With the thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters.
a) 40% of the flanges exceeds 1.01 millimeters.
b) 1.04 millimeters is the thickness that is exceeded by 90% of the flanges.
c) The mean of flange thickness is 1 millimeters and the variance of flange thickness is 0.01 millimeters^2.
a) To determine the proportion of flanges that exceeds 1.01 millimeters, we need to find the area under the probability density function (pdf) of the thickness that is greater than 1.01 millimeters.
Let's call the random variable X representing the thickness of the flange. The pdf of X is uniform, so it has constant value over the interval [0.95, 1.05]. Therefore, the proportion of flanges that exceeds 1.01 millimeters can be found as follows:
P(X > 1.01) = (1.05 - 1.01) / (1.05 - 0.95) = (1.05 - 1.01) / 0.1 = 0.04 / 0.1 = 0.4
So, 40% of the flanges exceed 1.01 millimeters.
b) To find the thickness that is exceeded by 90% of the flanges, we need to solve for X in the following equation:
P(X > X) = 0.9
Substituting the values for the pdf, we get:
(X - 0.95) / (1.05 - 0.95) = 0.9
Solving for X, we get:
X = 0.95 + 0.9 * (1.05 - 0.95) = 0.95 + 0.9 * 0.1 = 0.95 + 0.09 = 1.04
So, 1.04 millimeters is the thickness that is exceeded by 90% of the flanges.
c) The mean of X can be calculated as follows:
Mean = (0.95 + 1.05) / 2 = 1
The variance of X can be calculated as follows:
Variance = (1.05 - 0.95)^2 / 12 = 0.01
So, the mean and variance of flange thickness are:
Mean = 1 millimeters
Variance = 0.01 millimeters^2
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How do you prove a contrapositive?
Answer:
Step-by-step explanation:
A contrapositive is a logical equivalent of the original statement that has the opposite direction and negated conclusion. It can be proven by using the following steps:
Start with the original statement in the form of "If P, then Q".
Negate both the hypothesis (P) and the conclusion (Q) of the original statement.
Conjoin the negated hypothesis and the negated conclusion to form a new statement.
Show that the contrapositive is logically equivalent to the original statement, meaning that it has the same truth value as the original statement for all possible cases.
For example, consider the statement: "If it rains, the roads will be wet." The contrapositive of this statement is "If the roads are not wet, it did not rain." To prove the contrapositive, we can use the following steps:
Start with the original statement "If it rains, the roads will be wet."
Negate both the hypothesis and the conclusion: "It does not rain" and "The roads are not wet".
Conjoin the negated hypothesis and the negated conclusion: "It does not rain and the roads are not wet."
Show that the contrapositive is logically equivalent to the original statement by considering all possible cases:
If it rains, the roads will be wet (as stated in the original statement), and the contrapositive "It does not rain and the roads are not wet" is false.
If it does not rain, the roads will not be wet (as stated in the contrapositive), and the original statement "If it rains, the roads will be wet" is false.
This shows that the contrapositive is logically equivalent to the original statement, and we can use it to draw the same conclusion with a different proof.
Andrea backyard is 400 square feet.her rectangular swimming pool is 10 feet long and 6 feet wide what is the area Andrea's backyard not including the swimming
pool
The area of Andrea’s backyard, not including the swimming pool, is 340 feet²
What is area of Rectangle?The Area of rectangle is the product of its length to its width.
i.e., Area of rectangle = length x width.
Given:
A rectangular swimming pool has 10 feet long and 6 feet wide.
The area of a rectangle is:
A= L x W
A = 10 x 6
A = 60 ft²
Now, the area of the Andrea’s backyard (A2) is 400 ft²,
So, area of backyard not including the swimming pool
Area = Area of backyard - area of pool
A =400 ft²-60 ft²
A =340 ft²
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The diameter of a circle is 7 ft. Find the circumference to the nearest tenth.
Answer:
Step-by-step explanation:
C=[tex]2\pi R=\pi d[/tex]
if [tex]\pi = 3.14[/tex]
c=3.14*7=21.98
what is the image of (7,3)?
use the translation: T<3,-5>
HELP ASAP
The image of (7, 3) after a translation of T(3, - 5) would be at (10, - 2).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
Given, A point has a coordinate of (7, 3).
We know, Translation shifts coordinate into the x-y coordinate.
Therefore, The image of (7, 3) after a translation of (3, - 5) would be,
(7 + 3, 3 - 5) which is now at (10, - 2).
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The scores from a 20 point algebra quiz are shown.
7, 9, 10, 12, 13, 15, 17, 18, 19, 20
The percentile of a test score can be defined as the percent of test scores less than or equal to that test score
Use this definition to find the percentile of the test score 12
The test score 12 is at the ___th percentile
The test score of 12 is at the 40th percentile.
