Explanation:
Sand Timer Volume Calculation
Puranik Dewangan
need an explanation
It takes 15 minutes for all of the sand to flow through a sand timer. The sand timer contains 475 grams of sand. Each millilitre of sand weighs 1.5 grams. How many millilitres of sand flow through the timer per minute?
To solve the problem, we need to find the total volume of sand that flows through the timer in 15 minutes, and then divide it by 15 to find the volume per minute.
First, let's find the total weight of the sand in grams:
475 grams
Next, we can convert the weight to volume by dividing by the weight of one milliliter of sand:
475 grams ÷ 1.5 grams/mL = 316.67 mL
So 316.67 mL of sand flows through the timer in 15 minutes. To find the volume per minute, we divide by 15:
316.67 mL ÷ 15 minutes = 21.11 mL/minute
Therefore, 21.11 millilitres of sand flow through the timer per minute.
Puranik Dewangan
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the first equation is substituted into the second equation. 12x − y = −4 4x − 3y = −6 a 4x − 3(−12x − 4) = −6 b 4x − 3(12x + 4) = −6 c 4(12x + 4) − 3y = −6 d 4(−12x − 4) − 3y = −6
To use the substitution method, we need to solve one of the equations for one of the variables in terms of the other variable, and then substitute the resulting expression into the other equation. In this case, we can solve the first equation for y:
12x - y = -4
y = 12x + 4
Now we can substitute this expression for y into the second equation:
4x - 3y = -6
4x - 3(12x + 4) = -6
Simplifying this equation gives:
4x - 36x - 12 = -6
-32x = 6
x = -6/32 = -3/16
Now we can substitute this value of x back into either of the original equations to find y. Let's use the first equation:
12x - y = -4
12(-3/16) - y = -4
-27/4 = y
So the solution to the system is (x, y) = (-3/16, -27/4).
Therefore, the answer to the given question is (b) 4x − 3(12x + 4) = −6, which is the second equation after the substitution of y = 12x + 4.