Answer:
(a)[tex]D(x)=-2,500x+60,000[/tex]
(b)[tex]R(x)=60,000x-2500x^2[/tex]
(c) x=12
(d)Optimal ticket price: $12
Maximum Revenue:$360,000
Step-by-step explanation:
The stadium holds up to 50,000 spectators.
When ticket prices were set at $12, the average attendance was 30,000.
When the ticket prices were on sale for $10, the average attendance was 35,000.
(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)
Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).
[tex]\text{Slope, m}=\dfrac{30000-35000}{12-10}=-2500[/tex]
Therefore, we have:
[tex]y=-2500x+b[/tex]
At point (12,30000)
[tex]30000=-2500(12)+b\\b=30000+30000\\b=60000[/tex]
Therefore:
[tex]D(x)=-2,500x+60,000[/tex]
(b)Revenue
[tex]R(x)=x \cdot D(x) \implies R(x)=x(-2,500x+60,000)\\\\R(x)=60,000x-2500x^2[/tex]
(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.
[tex]R(x)=60,000x-2500x^2\\R'(x)=60,000-5,000x\\60,000-5,000x=0\\60,000=5,000x\\x=12[/tex]
The critical value of R(x) is x=12.
(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]
Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.
[tex]R(x)=60,000x-2500x^2\\R(1)=60,000(1)-2500(1)^2=\$57,500\\R(12)=60,000(12)-2500(12)^2=\$360,000\\R(24)=60,000(24)-2500(24)^2=\$0[/tex]
Therefore:
Optimal ticket price:$12Maximum Revenue:$360,000Which of the following relations is a function?
A{(3,-1), (2, 3), (3, 4), (1,7)}
B{(1, 2), (2, 3), (3, 4), (4, 5)}.
C{(3, 0), (4, -3), (6, 7), (4,4)}
D{(1, 2), (1, 3), (2, 8), (3, 9)}
Answer:
B
Step-by-step explanation:
A is not a function because the same x value is repeated twice with different y values. The same goes for C and D so the answer is C.
Answer:
B.
Step-by-step explanation:
Well a relation is a set of points and a function is a relation where every x value corresponds to only 1 y value.
So lets see which x values in these relations have only 1 y value.
A. Well a isn’t a function because the number 3 which is a x value had two y values which are -1 and 4.
B. This relation is a function because there are no similar x values.
C. This is not a function because the x value 4 has two y values which are 4 and -3.
D. This is not a function because the number 1 has 2 and 3 as y values.
Given a right triangle with a hypotenuse length of radical 26 and base length of 3. Find the length of the other leg (which is also the height).
Answer:
√17
Step-by-step explanation:
The Pythagorean theorem can be used for the purpose.
hypotenuse² = base² +height²
(√26)² = 3² +height²
26 -9 = height²
height = √17
The length of the other leg is √17.
A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Three hundred feet of fencing is used
dimensions of the playground that maximize the total enclosed area. What is the maximum area?
The smaller dimension is
feet
Answer:
50 ft by 75 ft3750 square feetStep-by-step explanation:
Let x represent the length of the side not parallel to the partition. Then the length of the side parallel to the partition is ...
y = (300 -2x)/3
And the enclosed area is ...
A = xy = x(300 -2x)/3 = (2/3)(x)(150 -x)
This is the equation of a parabola with x-intercepts at x=0 and x=150. The line of symmetry, hence the vertex, is located halfway between these values, at x=75.
The maximum area is enclosed when the dimensions are ...
50 ft by 75 ft
That maximum area is 3750 square feet.
_____
Comment on the solution
The generic solution to problems of this sort is that half the fence (cost) is used in each of the orthogonal directions. Here, half the fence is 150 ft, so the long side measures 150'/2 = 75', and the short side measures 150'/3 = 50'. This remains true regardless of the number of partitions, and regardless if part or all of one side is missing (e.g. bounded by a barn or river).
1. Growth of Functions (11 points) (1) (4 points) Determine whether each of these functions is O(x 2 ). Proof is not required but it may be good to try to justify it (a) 100x + 1000 (b) 100x 2 + 1000
Answer:
See explanation
Step-by-step explanation:
To determine whether each of these functions is [tex]O(x^2)[/tex], we apply these theorems:
A polynomial is always O(the term containing the highest power of n)Any O(x) function is always [tex]O(x^2)[/tex].(a)Given the function: f(x)=100x+1000
The highest power of n is 1.
