<h3>
Answer: 9/100</h3>
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Explanation:
There are 3 pink marbles out of 10 total (we can see that 2 yellow + 3 pink + 5 blue = 10 total)
The fraction 3/10 represents the probability of pulling out a pink marble at random. Since the first one is put back, this means the fraction 3/10 stays the same on the second draw as well.
We use the idea mentioned in the hint to multiply the fractions:
(3/10)*(3/10) = (3*3)/(10*10) = 9/100
The probability of pulling two pink marbles in a row is 9/100, where the first marble is put back.
Effectively, if you were given 100 tries at doing this, you should expect about 9 of those times you get 2 pink marbles in a row.
Answer:
53.33
Step-by-step explanation:
finding area of ΔPAM
using similar triangles

16 = 12x; x = 
ΔPAM = 4/3 * 4 * 1/2 = 16/6 = 8/3
ΔPAL = 4 * 12 * 1/2 = 24
24 + 8/3 = 80/3 (using fraction form for now, will round later)
since there are two ΔPLM (ΔLMU has same area since they are congruent)
we can multiply 80/3 by 2
80/3 * 2 = 160/3 = 53.33
Answer:
225
Step-by-step explanation:
When you fill in values of n, you find the series is an arithmetic series of 15 terms with a first term of 1 and a common difference of 2. The formula for the sum of such a series can be used.
<h3>Terms</h3>
Looking at terms of the series for different values of n, we find ...
for n = 1: 2(1) -1 = 1 . . . . . the first term
for n = 2: 2(2) -1 = 3 . . . . the second term; differs by 3-1=2
for n = 15: 2(15) -1 = 29 . . . . the last of the 15 terms
<h3>Sum</h3>
The sum of the terms of an arithmetic series is the product of the average term and the number of terms. The average term is the average of the first and last terms.
Sum = (1 +29)/2 × 15 . . . . . . average term × number of terms
Sum = 15 × 15 = 225
The sum of the series is 225.
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<em>Additional comment</em>
Based on the first term (a1), the common difference (d), and the number of terms (n), the sum can also be written ...
S = (2×a1 +d(n -1))(n/2)
For the parameters of this series, the sum is ...
S = (2(1) +2(15 -1))(15/2) = 30(15/2) = 225
Answer:
68 cm
Step-by-step explanation:
Using the concept of tangents drawn from external point to a circle are congruent, we can find the Perimeter of polygon.
