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guapka [62]
3 years ago
6

If M is the set of all square of integers that are less than 100 and N is the set of all positive even numbers that are under 30

Mathematics
1 answer:
irina [24]3 years ago
3 0

Answer:

a) M = {0 , 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81}

   N = {2 , 4, 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 , 26 , 28}

b) M ∩ N = {4 , 16 }

M ∪ N = {0 , 1 , 2 , 4 , 6 , 8 , 9 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 , 25 , 26 , 28 ,

               36 , 49 , 64 , 81}

a) X = {e , i , g , h , t , y}

   W = {e , n , s , t , v , y}

b) X ∪ W = {e , i , g , h , n , s , t , v , y}

X ∩ W = {e , t , y}

Step-by-step explanation:

* Lets explain how to solve the problem

- We can find a square number by multiply the number by itself

a)

- M is the set of all square integers that are less than 100

∵ The integers from -9 to 9 has square less than 100

∴ M = {0 , 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81}

- N is the set of all positive even numbers that are under 30

∵ Even number any number divisible by 2

∵ They are positive numbers

∴ They start with 2 because zero is not a positive or negative

∴ N = {2 , 4, 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 , 26 , 28}

b)

- M ∩ N means the common numbers between set M and set N

∵ The common elements of M ∩ N are square and even less

   than 30

∴ M ∩ N = {4 , 16 }

- M ∪ N means all the elements in M and N without reputation

∴ M ∪ N = {0 , 1 , 2 , 4 , 6 , 8 , 9 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 , 25 ,

  26 , 28 , 36 , 49 , 64 , 81}

a)

- X is the set of all letters of the word eighty

∵ The letters of word eighty are e i g h t y

∴ X = {e , i , g , h , t , y}

- W be the set of all letters of the word seventy

∵ The letters of word seventy are s e v e n t y

∵ We don't repeat any element in the set

∴ W = {e , n , s , t , v , y}

b)

- X ∪ W means all the elements in X and W without reputation

∴ X ∪ W = {e , i , g , h , n , s , t , v , y}

- X ∩ W means the common elements between set X and set W

∵ The common letters between X and W are e , t , y

∴ X ∩ W = {e , t , y}

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Prove that 2n^3 + 3n^2 + n is divisible by 6 for every integer n > 1 by mathematical induction. (7 marks)
notka56 [123]

Answer:

The answer is True

Step-by-step explanation:

A <em>mathematical induction</em> consists in only 2 steps:  

<u>First step</u>: Show the proposition is true for the first one valid integer number.

<u>Second step</u>: Show that if any one is true then the next one is true  

Finally, if first step and second step are true, then the complete proposition is true.

So, given 2*n^3+3*n^2+n

First step: using and replacing n=2 (the first valid integer number >1)

2*(2)^3 +3*(2)^2+2=30

\frac{30}{6} =5

As the result is an integer number, so the first step is true.

Second step: using any next number, n+1, let it replace

2*(n+1)^3+3*(n+1)^2+(n+1)\\2*(n^3+3*n^2+3*n+1)+3*(n^2+2*n+1)^2+(n+1)\\2*n^3+6*n^2+6*n+2+3*n^2+6*n+3+n+1\\(2*n^3+3*n^2+n)+(6*n^2+12*n+6)

As the First step is true, we know that

2*n^3+3*n^2+n=6*k,

So let it replace in the previous expression

6*k+6*(n^2+2*n+1)\\6*[k+(n^2+2*n+1)]

Finally

\frac{6*[k+(n^2+2*n+1)]}{6} =k+(n^2+2*n+1)

where the last expression is an integer number

So the second step is true, and the complete proposition is True

5 0
2 years ago
9. m+3 ]=7<br> How do you do this
LekaFEV [45]

Answer:

m=4

Step-by-step explanation:

7-3=4................

hope that helps

4 0
2 years ago
At an antique boat show, 90% of the boats are made of a natural, polished wood. 75% of the boats have some chrome accents on the
nadya68 [22]

Answer:

0.933 ; not independent

Step-by-step explanation:

Given :

A - made from natural polished wood

B - made from chrome accent

P(A) = 0.9

P(B) = 0.75

P(AnB) = 0.7

1.) probability of natural wood Giveb that it has chrome accent

P(A|B) = P(AnB) / P(B)

P(A|B) = 0.7 / 0.75

P(A|B) = 0.933

2.)

For an independent event :

P(AnB) = p(A) * p(B)

P(AnB) = 0.9 * 0.75 = 0.675

However, p(AnB) Given here is 0.7, thus the event aren't independent

3 0
3 years ago
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 89m long and 70m wide.
Sindrei [870]

Step One

Find the area of the rectangle

Area = L * W

Area = 89 cm * 70 cm

Area = 6230 cm^2

Step Two

What is the formula for the two end semicircles?

Two semicircles = 1 whole circle

Area of any circle = pi * r^2

Step Three

Find the area of the circle

r = the width / 2     This may not be true. You need the diagram. If the circles are drawn on the length then use r = the length / 2

r = 70/2  = 35 cm

Area of circle = pi * r^2

Area of circle = 3.14 * 35^2

Area of circle = 3846.5

Step Four

Find the total area

The total area = Area of the rectangle + area of circle

The total area = 6230 + 3846.5

The total area = 10076.5 cm^2 <<<< Answer

3 0
3 years ago
A car is driven 440 miles in 11 hours. What is the rate in miles per hour?
nikklg [1K]

Answer:

40 Mph

Step-by-step explanation:

440/11 is equal to 40

5 0
3 years ago
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