Answer:
Given that the events A and B are mutually exclusive.
P(A) = 0.1
P(B) = 0.4
Mutually Exclusive Events: When two events are Mutually Exclusive it is impossible for them to happen together i.e
If A and B are two events then; P(A and B) = 0
then;
P(A or B) = P(A) +P(B)
By the definition of mutually exclusive events;
P(A or B) = P(A) +P(B) ......[1]
Substitute the values of P(A) = 0.1 and P(B) = 0.4 in [1] we have;
P(A or B) = P(A) +P(B) = 0.1+0.4 = 0.5
Check the picture below.
so is really just a thick trapezoid, or namely a trapezoidal prism 5 inches thick.
so if we just get the area of the trapezoidal face and multiply by the thickness, we'd get it's volume
![\bf \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} a,b=\stackrel{parallel~sides}{bases}\\ h=height\\[-0.5em] \hrulefill\\ a = 8\\ b = 13\\ h = 6 \end{cases}\implies A=\cfrac{6(8+13)}{2}\implies A=63 \\\\\\ \stackrel{\textit{area of the trapezoidal prism}}{63\cdot 5\implies \stackrel{in^3}{315}}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20trapezoid%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7Bh%28a%2Bb%29%7D%7B2%7D~~%20%5Cbegin%7Bcases%7D%20a%2Cb%3D%5Cstackrel%7Bparallel~sides%7D%7Bbases%7D%5C%5C%20h%3Dheight%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20a%20%3D%208%5C%5C%20b%20%3D%2013%5C%5C%20h%20%3D%206%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Ccfrac%7B6%288%2B13%29%7D%7B2%7D%5Cimplies%20A%3D63%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Barea%20of%20the%20trapezoidal%20prism%7D%7D%7B63%5Ccdot%205%5Cimplies%20%5Cstackrel%7Bin%5E3%7D%7B315%7D%7D)
57,142 because it says standard
Answer:
Leah has 48 marbles.
Step-by-step explanation:
Represent the number of marbles that each person has by L and D.
Leah has 28 more marbles than Dan: L = D + 28.
Then (1/3)L = (4/5)D. Here the LCD is 15, and so multiplying this equation by 15 will remove the fractions: 15(1/3)L = 15(4/5)D.
Therefore, 5L = 12D, and D = 5L/12.
Then, since L = D + 28, L = (5/12)L + 28, or
12L = 5L + 336, or
7L = 336, or
L = 336/7 = 48.
Leah has 48 marbles. That means that Dan has 20 marbles.
Find the least common multiple of 8, 15, and 21. . . . . . It's 280 .
So all the numbers divisible by 8, 15, and 21 are all the multiples of 280.
The smallest 6-digit number is 100,000 .
100,000 / 280 = 357.1 , so the next whole-number multiple is the 358th one.
280 x 358 = <u>100,240</u> .
You can tell right away that this is the smallest one that qualifies,
because if you take away 280 and go to the next smaller multiple,
it won't have 6 digits anymore.
