a. Probability density function (pdf) of X: 0.247 for 0.20 < x < 4.25.
b. Probability that diameter exceeds 2 mm: 0.556.
c. Probability that diameter is within 2 mm of the mean diameter: 0.988.
(a) Probability density function (pdf) of X:
For a uniform distribution with A = 0.20 and B = 4.25, the pdf is constant within the range A to B and 0 elsewhere. Therefore:
f(x) = 1 / (B - A) = 1 / (4.25 - 0.20) = 1 / 4.05 ≈ 0.247 for 0.20 < x < 4.25
(b) Probability that diameter exceeds 2 mm:
P(X > 2) = (4.25 - 2) * f(x) = 2.25 * 0.247 ≈ 0.556
(c) Probability that diameter is within 2 mm of the mean diameter:
The mean of a uniform distribution is (A + B)/2 = (0.20 + 4.25)/2 = 2.225.
So, we need to find P(2.225 - 2 < X < 2.225 + 2), which is P(0.225 < X < 4.225).
P(0.225 < X < 4.225) = (4.225 - 0.225) * f(x) = 4 * 0.247 ≈ 0.988
Complete question:
An article considered the use of a uniform distribution with
A = 0.20 and B = 4.25
for the diameter X of a certain type of weld (mm).
(a) Determine the pdf of X. (Round your answers to three decimal places.)
0.2<x<4.25
(b) What is the probability that diameter exceeds 2 mm? (Round your answer to three decimal places.)
(c) What is the probability that diameter is within 2 mm of the mean diameter? (Round your answer to three decimal places.)
How to order decimals from least to greatest with different decimals places?
According to bmi, a woman who is 5 feet 6 inches tall and weighs 175 pounds is considered to be
A woman who is 5 feet 6 inches tall and weighs 175 pounds has a BMI of 28.2 and would be classified as overweight.
The Body Mass Index (BMI) is a tool commonly used to assess whether a person has a healthy weight relative to their height. To calculate BMI, you divide a person's weight in pounds by their height in inches squared and multiply by 703.
For a woman who is 5 feet 6 inches tall and weighs 175 pounds:
Height: 66 inchesWeight: 175 poundsThe calculation for BMI would be:
BMI = (175 / (66×66)) × 703
BMI = 28.2
According to the BMI weight status categories:
BMI between 25 and 29.9 is considered overweight, and a BMI of 30 or higher is considered obese.
Therefore, a woman who is 5 feet 6 inches tall and weighs 175 pounds would be classified as overweight.
Ms. Frazier chooses two students to come to the board from a class of 12 boys and 8 girls. What is the probability that she will select a girl student first and a boy student second?
The probability that Ms. Frazier selects a girl first and a boy second from her class is 24/95, calculated by multiplying the probability of selecting a girl (8/20) by the probability of selecting a boy thereafter (12/19).
Explanation:To calculate the probability that Ms. Frazier will select a girl student first and a boy student second from her class of 12 boys and 8 girls, we need to use the concept of conditional probability because the selection of the second student depends on the first.
The total number of students is 12 boys + 8 girls = 20 students. The probability of selecting a girl first is the number of girls divided by the total number of students, which is 8/20. Once a girl is selected, there are now 19 students left. The probability of selecting a boy next is the number of boys left (which is still 12) divided by the new total, which is 12/19. The joint probability of both events happening in succession (selecting a girl then a boy) is found by multiplying the probabilities of the two individual events.
So, the probability of selecting a girl first and a boy second is (8/20) × (12/19) = 96/380. This simplifies to 24/95 when we divide both numerator and denominator by 4.
Therefore, Ms. Frazier has a probability of 24/95 to choose a girl first and a boy student second.
The probability of selecting a girl student first and a boy student second is approximately 0.2526.
Explanation:To find the probability of selecting a girl student first and a boy student second, we need to calculate the probability of each event separately and then multiply them together.
Step 1: Probability of selecting a girl student first
Number of girls: 8Total number of students: 12 boys + 8 girls = 20Probability of selecting a girl student first = Number of girl students / Total number of students = 8/20 = 0.4Step 2: Probability of selecting a boy student second
Number of boy students: 12Total number of students after selecting a girl student: 20 - 1 = 19Probability of selecting a boy student second = Number of boy students / Total number of students after selecting a girl student = 12/19 ≈ 0.6316Step 3: Multiply the probabilities from Step 1 and Step 2:
Probability of selecting a girl student first and a boy student second = Probability of selecting a girl student first × Probability of selecting a boy student second = 0.4 × 0.6316 ≈ 0.2526How do you find the x intercepts of a polynomial function with a zero constant?
