A 292 kg motorcycle is accelerating up along a ramp that is inclined 30.0° above the horizontal. The propulsion force pushing the motorcycle up the ra

Jones figures that the total number of thousands of miles that a used auto can be driven before it would need to be junked is an exponential random variable with parameter ${\displaystyle \frac{1}{20}}$.
Smith has a used car that he claims has been driven only 10,000 miles.
If Jones purchases the car, what is the probability that she would get at least 20,000 additional miles out of it?
Repeat under the assumption that the lifetime mileage of the car is not exponentially distributed but rather is (in thousands of miles) uniformly distributed over (0, 40).

In Figure, a stationary block explodes into two pieces and R that slide across a frictionless floor and then into regions with friction, where they stop. Piece L, with a mass of 2.6 kg, encounters a coefficient of kinetic friction ${\displaystyle \mu L=0.40}$ and slides to a stop in distance deal = 0.15 m. Piece R encounters a coefficient of kinetic friction ${\displaystyle \mu R=0.50}$ and slides to a stop in distanced R=0.30 m. What was the mass of the original block?

In a scene in an action movie, a stuntman jumps from the top of one building to the top of another building 4.0m away. After a running start, he leaps at a velocity of 5.0 m/s at an angle of 15degrees with respect to the flat roof. Will he make it to the other roof, which is 2.5m shorter than the building he jumps from?

Assign a binary code in some orderly manner to the 52 playingcards. Use the minimum number of bits.

To calculate:
To evaluate the expression $\sqrt[5]{(-7{)}^5}$.

Identify the functions represented by the following power series. ${\displaystyle \sum _{k=0}^{\mathrm{\infty }}{(-1)}^k\frac{x^k}{3^k}}$

1. Consider the quadratic function.
${\displaystyle f\left(x\right)=-(x+4)(x-1)}$
a.What are the x-intercepts and y-intercepts?
b.What is the equation of the axis of symmetry?
c. What are the coordinates of the vertex? yurm quadratic function,
${\displaystyle f\left(x\right)=-(x+4)(x-1)}$
f) For x-intercepts, put ${\displaystyle f\left(x\right)=0}$
${\displaystyle \Rightarrow -(x+4)(x-1)=0}$
${\displaystyle =x+4=0\text{and}x-1=0}$
${\displaystyle x=4\text{and}x=1}$
are ${\displaystyle (-4,0)\text{and}(1,0)}$
Thus, x-intercepts are ${\displaystyle (-4,0)\text{and}(1,0)}$
For y intercepts put ${\displaystyle x=0inf\left(x\right)}$
${\displaystyle f\left(x\right)=+(0+4)(x-1)=-4}$
Thus, y-intercepts is (0, -4)
b)Reusiting the function as below:
${\displaystyle f\left(x\right)=-(x+4)(x-1)=-(x^2-x+4x-4)}$
${\displaystyle f\left(x\right)=-(x^2+3x-4)}$
${\displaystyle f\left(x\right)=-(x^2+3x+{\left(\frac{3}{2}\right)}^2-\left({\frac{3}{2}}^2\right)+4}$
${\displaystyle f\left(x\right)=-{(x+\frac{3}{2})}^2+4}$
Comparising it with vertex form, ${\displaystyle y=a{(z-h)}^2+k}$
here, ${\displaystyle a=-1,h=\frac{-3}{2}\text{and}k=4}$
Thus, axis of symmetry is ${\displaystyle x=h=\frac{-3}{2}}$
c) Vertex coordinates: ${\displaystyle (h,k)=(\frac{-3}{2,4})}$