1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
liubo4ka [24]
3 years ago
12

In a game of checkers, there are 12 red game pieces and 12 black pieces. What is the probability that the first two checkers he

pulls from the box at random will be two red checkers?
P.S pls show steps
Mathematics
1 answer:
allsm [11]3 years ago
5 0
2/24 

add the red checkers and the black checkers together. (This will be the denominator)

Then add the 2 which is the numerator 

So the chances are 2/24 or 1/12

Hope this helped!


You might be interested in
The diameter of Jim’s circular flower bed is 10 feet. What is the area, in square feet, of Jim’s flower bed?
Setler79 [48]
The area of a circle is PiR^2
Divide 10 by 2, to get the radius.
Square the radius, 5, which gives you 25.
25Pi is your answer, which is C.)
8 0
3 years ago
Read 2 more answers
Linear Algebra question! Please help!
kozerog [31]

Answers:

  1. false
  2. false
  3. true
  4. false
  5. True

==================================================

Explanation:

Problem 1

This is false because the A and B should swap places. It should be (AB)^{-1} = B^{-1}A^{-1}.

The short proof is to multiply AB with its inverse (AB)^{-1}  and we get: (AB)*(AB)^{-1} = (AB)*(B^{-1}A^{-1}) = A(B*B^{-1})*A^{-1} = A*A^{-1} = I

The fact we get the identity matrix proves that we have the proper order at this point. The swap happens so that B matches up its corresponding inverse B^{-1} and the two cancel each other out.

Keep in mind matrix multiplication is <u>not</u> commutative. So AB is not the same as BA.

-------------------------

Problem 2

This statement is true if and only if AB = BA

(A+B)^2 = (A+B)(A+B)

(A+B)^2 = A(A+B) + B(A+B)

(A+B)^2 = A^2 + AB + BA + B^2

(A+B)^2 = A^2 + 2AB + B^2 ... only works if AB = BA

However, in most general settings, matrix multiplication is <u>not</u> commutative. The order is important when multiplying most two matrices. Only for special circumstances is when AB = BA going to happen. In general,  AB = BA is false which is why statement two breaks down and is false in general.

-------------------------

Problem 3

This statement is true.

If A and B are invertible, then so is AB.

This is because both A^{-1} and B^{-1} are known to exist (otherwise A and B wouldn't be invertible) and we can use the rule mentioned in problem 1. Make sure to swap the terms of course.

Or you can use a determinant argument to prove the claim

det(A*B) = det(A)*det(B)

Since A and B are invertible, their determinants det(A) and det(B) are nonzero which makes the right hand side nonzero. Therefore det(A*B) is nonzero and AB has an inverse.

So if we have two invertible matrices, then their product is also invertible. This idea can be scaled up to include things like A^4*B^3 being also invertible.

If you wanted, you can carefully go through it like this:

  1. If A and B are invertible, then so is AB
  2. If A and AB are invertible, then so is A*AB = A^2B
  3. If A and A^2B are invertible, then so is A*A^2B = A^3B

and so on until you build up to A^4*B^3. Therefore, we can conclude that A^m*B^n is also invertible. Be careful about the order of multiplying the matrices. Something like A*AB is different from AB*A, the first of which is useful while the second is not.

So this is why statement 3 is true.

-------------------------

Problem 4

This is false. Possibly a quick counter-example is to consider these two matrices

A = \begin{bmatrix}1 & 0\\0 & 1\end{bmatrix} \text{ and } B = \begin{bmatrix}-1 & 0\\0 & -1\end{bmatrix}

both of which are invertible since their determinant is nonzero (recall the determinant of a diagonal matrix is simply the product along the diagonal entries). So it's not too hard to show that the determinant of each is 1, and each matrix shown is invertible.

However, adding those two mentioned matrices gets us the 2x2 zero matrix, which is a matrix of nothing but zeros. Clearly the zero matrix has determinant zero and is therefore not invertible.

There are some cases when A+B may be invertible, but it's not true in general.

-------------------------

Problem 5

This is true because each A pairs up with an A^{-1} to cancel out (similar what happened with problem 1). For more info, check out the concept of diagonalization.

5 0
2 years ago
A student has two identical sheets of paper. he crumples one up into a small ball. if he drops the sheet of paper and the ball o
Vilka [71]
The air resistance acting on the un-crumbled sheet is greater.
5 0
3 years ago
Read 2 more answers
Select all the ordered pairs that make this statement true?
Ierofanga [76]

Answer: (24,-9)

(0,9)

(4,6)

Step-by-step explanation:

3x + 4y = 36

Using (3,-2) will be:

= 3(3) + 4(-2)

= 9 - 8 = 1

Using (1,7) will be

= 3(1) + 4(7)

= 3 + 28 = 31

Using (0,0) equals to 0

Using (24,-9) will be:

= 3(24) +4( -9)

= 72 - 36 = 36

Using (0,9) will be:

= 3(0) + 4(9)

= 0 + 36 = 36

Using (4,6) will be:

3(4) + 4(6)

= 12 + 24

= 36

Using (-12,18) will be:

= 3(-12) + 4(-18)

= -36 - 72

= -108

The correct options are (24,-9), (0,9 and (4,6)

5 0
3 years ago
PLEASE ANSWER THIS!! 16 POINTS!<br><br> (2/3)*2 + 1/2
alexira [117]

Answer:

=7/6

Step-by-step explanation:

Join 4/3=1:7/3

7/3/2

Apply the fraction rule:=

7/3x2

Multiply the numbers=

7/6

5 0
3 years ago
Read 2 more answers
Other questions:
  • Deals with Area of Triangle, thankyou so very much for your help!
    7·1 answer
  • Harvey practiced the piano for 5/8 hour.Annika practiced the piano for 5/6 of an hour.
    5·2 answers
  • 18 first-graders and 72 other students attended a school assembly. What percentage of the students at the assembly were first-gr
    9·2 answers
  • Which statements are true about the regular polygon? Select three options. The sum of the measures of the interior angles is 900
    11·2 answers
  • 12) The sum of two natural numbers is 30. If one of the numbers is one-
    12·2 answers
  • My sister is 18 years old. My brother says that his age minus nineteen Is equal
    5·2 answers
  • Explain two different ways to find a new value after an original value is increased by 30%.
    15·1 answer
  • There were 215 students who attended the school play. If there are a total of 250 students in the school, what percent of the st
    9·2 answers
  • Shelly charges$10 per hour for her babysitting services. Last month Shelly babysat for 15 hours. This month she babysat for n ho
    7·1 answer
  • ese Missy wants to determine whether x + 3 is a factor of the polynomial the x^4 + x² +6x-9 by using the factor theorem How does
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!