To find the x-intercepts of a polynomial function, set y equal to zero and solve for x. Use the quadratic formula -b±sqrt(b²-4ac)/2a to solve, where a, b, and c are coefficients of the function.
Explanation:The 'x' intercepts of a function are the values of 'x' where 'y' equals zero. Take the given polynomial equation x² +0.0211x -0.0211 = 0; here a=1, b=0.0211 and c=-0.0211. We can solve this using the quadratic formula which states: x = -b ± sqrt(b² - 4ac) / 2a. Plugging the values in we get: x = -0.0211 ± sqrt((0.0211)² - 4(1)(-0.0211)) / (2*1). Solve this to get the x-intercepts.
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Solve for x. x−14=38 Enter your simplified answer in the box.
Answer:
52
Step-by-step explanation:
simplify ( 1/2A + 1/2B )^2
Simplify: √5 x √12 x √50
a: 10√10
b: 7√30
c:10√30
d: 7√10
if x is 50 then what is x4+44+3.5
joanna bought 1 1/2 pounds of apples, 3/4 pounds of strawberries, 1/2 pound of grapes, 1 3/4 pounds of oranges, and 1 1/4 pounds of pears. How many pounds of fruit Joanna bought in all?
The distance between the baseball stadium and the airport is 1.6×106 centimeters. Which unit of measurement is most appropriate to measure this distance? inches kilometers feet milimeters
The correct answer would be kilometers
Answer:
Kilometers
Step-by-step explanation:
I took the test.
Mateo is draining a pool at a rate of 1/8 of a gallon every 1/2 hour. If he continues to drain the pool , how much waters will be drained in 1 hour?
Between which two integers does √64 lie?
Sort the sequences to whether they are arithmetic, geometric, or neither
1) 98.3 , 94.1 , 89.9 , 85.7
2) 1 ,0 , -1 ,0
3) 1.75 , 3.5 , 7 ,14
4) -1 ,1 , -1 ,1
5) -12, -10.8, -9.6, -8.4
her answer is right but you just have to switch 4 and 5 around 4 is geometric while 5 is arithmetic
Final Answer:
Each sequence is tested for a common difference or ratio to determine if it is arithmetic or geometric. The sequences 98.3, 94.1, 89.9, 85.7 and -12, -10.8, -9.6, -8.4 are arithmetic, 1.75, 3.5, 7, 14 is geometric, and 1, 0, -1, 0 as well as -1, 1, -1, 1 are neither.
Explanation:
To determine if a sequence is arithmetic, geometric, or neither, we look for a common difference or ratio between consecutive terms.
For the sequence 98.3, 94.1, 89.9, 85.7, we subtract consecutive terms: 94.1 - 98.3 = -4.2, 89.9 - 94.1 = -4.2, 85.7 - 89.9 = -4.2. The common difference is -4.2, so this sequence is arithmetic.The sequence 1, 0, -1, 0 does not have a common difference or ratio, so it is neither arithmetic nor geometric.For 1.75, 3.5, 7, 14, the ratios are 3.5/1.75 = 2, 7/3.5 = 2, and 14/7 = 2. The common ratio is 2, so this sequence is geometric.The sequence -1, 1, -1, 1 alternates signs without a common difference or ratio, so it is neither.For the sequence -12, -10.8, -9.6, -8.4, the difference is -10.8 - (-12) = 1.2, -9.6 - (-10.8) = 1.2, -8.4 - (-9.6) = 1.2. The common difference is 1.2, making it an arithmetic sequence.What equation allows you to calculate the force acting on an object
Sand dollars are animals that live buried in the sand of shallow coastal waters. The thin circular body of a sand dollar is usually 2 to 4 inches wide. Find the area of a sand dollar that is 3 inches wide.
