Answer:
Step-by-step explanation:
Part 1: Solve for the total amount of marbles
To solve for the probability of certain events, a population is needed to derive this information from. In order to find this population, add up the amounts of each marble.
8 + 14 + 12 = 34 marbles
Part 2: Determine the probabilities
Now, given the amounts of marbles, simply multiply the ratios of blue marbles to total marbles and the ratio of clear marbles to total marbles to get the combined probability.
The probability of these events occurring simultaneously is 15%.
Answer:
6/7
Step-by-step explanation:
5/7 + 1/7
Since the denominators are the same, we just add the numerators
5+1 = 6
Then we put the numerator over the denominator
6/7
<span> divide a polynomial p(x) by (x-3). Add and subtract the multiple of (x-3) that has the same highest-power term as p(x), then simplify to get a smaller-degree polynomial r(x) plus multiple of (x-3). </span>
<span>The multiple of (x-3) that has x^4 as its leading term is x^3(x-3) = x^4 - 3x^3. So write: </span>
<span>x^4 + 7 = x^4 + 7 + x^3(x - 3) - x^3(x - 3) </span>
<span>= x^4 + 7 + x^3(x - 3) - x^4 + 3x^3 </span>
<span>= x^3(x - 3) + 3x^3 + 7 </span>
<span>That makes r(x) = 3x^3 + 7. Do the same thing to reduce r(x) by adding/subtracting 3x^2(x - 3) = 3x^3 - 9x^2: </span>
<span>= x^3(x - 3) + 3x^3 + 7 + 3x^2(x - 3) - (3x^3 - 9x^2) </span>
<span>= x^3(x - 3) + 3x^2(x - 3) + 9x^2 + 7 </span>
<span>Again to reduce 9x^2 + 7: </span>
<span>= x^3(x - 3) + 3x^2(x - 3) + 9x^2 + 7 + 9x(x - 3) - (9x^2 - 27x) </span>
<span>= x^3(x - 3) + 3x^2(x - 3) + 9x(x - 3) + 27x + 7 </span>
<span>And finally write 27x + 7 as 27(x - 3) + 88; </span>
<span>x^4 + 7 = x^3(x - 3) + 3x^2(x - 3) + 9x(x - 3) + 27(x - 3) + 88 </span>
<span>Factor out (x - 3) in all but the +88 term: </span>
<span>x^4 + 7 = (x - 3)(x^3 + 3x^2 + 9x + 27) + 88 </span>
<span>That means that: </span>
<span>(x^4 + 7) / (x - 3) = x^3 + 3x^2 + 9x + 27 with a remainder of 88</span>
I can't tell the numbers apart as there are no colours so I did one answer a with them all being one digit numbers and another answer as them being 2 digit numbers...
1 digit:
5 + 4 + 3 + 3 + 2 + 2 +1 = 20
20 ÷ 7 = 2.86
2 digit:
54 + 33 + 22 + 1 = 110
110 ÷ 5 = 22
Answer:
Choice D
y = 3(2/3)^x
Step-by-step explanation:
a) y = 2(3/2)^x = 3^x (pretty close)
b) y = (2/3)^x (wrong, coming from the wrong side)
c) y = 2(3)^x = 6^x (too close to y line)
d) y = 3(2/3)^x = 2^x (looks right)
