Count the number of multiples of 3, 4, and 12 in the range 1-2005:
⌊2005/3⌋ ≈ ⌊668.333⌋ = 668
⌊2005/4⌋ = ⌊501.25⌋ = 501
⌊2005/12⌋ ≈ ⌊167.083⌋ = 167
(⌊<em>x</em>⌋ means the "floor" of <em>x</em>, i.e. the largest integer smaller than <em>x</em>, so ⌊<em>a</em>/<em>b</em>⌋ is what you get when you divide <em>a</em> by <em>b</em> and ignore the remainder)
Then using the inclusion/exclusion principle, there are
668 + 501 - 2•167 = 835
numbers that are multiples of 3 or 4 but not 12. We subtract the number multiples of 12 twice because the sets of multiples of 3 and 4 both contain multiples of 12. Subtracting once removes the multiples of 3 <em>and</em> 4 that occur twice. Subtracting again removes them altogether.
Answer:
D = 15
Step-by-step explanation:
|-10|+|5|=10+5=15
|-10|=10
|5|=5
Answer:
We conclude that the graph y = x² can be transformed into the graph of the given equation y = (x - 12)²+3 by shifting the graph of y = x² right 12 units and then up 3 units.
Hence, option D is true.
Please check the attached graph.
Step-by-step explanation:
Given the parent function
y = x²
Given the transformed function
y = (x - 12)²
Horizontal Translation:
The horizontal translation of y = x² is of the form
f(x-h)
so y = y = (x - 12)² means y = x² is shifted 12 right.
Vertical Translation:
y = x²
Then y = x² + b is a vertical translation of y = x²
if b > 0, then y = x² + b is the graph of y = x² 'b' units up.
if b < 0, then y = x² + b is the graph of y = x² 'b' units down.
Thus, y = x² + 3 means the graph y = x² is vertically shifted up by 2 units.
Please check the attached graph.
-
The blue graph is representing the graph of y = x².
- The red graph is representing the graph of y = (x - 12)²+3
Therefore, the graph y = x² can be transformed into the graph of the given equation y = (x - 12)²+3 by shifting the graph of y = x² right 12 units and then up 3 units.
Hence, option D is true.
Answer:
$28.3
Step-by-step explanation:
x=rate for 1km
y=initial fee
Mike: $35 for 15km -> 35 = 15x + y
Thomas: $24.50 for 10km -> 24.50 = 10x + y
Using those two equations we see the following:
Mike paid $10.5 more for 5 more km. The initial fee remains unchanged, so we can calculate the rate for 1km, which is 10.5/5=2.1.
35 = 15x + y
24.50 = 10x + y
10.5 = 5x
2.1=x
Using that value with one of the original equations we can calculate the initial fee.
35 = 15x + y
35 = 15*2.1 + y
35 = 31.5 + y
3.5 = y
Mike paid 15*2.1=31.5 ($2.1 for every km) plus the initial fee, his total was $35.
We subtract the 31.5 from the 35(total) and get the initial fee, which is $3.5.
<u>Let's see what Lex will pay:</u>
Km travelled times 2.1 (the rate for 1km) plus 3.5 (the initial fee).
12*2.1 + 3.5 = 28.3
Lex will pay $28.3 for the same taxi company to travel 12 km.
Principal amount = 12,000
Annual interest rate (r) = 6.99% = 0.0699
Time (years) = 4 years
Number of installments (t) = 12*4 = 48 months
Monthly payment, A = P/D
Where,
D= {(1+r/12)^t-1}/{r/12*(1+r/12)^t} = {(1+0.0699/12)^48-1}/{0.0699/12(1+0.0699/12)^48} = 42.47
Therefore, A = 12000/42.47 = 282.59
Total payments after 4 years = 282.59*4*12 = 13,564.17
Interest owed = 13,564.17 - 12,000 = 1,564.17