Answer:
The area of a sand dollar that is 3 inches wide is [tex]7.0686 inch^2[/tex]
Step-by-step explanation:
Width of sand dollar's circular body = d = 3 inches
Radius of the sand dollar's circular body = r
[tex]r=\frac{d}{2} = \frac{3 inch}{2}=1.5 inches[/tex]
Area of circle = [tex]\pi r^2[/tex]
So, the area of a sand dollar that is 3 inches wide:
[tex]A=3.14\times (1.5 inch)^2=7.0686 inch^2[/tex]
The area of a sand dollar that is 3 inches wide is [tex]7.0686 inch^2[/tex]
Suzanne works 25 hours a week for four weeks at $9.50 per hour. how much does she earn at the end of four weeks?
What is the answer to 3n-5=7n+11 with work shown
A coin is weighted so that the probability of obtaining a head in a single toss is 0.3. if the coin is tossed 35 times, what is the probability of obtaining between 9 and 14 heads, exclusive.
The probability of obtaining between 9 and 14 heads , exclusive is 0.510
What is Probability?
The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
The value of probability lies between 0 and 1
Given data ,
Let the probability of obtaining a head in a single toss be p = 0.3
Let the number of times the coin is tossed be n = 35
Now , the mean and the standard deviation is calculated by
Mean M = np
Substituting the values of n and p , we get
Mean M = 0.3 x 35
Mean M = 10.5
Now , the standard deviation S = √M ( 1- p )
Substituting the values in the equation , we get
Standard Deviation S = √10.5 ( 1 - 0.3 )
Standard Deviation S = √10.5 x 0.7
Standard Deviation S = 2.71
Now , the probability of obtaining between 9 and 14 heads , exclusive is represented as P ( 9 < x < 14 ) = P ( 8.5 < x < 14.5 )
And , the z - scores of 8.5 and 14.5 are
z ( 8.5 ) = ( x - M ) / S
= ( 8.5 - 10.5 ) / 2.71
= -0.3688
z ( 14.5 ) = ( x - M ) / S
= ( 14.5 - 10.5 ) / 2.71
= 1.1066
So , the probability of obtaining between 9 and 14 heads , exclusive is represented as P ( 9 < x < 14 ) = P ( -0.3688 < x < 1.1066 )
So , the equation can be written as
P ( 9 < x < 14 ) = P ( z < 1.1066 ) - P ( z < -0.3688 )
Using z-scores of probabilities, we have:
P ( 9 < x < 14 ) = 0.86577 - 0.3561
P ( 9 < x < 14 ) = 0.50967
P ( 9 < x < 14 ) = 0.510
Therefore , the value of P ( 9 < x < 14 ) is 0.510
Hence,
The probability of obtaining between 9 and 14 heads , exclusive is 0.510
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What is a reasonable percent error in chemistry?
2x-1
Evaluate the algebraic expressions for the given values of the variable
The graph of f(x) = 2^x + 1 is shown below. Explain how to find the average rate of change between x = 0 and x = 3.
At the movie theatre, child admission is $5.10 and adult admission is $9.00 . On Monday, 163 tickets were sold for a total sales of $1088.70 . How many adult tickets were sold that day?
a = adult tickets
c = child
c + a = 163 tickets total
rewrite as c = 163-a
5.10c + 9.00a = 1088.70
5.10(163-a) + 9.00a = 1088.70
831.30-5.10a + 9.00a = 1088.70
831.30 +3.9a = 1088.70
3.9a = 1088.70-831.30
3.9a = 257.40
a = 257.40 / 3.9 = 66
66 adult tickets were sold
Two angles of an isosceles triangle measure 70° and x°. What is the sum of three possible values of x? A. 95 B. 125 C. 140 D. 165 E. 180
The sum of three possible values of x° in the isosceles triangle is 180°. The angles are 40°, 70°, and 70°. The correct answer is E. 180.
In an isosceles triangle, two angles are congruent (equal). So, if one angle is 70°, the other angle must also be 70°.
Let's denote the third angle as y°.
Since the sum of the angles in any triangle is 180°, we can write the equation:
70° + 70° + y° = 180°
Solving for y:
2 × 70° + y° = 180°
y° = 180° - 140°
y° = 40°
So, the three possible values of x° are 40°, 70°, and 70°.
Now, let's find the sum of these three possible values:
Sum = 40° + 70° + 70°
Sum = 180°
Therefore, the sum of three possible values of x° is 180°. The correct answer is E. 180.
