<h3>
Answer:</h3>
- 32 kg of 30% copper
- 48 kg of 55% copper
<h3>
Step-by-step explanation:</h3>
Let x represent the mass of 55% copper alloy that is to be used in the mix. Then 80-x is the mass of 30% copper alloy to be used. The total amount of copper in the mix is then ...
... 0.55x + 0.30(80-x) = 0.45·80
... 0.25x = 12 . . . . . . simplify, subtract 24
... x = 48 . . . . . . . . . divide by the coefficient of x
... 80-x = 32 . . . . . . the mass of 30% copper alloy required
The metalworker should combine 32 kg of 30% copper alloy with 48 kg of 55% copper alloy to make 80 kg of 45% copper alloy.
Answer:
40.2 Yards
Step-by-step explanation:
To find the diagonal length of the orchard, we need to use the Pythagorean Theorem. The formula of the Pythagorean Theorem is:
c²= a² + b²
a = 36 Yards
b = 18 Yards
Now let's plug in our values to the formula.
c² = a² + b²
c² = 36² + 18²
c² = 1296 + 324
c² = 1620
Now to find the value of c we need to get the square root of both sides.
c = 40.2
So the diagonal length of Mr. Richard's orchard is 40.2 Yards.
Answer:
24 in
Step-by-step explanation:
Perimeter is adding the length of all the sides together. So, 10 + 6 + 8 = 24
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.
