Answer: ![\dfrac{11}{87}](https://tex.z-dn.net/?f=%5Cdfrac%7B11%7D%7B87%7D)
Step-by-step explanation:
Given : An automobile manufacturing plant produced 30 vehicles today: 10 were sedans, 9 were vans, and 11 were trucks.
Number of combinations of n things taking r at a time :
![^nC_r=\dfrac{n!}{r!(n-r)!}](https://tex.z-dn.net/?f=%5EnC_r%3D%5Cdfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D)
Number of ways to choose two vehicles out of 30 vehicles :-
![^{30}C_2=\dfrac{30!}{2!(28)!}\\\\=\dfrac{30\times29}{2}\\\\=435](https://tex.z-dn.net/?f=%5E%7B30%7DC_2%3D%5Cdfrac%7B30%21%7D%7B2%21%2828%29%21%7D%5C%5C%5C%5C%3D%5Cdfrac%7B30%5Ctimes29%7D%7B2%7D%5C%5C%5C%5C%3D435)
Number of ways to choose two trucks out of 11 vehicles :-
![^{11}C_2=\dfrac{11!}{2!(9)!}\\\\=\dfrac{11\times10}{2}\\\\=55](https://tex.z-dn.net/?f=%5E%7B11%7DC_2%3D%5Cdfrac%7B11%21%7D%7B2%21%289%29%21%7D%5C%5C%5C%5C%3D%5Cdfrac%7B11%5Ctimes10%7D%7B2%7D%5C%5C%5C%5C%3D55)
Now, the the probability that two trucks will be selected will be :-
![\dfrac{55}{435}=\dfrac{11}{87}](https://tex.z-dn.net/?f=%5Cdfrac%7B55%7D%7B435%7D%3D%5Cdfrac%7B11%7D%7B87%7D)
Answer:
#1 is B
Step-by-step explanation:
I think this is correct because iv done that many times before
___
/ ___ \ Let's imagine a trapezoid looks like this. The two parallel lines would be the top and the bottom lines.
The 10 in. side would be either the top or bottom line. The other parallel line is twice as long, meaning it's 2 times longer. So you multiply 10 in x 2 = 20 in.
The given side length = 10 inches.
Height = half as long, meaning it's half of 10 in. = 5 in.
Formula of a trapezoid =
![\frac{a+b}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%2Bb%7D%7B2%7D%20)
x height
Where a and b are bases. The top and bottom of the trapezoid are bases.
Area trapezoid =
![\frac{10 + 20}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B10%20%2B%2020%7D%7B2%7D%20)
x 5 =
![\frac{30}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B30%7D%7B2%7D)
x 5 = 15 x 5 = 75 in² <-- area means the unit is squared
7 x -2 = -14 therefore, d is your answer