Answer:
3:4.
Step-by-step explanation:
To work this out we need to find the highest multiple of 45 and 60.
15 is the largest number that goes into both of them so what we are going to do now is divide both number by 15.
45 divided by 15 = 3
60 divided by 15 = 4
Therefore the odds of selecting a red candy is 3:4.
Hope that helps. x
Answer:
h(8q²-2q) = 56q² -10q
k(2q²+3q) = 16q² +31q
Step-by-step explanation:
1. Replace x in the function definition with the function's argument, then simplify.
h(x) = 7x +4q
h(8q² -2q) = 7(8q² -2q) +4q = 56q² -14q +4q = 56q² -10q
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2. Same as the first problem.
k(x) = 8x +7q
k(2q² +3q) = 8(2q² +3q) +7q = 16q² +24q +7q = 16q² +31q
_____
Comment on the problem
In each case, the function definition says the function is not a function of q; it is only a function of x. It is h(x), not h(x, q). Thus the "q" in the function definition should be considered to be a literal not to be affected by any value x may have. It could be considered another way to write z, for example. In that case, the function would evaluate to ...
h(8q² -2q) = 56q² -14q +4z
and replacing q with some value (say, 2) would give 196+4z, a value that still has z as a separate entity.
In short, I believe the offered answers are misleading with respect to how you would treat function definitions in the real world.
Question # 14
Given the numbers
10 11 12 13 14 15 16 17 18 19 20
Let 'x' be the number
The condition breakdown:
I am less than 20.
- So the number 'x' must be less than 20 i.e. x < 20
I am more than 13.
- So the number 'x' must be greater than 13 i.e. x > 13
I am less than 17.
- So the number 'x' must be less than 17 i.e. x < 17
Finally:
I am 4 more than 12
i.e. 12+4 = 16
Thus, the number is x = 16
Question # 15
Part a)
Given the numbers
10 11 12 13 14 15 16 17 18 19 20
Let 'x' be the number
The condition breakdown:
I am more than 10.
I am less than 20.
I am more than 12.
I am less than 15.
As the numbers left after all the conditions are fulfilled are 13 and 14.
- But the last condition is, of the numbers that left, the number is greater than all the remaining numbers.
So, from the remaining number 13 and 14;
14 > 13
Thus, the number x = 14
Part b)
Drawing the number 14 in the place value:
Chart
Tens Ones
1 4
Answer:
x + y = ±15
Step-by-step explanation:
Step 1: Write out systems of equations
x - y = 1
xy = 56
Step 2: Rearrange 1st equation
x = y + 1
Step 3: Substitution
(y + 1)y = 56
Step 4: Distribute
y² + y = 56
Step 5: Solve for <em>y</em>
y² + y - 56 = 0
(y - 7)(y + 8) = 0
y = -8, 7
Step 6: Plug in <em>y </em>to find <em>x</em>
x - 7 = 1
x = 8
x - (-8) = 1
x + 8 = 1
x = -7
Step 7: Find answer
x + y = ?
8 + 7 = 15
-7 + -8 = -15
So both 15 and -15 could be the answer.
