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Ulleksa [173]
3 years ago
13

Jeremy is playing a board game and rolls two number cubes. Let A = {the sum of the number cubes is even} and let B = {the sum of

the number cubes is divisible by 3}. List the outcomes in A ∩ B.
{6, 12}
{3, 6, 9, 12}
{2, 4, 6, 8, 10, 12}
{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
Mathematics
1 answer:
Roman55 [17]3 years ago
7 0

Answer:

A ∩ B = {12}

Step-by-step explanation:

What are the possible even outcomes?  

Assuming the number cubes are 1-6,

our possible outcomes run from 2-12, but we are looking for even rolls, so A={2,4,6,8,10,12}.  

How many of those are divisible by 3?  B={12}.  

We are looking for what is in common between these, so

A ∩ B= {12}

You might be interested in
Check whether x² +4x +4 is prefect spuare expression or not . if so factorise the expression<br>​
irinina [24]

Answer:

It is a perfect square expression.

It factors to (x+2)^2

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

Explanation:

The general format for a perfect square is

(a+b)^2 = a^2 + 2ab + b^2

Which can be seen through the use of the FOIL rule.

Compare x^2+4x+4 with a^2+2ab+b^2, and we have these three equivalences:

  • x^2 = a^2 .... first terms
  • 4x = 2ab .... middle terms
  • 4 = b^2 .... last terms

Since x^2 = a^2, we can apply the square root to both sides to get a = x. Similarly, 4 = b^2 leads to b = 2. We could get b = -2, but that would mean 2ab = 2x*(-2) = -4x instead of 4x. So we'll stick with b = 2 instead.

Because a = x and b = 2, we then can say:

(a+b)^2 = a^2 + 2ab + b^2

(x+2)^2 = x^2 + 2*x*2 + 2^2

(x+2)^2 = x^2 + 4x + 4

Showing that x^2+4x+4 factors to (x+2)^2.

7 0
2 years ago
What is c - b for six grade math
JulsSmile [24]

Answer:

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Step-by-step explanation:

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4 0
2 years ago
Which is the box-and-whisker plot for the data set?
ivann1987 [24]
It is the first graph. The median of the number list is 14. The Q1 is 9 ((7+11)/2) and the Q3 is 17 ((19+15)/2) the two outliers are 6 and 21
8 0
3 years ago
The price of a coat increased from $78 to $92. What is the price increase percentage?
blagie [28]

Answer:

18%

Step-by-step explanation:

Since the original price is $78 then this is the original 100% of the price. The new price will be marked up x percent and be $92. To find the new price set up a proportion with these values:

\frac{92}{78}=\frac{x}{100}

Solve for the original price by cross multiplying numerator with denominator.

x(78) = 92(100)

78x = 9200

x= 117.9 = 118%

This is 18% more or over the original price.


5 0
2 years ago
What is the mass of a baseball that has a kinetic energy of 100 J and is traveling at 5 m/s?
Andrei [34K]
The formula of the kinetic energy is:
K.E = \frac{1}{2}mv²

The given are
K.E = 100 J
v = 5 m/s

Plug them in:

100 = \frac{1}{2}m × (5)²
100 = \frac{1}{2}m × 25
100 = 12.5m
Divide by 12.5 on either sides to isolate m

\frac{100}{12.5} = \frac{12.5m}{12.5}
12.5 and 12.5 cancels out
8 kg = m
The mass of the baseball that has a kinetic energy of 100 J and speed of 5 m/s is 8 kg

4 0
3 years ago
Read 2 more answers
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