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What is the area of the rectangle?
60 units²
66 units²
70 units²
74 units²
A translation of directed line segment from the origin to (0,-3) followed by a reflection around the line y=x
To translate a directed line segment from the origin to (0,-3), simply subtract 3 from the y-coordinate. To reflect a point across the line y=x, swap the x and y coordinates. The reflected point of (0,-3) would be (-3,0).
Explanation:To translate a directed line segment from the origin to (0,-3), we can simply subtract 3 from the y-coordinate. The new coordinate would be (0,-3).
To reflect a point across the line y=x, we swap the x and y coordinates. So the reflected point of (0,-3) would be (-3,0).
Dawn Lingua bought three yards of cloth to make some curtains. The cloth was on sale for $2.25 per yard. How much did Dawn pay for the cloth if the sales tax was 5%?
Answer:
Dawn paid $7.09.
Step-by-step explanation:
Dawn Lingua bought cloth to make curtains = 3 yards
Cost of the cloth = $2.25 per yard
Cost of 3 yard cloth = $2.25 × 3 = $6.75
Sales tax was = 5%
Sales tax on the total cost = 5% of 6.75
= (5/100) × 6.75 = 0.05 × 6.75 = $0.3375
Now we add sales tax to the total cost
= 6.75 + 0.3375 = $7.0875 rounded to $7.09
Dawn paid for the cloth with sales tax was $7.09
Jacob held different part-time jobs during his summer holiday. The table below shows the total money he earned for different amounts of time, in hours: Hours Worked 1 2 3 4 5 6 7 8 9 Money Earned (dollars) 4 8 12 16 20 24 28 32 36 What type of association will the scatter plot for this data represent between the number of hours worked and the total money earned?
The type of association scatter plot for this data represents the number of hours worked and the total money earned is a positive correlation.
How to find the type of association that represent the data?The number of hours and the amount of money increases at an even rate, 4 dollars for each hour.
The given table;
Hours Worked 1 2 3 4 5 6 7 8 9
Money Earned (dollars) 4 8 12 16 20 24 28 32 36
We can see here as the number of hours increases the amount of money is increasing, so it indicates that there is a positive association.
Also, there is an unequal change in equal intervals of time, so it represents a positive nonlinear association.
Hence, the graph is a line, y=4x,
The type of association scatter plot for this data represents the number of hours worked and the total money earned is a positive correlation.
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ROUND 4,719,429 TO THE NEAREST 10,000
Which should be the first step in solving the equation 1.2 w -3.8= 12.4
1. Add 3.8 to both sides of the equation.
2. Subtract 1.2 from both sides of the equation.
3. Multiply both sides of the equation by 1.2.
4. Divide both sides of the equation by 3.8.
Answer:
Option 1 - Add 3.8 to both sides of the equation.
Step-by-step explanation:
Given : Equation [tex]1.2w-3.8=12.4[/tex]
To find : Which should be the first step in solving the equation?
Solution :
Equation [tex]1.2w-3.8=12.4[/tex]
Step 1 - Adding 3.8 both side,
[tex]1.2w-3.8+3.8=12.4+3.8[/tex]
[tex]1.2w= 16.2[/tex]
Step 2 - Divide 1.2 both side,
[tex]\frac{1.2w}{1.2}=\frac{16.2}{1.2}[/tex]
[tex]w=13.5[/tex]
Therefore, The first step in solving the equation is 'Add 3.8 to both sides of the equation.'
So, Option 1 is correct.
Can you guys please help me with math? (Pt 2.)
(I've attached the picture)
Elian is placing a rectangle in the coordinate plane. He knows that the shorter side of the rectangle is half the length of the longer side. He places the longer side on the x-axis.
What coordinates should he assign to the top-left vertex of the rectangle?
Enter your answer in the boxes.
Let
x--------> the length side of the rectangle
y-------> the width side of a rectangle
we know that
[tex]y=\frac{1}{2}x[/tex] ------> equation A
[tex]x=2a\ units[/tex] ---------> given problem (see the graph)
substitute the value of x in the equation A
[tex]y=\frac{1}{2}2a=a\ units[/tex]
therefore
the answer is
the top-left vertex of the rectangle is the point [tex](0,a)[/tex]