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1 year ago

A student was asked to rewrite using only the associative property of multiplication. Which is the correct response?

1 answer:

3 0

Given that the associative property of multiplication says that you can group the numbers in any combination, we can reorganize the expression as: 7·(10·3)=210. So the answer would be the first option.

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An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated.(

photoshop1234 [79]

Answer:

(a) Shown below.

(b) Explained below.

Step-by-step explanation:

(a)

The sample space of rolling an 8-sided die twice is as follows:

S = {(1 , 1) , ( 1 , 2) , ( 1, 3) , ( 1, 4 ) , ( 1, 5) , ( 1 , 6 ) , ( 1, 7 ) , ( 1, 8) ,

(2 , 1) , (2 , 2) , ( 2, 3) , ( 2, 4 ) , ( 2, 5) , (2 , 6 ) , ( 2, 7 ) , ( 2, 8) ,

(3 , 1) , ( 3, 2) , ( 3, 3) , ( 3, 4 ) , ( 3, 5) , ( 3 , 6 ) , (3, 7 ) , ( 3, 8) ,

(4, 1) , ( 4 , 2) , ( 4, 3) , ( 4, 4 ) , ( 4, 5) , (4 , 6 ) , (4, 7 ) , (4, 8) ,

(5, 1) , ( 5 , 2) , ( 5, 3) , (5, 4 ) , ( 5 ,5) , (5, 6 ) , ( 5, 7 ) , ( 5, 8) ,

(6 , 1) , ( 6 , 2) , ( 6, 3) , (6, 4 ) , ( 6, 5) , (6 , 6 ) , ( 6, 7 ) , ( 6, 8) ,

(7 , 1) , ( 7 , 2) , ( 7, 3) , ( 7, 4 ) , ( 7 , 5) , ( 7, 6 ) , ( 7, 7 ) , (7, 8) ,

(8 , 1) , ( 8 , 2) , (8, 3) , ( 8, 4 ) , ( 8, 5) , ( 8 , 6 ) , ( 8, 7 ) , ( 8, 8)}

There are a total of N = 64 elements.

(b)

(i)

The product of the two numbers is a prime number:

Product is a prime number samples:

2 = ( 1, 2) , ( 2, 1)

3 = ( 1 , 3) , ( 3 , 1)

5 = ( 1, 5) , ( 5 , 1)

7 = ( 1, 7) , ( 7 , 1)

Number of samples, n = 8

P (Product is a prime number) = 8/64 = 1/8 = 0.125.

(ii)

The product of the two numbers is not a perfect square :

Product is not a perfect square samples:

2 = ( 1, 2) , ( 2, 1)

3 = ( 1 , 3) , ( 3 , 1)

5 = ( 1, 5) , ( 5 , 1)

6 = ( 1, 6) , ( 2, 3) , ( 3, 2) , ( 6 , 1)

7 = ( 1, 7) , ( 7 , 1)

8 = ( 1 , 8) , ( 2, 4) , ( 4 , 2) , ( 8 , 1)

10 = ( 2, 5) , ( 5, 2)

12 = (2 , 6) , ( 3 , 4) , ( 4 3) , ( 6 , 2)

14 = ( 2, 7) , ( 7 , 2)

15 = (3 , 5) , ( 5 , 3)

18 = ( 3, 6) , ( 6 , 3)

20 = ( 4, 5) , ( 5, 4)

21 = ( 3 , 7) , ( 7 , 3)

24 = ( 3 , 8) , ( 4 , 6 ) , ( 6 , 4) , ( 8 , 3)

28 = ( 4 , 7) , ( 7 , 4)

30 = ( 5 , 6) , ( 6 ,5 )

32 = ( 4 , 8) , ( 8 , 4)

35 = ( 5 , 7) , ( 7 , 5)

40 = ( 5 , 8) , ( 8 , 5)

42 = ( 6 , 7) , ( 7 , 6)

48 = ( 6 , 8) , ( 8 , 6)

56 = ( 7 , 8) , ( 8 , 8)

Number of samples, n = 52

P (Product is not a perfect square) = 52/64 = 0.8125

(iii)

The product of the two numbers is a multiple of 5:

Product is a multiple of 5 samples:

5 = ( 1, 5) , ( 5 , 1)

10 = ( 2, 5) , ( 5, 2)

15 = (3 , 5) , ( 5 , 3)

20 = ( 4, 5) , ( 5, 4)

25 = ( 5 , 5)

30 = ( 5 , 6) , ( 6 ,5 )

35 = ( 5 , 7) , ( 7 , 5)

40 = ( 5 , 8) , ( 8 , 5)

Number of samples, n = 15

P (Product is a multiple of 5 ) = 15/64 = 0.2344.

