Answer and Step-by-step explanation:
A. 4 inches: An object that's 4 inches is about 2.54 centimeters or 25.4 millimeters. An business envelope is typically about 4 inches by 9 inches for example.
B. 6 feet: A 6 feet object is quite big when compared to just 4 inches. A feet is 12 inches hence 6 feet is 72 inches. A very tall human being is typically 6 feet.
C. 1 meter: A meter is about 39.37 inches hence it is quite big when compared to a feet. A baseball bat is one meter long.
D. 5 yards: A yard is 36 inches hence a bit smaller than a meter. A trampoline could be 5 yards for example
E. 6 centimeters: one centimeter is 0.394 inches hence smaller than an inch. A 6 centimeters object for example is pencil for writing.
F. 2 millimeters: a millimeter is 0.0394 inches hence smaller than a centimeter and an inch. An orange seed could be 2 millimeters long
G. 3 kilometers: one kilometer is 39370.079 inches hence a kilometer is bigger than inches, meter, feet, yards, centimeters, millimeters. A very big tree could be 3 kilometers long
Answers:
(a) p + m = 5
0.8m = 2
(b) 2.5 lb peanuts and 2.5 lb mixture
Explanations:
(a) Note that we just need to mix the following to get the desired mixture:
- peanut (p) - peanuts whose amount is p
- mixture (m) - mixture (80% almonds and 20% peanuts) that has an amount of m; we denote this as
By mixing the peanuts (p) and the mixture (m), we combine their weights and equate it 5 since the mixture has a total of 5 lb.
Hence,
p + m = 5
Note that the desired 5-lb mixture has 40% almonds. Thus, the amount of almonds in the desired mixture is 2 lb (40% of 5 lb, which is 0.4 multiplied by 5).
Moreover, since the mixture (m) has 80% almonds, the weight of almonds that mixture is 0.8m.
Since we mix mixture (m) with the pure peanut to get the desired mixture, the almonds in the desired mixture are also the almonds in the mixture (m).
So, we can equate the amount of almonds in mixture (m) to the amount of almonds in the desired measure.
In terms mathematical equation,
0.8m = 2
Hence, the system of equations that models the situation is
p + m = 5
0.8m = 2
(b) To solve the system obtained in (a), we first label the equations for easy reference,
(1) p + m = 5
(2) 0.8m = 2
Note that using equation (2), we can solve the value of m by dividing both sides of (2) by 0.8. By doing this, we have
m = 2.5
Then, we substitute the value of m to equation (1) to solve for p:
p + m = 5
p + 2.5 = 5 (3)
To solve for p, we subtract both sides of equation (3) by 2.5. Thus,
p = 2.5
Hence,
m = 2.5, p = 2.5
Therefore, the solution to the system is 2.5 lb peanuts and 2.5 lb mixture.
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-Emilie Xo
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192 cakes. This is because the average cakes per minute is 4.8, you the multiply 4.8 by 40 to get 192.
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