Hi

Line passing thru point(3,9) perpendicular to x = 3 (Blue) 

 y = 9 (green line)

 

Hi

*Note: 

mean of 50 and a std. deviation of 10

 z = -20/10 = -2  and z = 15/10 = 1.5

P(between 30 and 65) = P( -2 > z < 1.5) = .9332 - .0228 = .9104  

91.04% of them are between 30 and 65

Area under the graph between z = -2 and z = 1.5

 

Hi

IQ = 100 is the mean score used

P(lower than 100) = .5

 

Hi



 L = 9m and W =6m

P = 18m + 12m = 30m

 

Hi



If it is:

 [9(U^2)^5/2] then 9^(5/2)U^5 = 3^5*U^5 = 243U^5

 

Hi

 p/q = 5/2

     | Cross Multiplying 

  2p = 25

  p = 12.5

 

CHECKING our answer***

  |Cross Multiplying 

  25 = 25

          

 

Hi

Let x represent his speed on the freeway & his speed off freeway be(x-20mph)

 Question states*** reduced speed to (x-20)mph when off the freeway for last 3hrs

 3x + 3(x-20mph) = 324

     6x = 384

      x =64mph, freeway speed

 

Hi

 (9a^3-6b^2-8ab)

-(5a^3-9b^2+3ab)



  9a^3-6b^2-8ab

 -5a^3+9b^2-3ab



 4a^3 +3b^2-11ab

 

Hi

*Note: 

 z =(55-50)/10 = 5/10 = .5

 P( x <55) = .6915   69.15% of the scores

Percentage under the graph to the left of the green line: z=.5

 

Hi

 

Hi

y = x^2 (Green)

y = -(x+1)^2 -4 (Blue) Vextex(-1,-4)

 

Hi

2x-3y ≤ 6

(2/3)x-2 ≤ y

 y ≥ (2/3)x-2

I. graph y = (2/3)x-2

II. Shade area above/including the line

 

Hi



ln x =9

 e^9 = x

 8103.0839 = x    |Calculator makes short work of finding x

 

Hi

Recommend for 1-3 to multiply the factors using FOIL to verify those factors

F	First terms

O	Outside terms

I	Inside terms

L	Last terms

(1) 9-x^2                  (3-x)(3+x)

(2) 4x^2-36x+81            (2x-9)(2x-9)

(3) 4(y^2+4y+4)            4(y+2)(y+2)





(4)            

 

Hi, 

You did not state the exact nature of your Question:

h=-16t^2+96t+112   |Represents a parabola opening downward

h= -16(t-3)^2 + 144 + 160 |completing Square to find Vertex

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

 Vertex(3,304)  h reaches a maximum of 304 when t = 3

 

Hi

Let x represent the number

Question states***

 3n+4 = 2n  

   n = -4



CHECKING our answer***

 3*-4 + 4 = 2*-4 = -8

 

Hi

 e^x = 12

 ln12 = x    |calculator makes short work of this

 2.4849 = x

 

 

Hi

*Note: 

 z = -2000/3900 = -.5128   and z = 8000/3900 = 2.0513

 P(between 40,000 and 50,000) = P(-.5128 < z < 2.0513) = .6758

 

Hi

Add 

1*(8x^2-3y^2-5xy) +1*(-12x^2-6y^2+9xy)   |applying distributive Principle

 8x^2-3y^2-5xy -12x^2-6y^2+9xy           |combining Like terms

   -4x^2-9y^2+4xy

or -(4x^2-4xy+ 9y^2)

 

Hi

Multiply

(3x-4)^2 = (3x-4)(3x-4) = 9x^2 -24x +16

           F	First terms     9x^2

           O	Outside terms   -12x

           I	Inside terms    -12x

           L	Last terms       16

 

Hi

Let x represent speed of a car making the trip in 2hr

D  = 5hr*26mph = 130mi

  2hr*x = 130mi

   x = 65mph

 

Hi

Multiply 

(4a-5)(2a+3) 

 8a^2 +2a -15

F	First terms   8a^2

O	Outside terms 12a

I	Inside terms -10a

L	Last terms   -15

 

 

Hi

 |multiplying thru by x(x-1)(x+1)

   x^2 -(x+3)(x+1) = -3(x-1)

   x^2-x^2-4x-3 = -3x+3

             -6 = x

              

 

 

Hi

18 less boys than girls

Let x and (x+18) represent th enumber of boys and girls respctively

Question states***

  .40(x + (x+18) = x

  .40(2x + 18) = x

       7.2 = .2x

       x = 36, the number of boys.  Number of girls is 54.  Total of 90 students



CHECKING our answer***

     .40*90 = 36

    

        

 

Hi

q^2-49/ q^2-14q+49

 

Hi

Let x represent the number of women

Note: ratios Set Up Proportions!

 4/5 = 36/x     | Cross Multiplying 

  4x = 5*36

   x = 5*36/4 

   x = 45



CHECKING our Answer***

  4/5 = 36/45

 

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.

(x-1)^2/25 + (y+2)^2/16 = 1     | a = 5 and b = 4  C(1,-2)

 f = sqrt(25-16) = 3  (foci are located 3 each side of center along major axis)  

 |foci are (-2,-2) and (4,-2)

 

Hi

Let x represent the number

Question states***

  (1/2)n = (1/3)n + 25  |Multipying thru by 6 so as all denominators = 1

     3n = 2n + 150

      n = 150



CHECKING our Answer***

  75 = 50 + 25

 

Hi

Note: 30-60-90 triangle, sides have a ratio 1:sqrt(3):2  

Area[short leg = 8in] = (1/2)*8*8sqrt(3) = 32sqrt(3)

Area[short leg = 24in] = (1/2)*24*24sqrt(3) = 288sqrt(3)

ratio of the areas is 32/288 = 1/9  or 1:9

Why 1:9 because 1:3^2 is 1:9  

larger triangle: shortest leg of that is 3 times the smaller's shortest leg



What would be the ratio of the areas of two triangles 

with short legs 5 and 20 inches long?

  1:4^2 or 1:16

 

Hi

Volume(Sphere) = 4/3pir^3  and r = 

 4/3pi2^3  +  4/3pi3^3 +  4/3pi4^3  = 4/3*99pi = 



 r = 

 r =  = 4.63 mm (to nearest hundredth of a mm)