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denis23 [38]
3 years ago
10

Roger 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 5}. List the outcomes in A ∪ B.
Mathematics
1 answer:
____ [38]3 years ago
5 0
The answer is A ∪ B = {2, 4, 5, 6, 8, 10, 12}

A = {2, 4, 6, 8, 10, 12}
B = {5, 10}

A ∪ B. The union of two sets is everything in both sets. So we will combine the outcomes in set A and set B. Since in set B 10 is an even number, we will just add number 5 in <span>A ∪ B.
</span>
A ∪ B = {2, 4, 5, 6, 8, 10, 12}
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5-6. Find the constant of proportionality (unit rate) for each set of values. Then use the constant of proportionality to write
kakasveta [241]

5. The constant of proportionality is 1.5

The equation is <em>p </em>= 1.5×s

6. The constant of proportionality is 1.99

The equation is p = 1.99 × a

7. The variables Number of Pens and Cost  are not proportional

Please find attached the required graph

8. The variables Number of minutes and Words Typed are not proportional

Please find attached the required graph

The procedure for finding the answers are as follows;

5. The given data are presented as follows;

\begin{array}{ccc}Shirts \ (s)&&Profit \ (p)\\5&&7.50\\10&&15.00\\15&&22.50\end{array}

Where two variables, <em>s</em> and <em>p</em> are proportional, we get;

p ∝ s

Therefore;

p = C × s

C = p/s

Where;

C = The constant of proportionality

Therefore, the constant of proportionality, <em>C</em>, of the given variables, (number of shirts, <em>s</em>, and profit, <em>p</em>, is found as follows;

C = 7.50/5 = 15.00/10 = 22.50/15 = 1.5

The constant of proportionality, C = 1.5

The equation that relates the two values is <em>p </em>= 1.5×s

6.  For the apples to price relationship, we have;

\begin{array}{ccc}Apples \ (a)&&Price\ (p)\\4&&7.96\\5&&9.95\\6&&11.94\end{array}

Therefore;

p ∝ a

p = C × a

C = p/a

Plugging in the values gives;

C = 7.96/4 = 9.95/5 = 11.94/6 = 1.99

The constant of proportionality, C = 1.99

Therefore, the equation relating the two values is p = 1.99 × a

7. The given data is presented in a tabular form as follows;

\begin{array}{ccc}Number \ of \ pens  &&Cost\ \\1&&52\\2&&54\\3&&56\\4&&58\end{array}

A set of data is proportional or has a proportional relationship if their <em>x</em>, and therefore, y-intercept is (0, 0)

From the graph of the data, created with MS Excel, the y-intercept is 50 which is not equal to zero, therefore, the relationship between the data is not a proportional relationship

8. The given data is presented in a tabular form as follows;

\begin{array}{ccc}Number \ of \ Minutes&&Words \ Typed\ \\1&&50\\2&&90\\3&&140\\4&&180\end{array}

From the graph of the data, we have that the y-intercept of the line of best fir is 5, therefore, the relationship is not a proportional relationship

Learn more about proportional relationships here;

brainly.com/question/24289972.

5 0
3 years ago
Simplyfy the given equation 5x+2(x-3)=-2(x-1)
Blizzard [7]

5x+2x−6=−2x+2

7x−6=−2x+2

7x=−2x+2+6

7x=−2x+8

7x+2x=8

9x=8

x=8/9

Hope this helps, have a blessed day! :-)

5 0
3 years ago
WILL GIVE BRAINLIEST ian solved the system of equations by making a substitution for y in the second equation. What equation did
Aleonysh [2.5K]

5x -2(-3x+1) =31

5x +6x-2=31

Choice B

6 0
3 years ago
What is an equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 ?
Natali5045456 [20]

Answer:

The equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 is

6x+y=-5

Step-by-step explanation:

Given:  

Let,  

point A( x₁ , y₁) ≡ ( -2 , 7)

To Find:  

Equation of Line  that passes through the point (-2,7) and is perpendicular to the line x-6y=42=?  

Solution:  

x-6y=42    ..................Given

which can be written as

y=mx+c

Where m is the slope of the line

∴ y=\dfrac{x}{6}-7

On Comparing we get

Slope = m = \dfrac{1}{6}

The Required line is Perpendicular to the above line.

So,

Product of slopes = - 1

m\times m_{1}=-1\\Substituting\ m\\ \dfrac{1}{6} m_{1}=-1\\\\m_{1}=-6

Slope of the required line is -6

Equation of a line passing through a points A( x₁ , y₁) and having slope m is given by the formula,  

i.e equation in point - slope form

(y-y_{1})=m(x-x_{1})

Now on substituting the slope and point A( x₁ , y₁) ≡ ( -2, 7) and slope = -6 we get

(y-7)=-6(x--2)=-6(x+2)=-6x-12\\\\\therefore 6x+y=-5.......is\ the required\ equation\ of\ the\ line

The equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 is

6x+y=-5

3 0
3 years ago
Alberto bought his bicycle for$275. He sold for $350. What was the amount of his Percentage profit?
juin [17]

Answer:

Step-by-step explanation:

$350 -$275= $75 profit

6 0
3 years ago
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