Answer: The answer is 300 gallons.
Step-by-step explanation: Riemann sum is a method of calculating the total area under a curve on a graph, which is also known as Integral.
To calculate that area, we divide it into a number of rectangles with one point touching the curve. The curve has a closed interval [a,b] that can be subdivided into n subintervals, each having a width of Δ
= ![\frac{b-a}{n}](https://tex.z-dn.net/?f=%5Cfrac%7Bb-a%7D%7Bn%7D)
If a function is defined on the closed interval [a,b] and
is any point in [
,
], then a Riemann Sum is defined as ∑f(
)Δ
.
For this question:
Δ
=
= 1.4
Now, we have to find s(t) for each valor on the interval:
s(t) = 0.29
- t +25
s(0) = 25
s(1) = 24.29
s(2) = 24.16
s(3) = 24.61
s(4) = 25.64
s(5) = 27.25
s(6) = 29.44
s(7) = 32.21
Now, using the formula:
∑f(
)Δ
= 1.4(25+24.29+24.16+24.61+25.64+29.44+32.21)
∑f(
)Δ
= 1.4(212.6)
∑f(
)Δ
≅ 300
With Riemann Sum, it is estimated the total country's per capita sales of bottled water is 300 gallons.
Answer: d = 11/2 or 5 1/2
Step-by-step explanation:
2d - 6 = 5
+ 6 + 6
2d = 11
/2 /2
d = 11/2 or 5 1/2
parallel means "same slope (m)"
m =
= ![\frac{0 - 5}{-3 - (-6)} = \frac{-5}{-3 + 6} = \frac{-5}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B0%20-%205%7D%7B-3%20-%20%28-6%29%7D%20%3D%20%5Cfrac%7B-5%7D%7B-3%20%2B%206%7D%20%3D%20%5Cfrac%7B-5%7D%7B3%7D)
Now, input the point (0, 0) and the slope
into the Point-Slope formula:
y - y₁ = m(x - x₁)
y - 0 =
(x - 0)
y = ![\frac{-5}{3}x](https://tex.z-dn.net/?f=%5Cfrac%7B-5%7D%7B3%7Dx)
3y = -5x <em>multiplied both sides by 3</em>
0 = -5x - 3y <em>subtracted 3y from both sides</em>
Answer: C
Answer:Gcf=1.
Step-by-step explanation: The factors of 2 are: 1, 2
.
The factors of 6 are: 1, 2, 3, 6
.
The factors of 15 are: 1, 3, 5, 15.