profit

 

Hi, 



cyclindrical aquarium is designed with a base diameter of 5 feet and a height of 6 feet.

V =  = 118 ft^3, rounded to the nearest whole number

 

Hi, 

At 10 weeks old a puppy weighs 9 pounds. At 30 weeks old the puppy weighs 24 pounds

(30,24)

(10,9)   m = 

 y = (13/20)x + b

 9 = (13/20)10 + b

 5/2 = b

  when born (x=0) weighed 2.5 lbs



   

    At 42.3 wks, puppy will weigh 30lbs

 

Hi, Re:TY, 

The display below are the  possible outcomes rolling a pair of dice

Only one of the outcomes is >9 'and' is a 12, thus the 1/36

There are 6 possible outcomes >9 and therefore the 6/36

P(A|B) = P(A and B)/P(B)

P(12|>9) =  = 1/6



___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_

 

Hi, 

is -1 larger than -100

picture the numbers on a Number line: Yes, -1 is larger than-100

 

Hi, 

 x + x + x + x + 2x = 1

   6x = 1

    x = 1/6, fraction of the final grade determined by each quiz

Exam is 2(1/6) = 1/3

 1/6 + 1/6 + 1/6 + 1/6 + 1/3 = 4/6 + 1/3 = 1

 

Hi, 

Am assuning You meant 12 'ounces'

Letting x represent the maximum number of tablespoons of bread flour in 12 ounces:

     |Cross Multiplying to solve

   x = 48 TBSP, the maximum number of tablespoons of bread flour in 12 ounces

 

Hi, 

(4,6)

(2,3)   m = 3/2 

positve correlation

scatter plot of this data shows a linear regression: y = (3/2)x

 

Hi, 

(y-3)^2/(4) - (x+1)^2/(9) = 1

 y = 3 +(2)sqrt(1+(x+1)^2/9)

 y = 3 -(2)sqrt(1+(x+1)^2/9)

 

Hi, 





         72 = 9d

          8 = d

     

     



OR



   

 

Hi, 

equation of the line passing through (4,7) and parallel to 6x-7y=10 OR y = (6/7)x -10/7

y = (6/7)x + b

7 = (6/7)4 + b    ||Using pt(4,7) to solve for b

25/7 = b

y = (6/7)x + 25/7  or in Standard form:  6x-7y = -25

 

Hi, 

Note:  

 

 

Hi,

My recommendation would be to Plot 'easy Pts'...using for ex: x = 0,1,2 

and sketch the parabola

 

Hi, 

 

  Yes!!!



 Parabola opening right, Vertex (2,-1)

 

Hi, 

express bus is traveling 10 mph faster than the local bus

Let x and (x+10) represent speeds of local and express respectively

Question states*** D = rt

  3x + 3(x+10) = 300mi

      6x = 270

       x = 45mph, speed of local train.  Express is 55mph

 

Hi, 

 width of the rectangle is 4 centimeters less than its length

Let x and (x-4) represent length and width respectively

Question states***

x(x-4)= 96 in^2

 x^2 - 4x - 96 = 0

 (x-12)(x+8) = 0

    x = 12, throwing out negative solution for unit measure

 Length is 12cm and width is 8cm

   12in*8in = 96cm^2

 

Hi, 

 

  

  

Parabola opening right Vertex(2,-1)

 

Hi, 

Jeff takes 5hrs longer to build a fence than it takes Bill.

Letting x and (x+5) represent Bill's and Jeff's times respectively



PER HOUR Key:

    Yes!!

Multiplying thru with 6x(x+5) so as all denominators= 1

 6x + 6(x+5) = x(x+5)

   12x +30= x^2 + 5x

    x^2 - 7x - 30

factoring:

(x-10)(x+3)= 0

   x = 10 , x = -3  Throwing out x = -3

   x = 10hr is Bill's time and Jeff's is 15hr

  1/10 +1/15 = 25/150 = 1/6

 

Hi,

 total amount for an investment of $100 invested at 3.5% for 8 years and compounded continuously? 

 A =  = $132.31

 

Hi, 

How many different 10 letters word (real or imaginary) can be formed from the following letters TPIOOYPUTM

TPIOOYPUTM has 2-Ts,2-Ps, 2-Os

 10!/(2!2!2!) = 453,600 ways

 

Hi, 

hyperbola that has a center at (10,4), a focus at (15,4), and a vertex at (13,4)

Opens right and left,Distance of the vertices from center = 3  

 Distance of the foci from center = 5 = , b = 4

 

Hi, 

In General 

A = Accumulated Amount = 250,000

P[n]= Savings Amount per period

r= annual rate = .08

n= periods per year = 12

t= years = 10 





, the monthly savings amount necessary = $1366.52

 

Hi, 

8 boys and 12 girls can finish the work in 10 days, while 6 boys and 8 girls can finish it in 14 days

Note: work PER Day KEY

Let x and y represent work done per day by boy and girl respectively:

 8x + 12y = 1/10     

 6x  + 8y = 1/14    |multiplying thru by -3/2 to  eliminate the y variable



 8x + 12y = 1/10     

-9x  -12y = -3/28    |result of multiplying thru by -3/2 to  eliminate the y variable

     x = 1/140  and y = 1/280, work PER Day by each

time taken by 1 boy alonedays and 1 girl alonedays to finish the work.

 

Hi, 

16x^2 - 25y^2=400



Note:Standard Form of an Equation of an Hyperbola is   opening right or left 

where Pt(h,k) is a center  with vertices 'a' units right and left of center. V are (±5,0)

 Asymptotes passing thru the center with slope = ± b/a , y = ±4/5x

foci being ± sqrt(a^2 + b^2) from center  along axis of symmetry y = b

 foci are (±,0)

 

Hi, Hi re TY, 

1) Note: no mention of the  who smoked and used alcohol...Note: says only  smokers total

2) 6 with all habits listed.

100 people surveyed 34 smoked, 61 cursed, 50 drank alcohol, 25 smoked and cursed, 

30 cursed and drank alcohol, and 6 had all 3 habits.

a) How many had none of these habits: 

 b) Only had the smoking habit  

 

Hi, 

Find the slope of the line through each pair of points:

 



(-5,4) 

(-1,11)   m = -7/-4 = 7/4

 y = (7/4)x + b    ||Using Pt(-1,11) to solve for b

 11 = (7/4)(-1) + b 

51/4 =  b 

 0 = b

 y = (7/4)x + 51/4    OR in Standard form:  7x -4y = 51

 

Hi, 

Find the slope of the line through each pair of points:

 



(-2,-8) 

 (1,4) m = -12/-3 = 4

 y = 4x + b    ||Using Pt(1,4) to solve for b

 4 = 4*1 + b 

 0 = b

 y = 4x    OR in Standard form:  4x -y = 0