What is a percentile?
A Percentile divides a data set into the 100 equal parts. A percentile is a measurement that tells us what percent of the total frequency of a data set was at or below that measure.
From the question,
The test score of 12 is less than or equal to 7, 9, 10, 12, so 4 out of the 10 scores are less than or equal to 12.
So, the percentile of the test score 12 can be calculated as:
Percentile = (number of scores less than or equal to 12) / (total number of scores) x 100
percentile = (4) / (10) x 100
percentile = 40
Hence, the test score of 12 is at the 40th percentile.
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A marketing assistant for a technology firm plans to randomly select 1000 customers to estimate the proportion who are satisfied with the firm's performance. Based on the results of the survey, the assistant will construct a 95% confidence interval for the proportion of all customers who are satisfied. The marketing manager, however, says that the firm can afford to survey only 250 customers. How will this decrease in sample size affect the margin of error and confidence interval? True Statements or False Statements
False: The decrease in sample size will increase the margin of error and decrease the confidence interval.
What is interval?Interval is a set of values that are located between two specific points on a line. It can be used to measure the amount of time between two events, the difference between two numbers, or the distance between two points. Intervals can also be used in data analysis to identify patterns or trends. In mathematics, intervals are often represented as a pair of numbers, such as (1, 5).
The decrease in sample size will decrease the margin of error and increase the confidence interval. This is because when the sample size is decreased, the margin of error is increased and the confidence interval is decreased since the precision of the estimate is lower. This means that the range of the confidence interval is wider and the estimates are less precise.
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A boat leaves the dock and travels 10 miles due south, then 24 miles due west. How far is the boat from the dock? Boat 24 mi OA. 676 mi OB. 14 mi OC. 34 mi O D. 26 mi Dock 10 mi
The distance from the boat to the dock will be 26 miles. Then the correct option is D.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
A boat leaves the dock and travels 10 miles due south, then 24 miles due west.
Then the distance from the boat to the dock is given as,
d² = 10² + 24²
d² = 100 + 576
d² = 676
d = 26 miles
The distance from the boat to the dock will be 26 miles. Then the correct option is D.
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Suppose "n" can't equal 0 or 1. Show that substitution v=y^(1-n) transforms the Bernoulli equation dy/dx + P(x)y=Q(x)y^(n)into the linear equation dv/dx + (1-n)P(x)v(x)=(1-n)Q(x).
Answer:v = y(1-n)dv/dx = (1-n)y-n dy/dxso dy
Step-by-step explanation:
WORTH 100 POINTS!!!
OPEN RESPONSE A city parking garage charges $4 to park for up to two hours. After that, an additional charge of $2.50 per hour applies. Write an equation in point-slope form that models the total cost y for parking x hours, where x > 2
Answer: y = 4 + 2.50(x > 2)
Step-by-step explanation: y is the outcome, the fixed cost is 4, and the variable cost is 2.50 × (x > 2).
True or False? All of these figures are similar
Answer:
True
Step-by-step explanation:
They Are all Equal and The Same By the Degrees and Angles and Numbers
What is equation of a semicircle?
The equation of the semicircle upper side of the x-axis will be x = √[r² - (y - k)²] + h.
What is the equation of a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the radius of the circle and the location of the center of the circle be (h, k). Then the equation of the circle is given as,
(x - h)² + (y - k)² = r²
The equation of the semicircle upper side of the x-axis will be given as,
(x - h)² + (y - k)² = r²
x - h = √[r² - (y - k)²]
x = √[r² - (y - k)²] + h
The equation of the semicircle upper side of the x-axis will be x = √[r² - (y - k)²] + h.
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is the value of Y+6 greater in4(y+6)=48 or 12(y+6)=48 how do you know?
To determine which expression has a greater value for Y + 6, we need to isolate Y + 6 on one side of the equation and compare the two expressions.
Starting with 4(y + 6) = 48, we can distribute the 4 to get 4y + 24 = 48. Subtracting 24 from both sides gives us 4y = 24, and then dividing both sides by 4 gives us y = 6. So, for this expression, the value of Y + 6 is 6 + 6 = 12.
Next, for 12(y + 6) = 48, we can distribute the 12 to get 12y + 72 = 48. Subtracting 72 from both sides gives us 12y = -24, and then dividing both sides by 12 gives us y = -2. So, for this expression, the value of Y + 6 is -2 + 6 = 4.
Therefore, the value of Y + 6 is greater in 4(y + 6) = 48 than in 12(y + 6) = 48.
Answer:
The value of y + 6 is greater in the first equation.
