The volume of a sphere is given by:
So, we need to deduct this equation. We will walk through Calculus on the concept of a solid of revolution that is a solid figure that is obtained by rotating a plane curve around some straight line (the axis of revolution<span>) that lies on the same plane. We know from calculus that:
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![V=\pi \int_{a}^{b}[f(x)]^{2}dx](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Cint_%7Ba%7D%5E%7Bb%7D%5Bf%28x%29%5D%5E%7B2%7Ddx)
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Then, according to the concept of solid of revolution we are going to rotate a circumference shown in the figure, then:
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Isolationg y:
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So,
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![V=\pi \int_{a}^{b}[\sqrt{r^{2}-x^{2}}]^{2}dx](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Cint_%7Ba%7D%5E%7Bb%7D%5B%5Csqrt%7Br%5E%7B2%7D-x%5E%7B2%7D%7D%5D%5E%7B2%7Ddx)
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being -r and r the limits of this integral.
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Solving:
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![V=\pi[r^{2}x-\frac{x^{3}}{3}]\right|_{-r}^{r}](https://tex.z-dn.net/?f=V%3D%5Cpi%5Br%5E%7B2%7Dx-%5Cfrac%7Bx%5E%7B3%7D%7D%7B3%7D%5D%5Cright%7C_%7B-r%7D%5E%7Br%7D)
Finally:
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The better deal is the Full Warranty, by approximately 174 dollars. To solve the cost of the full warranty, simply multiply 30 percent times the cost of the washer/dryer.30 x 1,179 = 353.70. You do not need to add anything to this because the warranty covers the extra costs. To solve for the cost of the limited warranty, multiply 14 percent times the cost of the washer/dryer, plus the cost of the new parts and the repair center costs (the warranty only covers the labor repair costs): (.14 x 1,179) + 211 + 152 --> 165.06 + 211 + 152 = 528.06. The full warranty is clearly cheaper. To figure out by how much, simply subtract the full warranty from the limited warranty: 528.06 - 353.70 = 174.36. To round to the nearest number, take off the decimal: 174. So that means your answer is D hope this helps.
The total number of people that will be selected is 14.
<u>Step-by-step explanation:</u>
For stratified random sampling at first we need to divide the population into some strata and then choose sample from each. For the given problem the response category is
Sample size of strata = (Size of entire sample by populaion size) multiply strata size
= (20 by 300) multiply 210
after solving we get, 14
therefore, 14 people will be selected.
One merit is that here since we divide the whole data into stratas and then select samples from that so it can be used as a guard against unwanted samples and also gives more accurate sample measure. Here since we required samples from the population who gave yes and no opinion so it is better to use stratified sampling method otherwise if we use simple random sampling then we may choose those samples who gave no opinion. But since we don't use that method so we can avoid this.
Answer: option D is the correct answer
Step-by-step explanation:
The shaded portion of the circle is the smaller sector whose radius is the same as the radius of the circle which is given as 4 units. The sector is always bounded by two radii with a common point which is the center of the circle and forming an angle at that point. The given sector forms an angle of 45 degrees.
Area of a sector is expressed as
#/360 × π × r^2 and # is in degrees
Therefore, area of the shaded portion or sector = 45/360 × π × 4^2
= 45/360 × 16π
= 45/360 (16π)
Well, the correlation coefficient is represented by the slope of the line which appears to be close to 2/3 (meaning 2 up, 3 right) therefore the coefficient is (+) and 2 / 3 = approx. 0.667. sooooo.<span> the correlation coefficient is most likely </span>0.872
