Answer:
Concave down
Y-intercept: (0,-3)
X-intercepts: (-1,0) (-3,0)
Vertex: (-2,1)
Answer:
The kinetic energy of an object is given by: Kinetic energy = 1/2 * mass * velocity If the kinetic energy of the pendulum at the top of its swing is 0, then this tells us that the velocity of the pendulum at that point is 0
Answer:
80.0456<
<81.1210
Step-by-step explanation:
-Given the mean,
and
, the confidence interval can be calculated using the formula:

#We substitute our values in the formula to solve for CI:
![=\bar x\pm z\times \frac{\sigma}{\sqrt{n}}\\\\=\bar y\pm z_{0.05}\times \frac{s}{\sqrt{72}}\\\\=80.5833\pm 1.645\times \frac{2.77369}{\sqrt{72}}\\\\=80.5833\pm0.5377\\\\=[80.0456,81.1210]](https://tex.z-dn.net/?f=%3D%5Cbar%20x%5Cpm%20z%5Ctimes%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%5C%5C%5C%5C%3D%5Cbar%20y%5Cpm%20z_%7B0.05%7D%5Ctimes%20%5Cfrac%7Bs%7D%7B%5Csqrt%7B72%7D%7D%5C%5C%5C%5C%3D80.5833%5Cpm%201.645%5Ctimes%20%5Cfrac%7B2.77369%7D%7B%5Csqrt%7B72%7D%7D%5C%5C%5C%5C%3D80.5833%5Cpm0.5377%5C%5C%5C%5C%3D%5B80.0456%2C81.1210%5D)
Hence, the confidence interval lies between 80.0456 and 81.1210
Answer:
1. x = ±9
2.
3. 12 and -12.
4. Antoine is incorrect. There exists two solutions x=5 and x= -5.
Step-by-step explanation:
According to the questions,
Problem 1.
i.e.
i.e. x = ±9.
Problem 2.
i.e.
i.e.
i.e.
Problem 3. [tex]f(x)=x^{2}-144[tex]
To find the roots, we take, [tex]x^{2}-144=0[tex] i.e. [tex]x^{2}=144[tex] i.e. x = ±12.
Thus, the options are 12 and -12.
Problem 4. We have [tex]f(x)=x^{2}+25[tex]
For the roots, we take, [tex]x^{2}+25=0[tex] i.e. [tex]x^{2}=25[tex] i.e. x = ±5.
Thus, Antoine is not correct and two solutions namely x=5 and x= -5 exists.