Hi,

An employer interviews  8 people for 4 technical support positions in a company, and 3 of the 8 people are men. 

If all 8 are qualified, in how many ways can the employer fill the technical support positions if exactly 2 are men

 3C2*5C2= 3*10 = 30 ways

 

Hi,

A ladder leans agains a building forming an angle of 58 degrees with the ground.  

The bae of the ladder is 3 feet from the building.  

Usethe cosine determine the length of the ladder.

Let h represent the length of the ladder.

 cos(58) = adj/hyp = 3/h

    h = 3ft/cos(58) = 5.66ft

 

Hi,

A bank loaned out $17,000, part of it at 6% per year, and the rest at 16% per year. 

If the interest received in one year totaled $1500, how much was loaned out at 6%? 

Question states***

 .06(17000-x) + .16x = $1500

                 .10x = 1500-1020

                     x = $4800, amount loaned at 16%. $12,200 at 6%

and...

CHECKING our Answer***

 

Hi,

The diameter of  a bicycle wheel is 26 inches .   

How many times did the wheel revolve when the bicycle travels one mile? 

  

 

Hi,

Mrs. Jones Algebra 2 class scored very well on yesterday’s quiz: 91, 92, 94, 88, 96, 99, 91, 93, 94, 97, 95, 97 

With one exception, everyone received an A. Within how many standard deviations from the mean do all the quiz grades fall? 

Mean =  93.9 , SD = 3.12  (Using Excel Data Analysis Tool)

 (99-93.9)/3.12 = 1.6 

 (88 - 93.9)/3.12 = -1.89

all the quiz grades fall within 2 SD from the mean.

Important to Understand z -values as they relate to the Standard Normal curve:

Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and 50% to the right





 

 

Hi,

finding two ordered pairs (x,y) for each line:

x+y=1 ⇒ (0,1) and (1,0) on this line (green)

y=2x+13 ⇒ (0,13) and (-13/2,0) on this line (blue)

plot points and connect with their respective lines

Intersect at (-4,5), the ordered pair that is the solution for this system

 

Hi, Re: TY, Please repost with more detail.  Thanks.

a rectangle length is 40cm and its diagonals is 41 cm. w = 

 

Hi,

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

The probability that a dessert sold at a certain cafe contains chocolate is 86%. 

The probability that a dessert containing chocolate also contains nuts is 30%. 

 Find the probability that a dessert chosen at random contains nuts given that it contains chocolate

P(nuts given chocolate) = .30/.86 = .349  or 34.9% (rounded to the nearest tenth

 

Hi,

Important to Understand z -values as they relate to the Standard Normal curve:

Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and %50 to the right



For the normal distribution: 

one  standard deviation from the mean accounts for about 68.2% of the set 

two standard deviations from the mean account for about 95.4%

and three standard deviations from the mean account for about 99.7%.

a normal distribution that has a mean of 100 and a standard deviation of 8.

p(92 < x < 108)= .682

 p(84 < x < 116) = .954

 p(x < 84) = (1-.954)/2

 

Hi,

Line ab

(-2,11)

( 5, 7) m = -4/7

line bc

(5,7)

(1,0)   m = 7/4

triangle abc is a right triangle as ab is perpendicular to bc

(-2,11)

( 5, 7)  

(5,7)

(1,0)     

A = 

 

Hi,

Solve the system of linear equations by graphing:

I. finding two ordered pairs (x,y) for each 

4x-y=0  If x = 0 ⇒ y = 0, Pt(0,0)  and If x = 1 ⇒ y = 4, Pt(1,4) 

2x-y=-2  If x = 0 ⇒ y = 2, Pt(0,2)  and If y = 0 ⇒ x = -1, Pt(-1,0) 

II.  Plotting the points and connecting with a line for each case.

III. Intersect at (1,4) which is the ordered pair that is the solution for this System

 

Hi,



Forgot about the x-coefficient of the middle term

 

Hi,

Find the largest of 2 consecutive integersand  whose sum is 214

   x + (x+1) = 214

       2x = 213

        x = 106 1/2, there are NO 2 consecutive integers with a sum of 214

      

 

Hi,

A one-cup serving of orange juice contains 3 mg less than four times the amount  of vitamin C as a one-cup serving of pineapple juice. 

