Answer:

Step-by-step explanation:

Applying the Laplace transform:
![\mathcal{L}[y'']+5\mathcal{L}[y']+4\mathcal{L}[y']=0](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5By%27%27%5D%2B5%5Cmathcal%7BL%7D%5By%27%5D%2B4%5Cmathcal%7BL%7D%5By%27%5D%3D0)
With the formulas:
![\mathcal{L}[y'']=s^2\mathcal{L}[y]-y(0)s-y'(0)](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5By%27%27%5D%3Ds%5E2%5Cmathcal%7BL%7D%5By%5D-y%280%29s-y%27%280%29)
![\mathcal{L}[y']=s\mathcal{L}[y]-y(0)](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5By%27%5D%3Ds%5Cmathcal%7BL%7D%5By%5D-y%280%29)
![\mathcal{L}[x]=L](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5Bx%5D%3DL)

Solving for 




Apply the inverse Laplace transform with this formula:
![\mathcal{L}^{-1}[\frac1{s-a}]=e^{at}](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5E%7B-1%7D%5B%5Cfrac1%7Bs-a%7D%5D%3De%5E%7Bat%7D)
![y=3\mathcal{L}^{-1}[\frac1{s+4}]=3e^{-4t}](https://tex.z-dn.net/?f=y%3D3%5Cmathcal%7BL%7D%5E%7B-1%7D%5B%5Cfrac1%7Bs%2B4%7D%5D%3D3e%5E%7B-4t%7D)
Answer:
61,239,550
Step-by-step explanation:
We let the random variable X denote the IQ scores. This would imply that X is normal with a mean of 100 and standard deviation of 17. We proceed to determine the probability that an individual chosen at random from the population would be a genius, that is;
Pr( X>140)
The next step is to evaluate the z-score associated with the IQ score of 140 by standardizing the random variable X;

The area to the right of 2.3529 will be the required probability. This area from the standard normal tables is 0.009314
From a population of 6,575,000,000 the number of geniuses would be;
6,575,000,000*0.009314 = 61,239,550
Multiply the amount of seconds to ring up items by the amount of items.
1 × 17 = 17
Now add the amount of seconds to process a payment to the product.
17 + 25 = 42
<h2>Answer:</h2>
<u>It takes </u><u>42 seconds</u><u> to ring up a customer with 17 items.</u>
Answer:
A. 502.4 cm^3
Step-by-step explanation:
r=8/2=4 cm
V=pi*r^2*h=3.14*16*10=502.4 cm^3 (A)
Using 3.14 for PI.
The radius of a ball and the can is half the diameter = 1.25
The height of the can is the height of 3 diameters = 7.5
Volume of one tennis ball:
4/3 x PI x 1.25^3 = 8.18 cubic inches.
Volume of 3 tennis balls: 3 x 8.18 = 24.54 cubic inches.
Volume of can:
PI x 1.25^2 x 7.5 = 36.80 cubic inches.
Space = 36.80 - 24.54 = 12.26 cubic inches.