What is the result when 4x^3 + 18x^2 + 28x + 15 is divided by 2x + 3?
1 answer:
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Answer:
A. P(x<3.85 or x>4.15)= P(x<3.85)+P(x>4.15) = 0.1336
Step-by-step explanation:
Working with an ordinary Normal Distribution of probability and trying to find the probabilities asked in it could be difficult, because there´s no easy method to find probabilities in a generic Normal Distribution (with mean μ=4 and STD σ=0.1). The recommended approach to this question is to use a process called "Normalize", this process let us translate the problem of any Normal Distribution to a Standard Normal Distribution (μ=0 and σ=1) where there´s easier ways to find probabilities in there. The "Normalization" goes as follows:
Suppose you want to know P(x<a) of the Normal Distribution you are working with:
P(x<a)=P( (x-μ)/σ < (a-μ)/σ )=P(z<b) ( b=(a-μ)/σ )
Where μ is the mean and σ is the STD of your Normal Distribution. Notice P(z<b) now it´s a probability in a Standard Normal Distribution, now we can find it using the available method to do so. My favorite is a chart (It´s attached to this answer) that contains a lot of probabilities in a Standard Normal Distribution. Let´s solve this as an example
A. We want to find the probability of the cork being defective (P(x<3.85) + P(x>4.15)). Now we find those separated and, then, add them for our answer.
Let´s begin with P(x<3.85), we start by normalizing that probability:
P(x<3.85)= P( (x-μ)/σ < (3.85-4)/0.1 )= P(z<-1.5)
And now it´s time to use the chart, it works like this: If you want P(z<c) and the decimal expansion of c=a.bd... , then:
P(z<c)=(a.b , d)
Where (a.b , d) are the coordinates of the probability in the chart. Keep in mind that will only work with "<" (It won´t work directly with P(z>c)) and we will do some extra work in those cases.
P(z<-1.5) is in the coordinates (-1.5 , 0)
P(z<-1.5)= 0.0668
P(x<3.85)= 0.0668
Now we are looking for P(x>4.15), let´s Normalize it too:
P(x>4.15)=P( (x-μ)/σ < (4.15-4)/0.1 )=P(z>1.5)
But remember the chart only work with "<", so we need to use a property of probability:
P(z>1.5)= 1 - P(z<1.5)
Using the chart:
P(z<1.5)=0.9332 (1.5 , 0)
P(z>1.5)= 1 - 0.9332
P(z>1.5)= 0.0668
P(x>4.15)= 0.0668
And our final answer will be:
P(x<3.85 or x>4.15)= P(x<3.85)+P(x>4.15) = 0.1336
Answer:
Question 3: 582 ft²
Question 4: 348 in²
Step-by-step Explanation:
Question 3:
Consider the solid shape given as being consisting of two rectangular prism. With careful examination, you'd observe that the offer one beneath has dimensions,
The second one has
Surface area of the bigger rectangular prism = total surface area - area of the surface that is joined to the smaller rectangular prism.
Area of the face joined to the smaller rectangular prism = 4*6 = 24 ft²
Surface area of the bigger rectangular prism =
Surface area of the bigger rectangular prism = 438 ft²
Surface area of the smaller rectangular prism = total surface area of rectangular prism - area of the surface that is joined to the bigger rectangular prism.
=
<em><u>Surface area of the solid = 438 + 144 = 582 ft²</u></em>
Question 4:
Surface area of the triangular prism is given as: 2(B.A) + P*L
Where,
B.A = area of 1 triangular base = ½*height of the triangle*base of the traingle
B.A = ½*6*16 = 3*16 = 48 in²
P = perimeter of 1 triangular base = sum of all sides of the triangle.
P = 16+10+10 = 36 in
L = length or height of prism =
Plug in the values to find surface area of the prism
Surface area = 2(B.A) + P*L
= 2(48) + 36*7 = 96 + 252 = 348 in²
<em><u>Surface area of prism = 348 in²</u></em>