Answer:
55 lbs of $0.40 and 45 lbs of $1.40
Step-by-step explanation:
Let's say that we have two buckets, one that weighs x pounds and the candies in it are $0.40 per pound and another that weighs 100-x pounds (because we know the two added together must be 100 pounds) and the candies in it are $1.40 per pound.
There is a third bucket that is made when you combine the two, it weighs 100 pounds and the candies in it are $0.85. Multiply the cents per pound by the pounds of the candy for each bucket and you get this equation:
0.4 * x + 1.4 (100-x) = 0.85 * 100
Solve!
0.4x + 140 - 1.4x = 85
-x + 140 = 85
-x = -55
x = 55
From this we get that 100 - x = 45.
So, the answer is 55 lbs of $0.40 and 45 lbs of $1.40
Answer is 39.55 I’m pretty sure
Answer:
![z(t) = (0.9808)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%280.9808%29%5Et)
![z(t) = (1.0196)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%281.0196%29%5Et)
![z(t) = (0.9808)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%280.9808%29%5Et)
![z(t) = (1.03)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%281.03%29%5Et)
![z(t) = (1.0404)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%281.0404%29%5Et)
![z(t) = (1.0001)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%281.0001%29%5Et)
Step-by-step explanation:
We are given the following in the question:
![x(t)=(1.04)^t\\y(t)t=(1.02)^t](https://tex.z-dn.net/?f=x%28t%29%3D%281.04%29%5Et%5C%5Cy%28t%29t%3D%281.02%29%5Et)
We have to find the growth rate z(t) in each of the following cases:
(a) z = xy
![z(t) = x(t)y(t)\\z(t) = (1.04)^t.(1.02)^t\\z(t) = (1.04\times 1.02)^t\\z(t) = (1.0608)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20x%28t%29y%28t%29%5C%5Cz%28t%29%20%3D%20%281.04%29%5Et.%281.02%29%5Et%5C%5Cz%28t%29%20%3D%20%281.04%5Ctimes%201.02%29%5Et%5C%5Cz%28t%29%20%3D%20%281.0608%29%5Et)
(b) z=x/y
![z(t) =\displaystyle\frac{x(t)}{y(t)}\\\\z(t) = \frac{(1.04)^t}{(1.02)^t} = \bigg(\frac{1.04}{1.02}\bigg)^t\\\\z(t) = (1.0196)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%5Cdisplaystyle%5Cfrac%7Bx%28t%29%7D%7By%28t%29%7D%5C%5C%5C%5Cz%28t%29%20%3D%20%5Cfrac%7B%281.04%29%5Et%7D%7B%281.02%29%5Et%7D%20%3D%20%5Cbigg%28%5Cfrac%7B1.04%7D%7B1.02%7D%5Cbigg%29%5Et%5C%5C%5C%5Cz%28t%29%20%3D%20%281.0196%29%5Et)
(c) z=y/x
![z(t) =\displaystyle\frac{y(t)}{x(t)}\\\\z(t) = \frac{(1.02)^t}{(1.04)^t} = \bigg(\frac{1.02}{1.04}\bigg)^t\\\\z(t) = (0.9808)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%5Cdisplaystyle%5Cfrac%7By%28t%29%7D%7Bx%28t%29%7D%5C%5C%5C%5Cz%28t%29%20%3D%20%5Cfrac%7B%281.02%29%5Et%7D%7B%281.04%29%5Et%7D%20%3D%20%5Cbigg%28%5Cfrac%7B1.02%7D%7B1.04%7D%5Cbigg%29%5Et%5C%5C%5C%5Cz%28t%29%20%3D%20%280.9808%29%5Et)
(d) z=x^(1/2) y^(1/2)
![z(t) = (x(t))^{\frac{1}{2}}(y(t))^{\frac{1}{2}}\\z(t) = ((1.04)^t)^\frac{1}{2} ((1.02)^t)^\frac{1}{2}\\z(t) = (1.0608)^{\frac{t}{2}}\\z(t) = (1.03)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%28x%28t%29%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%28y%28t%29%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5C%5Cz%28t%29%20%3D%20%28%281.04%29%5Et%29%5E%5Cfrac%7B1%7D%7B2%7D%20%28%281.02%29%5Et%29%5E%5Cfrac%7B1%7D%7B2%7D%5C%5Cz%28t%29%20%3D%20%281.0608%29%5E%7B%5Cfrac%7Bt%7D%7B2%7D%7D%5C%5Cz%28t%29%20%3D%20%281.03%29%5Et)
(e) z=(x/y)^2
![z(t) =\bigg(\displaystyle\frac{x(t)}{y(t)}\bigg)^2\\\\z(t) =\bigg( \frac{(1.04)^t}{(1.02)^t}\bigg)^2 = \bigg(\frac{1.04}{1.02}\bigg)^{2t}\\\\z(t) = (1.0404)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%5Cbigg%28%5Cdisplaystyle%5Cfrac%7Bx%28t%29%7D%7By%28t%29%7D%5Cbigg%29%5E2%5C%5C%5C%5Cz%28t%29%20%3D%5Cbigg%28%20%5Cfrac%7B%281.04%29%5Et%7D%7B%281.02%29%5Et%7D%5Cbigg%29%5E2%20%3D%20%5Cbigg%28%5Cfrac%7B1.04%7D%7B1.02%7D%5Cbigg%29%5E%7B2t%7D%5C%5C%5C%5Cz%28t%29%20%3D%20%281.0404%29%5Et)
(f) z=x^(-1/3)y^(2/3)
![z(t) = (x(t))^{\frac{-1}{3}}(y(t))^{\frac{2}{3}}\\z(t) = ((1.04)^t)^{\frac{-1}{3}}((1.02)^t)^{\frac{2}{3}}\\z(t) = ((1.04)^{\frac{-1}{3}})^t((1.02)^{\frac{2}{3}})^t\\z(t) = (1.04^{\frac{-1}{3}}\times 1.02^{\frac{2}{3}})^t\\z(t) = (1.0001)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%28x%28t%29%29%5E%7B%5Cfrac%7B-1%7D%7B3%7D%7D%28y%28t%29%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%5C%5Cz%28t%29%20%3D%20%28%281.04%29%5Et%29%5E%7B%5Cfrac%7B-1%7D%7B3%7D%7D%28%281.02%29%5Et%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%5C%5Cz%28t%29%20%3D%20%28%281.04%29%5E%7B%5Cfrac%7B-1%7D%7B3%7D%7D%29%5Et%28%281.02%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%5Et%5C%5Cz%28t%29%20%3D%20%281.04%5E%7B%5Cfrac%7B-1%7D%7B3%7D%7D%5Ctimes%201.02%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%5Et%5C%5Cz%28t%29%20%3D%20%281.0001%29%5Et)
Answer:1800 words
Step-by-step explanation:
Multiply how many words per minute she types by how many minutes she types. In this case 60x30=?. The easy way to do this is drop the 2 zeros and do 6x3=18. In the original equation we dropped the 2 zeros. Now we add them back on the back of the 18 and get 1800.
Answer:
x = -12.5
Step-by-step explanation:
Solve : -2x - 10 =15
-2x - 10 = 15
-2x = 15 + 10
-2x = 25
x = -25/2
x = -12.5