Answer:
The side lengths are 30, 36 and 39.
Step-by-step explanation:
To find the missing side, write a proportion using side lengths from each similar shape. A proportion is an equation that sets equal two ratios.
Find y by cross multiplying numerator and denominator of each fraction.
13y = 39(12)
13y = 468
y = 36
Find the other missing side by repeating the process.
Find y by cross multiplying numerator and denominator of each fraction.
13y = 39(10)
13y = 390
y = 30
The side lengths are 30, 36 and 39.
Answer:
Through open market operations Government can fluctuate the money supply in the economy. One of the short-term effects is to drive the price level from 100 down to 93.3. In short run, decrease in money supply will leads to higher interest rate, this will discourage the investors. Thus, investing and spending will fall which will shift the aggregate demand curve leftward.
<em>check the attached file for the curve</em>
In long run adjustment in wages tale place and firm will pay lower wage rate to workers. Since nominal wages will decrease overtime causing the SRAS curve to shift rightward. Because unemployment is created in the short run which decreases wages, so supply increase from SRAS to SRAS (1). Long run equilibrium will attain at (8,87.5).
![\Bbb E[Y^2] = \Bbb E[(4X - 2)^2]](https://tex.z-dn.net/?f=%5CBbb%20E%5BY%5E2%5D%20%3D%20%5CBbb%20E%5B%284X%20-%202%29%5E2%5D)
so by definition of expectation,
![\Bbb E[Y^2] = \displaystyle \int_{-\infty}^\infty (4x-2)^2 f_X(x) \, dx = \int_0^\infty 3(4x-2)^2 e^{-3x} \, dx](https://tex.z-dn.net/?f=%5CBbb%20E%5BY%5E2%5D%20%3D%20%5Cdisplaystyle%20%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20%284x-2%29%5E2%20f_X%28x%29%20%5C%2C%20dx%20%3D%20%5Cint_0%5E%5Cinfty%203%284x-2%29%5E2%20e%5E%7B-3x%7D%20%5C%2C%20dx)
Integrate by parts (twice).
First, let
so that
![\displaystyle \Bbb E[Y^2] = -(4x-2)^2 e^{-3x} \bigg|_{x=0}^{x\to\infty} + 8 \int_0^\infty (4x-2) e^{-3x} \, dx \\\\ ~~~~ = 4 + 8 \int_0^\infty (4x-2) e^{-3x} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5CBbb%20E%5BY%5E2%5D%20%3D%20-%284x-2%29%5E2%20e%5E%7B-3x%7D%20%5Cbigg%7C_%7Bx%3D0%7D%5E%7Bx%5Cto%5Cinfty%7D%20%2B%208%20%5Cint_0%5E%5Cinfty%20%284x-2%29%20e%5E%7B-3x%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%20~~~~%20%3D%204%20%2B%208%20%5Cint_0%5E%5Cinfty%20%284x-2%29%20e%5E%7B-3x%7D%20%5C%2C%20dx)
Next,
so that
![\displaystyle \Bbb E[Y^2] = 4 + 8 \left(-\frac13 (4x-2) e^{-3x} \bigg|_{x=0}^{x\to\infty} + \frac43 \int_0^\infty e^{-3x} \, dx\right) \\\\ ~~~~ = 4 + 8 \left(-\frac23 - \frac49 e^{-3x}\bigg|_{x=0}^{x\to\infty}\right) \\\\ ~~~~ = 4 - \frac{16}3 + \frac{32}9 = \boxed{\frac{20}9}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5CBbb%20E%5BY%5E2%5D%20%3D%204%20%2B%208%20%5Cleft%28-%5Cfrac13%20%284x-2%29%20e%5E%7B-3x%7D%20%5Cbigg%7C_%7Bx%3D0%7D%5E%7Bx%5Cto%5Cinfty%7D%20%2B%20%5Cfrac43%20%5Cint_0%5E%5Cinfty%20e%5E%7B-3x%7D%20%5C%2C%20dx%5Cright%29%20%5C%5C%5C%5C%20~~~~%20%3D%204%20%2B%208%20%5Cleft%28-%5Cfrac23%20-%20%5Cfrac49%20e%5E%7B-3x%7D%5Cbigg%7C_%7Bx%3D0%7D%5E%7Bx%5Cto%5Cinfty%7D%5Cright%29%20%5C%5C%5C%5C%20~~~~%20%3D%204%20-%20%5Cfrac%7B16%7D3%20%2B%20%5Cfrac%7B32%7D9%20%3D%20%5Cboxed%7B%5Cfrac%7B20%7D9%7D)
The answer I got was 0.18
Answer:
Using 5.25 cups of flour would make 3 batches of cookies. He made 180 cookies.
Step-by-step explanation:
To see how many batches you make all you do is take the 5.25 and divide it by 1.75 because thats how much it takes to make 1. When you divide it you get 3. If there are 5 dozen in each batch thats 60 cookies because 1 dozen is 12. Then,since he made 3 batches you multiply the 60 by 3 and you get 180.
Hope this helps!