Therefore f(x) is O(x).
Since any O(x) function is always [tex]O(x^2)[/tex], 100x+1000 is [tex]O(x^2)[/tex].
[tex](b) f(x)=100x^ 2 + 1000[/tex]
The highest power of n is 2.
Therefore the function is [tex]O(x^2)[/tex].
Answer:
i think its 2000
Step-by-step explanation:
Determine the logarithmic regression of the data below using either a calculator or spreadsheet program. Then, estimate the x−value when the y−value is 5.2. Round your answer to one decimal place. (4.7,10.7),(7.8,20.6),(10.5,30.2),(15.6,41),(20.8,56.1),(22,65.1). Please help right away! Thank you so much!
Answer:
y ≈ 33.7·ln(x) -45.94.6Step-by-step explanation:
A graphing calculator can perform logarithmic regression, as can a spreadsheet. The least-squares best fit log curve is about ...
y ≈ 33.7·ln(x) -45.9
The value of x estimated to make y = 5.2 is about 4.6.
The dimensions of a closed rectangular box are measured as 96 cm, 58 cm, and 48 cm, respectively, with a possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error in calculating the surface area of the box.
Answer:
161.6 cm²Step-by-step explanation:
Surface Area of the rectangular box = 2(LW+LH+WH)
L is the length of the box
W is the width of the box
H is the height of the box
let dL, dW and dH be the possible error in the dimensions L, W and H respectively.
Since there is a possible error of 0.2cm in each dimension, then dL = dW = dH = 0.2cm
The surface Area of the rectangular box using the differentials is expressed as shown;
S = 2{(LdW+WdL)+(LdH+HdL)+(WdH+HdW)]
Also given L = 96cm W = 58cm and H = 48cm, on substituting this given values and the differential error, we will have;
S = 2{(96*0.2+58*0.2) + (96*0.2+48*0.2)+(58*0.2+48*0.2)}
S = 2{19.2+11.6+19.2+9.6+11.6+9.6}
S = 2(80.8)
S = 161.6 cm²
Hence, the surface area of the box is 161.6 cm²
a) Al usar un microscopio el microscopio se amplía una célula 400 veces. Escribe el factor de ampliación como cociente o como escala.
b) La imagen de una célula usando dicho microscopio mide 1,5 mm ¿ Cuánto mide la célula en la realidad?
Answer:
x = 0,00375 mm
Step-by-step explanation:
a) El factor de ampliación es 400/1 es decir el tamaño real se verá ampliado 400 veces mediante el uso del microscopio
b) De acuerdo a lo establecido en la respuesta a la pregunta referida en a (anterior) podemos establecer una regla de tres, según:
Si al microscopio el tamaño de la célula es 1,5 mm, cual será el tamaño verdadero ( que es reducido 400 en relación al que veo en el microscopio)
Es decir 1,5 mm ⇒ 400
x (mm) ⇒ 1 (tamaño real de la célula)
Entonces
x = 1,5 /400
x = 0,00375 mm
Can Someone help me!!! I need this ASAP! What number? Increased by 130% is 69? FYI: the answer is less than 69
Answer:
Hey there!
There are a few ways you could solve this problem, but the easiest would to be writing an equation.
You could say-
2.3x=69
Divide by 2.3
x=30
Hope this helps :)
Answer:
30
Step-by-step explanation:
the answer is 30 bc increasing something by 130% is multiplying it by 2.3 so technically you have to divide 69 by 2.3 which equals to 30
You spend 6,380.00 a year for rent. This is 22% of your income. What is your income?
Answer: 29,000.00
Step-by-step explanation:
Let the income=x. 22%=0.22.
So 6380/x=0.22
x=6380/0.22=29,000.00
The following data represent the miles per gallon for a particular make and model car for six randomly selected vehicles. Compute the mean, median, and mode miles per gallon 24.2. 22.2. 37.8, 22.7. 35 4. 31.61. Compute the mean miles per gallon. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mean mileage per gallon is _______B. The mean does not exist 2. Compute the median miles per gallon. Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The median mileage per gallon is __________B. The median does not exist. 3. Compute the mode miles per gallon. Select the correct choice below and, if necessary,fill in the answer box to complete your choice. A. The mode is _________B. The mode does not exist.