----------------------------
Divide both sides of the first equation by 4:
4(y + 6) = 48y + 6 = 12Divide both sides of the second equation by 12:
12(y + 6) = 48y + 6 = 4As we see the first expression has greater value since 12 > 4.
There's a 30% chance of it raining each day in Narnia. On how many days would you expect it to rain during your visit there that lasts 110 days?
Answer:
Step-by-step explanation:
Since there is a 30% chance of rain on any given day, there is a 70% chance that it will not rain on a given day.
To calculate the expected number of days it will rain during your visit, we can use the formula:
Expected number of rainy days = total number of days * probability of rain
Expected number of rainy days = 110 days * 0.3 = 33 days
Therefore, we can expect it to rain on approximately 33 days during a 110-day visit to Narnia.
This table shows a linear function.
x y
-1 7
0 5
1 3
2 1
3 -1
Based on the information given, how can you verify that the function is linear? Select all that apply. choices shown in image
Step-by-step explanation:
the 3rd, 5th and 6th answers are correct.
Answer:
3, 5, 6
Step-by-step explanation:
For every change in x of 1, there is a change in y of -2.
For an equation to be linear, equal changes in x must produce equal changes in y.
Since that is true here, it is a linear equation.
Point (0, 5) gives you the y-intercept, b = 5.
From (0, 5) to (1, 3), you can calculate the slope:
slope = m = (3 - 5)/(1 - 0) = -2
The equation is y = -2x + 5
The true statements are: 3, 5, 6
The measure of one interior angle of a parallelogram is 0. 25 times the measure of another angle.
If the measure of one interior angle of a parallelogram is 0.25 times the measure of another angle, let's call the measure of the larger angle "x". Then, the measure of the smaller angle would be 0.25x.
In a parallelogram, opposite angles are equal in measure. So, if one angle measures x, the opposite angle would also measure x. And if one angle measures 0.25x, the opposite angle would also measure 0.25x.
Therefore, the sum of the measures of the angles in a parallelogram would be x + x + 0.25x + 0.25x = 2x + 0.5x = 2.5x.
Since the sum of the measures of the interior angles in a parallelogram must equal 360 degrees, we can set up the following equation:
2.5x = 360
Solving for x, we get:
x = 144
0.25x = 0.25*144
= 36
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Can someone help me out with this? I haven't had any time to catch up on math work lately... It would be greatly appreciated.
Answer:8
Step-by-step explanation:
What is a proportion symbol in statistics?
The proportional symbol in statistics is to express the percentage of a population that possesses a particular feature.
To express the percentage of a population that possesses a particular feature, the proportion symbol in statistics, abbreviated "p," is employed. The number of people in a population who share an interest feature divided by the total number of people in the population is represented as a proportion, which is a fraction or ratio.
We can select a random sample of people from the population and count the number of people who own cars, for instance, if we are interested in the percentage of residents of a city who drive. In our sample, let "x" represent the number of car owners, and "n" represent the total number of participants. The sample percentage of cars is thus to express the percentage of a population that possesses a particular feature, the proportion symbol in statistics, abbreviated "p," is employed. The number of people in a population who share an interest feature divided by the total number of people in the population is represented as a proportion, which is a fraction or ratio.
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What is the sum of the 10th square number
and the 9th square number?
The sum of the 10th square number and the 9th square number is, 181
What is the squaring of numbers ?A number is multiplied by itself when it is squared. For instance, when you square the number 3, you get the result 9 (3 x 3). Superscript "2" is the symbol for squaring a number. For instance, 32 = 9 can be used to represent the square of 3.
Numerous crucial mathematical properties and applications of squaring a number can be found in number theory, algebra, and geometry. Squaring, for instance, can be used to solve quadratic equations or to determine the area of a square, the distance between two points, or both. A number's ability to form a perfect square can also be determined by squaring it.
The 10th square number is 10² = 100
and the 9th square number is 9² = 81.
So, the sum of the 10th square number and the 9th square number is:
= 100 + 81
= 181
Therefore, the sum of the 10th square number and the 9th square number is 181.
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what is 148 cm to inches
Answer:
58.2677
Step-by-step explanation:
148 divide the length value by 2.54
Answer:
1 inch = 2.54 cm
148 / 2.54 = 58.2677165354 inches
Step-by-step explanation:
1) There are three consecutive positive integers, such that the largest
is 44 less than twice the smallest. What is the value of the smallest
of these three consecutive integers?
The three consecutive integers are 46, 47, 48.
What is number?A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
here, we have,
Let the three consecutive integers be represented as x,x+1,x+2
As per the requirement, largest integer is 44 less than twice the smallest.
