What is the slope and write an equation in slope intercept form.
1 answer:
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Answer: 294.4 m²
<u>Step-by-step explanation:</u>
Separate the shaded region into two parts:
- The section containing the central angle of 230° (360° - 130°)
- The triangle with sides 11.1, 11.1 & 20.12 (use Law of Cosines)
Area of shaded region = Area of (1) + Area of (2)
= 247.3 + 47.1
= 294.4
Answer:
The probability hat the sample mean height for the 40 chimneys is greater than 102 meters is 0.1469.
Step-by-step explanation:
Let the random variable <em>X</em> be defined as the height of chimneys in factories.
The mean height is, <em>μ</em> = 100 meters.
The standard deviation of heights is, <em>σ</em> = 12 meters.
It is provided that a random sample of <em>n</em> = 40 chimney heights is obtained.
According to the Central Limit Theorem if we have an unknown population with mean <em>μ</em> and standard deviation <em>σ</em> and appropriately huge random samples (<em>n</em> > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
Then, the mean of the distribution of sample means is given by,
And the standard deviation of the distribution of sample means is given by,
Since the sample selected is quite large, i.e. <em>n</em> = 40 > 30, the central limit theorem can be used to approximate the sampling distribution of sample mean heights of chimneys.
Compute the probability hat the sample mean height for the 40 chimneys is greater than 102 meters as follows:
*Use a <em>z</em>-table fr the probability.
Thus, the probability hat the sample mean height for the 40 chimneys is greater than 102 meters is 0.1469.
Tow rates are equivalent if tow initial investments over a the same time, produce the same final value using different interest rates.
For the annually rate we have that:
Where
= initial investment.
= annually interest rate in decimal form.
And the exponent (1) represents the full year.
For the quarterly interest rate we have that:
Where
= initial investment.
= quarterly interest rate in decimal form.
And the exponent (4) the 4 quarters in the full year.
Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
Notice that we are not using the initial investment
since they are the same.
The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
![\sqrt[4]{1.07} =1+ i_{q}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B1.07%7D%20%3D1%2B%20i_%7Bq%7D%20)
![i_{q} = \sqrt[4]{1.07} -1](https://tex.z-dn.net/?f=%20i_%7Bq%7D%20%3D%20%5Csqrt%5B4%5D%7B1.07%7D%20-1)
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.
For the annually rate we have that:
Where
And the exponent (1) represents the full year.
For the quarterly interest rate we have that:
Where
And the exponent (4) the 4 quarters in the full year.
Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
Notice that we are not using the initial investment
The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.