(iv)

The product of the two numbers is less than or equal to 21:

Product is less than or equal to 21 samples:

1 = ( 1, 1)

2 = ( 1, 2) , ( 2, 1)

3 = ( 1 , 3) , ( 3 , 1)

4 = (1 , 4) , ( 2, 2) , ( 4, 1)

5 = ( 1, 5) , ( 5 , 1)

6 = ( 1, 6) , ( 2, 3) , ( 3, 2) , ( 6 , 1)

7 = ( 1, 7) , ( 7 , 1)

8 = ( 1 , 8) , ( 2, 4) , ( 4 , 2) , ( 8 , 1)

9 = ( 3, 3)

10 = ( 2, 5) , ( 5, 2)

12 = (2 , 6) , ( 3 , 4) , ( 4 3) , ( 6 , 2)

14 = ( 2, 7) , ( 7 , 2)

15 = (3 , 5) , ( 5 , 3)

16 = (2 , 8) , ( 4 , 4) , ( 8 , 2)

18 = ( 3, 6) , ( 6 , 3)

20 = ( 4, 5) , ( 5, 4)

21 = ( 3 , 7) , ( 7 , 3)

Number of samples, n = 40

P (Product is less than or equal to 21) = 40/64 = 0.625.

(v)

The product of the two numbers is divisible by 4 or 6:

Product is divisible by 4 or 6 samples:

4 = (1 , 4) , ( 2, 2) , ( 4, 1)

6 = ( 1, 6) , ( 2, 3) , ( 3, 2) , ( 6 , 1)

8 = ( 1 , 8) , ( 2, 4) , ( 4 , 2) , ( 8 , 1)

12 = (2 , 6) , ( 3 , 4) , ( 4 3) , ( 6 , 2)

16 = (2 , 8) , ( 4 , 4) , ( 8 , 2)

18 = ( 3, 6) , ( 6 , 3)

20 = ( 4, 5) , ( 5, 4)

24 = ( 3 , 8) , ( 4 , 6 ) , ( 6 , 4) , ( 8 , 3)

28 = ( 4 , 7) , ( 7 , 4)

30 = ( 5 , 6) , ( 6 ,5 )

32 = ( 4 , 8) , ( 8 , 4)

36 = (6 , 6)

40 = ( 5 , 8) , ( 8 , 5)

42 = ( 6 , 7) , ( 7 , 6)

48 = ( 6 , 8) , ( 8 , 6)

56 = ( 7 , 8) , ( 8 , 8)

64 = ( 8 , 8)

Number of samples, n = 42

P (Product is less than or equal to 21) = 42/64 = 0.6563.

3 0

3 years ago

4/18 is closest to: 1/2 or 1 whole

Anika [276]

Answer:

1/2, since 1 whole is 18/18 and 1/2 is equal to 9/18

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

3/4 + (1/3 ÷ 1/6) - (1/2) =

Mashcka [7]

9/4 is the answer :)

6 0

3 years ago

Read 2 more answers

What is the slope-intercept equation for the line below? (0,2) (5,4)

Alla [95]

Find the slope first
m = (y₂ - y₁)/(x₂ - x₁)
m = (4-2)/(5-0)
m = 2/5

Find the slope-intercept equation
y - y₁ = m(x - x₁)
y - 2 = 2/5 (x - 0)
y - 2 = (2/5)x
y = (2/5)x + 2

7 0

3 years ago

Read 2 more answers

F(x)=9 x^{3} +2x^2-5x+4 and g(x)=5x^3-7x+4. What is f(x)-g(x)? Show all of your steps and write your finial answer in factored f

olasank [31]

Answer:

{ -0.5 - √2, 0, -.5 + √2 }

Step-by-step explanation:

Let's rewrite these two functions in a vertical column:

f(x)=9 x^{3} +2x^2-5x+4

-g(x)=5x^3-7x+4

Now combine (through subtraction) like terms, in order of descending powers of x:

f(x) - g(x) = 4x^ 3 + 2x^2 + 2x

Let's do some preliminary factoring here. Factor 2x out of each term, obtaining

f(x) - g(x) = 2x(2x^2 + x + 1)

First setting 2x = 0, we find that x = 0 is one solution.

Applying the quadratic formula to 2x^2 + x + 1, we see that a = 2, b = 1 and c = 1. Then the two roots of this quadratic are:

-1 plus or minus √(1^2 - 4(2)(1) ) -1 ± √(8)

x = ----------------------------------------------- = ---------------

2(1) 2

This simplifies to:

-1 plus or minus √(1^2 - 4(2)(1) ) -1 ± 2√(2)

x = ----------------------------------------------- = ---------------

2(1) 2

Thus, the roots of f(x) - g(x) are { -0.5 - √2, 0, -.5 + √2 }

7 0

3 years ago