MATHEMATICS HIGH SCHOOL

(2a^2 +a + 3) (a - 1)

Answers

Answer 1

Answer:

Answer: 2a^3-a^2+2a-3

Step-by-step explanation:

(2a^2+a+3) (a-1)

2a^3-2a^2+a^2-a+3a-3

2a^3-a^2+2a-3

Note: If you need extra help with this topic, I suggest you should search up "how to multiply a trinomial by a binomial" on Google. It will help you a lot!

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Which equation is true when b = -4?A b/4 + 5.5 = 4.5
B -54 + 2b = -46
С 7b - 8 = -20
D b/8 - 6 = -8

Answers

Answer:

Step-by-step explanation:

-4/4 = -1

-1+5.5

=4.5

The answer is B. -54+2b=-46

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.(a) Draw the possibility diagram of the product of the two numbers appearing on the die in each throw (b) Use the possibility diagram to calculate the probability that the product of the two numbers is I) A prime number ii) Not a perfect square iii) A multiple of 5 iv) Less than or equal to 21 v) Divisible by 4 or 6

Answers

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.

What is the unit price of a 6 pack soda on sale for 2.99

Answers

It should be at least 50 cents for one can of soda. :)

so we will do 2.99/6 and we will get .498333333333

There were 15 cars and 25 trucks in the parking garage. what is the ratio of cars to total vehicles

Answers

15:25 = 3:5
simply divide 15 and 25 both by 5 to get 3:5.

Caitlin earns money as a lifeguard and as a pet sitter. In one week, she earned $25 pet sitting. The total amount of money she earned that week was less than $75. The inequality g + 25 less-than 75 represents g, the possible amount of money she made as a lifeguard.A number line. An open circle is at g. Everything to the left of g is shaded.

What is the value of g on the number line?

$25

$49.99

$50

$75