Answer:
X: discrete
Y: continuous
M: continuous
N: discrete
P: discrete
Q: continuous
Step-by-step explanation:
First, we have to know the difference between discrete and continuous variables:
- Discrete variables are those that represent things that are counted, 3 red cars, 2 chickens, etc.. They take positive integer values, {0, 1, 2, ..., n}, being [0, n] the interval from which the variable takes values, that means, there is a finite number of possible values.
- Continuous variables are those that represent things that are measured, 3.56 km of railway laid, 5.77 l of paint used. They take positive real values, that means that in the interval used for the variable there are infinite possible values.
Now, we classify each variable:
- The number of automobile accidents per year in Virginia (X) is a discrete variable, as there can't be half an accident, one counts how many accidents are per year to know X.
- The length of time to play 18 holes of golf (Y) is a continuous variable, as it can take 2 hours, or 2.5 hours, or 2 hours, 30 minutes, 2 seconds, one measures how long it took to play 18 holes to know Y.
- The amount of milk produced yearly by a particular cow (M) is a continuous variable, as one measures how much milk was produced to know M.
- The number of eggs laid each month by a hen (N) is a discrete variable, as one counts how much eggs were laid to know N.
- The number of building permits issued each month in a certain city (P) is a discrete variable, as one counts how many permits were issued to know P.
- The weight of grain produced per acre (Q) is a continuous variable, as one measures the weight per acre to know Q.
Step-by-step explanation:
∫₋₂² (f(x) + 6) dx
Split the integral:
∫₋₂² f(x) dx + ∫₋₂² 6 dx
Graphically, if f(-x) = -f(x), then ∫₋₂² f(x) dx = 0. But we can also show this algebraically.
Split the first integral:
∫₋₂⁰ f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx
Using substitution, write the first integral in terms of -x.
∫₂⁰ f(-x) d(-x) + ∫₀² f(x) dx + ∫₋₂² 6 dx
-∫₂⁰ f(-x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx
Flip the limits and multiply by -1.
∫₀² f(-x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx
Rewrite f(-x) as -f(x).
∫₀² -f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx
-∫₀² f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx
The integrals cancel out:
∫₋₂² 6 dx
Evaluating:
6x |₋₂²
6 (2 − (-2))
24
<span>Multiplication Property of –1</span>
Since the problem gives the number of values of how far away each Eaton and Wellington are from Baxter, you can add both of the miles together to get the total distance from Eaton to Wellington.
42 1/2+37 4/5=
Find the common denominator for both of them.
42 5/10 + 37 8/10=
Answer: 80 3/10 miles from each other
Your answer is:
(125 - 8x^3) / (25 + 10x + 4x^2) = - ((2x - 5) * (4x^2 + 10x + 25)) / (4x^2 + 10x + 25) = - (2x - 5) = - 2x + 5
The correct result would be - 2x + 5.
