Genius I need your help

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Everything4pageants

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1. find all pairs of prime numbers whose sum equals 999

2. A basketball player attempts a free throw. If she is successful she can attempt a second. If p is the probability of a successful throw and if her probability of making 0 points is equal to that of making 2 points what is P? Round to the nearest thousandth.

3. Total # of interior angels in two regular polygons is 17. and the total number of diagonals is 63. How many sides does each regular polygon have?

4.
5x10rect.gif


3 congruent rectangles are placed to form a larger rectangle as shown with an area of 1350cm squared. Find the area of a square that has the same perimeter of the larger rectangle.

Help I have two days to figure these out. I really need the EC.
 
Please read "Read before posting".
Then show your work, else we can't tell where you're stuck.
 
Everything4pageants said:
1. find all pairs of prime numbers whose sum equals 999

2. A basketball player attempts a free throw. If she is successful she can attempt a second. If p is the probability of a successful throw and if her probability of making 0 points is equal to that of making 2 points what is P? Round to the nearest thousandth.

3. Total # of interior angels in two regular polygons is 17. and the total number of diagonals is 63. How many sides does each regular polygon have?

Help I have two days to figure these out. I really need the EC.
Click to expand...

problem 1.

Sum of two numbers can be odd iff one number is even and the other one is odd.

There is only one even prime number.

Now continue....

Problem 2.

If 'p' is probability of making the shot

what is the probability of NOT making the shot ? [spoiler:1ts7cmff]1-p[/spoiler:1ts7cmff] ............................(1)

Then what is the probability of making both shots? ........................ (2)

Equate (1) and (2) and solve for 'p' ..........................edited
 
Okay number 2.

This is what I'm thinking:

Probability of making shot 1/2
probability of missing shot 1/2

Probability of missing both shots 1/4
Probability of making both shots 1/4

How do I solve for P

I am confused there.
 
Subhotosh Khan said:
Everything4pageants said:
1. find all pairs of prime numbers whose sum equals 999

2. A basketball player attempts a free throw. If she is successful she can attempt a second. If p is the probability of a successful throw and if her probability of making 0 points is equal to that of making 2 points what is P? Round to the nearest thousandth.

3. Total # of interior angels in two regular polygons is 17. and the total number of diagonals is 63. How many sides does each regular polygon have?

Help I have two days to figure these out. I really need the EC.
Click to expand...

problem 1.

Sum of two numbers can be odd iff one number is even and the other one is odd.

There is only one even prime number.

Now continue....

Problem 2.

If 'p' is probability of making the shot

what is the probability of NOT making the shot ? [spoiler:12amzt9o]1-p[/spoiler:12amzt9o]

Then what is the probability of making both shots? ........................ (3)

Then what is the probability of NOT making both shots? ................... (4)

Equate (3) and (4) and solve for 'p'
Click to expand...



So would you mind checking:

1. 2, 997
2. The probability of making both shoes 1/3 and the probability of NOT making both shots 1/3 So P= 1/3 or .337


I can not figure out how to do number 3 at all.
 
Everything4pageants said:
2. A basketball player attempts a free throw. If she is successful she can attempt a second. If p is the probability of a successful throw and if her probability of making 0 points is equal to that of making 2 points what is P? Round to the nearest thousandth.
.
Click to expand...

The chance of making first shot = p

The chance of not-making first shot = 1 - p (scoring 0 points)

The chance of making first and second shots = p[sup:10fwz1hb]2[/sup:10fwz1hb] (scoring 2 points)

her probability of making 0 points is equal to that of making 2 points

p[sup:10fwz1hb]2[/sup:10fwz1hb] = 1 - p

p[sup:10fwz1hb]2[/sup:10fwz1hb] + p - 1 = 0

p = [-1 ± ? (1 + 4)]/2 = 0.618033989 (only positive value considered) = 0.618
 
Hello, Everything4pageants!


4. Three congruent rectangles are placed to form a larger rectngle as shown.
The total area is 1350 cm\(\displaystyle ^2.\)

Find the area of the square that has the same perimeter as the large rectangle.
Click to expand...
Code: 
      :       L       :   L/2   :
    - * - - - - - - - * - - - - * -
    : |               |         | :
   L/2|               |         | :
    : |               |         | :
    - * - - - - - - - *         | L
    : |               |         | :
   L/2|               |         | :
    : |               |         | :
    - * - - - - - - - * - - - - * -
      :       L       :   L/2   :

\(\displaystyle \text{Let }L\text{ be the length of a small rectangle.}\)
\(\displaystyle \text{Then }\tfrac{1}{2}L\text{ is the width of a small rectangle.}\)

\(\displaystyle \text{The large rectangle has length }\tfrac{3}{2}L\text{ and width }L.\)
\(\displaystyle \text{Its area is: }\:\left(\tfrac{3}{2}L\right)(L) \:=\:1350 \quad\Rightarrow\quad L^2 \:=\:900 \quad\Rightarrow\quad L \:=\:30\)

\(\displaystyle \text{Hence, the large rectangle is: }\:45\times30\text{ cm.}\)
\(\displaystyle \text{Its perimeter is: }\:2(45) + 2(30) \:=\:150\text{ cm.}\)


\(\displaystyle \text{The square with the same perimeter has side }x.\)
\(\displaystyle \text{It perimeter is: }\:4x \:=\:150\)
\(\displaystyle \text{Its side is: }\:x \:=\:\tfrac{75}{2}\text{ cm.}\)

\(\displaystyle \text{Therefore, its area is: }\:x^2 \:=\:\left(\frac{75}{2}\right)^2 \:=\:\frac{5625}{4} \;=\;1406\tfrac{1}{4}\text{ cm}^2.\)

 
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