MATHEMATICS HIGH SCHOOL

Stephanie is playing a board game and rolls two number cubes. Let A = {the sum of the number cubes is odd} and let B = {the sum of the number cubes is divisible by 3}. List the outcomes in A ∩ B.{1,3,5,7,9,11}
{1,3,9}
{3,9}
{3,9,12}

Answers

Answer 1
Answer: The outcomes of rolling two cubes are shown in the table below (the outcomes is added up). The members of A are circled while the members of B are boxed. The members of A that also members of B is both circled and boxed.

P(A) = {3, 5, 7, 9, 11}
P(B) = {3, 6, 9, 12}
P(A∩B) = {3,9}
Answer 2
Answer:

The intersection between the sets are the values that are common to both sets that is {3, 9}

What are sets?

Sets are arrangement of values of elements in a specified way.

Given the following sets

A = {1, 3,5, 7, 9, 11}

B = {3, 6, 9,12}

The intersection between the sets are the values that are common to both sets, hence;

A ∩ B = {3, 9}

Learn more on set here: brainly.com/question/5660357

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A quadratic equation is written in four equivalent forms below. I. y = (x - 1)2 - 49 II. y = x2 - 2x - 48 III. y = (x + 6)(x - 8) IV. y = x(x - 2) - 48 Which of the forms shown above would be the most useful if attempting to find the x-intercepts of the quadratic equation?

Answers

The x-intercept also known as the root of a quadratic can be found by solving the equation with respect to x.

III is the most useful for finding the roots
you would simply equate each term to 

So y= x + 6                               AND                    y= x - 8        
     0= x + 6                                                           0= x - 8
      x= -6                                                                x= 8
 
: . x-intercepts are x= -6 & x= 8

Multiply or Divide

(i need this for school tomorrow)

Answers

Answer:

Ok so here are the simple rules of doing it (very easy) cause I’m not doing it all so . when multiplying a power with The same base keep the base but add the exponents. Dividing, keep the base (if their the same if not then its already simplified same with multiplication) but SUBTRACT the exponents. Also keep the parenthesis if it’s a negative number base.

I’ll do a few.

11) a^10.           11b) 5^4

12) (-2)^2.        

13) 10^2.          13b) s^6

14) -4s^5(t^6) <- [Im not sure of this one)

15) x^3(y^3)

4 x (22+5)
Simplify the expression.

Answers

Answer:

the simplified expression is 108x

Step-by-step explanation:

4x(22+5)

you can remove the parenthesis by multiplying 4x by everything inside of them.

4x * 22 + 4x * 5

88x + 20x

108x

A box contains 3 plains pencils and 7 pens . A second box contains 6 color pencils and 2 crayons one item from each box is chosen at random. What is the probability that a pen from the first box and crayon from the second box are selected

Answers

Well to solve these type of question it is very easy to make a tree diagram and then solve them. How ever i have done it here for you.

So basically we have to get a pen from the first box so its probability is 7 / 10.

Similarly, we have to get a crayon from the second box so its probability is 2 / 8.

Now by counting principle we can multiply the two probabilities so 7/10 * 1/4 which becomes equal to 7/40.

What is 43/24 as a mixed number?

Answers

(43)/(24)=(24+19)/(24)=(24)/(24)+(19)/(24)=1+(19)/(24)=1(19)/(24)

Write the explicit rule.

-21, -51, -81, -111, -141

Answers

Answer:

aₙ = - 30n + 9

Step-by-step explanation:

You can tell this is an arithmetic sequence, as there is a difference of 30 between each value. Therefore the equation we will use here is aₙ = a₁ + (n - 1)d.

aₙ = a₁ + (n - 1)d

= - 21 + (n - 1) * - 30

= - 21 - 30n + 30

= - 30n + 9

Your solution would be option d. aₙ = - 30n + 9
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