Answer:
correct option: 2 -> It would decrease.
Step-by-step explanation:
If the amount of gas is the same, the following relation needs to be constant:
![Pressure * Volume / Temperature](https://tex.z-dn.net/?f=Pressure%20%2A%20Volume%20%2F%20Temperature)
So, If the pressure is constant, the volume and the temperature are directly proportional (if one increases, the other also increases).
Then, an decrease of 3 times in the volume would cause an decrease of 3 times in the temperature.
So the correct option is 2.: It would decrease.
Answer:
$2400 in A rated bond and $3000 in B rated bond.
Step-by-step explanation:
We have been given that Maria has recently retired and requested an extra $444.00 per year in income.
We can represent this information in an equation as:
![A+B=5400...(1)](https://tex.z-dn.net/?f=A%2BB%3D5400...%281%29)
She has $5400 to invest in an A-rated bond that pays 10% per annum or a B-rated bond paying 6% per annum.
![0.10A+0.06B=444...(2)](https://tex.z-dn.net/?f=0.10A%2B0.06B%3D444...%282%29)
From equation (1), we will get:
![A=5400-B](https://tex.z-dn.net/?f=A%3D5400-B)
Substitute this value in equation (2):
![0.10(5400-B)+0.06B=444](https://tex.z-dn.net/?f=0.10%285400-B%29%2B0.06B%3D444)
![540-0.10B+0.06B=444](https://tex.z-dn.net/?f=540-0.10B%2B0.06B%3D444)
![540-0.04B=444](https://tex.z-dn.net/?f=540-0.04B%3D444)
![540-540-0.04B=444-540](https://tex.z-dn.net/?f=540-540-0.04B%3D444-540)
![-0.04B=-96](https://tex.z-dn.net/?f=-0.04B%3D-96)
![\frac{-0.04B}{-0.04}=\frac{-96}{-0.04}](https://tex.z-dn.net/?f=%5Cfrac%7B-0.04B%7D%7B-0.04%7D%3D%5Cfrac%7B-96%7D%7B-0.04%7D)
![A=2400](https://tex.z-dn.net/?f=A%3D2400)
Therefore, Maria should invest $2400 in A-rated bond.
Substitute
in equation (1):
![2400+B=5400](https://tex.z-dn.net/?f=2400%2BB%3D5400)
![2400-2400+B=5400-2400](https://tex.z-dn.net/?f=2400-2400%2BB%3D5400-2400)
![B=3,000](https://tex.z-dn.net/?f=B%3D3%2C000)
Therefore, Maria should invest $3000 in B-rated bond.
Step-by-step explanation:
0.48 is the decimal form of 12/25
Answer:
0.0062
Step-by-step explanation:
Given that the mount of orange juice in a 500 ml can from a certain company is a random variable with a mean of 500 ml and a standard deviation of 2 ml.
As per central limit theorem sample mean follows normal here with mean = 500 ml and std error - ![\frac{2}{\sqrt{100} } \\=0.2](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B%5Csqrt%7B100%7D%20%7D%20%5C%5C%3D0.2)
Sample mean is N(500, 0.2)
Required probability
= probability that the sample mean is less than 499.5 ml
= ![P(X](https://tex.z-dn.net/?f=P%28X%3C499.5%29%5C%5C%3DP%28Z%3C%5Cfrac%7B-0.5%7D%7B0.2%7D%20%29%5C%5C%3D%20P%28Z%3C-2.5%29%5C%5C%5C%5C%20%3D0.00621)
Rounding off
0.0062
Answer:
Option (1) will be the answer.
Step-by-step explanation:
Coordinates of the points A and B lying on the line f are (0, 2) and (2, 0) respectively.
Slope of the line f,
![m_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=m_%7B1%7D%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
![m_{1}=\frac{2-0}{0-2}](https://tex.z-dn.net/?f=m_%7B1%7D%3D%5Cfrac%7B2-0%7D%7B0-2%7D)
After dilation of line f by a scale factor of 2, coordinates of A' and B' will be,
Rule for dilation,
(x, y) → (kx, ky)
Where k = scale factor
A(0, 2) → A'(0, 4)
B(2, 0) → B'(4, 0)
Slope of line f',
![m_{2}=\frac{0-4}{4-0}](https://tex.z-dn.net/?f=m_%7B2%7D%3D%5Cfrac%7B0-4%7D%7B4-0%7D)
![m_{2}=-1](https://tex.z-dn.net/?f=m_%7B2%7D%3D-1)
Since, ![m_{1}=m_{2}=-1](https://tex.z-dn.net/?f=m_%7B1%7D%3Dm_%7B2%7D%3D-1)
Therefore, both the lines f and f' will be parallel.
Option (1) will be the answer.