Answer:
A. The mean mileage per gallon is _____ 28.99__
A. The median mileage per gallon is _____27.905_____
B. The mode does not exist.
Step-by-step explanation:
Mean= Sum of values/ No of Values
Mean = 24.2 + 22.2+ 37.8+ 22.7 + 35.4 +31.61/ 6
Mean = 173.91/6= 28.985 ≅ 28.99
The median is the middle value of an ordered data which divides the data into two equal halves. For an even data the median is the average of n/2 and n+1/2 value where n is the number of values.
Rearranging the above data
22.2 , 22.7 , 24.2 , 31.61 , 35.4, 37.8
Third and fourth values are =24.2 + 31.61 = 55.81
Average of third and fourth values is = 55.81/2= 27.905
Mode is the values which is occurs repeatedly.
In this data there is no mode.
Which proportion would convert 18 ounces into pounds?
Answer:
16 ounces = 1 pound
Step-by-step explanation:
You would just do 18/16 = 1.125 pounds. There are always 16 ounces in a pound, so it always works like this
A triangular plot of land has one side along a straight road measuring 147147 feet. A second side makes a 2323degrees° angle with the road, and the third side makes a 2222degrees° angle with the road. How long are the other two sides?
Answer:
81.23 ft and 77.88 ft long
Step-by-step explanation:
The sum of the internal angles of a triangle is 180 degrees, the missing angle is:
[tex]a+b+c=180\\a+23+22=180\\a=135^o[/tex]
According to the Law of Sines:
[tex]\frac{A}{sin(a)}= \frac{B}{sin(b)}= \frac{C}{sin(c)}[/tex]
Let A be the side that is 147 feet long, the length of the other two sides are:
[tex]\frac{A}{sin(a)}= \frac{B}{sin(b)}\\B=\frac{sin(23)*147}{sin(135)}\\B=81.23\ ft\\\\\frac{A}{sin(a)}= \frac{C}{sin(c)}\\C=\frac{sin(22)*147}{sin(135)}\\C=77.88\ ft[/tex]
The other two sides are 81.23 ft and 77.88 ft long
answer if u love cats & dogs
Answer:
(7, 5.25) lies on the graph.
Step-by-step explanation:
We are given the following values
x = 4, 6, 8, 12 and corresponding y values are:
y = 3, 4.5, 6, 9
Let us consider two points (4, 6) and (6, 4.5) and try to find out the equation of line.
Equation of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given as:
[tex]y=mx+c[/tex]
where m is the slope.
(x,y) are the coordinates from where the line passes.
c is the y intercept.
Here,
[tex]x_{1} = 4\\x_{2} = 6\\y_{1} = 3\\y_{2} = 4.5[/tex]
Formula for slope is:
[tex]m = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m = \dfrac{4.5-3}{6-4}\\\Rightarrow m = \dfrac{1.5}{2}\\\Rightarrow m = \dfrac{3}{4}[/tex]
Now, the equation of line becomes:
[tex]y=\dfrac{3}{4}x+c[/tex]
Putting the point (4,3) in the above equation to find c:
[tex]3=\dfrac{3}{4}\times 4+c\\\Rightarrow 3=3+c\\\Rightarrow c =0[/tex]
So, final equation of given function is:
[tex]y=\dfrac{3}{4}x[/tex]
OR
[tex]4y=3x[/tex]
As per the given options, the point (7, 5.25) satisfies the equation.
So correct answer is [tex](7, 5.25)[/tex].
The length of a rectangle is 5M more than twice the width and the area of the rectangle is 63M to find the dimension of the rectangle
Answer:
width = 4.5 m
length = 14 m
Step-by-step explanation:
okay so first you right down that L = 5 + 2w
then as you know that Area = length * width so you replace the length with 5 + 2w
so it's A = (5 +2w) * w = 63
then 2 w^2 + 5w - 63 =0
so we solve for w which equals 4.5 after that you solve for length : 5+ 2*4.5 = 14
the ellipse is centered at the origin, has axes of lengths 8 and 4, its major axis is horizontal. how do you write an equation for this ellipse?
Answer:
The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].
