Answer: 72.78% of the drivers are traveling between 70 and 80 miles per hour based on this distribution.
Step-by-step explanation:
Let X be a random variable that represents the speed of the drivers.
Given: population mean : M = 72 miles ,
Standard deviation: s= 3.2 miles
The probability that the drivers are traveling between 70 and 80 miles per hour based on this distribution:
![P(70\leq X\leq 80)=P(\frac{70-72}{3.2}\leq \frac{X-M}{s}\leq\frac{80-72}{3.2})\\\\= P(-0.625\leq Z\leq 2.5)\ \ \ \ \ [Z=\frac{X-M}{s}]\\\\=P(Z\leq2.5)-P(Z\leq -0.625)\\\\\\ =0.9938-0.2660\ \ \ [\text{Using p-value calculator}]\\\\=0.7278](https://tex.z-dn.net/?f=P%2870%5Cleq%20X%5Cleq%2080%29%3DP%28%5Cfrac%7B70-72%7D%7B3.2%7D%5Cleq%20%5Cfrac%7BX-M%7D%7Bs%7D%5Cleq%5Cfrac%7B80-72%7D%7B3.2%7D%29%5C%5C%5C%5C%3D%20P%28-0.625%5Cleq%20Z%5Cleq%202.5%29%5C%20%5C%20%5C%20%5C%20%5C%20%5BZ%3D%5Cfrac%7BX-M%7D%7Bs%7D%5D%5C%5C%5C%5C%3DP%28Z%5Cleq2.5%29-P%28Z%5Cleq%20-0.625%29%5C%5C%5C%5C%5C%5C%20%3D0.9938-0.2660%5C%20%5C%20%5C%20%5B%5Ctext%7BUsing%20p-value%20calculator%7D%5D%5C%5C%5C%5C%3D0.7278)
Hence, 72.78% of the drivers are traveling between 70 and 80 miles per hour based on this distribution.
<span>Formula for volume of cube: V = a³
</span>V = (5)³ = 5<span> × </span>5<span> × </span><span>5 = 125 cm</span>³
Using product rule;
f(x)=(1+6x²)(x-x²)
f'(x)=(12x)(x-x²) + (1-2x)(1+6x²) = 12x² -12x³ +1 +6x² -2x -12x³ = -24x³ +18x² -2x +1
Solving the bracket first;
f(x)=(1+6x²)(x-x²) = x -x² +6x³ -6x^4
f'(x)= 1 -2x +18x² -24x³ = -24x³ +18x² -2x +1
Answer:
y = -5/3x + 4/3z
Step-by-step explanation:
5x + 3y = 4z
3y = -5x + 4z
y = -5/3x + 4/3z