There are 36 possible ways of throwing two dices. The following lists are shown in ordered pair:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
a) a pair of 3's
The probability is 1/36 because there is only one pair which is (3,3).
b) any pair
The probability is 6/36 or 1/6 because the number of pairs are (1,1) (2,2) (3,3) (4,4) (5,5) and (6,6).
c) at least one 4
The probability is 10/36 or 5/18 because there would be (4,1) (4,2) (4,3) (4,5) (4,6) (1,4) (2,4) (3,4) (5,4) (6,4) for any combination.
d) a total of 9
The probability is 4/26 or 2/13 because (4,5) (5,4) (3,6) (6,3) are the totals of 9.
5) a total greater than 8
The probability is 10/36 or 5/18. Just find the ordered pair having a sum greater than 8.
Hope this helps.
f(g(x)) means to plug the value of g(x) into every x you see in f(x) and do the math.
g(x) = 3x
f(3x) = 2(3x) - 1
f(3x) = 6x - 1
So, f(g(x)) = 6x - 1.
Understand?
h(f(x)) means to plug the value of f(x) into every x you see in h(x) and do the math.
h(x) = x^2 + 1
h(2x - 1) = (2x - 1)^2 + 1
h(2x - 1) = (2x - 1)(2x - 1) + 1
h(2x - 1) = 4x^2 - 4x + 1 + 1
h(2x - 1) = 4x^2 - 4x + 2
So, h(f(x)) = 4x^2 - 4x + 2
Understand?
This is called COMPOSITION OF FUNCTIONS.
<span>The answer two this question is C.
You can get this answer by multiplying the two polynomials and then simplifying. See the steps below:
(4x^2 - 5)(x + 3) ---> Now multiply the two parenthesis.
4x^3 - 5x + 12x^2 - 15 ---> Arrange the numbers by decreasing exponents.
4x^3 + 12x^2 - 5x - 15
No simplifying can be done since there are no like terms. </span>
Answer:
An inequality to model the situation is : ( 10 m + 3 n) ≥ 150
Here, m : The number of jeans sold
n : The number of shirts sold.
Step-by-step explanation:
Here, the profit on each sale of jeans = $ 10
The profit on each sale of shirt = $ 3
The profit needed to be made = AT LEAST $150
Now, here: Let us assume the number of jeans sold = m
And, The number of shorts sold =n
So, the profit on m jeans = m x ( Profit on 1 jeans) = m x ( $ 10) = 10 m
So, the profit on n shirts = n x ( Profit on 1 shirt) = n x ( $ 3) = 3 n
⇒ The total profit on m jeans + n shirts = ( 10 m + 3 n)
But, according to the question, the profit should AT LEAST $150.
⇒ TOTAL PROFIT ≥ $ 150
⇒ ( 10 m + 3 n) ≥ 150
Hence, an inequality to model the situation is : ( 10 m + 3 n) ≥ 150