First, simplify this system:
<span>2x = -10y + 6 and x + 5y = 3
by dividing the first equation by 2. Result: </span><span>x = -5y + 3
Subbing this into the 2nd equation, -5y + 3 + 5y = 3
This equation is always true, so this system has infinitely many sol'ns.</span>
<u>44%</u>
Sample space is 36C4
Now, we want to know all of the combinations that have 1 digit in it.
So, we can have one here:
1XXX
X1XX
XX1X
XXX1
But we have 10 different digits to choose from. So, we need to introduce the combination term, nCr, where n is a list of all digits and r is how many we want.
Since we only want one, we will need 10C1 for the number of digits. But we need to choose three lowercases, so it becomes 10C1 × 26C3
Since it's a probability question, we need to divide that by our sample space, 36C4, and our percentage becomes 44%
Check the picture below.
we could also look at it from the inscribed angle theorem, bearing in mind that the intercepted arc is 180°.
1. Cross multiply
35x = 5(11)
35x = 55
Divide both sides by 35
x = 55/35
x = 11/7
2. (x - 2)/x = 3/8
Cross multiply
3x = 8(x - 2)
3x = 8x - 16
Subtract 8x from both sides
-5x = -16
divide both sides by -5
x = -16/-5
x = 16/5 OR 3 1/5
3. (a + 1)/(a - 1) = 5/6
cross multiply
6(a + 1) = 5(a - 1)
distribute
6a + 6 = 5a - 5
subtract 5a from both sides
a + 6 = -5
subtract 6 from both sides
a = -11
4. (1/3)x - 4 = (2/3)x + 6
multiply each term by 3 to clear the fractions
x - 12 = 2x + 18
subtract x from both sides
-12 = x + 18
subtract 18 from both sides
-30 = x
The CPI increased from 29.6 to 82.4.
The rate of increase, is:
82.4/29.6 = 2.78
Now multiply this rate to the $0.14 price of grapes from 1960.
$0.14 x 2.78 = $0.39
Now to get the amount of increase subtract the new price from the original price:
$0.39 - $0.14 = $0.25 increase.
