<span>2n + 5 + n + 3n = (2n + n + 3n) + 5 = 6n +5
</span>Expression I is equivalent to the expression II.
Answer:
The volume of cone is
unit³.
Step-by-step explanation:
<u>Solution</u> :
As per given question we have provided :
- ➝ Radius of cone = 4 units
- ➝ Height of cone = 10 units
Here's the required formula to find the volume of cone :
![{\longrightarrow{\pmb{\sf{V_{(Cone)} = \dfrac{1}{3}\pi{r}^{2}h}}}}](https://tex.z-dn.net/?f=%7B%5Clongrightarrow%7B%5Cpmb%7B%5Csf%7BV_%7B%28Cone%29%7D%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%5Cpi%7Br%7D%5E%7B2%7Dh%7D%7D%7D%7D)
- V = Volume
- π = 3.14
- r = radius
- h = height
Substituting all the given values in the formula to find the volume of cone :
![{\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{1}{3}\pi{r}^{2}h}}}](https://tex.z-dn.net/?f=%7B%5Clongrightarrow%7B%5Csf%7BVolume_%7B%28Cone%29%7D%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%5Cpi%7Br%7D%5E%7B2%7Dh%7D%7D%7D)
![{\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{1}{3} \times 3.14{(4)}^{2}10}}}](https://tex.z-dn.net/?f=%7B%5Clongrightarrow%7B%5Csf%7BVolume_%7B%28Cone%29%7D%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20%5Ctimes%203.14%7B%284%29%7D%5E%7B2%7D10%7D%7D%7D)
![{\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{1}{3} \times 3.14{(4 \times 4)}10}}}](https://tex.z-dn.net/?f=%7B%5Clongrightarrow%7B%5Csf%7BVolume_%7B%28Cone%29%7D%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20%5Ctimes%203.14%7B%284%20%5Ctimes%204%29%7D10%7D%7D%7D)
![{\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{1}{3} \times 3.14{(16)}10}}}](https://tex.z-dn.net/?f=%7B%5Clongrightarrow%7B%5Csf%7BVolume_%7B%28Cone%29%7D%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20%5Ctimes%203.14%7B%2816%29%7D10%7D%7D%7D)
![{\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{1}{3} \times 3.14 \times 16 \times 10}}}](https://tex.z-dn.net/?f=%7B%5Clongrightarrow%7B%5Csf%7BVolume_%7B%28Cone%29%7D%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20%5Ctimes%203.14%20%5Ctimes%2016%20%5Ctimes%2010%7D%7D%7D)
![{\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{1}{3} \times 3.14 \times 160}}}](https://tex.z-dn.net/?f=%7B%5Clongrightarrow%7B%5Csf%7BVolume_%7B%28Cone%29%7D%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20%5Ctimes%203.14%20%5Ctimes%20160%7D%7D%7D)
![{\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{1\times 3.14 \times 160}{3}}}}](https://tex.z-dn.net/?f=%7B%5Clongrightarrow%7B%5Csf%7BVolume_%7B%28Cone%29%7D%20%3D%20%5Cdfrac%7B1%5Ctimes%203.14%20%5Ctimes%20160%7D%7B3%7D%7D%7D%7D)
![{\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{3.14 \times 160}{3}}}}](https://tex.z-dn.net/?f=%7B%5Clongrightarrow%7B%5Csf%7BVolume_%7B%28Cone%29%7D%20%3D%20%5Cdfrac%7B3.14%20%5Ctimes%20160%7D%7B3%7D%7D%7D%7D)
![{\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{502.4}{3}}}}](https://tex.z-dn.net/?f=%7B%5Clongrightarrow%7B%5Csf%7BVolume_%7B%28Cone%29%7D%20%3D%20%5Cdfrac%7B502.4%7D%7B3%7D%7D%7D%7D)
![{\longrightarrow{\sf{Volume_{(Cone)} \approx 167.47}}}](https://tex.z-dn.net/?f=%7B%5Clongrightarrow%7B%5Csf%7BVolume_%7B%28Cone%29%7D%20%20%5Capprox%20167.47%7D%7D%7D)
![\star{\underline{\boxed{\sf{\purple{Volume_{(Cone)} \approx 167.47\: {unit}^{3}}}}}}](https://tex.z-dn.net/?f=%5Cstar%7B%5Cunderline%7B%5Cboxed%7B%5Csf%7B%5Cpurple%7BVolume_%7B%28Cone%29%7D%20%5Capprox%20167.47%5C%3A%20%20%7Bunit%7D%5E%7B3%7D%7D%7D%7D%7D%7D)
Hence, the volume of cone is 167.47 unit³.
![\rule{300}{2.5}](https://tex.z-dn.net/?f=%5Crule%7B300%7D%7B2.5%7D)
Answer:
1x - 1
Step-by-step explanation:
So first you distribute; and that should give you 1x - 1
Answer:
There is enough evidence at the 1% level of significance to suggest that the mean stopping distance of the truck is greater than 30
Step-by-step explanation:
We will conduct a hypothesis test for the mean. We will compare the mean stopping distance of the truck to the maximum distance of 30 and see if there is any significant difference.
We first need to find the mean and standard deviation of the stopping distance of the sample. See the first attached photo for the calculations of these values..
We get a sample mean of: 31.2333
and a sample standard deviation of: 0.2813
We will use these to conduct a hypothesis test. See the calculations for the test on the second attached photo
9514 1404 393
Answer:
a) 4
b) 3
Step-by-step explanation:
a. The total number of real and complex zeros is equal to the degree of the polynomial. That total is (1 negative real) + (3 positive real/complex) = 4 total zeros. The degree of the polynomial is 4.
The even degree is confirmed by the answer to part b, and by the end-behavior shown in the table, which has a tendency to -∞ for |x|→∞.
__
b. The intermediate value theorem tells you there will be zeros in the intervals (0, 1), (1, 2), and (2, 3) according to the values in the table. (The function changes sign in those intervals.) Thus there are 3 positive real zeros.
_____
<em>Additional comment</em>
Stanley cannot tell anything about Descartes' rule of signs by analyzing the table of function values. To use that rule, he must have terms of the polynomial. If he has those terms, he already knows the degree of the polynomial.