A. Sigma notation
The formula for finding the nth value of the geometric series
is given as:
an = a1 * r^n
Where,
an = nth value of the series
<span>a1 = 1st value in the geometric series = 940</span>
r = common ratio = 1/5
n = nth order
The sigma notation for the sum of this infinite geometric
series is therefore,
(see attached photo)
B. Sum of the infinite geometric series
The formula for calculating the sum of an infinite
geometric series is given as:
<span>S = a1 / (1 – r)</span>
Substituting the given values:
S = 940 / (1 – 1/5)
<span>S = 1,175</span>
The solution set is { y | y < -3 or y > 7}
Graph is attached
Answer:
x = 1/4
y = 5 2/4
Step-by-step explanation:
Given two equations
1. 10x + 3y = 19
2. y = 2x + 5
Substitute 2x + 5 for y in the first equation
We have
10x + 3y = 19
10x + 3(2x + 5) = 19
Expand the bracket
10x + 3 X 2x + 3 X 5 = 19
10x + 6x + 15 = 19
16x + 15 = 19
Subtract 15 from both sides to eliminate 15 on the left
16x + 15 - 15 = 19 - 15
16x = 4
Divide both sides by 16 to isolate x
16x/16 = 4/16
x = 1/4
Now, substitute 1/4 for x in either equation to get y.
Using equation 2 , we have
y = 2x + 5
= 2(1/4) + 5
= 2/4 + 5
LCM of the denominator is 4.
Divide the LCM by the denominators and multiply the results by the numerators. Also, the LCM becomes the denominator of the results
Therefore
= 2 + 20/4
= 22/4
y= 5 2/4
x = 1/4 , y = 5 2/4
Step-by-step explanation:
If we count for both numbers up to 36, we start seeing a pattern...
Candy: 6 12 18 24 30 36
Danny: 4 8 12 16 20 24 28 32 36
Every other number in Candy's counting is also counted by Danny. So here's what we'll do:
600/6 = 100
This is how many numbers Candy counted overall.
100/2 = 50
This is how many numbers Danny counted that were also numbers Candy counted.
Answer:
50 of the numbers that candy counted were also counted by Danny.
Answer:
63%
Step-by-step explanation:
2 dozen eggs is 24
24-9=15
15/24=.625 but when you rounded .63
