Hi

log5 m=1/3 log5 125







  5^0 = m/125^(1/3)=

   1 = 

= m

     5 = m

 

Hi

In how many ways can a group of 7 students be selected from 8 students

 8C7 = 8 ways

 

Hi

a certain mathematics test consist of 10 "true" and "false" questions

 2^10 or 1024 is the number of ways the test can be answered

 

Hi

T = 420 - 350 (3.2)^-.1m  |where m represents the number of minutes after the oven is turned on 

and T represents the temperature of the oven in degrees Fahrenheit.

T = 420 - 350 (3.2)^-.1m 

 (T-420)/-350 = 3.2^.1m

 log[(T-420)/-350]/log(3.2) = -.1m

 T = 320

 log[(-100)/-350]/log(3.2) = -.1m



 log .2857/log(3.2) = -.544/.5 = -.1m

                   -1.08 = -.1m

                    m = 10.8 min, time it takes to reach a temperature of 320F



 

 

Hi



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

f(x) = -x^2 + 6x   |Completing Square to find the Vertex

y = -[(x-3)^2 - 9]

y = -(x-3)^2 + 9      |represents parabola opening downward, a<0 

vertex Pt(3,9) f(3) = 9 is a maximum point

Domain:  and Range: {y|y ≤ 9}

 

Hi

solve the system by graphing

8x-5y=20  (0,-4) and (20/8,0)

5y-8x=-20 ( 0,-4) and (20/8,0) 

Graphing points and connecting with a line: 

These are the same lines, infinite solutions.  System is Dependent.

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

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

vertex (0, 18) 

 y = ax^2 + 18      |passing through (-3, 0) 

 0 = a*9 + 18

-18 = 9a

-2 = a

 y = -2x^2 + 18



Write the quadratic function in the vertex form. 

y = -3x^2 - 30x - 71    |Completing the square to do so

y = -3[x^2 +10x] - 71 

y = -3[(x+5)^2 -25] - 71

y = -3(x+5)^2 + 75 - 71

y = -3(x+5)^2 + 4

 

 

Hi

If I am understanding Your Question properly

    A = lnP/-.000121

 -.000121A = lnP

   e^( -.000121A) = P

 

Hi

    g(x) =   

and f(x) = 2x + 1 

 f(g(x)) = 2() + 1   |substituting g(x) for x

 f(g(x)) = x - 1 + 1

 f(g(x)) = x 

 

Hi

If I am understanding Your Question properly:

  

     | 3 - 3/2 = 3/2

          3x+ 4 = 9/4

          3x = 9/4 - 16/4

          3x = -7/4

           x = -7/12

CHECKING our Answer***

  

  



   

 

Hi, Note use of ^ (uppercase 6)

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

f(x) = 0.0037x^2 – 0.41x +36.23  |graphically a parabola opening upward a>0

models the average age at which Kentucky men were first married x years 'after 1900'

f(x) = 0.0037x^2 – 0.41x +36.23  |Completing square to find the vertex (min point)

f(x) = .0037[(x - 55.4)^2 - 3069.7589] + 36.23

f(x) = .0037(x - 55.4)^2 - 11.36 + 36.23

f(x) = .0037(x - )^2 + 

The year, average age at a minimum: 1900+55 = 1955  

The average age at first marriage: 24.9





 

 

Hi

The number of fruit flies F(x) in a farming area depends on the spring rainfall x: 

 f(x) = -x^2+15x  |graphically a parabola opening downward a< 0

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

 f(x) = -(x -7.5)^2 + 56.25     | completing the square to find the vertex

 Vertex is Pt(7.5, 56.25)

     7.5" rainfall produces the maximum number of fruit flies 

 

Hi



In 1920 the record for a certain race was 45.1 sec

In, 1980, it was 4303 sec.

 (1980,4303)

 (1920, 45.1)   m = 4257.9 / 60 = 70.965

 R(t) = 70.965t + 45.1 where t= the number of years since 1920.

 

Hi

jacobs sixth bday he got a $3,000 cd it earns 5% interest,compounded quarterly.

 If the CD matures on his 16th bday what amount will be available then

    A=P(1+r/n)^nt

    A=$3000(1+.05/4)^4*10

    A=$3000(1.0125)^40 = $4930.86

 

Hi

A light bulb has an average life of 500 hours with a SD = 100 hours.

amusement park buys and installs 10,000 of such bulbs.