Servings of the two juices contain a total of 122 mg of vitamin C.

Yes! You have the idea of identifying the OJ and P...that is the KEY thing!

Set Up is to add the two,however

Question states***  OJ   +   P  = 122mg

 122mg = (4x-3mg) + x

 125 = 5x

  x = 25mg, amount on P.   OJ has 97mg   

 

Hi,

Adam drove a boat for 3 hours against a 5mph current.

He drove back in 1 hour. How fast would he be driving in still water.

Question states***  Note:  D = rt and distance up and back the same.

     |solve for r in mph  (2r = 18,  r = 9mph)

 

Hi,

In the 2008–2009 NBA regular season, the Boston Celtics won two more than three times as many as the games lost. 

The Celtics played  games. How many wins and losses did

 82 = Wins + losses     |Forgot to include games lost

 82 = (x+2) + x

 20 = x, games lost.  games won is 62.   

 

Hi,

If (a+1)(a+2) = 0

Then

(a + 1) = 0

    a = -1

or

(a + 2) = 0

   a = -2

If (a+1)(a+2) = 0,  then a = -1   or a = -2



n^2 + 3n -12 = 6

n^2 + 3n -18 = 0

factoring:

(n + 6)(n - 3) = 0

AND

(n + 6) = 0

or

(n - 3) = 0

  n = -6   or n = 3

 

Hi,Re:  TY, finish it Up and You get .011

according to police sources, a car with a certain protection system will be recovered 87% of the time. 

Find the probablity that 4 of 8 stolen cars will be recovered.

  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 = .87 & q = .13

 = nCx = 

 P(4 will be recovered) =  8C4(.87)^4(.13^4)  = 

 

Hi,

2 persons, A and B start running a certain distance at 8 and 10kmh respectively. 

B reaches the destination 6 minutes earlier than A's time 

Question states*** Note: each run the same distance and D = rt

  

       1 = 2t

           t = 1/2 hr   D = 4mi  

 

Hi,

Note:   D = rt   or t = D/r

Trevor drove 4 hours at the rate of 50 miles per hour.   

How long the same distance take trevor if he drove at 40mph? 

 

Hi,

Sarah is twice as old as her youngest brother's age

If the  between their ages is 15 years, how old is her youngest brother?

Question states***

  2x - x = 15

      x = 15 yr, age of the youngest brother

 

Hi,

John saves Nu. 2 in january, Nu. 6 in february, Nu. 18 in march and so on.

  , r = 3

 

 

Hi,

3/4th of number exceeds its 1/3rd by 60.

        |Multiplying thru by 12 so as all denominators = 1

       

        5x = 720

         x = 144 

and

CHECKING our Answer***

 

 

Hi,

there were chocolates in a box. 

santosh gave one fourth of choclates to pinki 

and one third of the choclates to praja and 50 choclates to pujana

   x = x/4 + x/3 + 50   |Multiplying thru by 12 so as all denominators = 1

  12x = 3x + 4x + 600

   5x = 600

    x = 120 chocolates in the box

  

 

Hi,

A carpenter is building a rectangular room with a fixed perimeter of 264 ft.

 What dimensions would yield the maximun area?  66' by 66'  (a square)



The length that would yield the maximum area is 66 ft. 

The width that would yield the maximum area is 66 ft.

 The maximum area is sq.ft.

 

Hi,

the sides of a parallelogram are in the sides of 2 is to 3 

Find the adjacent sides of parallelogram if the perimeter of the parallelogram is 20 cm

Let 2x and 3x  represent the adjacent sides:

 P = 2x + 3x + 2x + 3x = 20cm

                    10x = 20cm

                      x = 2cm



 the adjacent sides of parallelogram are 4cm  and 6cm

 

Hi,

if the perimeter of a pentagon(5 sides) is 60, its average size length is? 60/5

 

Hi,

a number when subtracted from 25 equals to it's one-fourth

   

       

        20 = x

 

Hi,

If you add 13 to four times a certain number, the sum is less than 265.

Question states***

   4x + 13 < 265

 

Hi,

55inches to 8feet is 

 

Hi,

 16^(1/2) =