The question tells us that Mallory's 2 years old than three times her brother Jake's age, but let's just start by saying she's 2 years older than <em>some age. </em>What would that look like? Well, we'd be taking some number and adding two to it, so something like this:
Mallory's age = (some age) + 2
What is that age though? The problem tells us it's three times Jake's age, j. We can write that as 3 × j, or 3j, to save space. Filling in our blank, we can write the expression for Mallory's age as 3j + 2
Answer:
Given the series,
∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1
I think the series is summation from n = 1 to ∞ of -4(-1/2)^(n-1)
So,
∑ − 4 ( − ½ )^(n − 1). From n = 1 to ∞
There are different types of test to show if a series converges or diverges
So, using Ratio test
Lim n → ∞ (a_n+1 / a_n)
Lim n → ∞ (-4(-1/ 2)^(n+1-1) / -4(-1/2)^(n-1))
Lim n → ∞ ((-4(-1/2)^(n) / -4(-1/2)^(n-1))
Lim n → ∞ (-1/2)ⁿ / (-1/2)^(n-1)
Lim n→ ∞ (-1/2)^(n-n+1)
Lim n→ ∞ (-1/2)^1 = -1/2
Since the limit is less than 0, then, the series converge...
Sum to infinity
Using geometric progression formula
S∞ = a / 1 - r
Where
a is first term
r is common ratio
So, first term is
a_1 = -4(-½)^1-1 = -4(-½)^0 = -4 × 1
a_1 = -4
Common ratio r = a_2 / a_1
a_2 = 4(-½)^2-1 = -4(-½)^1 = -4 × -½ = 2
a_2 = 2
Then,
r = a_2 / a_1 = 2 / -4 = -½
S∞ = -4 / 1--½
S∞ = -4 / 1 + ½
S∞ = -4 / 3/2 = -4 × 2 / 3
S∞ = -8 / 3 = -2⅔
The sum to infinity is -2.67 or -2⅔
<h2>
Step-by-step explanation: PHEW THAT TOOK A WHILE LOL IM A FAST TYPER</h2>
Answer:
(4, 0 ) and (0, - 10 )
Step-by-step explanation:
To find the x- intercept let y = 0 in the equation
5x - 0 = 20
5x = 20 ( divide both sides by 5 )
x = 4 ← x- intercept ⇒ (4, 0 )
To find the y- intercept let x = 0 in the equation
0 - 2y = 20
- 2y = 20 ( divide both sides by - 2 )
y = - 10 ← y- intercept ⇒ (0, - 10 )
6 * 105 = 630
the team scored approximately 630 points in 6 games.
The manager can do both but if he does 10 he will have 25 groups but if he does 5 he will have 50 groups so the simple way is 10 so he will have 25 groups