=> x+ 2 = 2x -44
=> 2x -x = 2+44
=> x= 46
So the three integers are 46, 47, 48
Verification:
Largest integer = 48
Smallest integer = 46
2 * smallest integer - 44
= 2* 46 - 44
= 48
Largest integer is also 48.
So the required condition in the question is satisfied by these three integers.
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What is the cost and area of the mat
1. The area of the mat is 1 in² and the cost is $0.05
2. The area of the mat is 4 in² and the cost is $0.2
What is area ?The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m².
The area of a square = l²
1. the area = 1×1 = 1 in²
since $0.05 is the cost per in²
therefore the cost of the mat is $0.05
2. the area = 2× 2 = 4 in²
therefore the cost = 4 × 0.05
= $0.2
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What is the y=mx+b formula for these points: (67,67), (65,65), (63,63), (69,69), (57,57), (65,65), (68,66), (48,48), (72,72)?
The y = mx + b formula for these points is y = 2x - 67.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (67, 65).Points on y-axis = (67, 65).At point (67, 67), a linear equation of this line can be calculated in slope-intercept form (y = mx + b) as follows:
y - 67 = (65 - 67)/(65 - 67)(x - 67)
y - 67 = 2(x - 67)
y = 2x - 134 + 67
y = 2x - 67
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what is the value of x? enter your answer in the box. units
The value of x or length of FD int the figure is 75.
image attached below,
EquationAn equation is a mathematical statement that is made up of two expressions connected by an equal sign.
side of triangleIn a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle.
This is similarities in sides questions. To solve make equation.
JY = 42
JS = 42 + 63 = 105
JD = 50
JF = 50 + x
Using the sides,
52/105 = 50/50+x
(42)(50+x) = (50)(105)
2100 + 42x = 5250
42x = 5250 - 2100
42x = 3150
x = 3150/42
x = 75.
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combine like terms 4x+4y^3-5+6-2y^3-5y^3+5x
A television and DVD player cost a total of $1140. The cost of the television is three times the cost of the DVD player. Find the cost of each item.
Answer:
cost of television + cost of DvD =1140
cost of television =3×cost of DVD
3×cost of DVD+cost of DVD =1140
4×cost of DVD =1140
cost of DVD =285$
Please help! Can’t seem to find anyone who has an explanation for this.
The steps to explain and show how to evaluate a·b for a = 5 and b = 8 include the following:
Steps a·b___
Substitute 5 for a 5·b
Substitute 8 for b 5·8
Multiply 40
What is an expression?In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).
Based on the information provided above, we have the following mathematical expression:
Expression = a·b
Expression = 5 × 8 (Substitute 5 for a and substitute 8 for b)
Expression = 40 (multiply).
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Kaj observes a marble travel along a horizontal path at a constant rate. The marble travels 1/20 of the length of the path in 2 1/2 seconds. At that rate, how many seconds does it take the object to travel the full length?
It takes 50 seconds to travel the full length at the constant rate R.
How many seconds does it take the object to travel the full length?Remember the relation between speed, distance and time:
distance = speed*time
Here we know that at a rate R (or speed S, these are equivalent) it moves (1/20) of the total distance D in (2 + 1/2) seconds, then we can write:
R*(2 + 1/2) = (1/20)*D
Now we only need to isolate D on the right side, to do so we need to multiply both sides by 20.
20*R*(2 + 1/2) = D
The time is:
20*(2 + 1/2) seconds
40 + 10 seconds
50 seconds
It takes 50 seconds to travel the full length,
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A company is designing a new cylindrical package. The volume of the package is 87.92 in.3. The radius is 2 inches. Use the formula V = Bh and 3.14 to approximate π
to answer the questions.
Part A
To the nearest inch, how many inches is the height of the cylindrical package?
Answer:
Step-by-step explanation:
to answer the questions.
Part A
To the nearest inch, how many inches is the height of the cylindrical package?
Part B
The company decides to keep the radius the same and double the height. Rounded to the nearest hundredth, how many cubic inches is the new volume of the package?
The points represented by the table lie on a line . Find the slope of the line x-1,1,3,5. Y 10, 5, 0,-5 m=
Answer: The slope of a line can be found using the formula:
m = (y2 - y1) / (x2 - x1)
We can choose any two points from the table to find the slope. Let's use the points (1, 10) and (5, -5):
m = (-5 - 10) / (5 - 1) = -15 / 4 = -3.75
So, the slope of the line represented by the table (x = 1, 3, 5, y = 10, 5, 0, -5) is -3.75.
Step-by-step explanation:
The coefficient of the term x6 is 6048
The coefficient of 6x is 6.
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
We have to write the coefficient of 6x.
As, coefficient is the number which is just before the variable like in 2x 'x' is the variable and '2' is the coefficient.
So, the coefficient 6x is 6.
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