Step-by-step explanation:
The standard equation of the ellipse is described by the following expression:
[tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1[/tex]
Where [tex]a[/tex] and [tex]b[/tex] are the horizontal and vertical semi-axes, respectively. Given that major semi-axis is horizontal, [tex]a > b[/tex]. Then, the equation for this ellipse is written in this way: (a = 8, b = 4)
[tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex]
The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].
Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter: 116 meters
Answer:
Length = 29 m
Width = 29 m
Step-by-step explanation:
Let x and y be the length and width of the rectangle, respectively.
The area and perimeter are given by:
[tex]A=xy\\p=116=2x+2y\\y=58-x[/tex]
Rewriting the area as a function of x:
[tex]A(x) = x(58-x)\\A(x) = 58x-x^2[/tex]
The value of x for which the derivate of the area function is zero, is the length that maximizes the area:
[tex]A(x) = 58x-x^2\\\frac{dA}{dx}=0=58-2x\\ x=29\ m[/tex]
The value of y is:
[tex]y = 58-29\\y=29\ m[/tex]
Length = 29 m
Width = 29 m
The problem is: On a Map, 3 inches represents 40 miles, How many inches represents 480 miles?
The graphs below are the same shape what is the equation of the blue graph
Answer:
B. g(x) = (x-2)^2 +1
Step-by-step explanation:
When you see this type of equation your get the variables H and K in a quadratic equation. In this case the (x-2)^2 +1 is your H. The (x-2)^2 +1 is your K.
For the H you always do the opposite so in this case instead of going to the left 2 times you go to the right 2 times (affects your x)
For the K you go up or down which in this case you go up one (affects your y)
And that's how you got your (2,1) as the center of the parabola
-Hope this helps :)
In a survey, 205 people indicated they prefer cats, 160 indicated they prefer dots, and 40 indicated they don’t enjoy either pet. Find the probability that if a person is chosen at random, they prefer cats
Answer: probability = 0.506
Step-by-step explanation:
The data we have is:
Total people: 205 + 160 + 40 = 405
prefer cats: 205
prefer dogs: 160
neither: 40
The probability that a person chosen at random prefers cats is equal to the number of people that prefer cats divided the total number of people:
p = 205/405 = 0.506
in percent form, this is 50.6%
Want Brainliest? Get this correct Which of the following is the quotient of the rational expressions shown below?
Answer:
[tex]\dfrac{4x^2+12x+5}{6x^2-3x}[/tex]
Step-by-step explanation:
Invert the denominator and multiply.
[tex]\dfrac{2x+5}{3x}\div\dfrac{2x-1}{2x+1}=\dfrac{2x+5}{3x}\cdot\dfrac{2x+1}{2x-1}\\\\=\dfrac{(2x+5)(2x+1)}{(3x)(2x-1)}=\boxed{\dfrac{4x^2+12x+5}{6x^2-3x}}\qquad\text{matches choice A}[/tex]
Answer:
[tex]\frac{4x^2+12x+5}{6x^2-3x}[/tex]
Step-by-step explanation:
After using the reciprocal of the second term, the denominator will multiply out to be [tex]6x^2-3x[/tex]. There is only one option with that as the denominator so it must be the correct answer.
Simplify the expression (5j+5) – (5j+5)
Answer:
0
Step-by-step explanation:
multiply the negative thru the right part of the equation so, 5j+5-5j-5. The 5j and the 5 than cancel out with each other. Hope this helps!
Answer:
0
Explanation:
step 1 - remove the parenthesis from the expression
(5j + 5) - (5j + 5)
5j + 5 - 5j - 5
step 2 - combine like terms
5j + 5 - 5j - 5
5j - 5j + 5 - 5
0 + 0
0
therefore, the simplified form of the given expression is 0.
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━━━━━━━☆☆━━━━━━━
▹ Answer
0.25 = 1/4 because 25/100 = 1/4
▹ Step-by-Step Explanation
0.25 to a fraction → 25/100
25/100 = 1/4
Therefore, this statement is true. (0.25 = 1/4 because 25/100 = 1/4)
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
7. The mean age at first marriage for respondents in a survey is 23.33,
with a standard deviation of 6.13. For an age at first marriage of 33.44,
the proportion of area beyond the Z score associated with this age is
.05. What is the percentile rank for this score?
