Given:
To find:
The exponential form of given equation.
Solution:
We have,
According to the property of the logarithm,
Using the above property of the logarithm, we get
Therefore, the required equation in exponential form is .
Answer:
-2x
Step-by-step explanation:
Rise over run,
This line goes up 4 (It goes up so it's positive).
and it goes to the left -2 times (Since it's left it's negative).
Slope: 4/-2 or -2/1 which is -2x
Answer:
(-y, x)
Step-by-step explanation:
See the image attached.
We start with (x,y), this is, x in the abscissa axis and y in the ordinates axis. When we rotate it 90 degrees clock wise, the measure on the ordinates goes to the abscissa while the abscissa goes to the ordinates. You have to notice that this last movement is to the negative part of the ordinate axis. Here we pass from (x, y) to (y, -x).
Then you rotate again, going to a 180 degrees rotation in total. The movement is the same: ordinates values go to the abscissa value. So, the -x that was on ordinates goes to the abscissa and the y in the abscissa goes to ordinates. However this last movement implies a negative sign in the y value, as we are going from positive to negative values. So, we pass from (y, -x) yo (-x, -y).
Finally we move again for reaching the 270 degrees rotation. Similar to the last 2 movements, -x passes from abscissa to ordinates and becoming x as we the sign is positive. In the same way, the -y in the ordinates goes to the abscissa and still being -y as we still on negative values. So, we finish with (-y, x).
So, this is the final answer: (-y, x)
Here I also attach a numerical example.
Answer:
The probability that computers work more than 41 minutes is 0.15866 or 15.87%.
Step-by-step explanation:
We are given that a computer tallied the time to work for 200 days and found it reasonable to the normal curve. The mean is 35 minutes, and the standard deviation with six minutes.
Let X = <u><em>the time taken by computer to work for 200 days</em></u>.
So, X ~ Normal()
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = population mean time = 35 minutes
= standard deviation = 6 minutes
Now, the probability that computers work more than 41 minutes is given by = P(X > 41 minutes)
P(X > 41 minutes) = P( > ) = P(Z > 1) = 1 - P(Z 1)
= 1 - 0.84134 = <u>0.15866</u>
The above probability is calculated by looking at the value of x = 1 in the z table which has an area of 0.84134.