<h3>
Answer: 17/24</h3>
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Explanation:
We have these four cases or possible outcomes
- Case 1) We select 0 black marbles and 3 red marbles.
- Case 2) We select 1 black marble and 2 red marbles.
- Case 3) We select 2 black marbles and 1 red marble.
- Case 4) We select 3 black marbles and 0 red marbles.
Let's calculate the probability for case 4.
There are 7 black marbles out of 10 total. The probability of picking black is 7/10. If no replacement is made, then 6/9 is the probability of picking black again (subtract 1 from the numerator and denominator separately). Finally, 5/8 is the probability of getting black a third time.
The probability of getting 3 black marbles in a row is
(7/10)*(6/9)*(5/8) = (7*6*5)/(10*9*8) = 210/720 = 7/24.
That fraction 7/24 means that if you had 24 chances, then you expect about 7 of them will lead to getting three black marbles in a row (aka case 4). Therefore, 24-7 = 17 occurrences are expected where we get cases 1 through 3 occur in some fashion (pick one case only).
Notice how cases 1 through 3 encapsulate the phrasing "at most 2 black marbles" which is another way of saying "2 black marbles is the highest we can go".
So that's why the answer is 17/24.
<h3>
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➷ 
can be simplified to 2
Multiply 2 by 6 to get the simplified version for part 1
= 
can be simplified to 
Multiply 2 by 3 to get the simplified version:
= 
It would be:
<h3><u>
✽</u></h3>
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Answer:
x²+5x - 150 = 0
Step-by-step explanation:
Let the length be y and width be x
If the length of a swimming pool is 10 more than 2 times the width, then;
y = 2x+10 ...1
Since the Area is 300m²
A = xy
300 = xy .... 2
Substitute 1 into 2
300 = x(2x+10)
300 = 2x²+10x
Rearrange
2x²+10x - 300 = 0
Divide through by 2
x²+5x - 150 = 0
This gives the required quadratic expression
<h3>
Answer: Choice A) 29.5 </h3>
This value is approximate.
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Work Shown:
First we need to find angle C
A+B+C = 180
46+73+C = 180
119+C = 180
C = 180 - 119
C = 61
This is not the final answer, so answer choice B is likely a trick/trap answer.
We'll use this angle value to help find side c. Use the law of sines
c/sin(C) = b/sin(B)
c/sin(61) = (32.3)/sin(73)
c = sin(61)*(32.3)/sin(73)
c = 29.5410185554849 which is approximate
c = 29.5 which points us to choice A as the final answer.
