The perimeterhof a rectangle is 48 inches. The rectangle is twice as long as it is wide. What is the length of the rectangle?
1 answer:
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Answer:
(a) 0.6579
(b) 0.2961
(c) 0.3108
(d) 240
Step-by-step explanation:
The random variable <em>X</em> can be defined as the number of particles in a suspension.
The concentration of particles in a suspension is 50 per ml.
Then in 5 mL volume of the suspension the number of particles will be,
5 × 50 = 250.
The random variable <em>X</em> thus follows a Poisson distribution with parameter, <em>λ</em> = 250.
The Poisson distribution with parameter λ, can be approximated by the Normal distribution, when λ is large say λ > 10.
The mean of the approximated distribution of X is:
μ = λ = 250
The standard deviation of the approximated distribution of X is:
σ = √λ = √250 = 15.8114
Thus,
(a)
Compute the probability that the number of particles withdrawn will be between 235 and 265 as follows:
Thus, the value of P (235 < <em>X</em> < 265) = 0.6579.
(b)
Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:
Thus, the value of .
(c)
A 10 mL sample is withdrawn.
Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:
Thus, the value of .
(d)
Let the sample size be <em>n</em>.
The value of <em>z</em> for this probability is,
<em>z</em> = 1.96
Compute the value of <em>n</em> as follows:
Thus, the sample selected must be of size 240.
Answer:
a) f(0)=4
b) f(-2)=2
c) x∈{-8,-4,4,8}
d) x∈{-9,-3,3,9}
e) x∈(-∞,-9)∪(-3,3)∪(9,∞).
f) x∈[-9,-3]∪[3,9]
g) Domain is x∈[-10,10]. Range is y∈[-4,4]. Zeros are at elements of x in {-9,-3,3,9}
h) Increasing on x∈ (-6,0) ∪ (6,10) and
decreasing on x∈ (-10,-6) ∪ (0,6).
Step-by-step explanation:
a) f(0) means what is the y-coordinate of the point at x=0.
So find 0 on the x-axis. I'm going to go up because the curve is at y=4 there.
Conclusion: f(0)=4.
b) f(-2) means what is the y-coordinate of the point at x=-2.
So find -2 on the x-axis. I'm going to go up because the curve is at y=2 there.
Conclusion: f(-2)=2.
c) f(x)=-2 means what is x when y=-2. So go on the y-axis and find -2. Now anything on that line y=-2 (horizontal line going through y=-2 on the y-axis) we need to look at.
There are 4 value we need to look at then.
x=-8
x=-4
x=4
x=8
At all of these the y-coordinate is -2.
d) f(x)=0 means what is x when y=0. So go on the y-axis and find 0. Now anything on that line y=0 (horizontal line going through y=0 on the y-axis; also knowing as the x-axis for y=0) we need to look at.
There are 4 values we need to look at then.
x=-9
x=-3
x=3
x=9
e) f(x)>0 means where is the curve above the x-axis.
The curve is above the x-axis:
- Before x=-9
- Between x=-3 and x=3
- After x=9
The interval notation is:
(-∞,-9)∪(-3,3)∪(9,∞).
d) f(x)≥0 means where is the curve below or on the x-axis (also known as y=0).
The curve is below or on the x-axis:
- Between -9 and -3 (inclusive of both endpoints because they include y=0).
- Between 3 and 9 (inclusive of both endpoints because they include y=0).
The interval notation is:
[-9,-3]∪[3,9]
g) The domain is where the curve exists for the x-values.
The domain is all real numbers between -10 and 10 (inclusive of both).
The curve starts at x=-10 and stops at x=10. The function exists a y value for any number between -10 and 10 (including both).
Interval notation is:
[-10,10]
The range is where the curve exists for the y-values.
Looking from bottom to top I see that it starts at y=-4 and stops at y=4. I notice the curve exists at some point between those two horizontal lines. It also exists at both of those endpoints" -4 and 4.
The range is between -4 and 4 (including both).
Interval notation is:
[-4,4]
The zeros are where the graph crosses the x-axis.
The graph crosses the x-axis at:
x=-9
x=-3
x=3
x=9
h) Reading left to right the graph increases when you see the curve going up.
I see this from x=-6 to x=0 (exclusive of both).
I see this from x=6 to x=10 (exclusive of both).
So interval notation is (-6,0) ∪ (6,10).
Reading left to right the graph decreases when you see the curve going down.
I see this from x=-10 to x=-6 ( exclusive of both).
I see this from x=0 to x=6 (exclusive of both).