Answer:
[tex] \mu = 23.33, \sigma =6.13[/tex]
And for this case we are analyzing the value os 33.44 and we can use the z score formula given by:
[tex] z=\frac{X -\mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{33.44 -23.33}{6.13}= 1.649[/tex]
We know that the proportion of area beyond the Z score associated with this age is .05 so then the percentile would be: 95
Step-by-step explanation:
For this case we have the following parameters:
[tex] \mu = 23.33, \sigma =6.13[/tex]
And for this case we are analyzing the value os 33.44 and we can use the z score formula given by:
[tex] z=\frac{X -\mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{33.44 -23.33}{6.13}= 1.649[/tex]
We know that the proportion of area beyond the Z score associated with this age is .05 so then the percentile would be: 95
Good Morning can I get some help please?
Answer:
5x + 10 = 25
Subtract 10 on each side to make x alone
5x = 15
divide by 5 on each side
x=3 so x=3
3x + 12 = 48
48-12=36
3x=36
divide by 3
x=12
4x + 8 = 16
4x = 8
x=2
2x + 15=25
2x=10
x=5
5x + 20 = 50
5x=30
x=6
hope this helps
1. 3
2.12
3.2
4.5
5.6
Step-by-step explanation:
Answer:
x = 3x = 12x = 2x = 5x = 6Step by step explanation
First:
Move the constant to the Right Hand Side and change its signCalculate the differenceDivideCalculateSolution,
1. 5x + 10 = 25
Move constant to the R.H.S and change its sign:
5x = 25 - 10
Calculate the difference
5x = 15
Divide both sides by 5
5x/5 = 15/5
calculate
X = 3
2. 3x + 12 = 48
or, 3x = 48 - 12
or, 3x = 36
or, 3x/x = 36/3
x = 12
3. 4x + 8 = 16
or, 4x = 16 - 8
or, 4x = 8
or, 4x/x = 8/4
x = 2
4. 2x + 15 = 25
or, 2x = 25 - 15
or, 2x = 10
or, 2x/x= 10/2
x = 5
5. 5x + 20 = 50
or, 5x = 50-20
or, 5x = 30
or, 5x/x = 30/5
x = 6
Hope this helps...
Good luck on your assignment...
An instructor asks students to rate their anxiety level on a scale of 1 to 100 (1 being low anxiety and 100 being high anxiety) just before the students take their final exam. The responses are shown below. Construct a relative frequency table for the instructor using five classes. Use the minimum value from the data set as the lower class limit for the first row, and use the lowest possible whole-number class width that will allow the table to account for all of the responses. Use integers or decimals for all answers.
48,50,71,58,56,55,53,70,63,74,64,33,34,39,49,60,65,84,54,58
Provide your answer below:
Lower Class Limit Upper Class Limit Relative Frequency
Answer:
The frequency table is shown below.
Step-by-step explanation:
The data set arranged ascending order is:
S = {33 , 34 , 39 , 48 , 49 , 50 , 53 , 54 , 55 , 56 , 58 , 58, 60 , 63 , 64 , 65 , 70 , 71 , 74 , 84}
It is asked to use the minimum value from the data set as the lower class limit for the first row.
So, the lower class limit for the first class interval is 33.
To determine the class width compute the range as follows:
[tex]\text{Range}=\text{Maximum}-\text{Minimum}[/tex]
[tex]=84-33\\=51[/tex]
The number of classes requires is 5.
The class width is:
[tex]\text{Class width}=\frac{Range}{5}=\frac{51}{2}=10.2\approx 10[/tex]
So, the class width is 10.
The classes are:
33 - 42
43 - 52
53 - 62
63 - 72
73 - 82
83 - 92
Compute the frequencies of each class as follows:
Class Interval Values Frequency
33 - 42 33 , 34 , 39 3
43 - 52 48 , 49 , 50 3
53 - 62 53 , 54 , 55 , 56 , 58 , 58, 60 7
63 - 72 63 , 64 , 65 , 70 , 71 5
73 - 82 74 1
83 - 92 84 1
TOTAL 20
Compute the relative frequencies as follows:
Class Interval Frequency Relative Frequency
33 - 42 3 [tex]\frac{3}{20}\times 100\%=15\%[/tex]
43 - 52 3 [tex]\frac{3}{20}\times 100\%=15\%[/tex]
53 - 62 7 [tex]\frac{7}{20}\times 100\%=35\%[/tex]
63 - 72 5 [tex]\frac{5}{20}\times 100\%=25\%[/tex]
73 - 82 1 [tex]\frac{1}{20}\times 100\%=5\%[/tex]
83 - 92 1 [tex]\frac{1}{20}\times 100\%=5\%[/tex]
TOTAL 20 100%
Legal descriptions tend to prefer neat straight lines from point to point, regardless of describing a square, rectangle, triangle or even a smooth circle. When might a property boundary end up being a squiggly line?