 Number lasting <500hr: 50% of them OR 5,000

 Number lasting more than 440 hours = .7557*10,000 = 7,557 

*Note: 

   z = (440-500)/100 = -.6

 P(z > -.6) = 1 -  NORMSDIST(-.6)= 1 - .2743 = .7557  OR 75.57%

 

Hi

*Note: 

   z = (17.50-13.40)/2.10 = 1.9524

 P(z > 1.9524) = 1 -  NORMSDIST(1.9524)= 1 - .9746 = .0254

 

Hi

*Note: 

   z = (9.7-15)/2.5 = -2.12

 P(z < -2.12) = NORMSDIST(-2.12)= .017

 

Hi

*Note: 

   z = (80.24-83)/6 = -.46    and z =(96.26-83)/6 = 2.21

 P(.46 < z < 2.21) = NORMSDIST(2.21)-NORMSDIST(-0.46) = .9864 - .3228 = .6637

 

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(defective) = 5/80 =.0625    and q = .9375

  nCx = 

randomly take three light bulbs from the box 

P(none are defective) = (.9375)^3 = .824

P(at least one is defective) =  1 - P(none are defective) = 1 -.824 = .176

 

Hi

        A  B  C  Total 

Male    7    3  18 

Female 10 14 11  35 

Total  17 22 14   

 P( student was NOT a male that got a "B") = 1 -(male with a "B") 

                                           = 1 - 8/53

                                           = 45/53

 

Hi

     

    2x+ 7 = 125   |Cubing both sides of the EQ

     2x = 118

      x = 59

 

Hi

Re: Plot ordered pair Pt(0,-3) on the coordinate axis

 Note: (0,-3) the 1st value (0) represents the x-value and (-3) the y-value

 

Hi

The perimeter of a rectangle is 54 inches:  

2L + 2W = 54  OR L + W = 27  AND L = 27-W  

Let x AND (27-x) represent the width and length respectively

Question states***area is 176 square inches  Area(rectangle) = L*W

  (27-x)x = 176

     x^2 - 27x + 176 = 0





   x = 22/2 = 11, the width.  Length 16 

or x = 32/2 = 16, the width.  Length 11

 

Hi



Malome is presently half his brother's age

Let x and 2x represent Malome and his brother's ages NOW

Question states***5 years ago...

 (x-5) + (2x - 5) = 26

    3x = 36

     x = 12, Malome's age NOW.  His brother is 24.  (2*12)



CHECKING our Answer***5 years ago...

      7 + 19 = 26

 

Hi

Find two numbers such that their sum is 8 

Let x and (8-x) represent the numbers

Question states***their product is 9

  x(8-x) = 9

   8x-x^2=9

   x^2 - 8x + 9 = 0

factoring

 (x-9)(x+1) = 0

 (x-9)= 0   x =  9  and (8-x) = -1

 (x+1) = 0  x = -1  and (8-(-1) = 9

 In either event, The numbers are 9 and -1

 

Hi

 Tom has taken 5 of the 8 equally weighted tests in his US History class.  

He has an average score of 78.0 points.  Total point thru 5 tests = 5*78 = 390

How many points does he need to earn on the 6th test to bring his 

average score to 80 points?  Let x represent his points on his 6th test 

  (390 + x)/6 = 80

   390 + x = 480

         x =  90 points

 

Hi

Let x, y, z represent the numbers:

The sum of three numbers is 4:  x + y + x = 4

The first, minus the second, plus 4 times the third, is 11: x - y +4z = 11

The third plus 3 times the first, plus the second, is -6: 3x + y + z = -6

Solving for x by substitution

x + y + z = 4  OR (y + z) = (4 - x)

x - y +4z = 11

3x + y + z = -6 AND 3x + (4-x) = -6   x = -5 

Solving for z by Eliminating y

x + y + z = 4  

x - y +4z = 11

 2x + 5z = 15

 2*-5 + 5z = 15

         z = 5  and y = 4  (x+y+z = -5 + 5 + z = 4)

the Numbers are -5,4,5

 

Hi

A(triangle) = 1/2bh

Find the area when b=22m (meters) and h=24m. 

substituting the b and h values   

A(triangle) = (1/2)22m*24m = 264 m^2 

 

Hi

Determine the time necessary for $1000 to double 

if it is invested at interest rate r=10% compounded continously.

  2000 = $1000e^(.10*t) Compounding continously

 ln (2000/1000) = .10t

   6.9315 yrs  = t

 

Hi





  

   x^2 = 1/49

   x = 1/7  |Negative solution is Extraneous

   

 

Hi