Answer:
The bus travelled 60 miles in 1 hour.
Step-by-step explanation:
To solve this problem we need to calculate the average speed at which the bus travelled. This is given by the distance travelled divided by the time that they took to get there. So we have:
average speed = distance/time
average speed = 360/6
average speed = 60 miles/h
Therefore in 1 hour they travelled 60 miles.
Answer:
The probability that he chooses a yellow ball is 5/14. If he removes all the orange balls, the probability that he will choose a red ball is 2/10.
Step-by-step explanation:
Simple logic.
Answer: If X = 5, z=<u>-3</u>
If X = 37, z= <u>3.4</u>
Step-by-step explanation:
We know that the formula to find the z-score for any random variable x is given by :-
![z=\dfrac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
, where
= Population mean
= Population standard deviation.
As per given , we have
![\mu=20\\\\\sigma=5](https://tex.z-dn.net/?f=%5Cmu%3D20%5C%5C%5C%5C%5Csigma%3D5)
Then , the z-score for x =5
![z=\dfrac{5-20}{5}=\dfrac{-15}{5}=-3](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B5-20%7D%7B5%7D%3D%5Cdfrac%7B-15%7D%7B5%7D%3D-3)
i.e. If X = 5, z=<u>-3</u>
When x =37,then ![z=\dfrac{37-20}{5}=\dfrac{17}{5}=3.4](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B37-20%7D%7B5%7D%3D%5Cdfrac%7B17%7D%7B5%7D%3D3.4)
i.e. If X = 37, z= <u>3.4</u>
Answer:
The value of x is:
![x=\dfrac{5\pm \sqrt{103}i}{8}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B5%5Cpm%20%5Csqrt%7B103%7Di%7D%7B8%7D)
Step-by-step explanation:
we have to use the quadratic formula to solve for x.
The equation is given as:
![4x^2-3x+9=2x+1](https://tex.z-dn.net/?f=4x%5E2-3x%2B9%3D2x%2B1)
which could also be written as:
![4x^2-3x+9-2x-1=0\\\\4x^2-3x-2x+9-1=0\\\\\\4x^2-5x+8=0](https://tex.z-dn.net/?f=4x%5E2-3x%2B9-2x-1%3D0%5C%5C%5C%5C4x%5E2-3x-2x%2B9-1%3D0%5C%5C%5C%5C%5C%5C4x%5E2-5x%2B8%3D0)
The quadratic formula for the quadratic equation of the type:
is given as:
![x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Here we have:
a=4, b=-5 and c=8.
Hence, by the quadratic formula we have:
![x=\dfrac{-(-5)\pm \sqrt{(-5)^2-4\times 8\times 4}}{2\times 4}\\\\x=\dfrac{5\pm \sqrt{25-128}}{8}\\\\\\x=\dfrac{5\pm \sqrt{103}i}{8}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-%28-5%29%5Cpm%20%5Csqrt%7B%28-5%29%5E2-4%5Ctimes%208%5Ctimes%204%7D%7D%7B2%5Ctimes%204%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7B5%5Cpm%20%5Csqrt%7B25-128%7D%7D%7B8%7D%5C%5C%5C%5C%5C%5Cx%3D%5Cdfrac%7B5%5Cpm%20%5Csqrt%7B103%7Di%7D%7B8%7D)
Hence, the value of x is:
![x=\dfrac{5\pm \sqrt{103}i}{8}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B5%5Cpm%20%5Csqrt%7B103%7Di%7D%7B8%7D)