Answer:
When describing a property line drawn down the center of a creek bed
Silver Lake has a population of 114,000. The population is decreasing at a rate of 1.5% each year. Which of the following choices is the correct function? a p(s) = 114000• 0.985x b p(s) = 114000x c p(s) = 114000x + 0.985 d None of these choices are correct.
Answer: D
Step-by-step explanation:
According to the question, Silver Lake has a population of 114,000. The population is decreasing at a rate of 1.5% each year
The initial population Po = 114000
Rate = 1.5% = 0.015
The declining population formula will be:
P = Po( 1 - R%)x^2
The decay formula
Since the population is decreasing, take away 0.015 from 1
1 - 0.015 = 0.985
Substitutes all the parameters into the formula
P(s) = 114000(0.985)x^2
P(s) = 114000× 0985x^2
The correct answer is written above.
Since option A does not have square of x, we can therefore conclude that the answer is D - non of the choices is correct.
Please help with this
Answer:
C) 42
Step-by-step explanation:
The parallel lines divide the transversals proportionally.
x/35 = 30/25
x = 35(6/5) . . . . multiply by 35, reduce the fraction
x = 42
The width of a casing for a door is normally distributed with a mean of 24 inches and a standard deviation of 1/8 inch. The width of a door is normally distributed with a mean of 23 7/8 inches and a standard deviation of 1/16 inch. Assume independence. a. Determine the mean and standard deviation of the difference between the width of the casing and the width of the door. b. What is the probability that the width of the casing minus the width of the door exceeds 1/4 inch? c. What is the probability that the door does not fit in the casing?
Answer:
a) Mean = 0.125 inch
Standard deviation = 0.13975 inch
b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25) = 0.18673
c) Probability that the door does not fit in the casing = P(X < 0) = 0.18673
Step-by-step explanation:
Let the distribution of the width of the casing be X₁ (μ₁, σ₁²)
Let the distribution of the width of the door be X₂ (μ₂, σ₂²)
The distribution of the difference between the width of the casing and the width of the door = X = X₁ - X₂
when two independent normal distributions are combined in any manner, the resulting distribution is also a normal distribution with
Mean = Σλᵢμᵢ
λᵢ = coefficient of each disteibution in the manner that they are combined
μᵢ = Mean of each distribution
Combined variance = σ² = Σλᵢ²σᵢ²
λ₁ = 1, λ₂ = -1
μ₁ = 24 inches
μ₂ = 23 7/8 inches = 23.875 inches
σ₁² = (1/8)² = (1/64) = 0.015625
σ₂ ² = (1/16)² = (1/256) = 0.00390625
Combined mean = μ = 24 - 23.875 = 0.125 inch
Combined variance = σ² = (1² × 0.015625) + [(-1)² × 0.00390625] = 0.01953125
Standard deviation = √(Variance) = √(0.01953125) = 0.1397542486 = 0.13975 inch
b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25)
This is a normal distribution problem
Mean = μ = 0.125 inch
Standard deviation = σ = 0.13975 inch
We first normalize/standardize 0.25 inch
The standardized score of any value is that value minus the mean divided by the standard deviation.
z = (x - μ)/σ = (0.25 - 0.125)/0.13975 = 0.89
P(X > 0.25) = P(z > 0.89)
Checking the tables
P(x > 0.25) = P(z > 0.89) = 1 - P(z ≤ 0.89) = 1 - 0.81327 = 0.18673
c) Probability that the door does not fit in the casing
If X₂ > X₁, X < 0
P(X < 0)
We first normalize/standardize 0 inch
z = (x - μ)/σ = (0 - 0.125)/0.13975 = -0.89
P(X < 0) = P(z < -0.89)
Checking the tables
P(X < 0) = P(z < -0.89) = 0.18673
Hope this Helps!!!
[!] Urgent [!] Find the domain of the graphed function.