math help please?

Question

1.In a standard deck of 52 cards,13 of the cards are diamonds.If two cards are drawn randomly without replacement, what is the probabilty that both cards are diamonds?

2.If the average of a and -5 is 10, whatis the value of a

3.find the sum of the measures of the interior angles of an octagon

Answer 1

PROBLEM 1:

Chance the first card is a diamond = 13/52 = 1/4
Chance the second card is also a diamond = 12/51

Combined probability of the two events (drawing 2 diamonds) is:
1/4 * 12/51 = 3/51 = 1/17

Answer: 1/17

PROBLEM 2:

Average is the sum of two numbers, divided by 2:

(a + -5) / 2 = 10

Multiply both sides by 2:
a - 5 = 20

Add 5 to both sides:
a = 25

Answer: 25

PROBLEM 3:

An octagon can be divided into 6 triangles (just draw lines from one vertex to the 5 available other vertices which will subdivide it into 6 triangles).

Each triangle has angles that add up to 180°. So an octagon would have interior angles that add up to 6 * 180° = 1080°.

In general an n-sided polygon has interior angles that add up to (n - 2) * 180°

Answer: 1080°

Answer 2

1. For the first choice, you have 13/52 chances of getting a diamond. For the second choice, it becomes 12/51. For both to be diamonds, multiply those fractions: 13/52 * 12/51= ?, you do the math. Hint: reduce the fractions.

2. Your two numbers are a and -5. The average is 10. The general formula is (a + b)/2 = c. Plug in your numbers: (a - 5)/2 = 10 ==> a - 5 = 20 ==> a = 25.

3. An octagon has six isoceles triangles. The angle formed with the vertex at the center of the octagon is a 45 degree angle, thus the two base angles equal 135 degrees and there are eight such pairs. These pairs also constitute the eight interior angles (draw a picture if need be). You're looking for one base angle in one triangle and the nearest base angle in the adjacent triangle. The base angles are all equal, you just need to pair two together that make up one interior angle. Now 8 deg * 135 deg = 1080 deg. And you're done. Not elegant, but pictures make a world of difference.

Answer 3

1) Assuming the first time you pick a diamond. Chance is 13/52. Second time you pick a diamond again, chance is 12 (as 1 diamond is already picked)/51 (as 1 card is already picked). According to the AND rule, the answer is 13/52 * 12/51. Go figure.
2) Average is found by 1st number + 2nd number /2. Therefore for this, you get equation of a+ -5 which equals to (a-5)/2=10.
Times 2 on both sides.
a-5=20
Add 5 to 20.
Go figure.

3) Formula for calculating this is:
(Number of sides-2)*180. Octagon has 8 sides. Go figure.

Answer 4

for the first answer it may be that you may get a dimond with a heart or a diamontd with a leaf
for the second the answer is a=25
since 25+(-5)/2
=20/2=10
for the third one i have no idea please tell me how many sides does a octagon have

Answer 5

1. 1/17

2. 25

3. 1080

Answer 6

1. (13/52)(12/51) is answer to one

2. 25

3. 135

did it all in my head.
piece of cake :)