Problem # 6: (15pts) A batch of 30 injection-molded parts contains 6 parts that have suffered excessive shrinkage. a) If two parts are selected at random, and without replacement, what is the probabil
Answers
The probability of randomly selecting two parts without replacement and having both of them be from the batch of parts with excessive shrinkage is approximately 0.9563.
To find the probability of selecting two parts without replacement and having both of them be from the batch of parts that have suffered excessive shrinkage, we can use the concept of hypergeometric probability.
Given:
Total number of parts in the batch (N) = 30
Number of parts with excessive shrinkage (m) = 6
Number of parts selected without replacement (n) = 2
The probability can be calculated using the formula:
P(both parts are from the batch with excessive shrinkage) = (mCn) * (N-mCn) / (NCn)
Where (mCn) denotes the number of ways to choose n parts from the m parts with excessive shrinkage, and (N-mCn) denotes the number of ways to choose n parts from the remaining (N-m) parts without excessive shrinkage.
Using the formula and substituting the given values, we get:
P(both parts are from the batch with excessive shrinkage) = (6C2) * (30-6C2) / (30C2)
Calculating the combinations:
(6C2) = 6! / (2! * (6-2)!) = 6! / (2! * 4!) = (6 * 5) / (2 * 1) = 15
(30-6C2) = (30-6)! / (2! * (30-6-2)!) = (24 * 23) / (2 * 1) = 276
Calculating the combinations for the denominator:
(30C2) = 30! / (2! * (30-2)!) = 30! / (2! * 28!) = (30 * 29) / (2 * 1) = 435
Now, substituting the calculated combinations into the probability formula:
P(both parts are from the batch with excessive shrinkage) = (6C2) * (30-6C2) / (30C2) = 15 * 276 / 435 ≈ 0.9563
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Related Questions
Consider the following function on the given interval f(x) = 14 + 4x - x², [0,5]Find the derivative of the function.f'(x) = Find any critical numbers of the function.x =Find the absolute maximum and absolute minimum values of f on the given interval.absolute minimum value =absolute maximum value =
Answers
The absolute minimum value of f on the interval [0,5] is 9, and the absolute maximum value is 18.
To find the derivative of the function f(x) = 14 + 4x - x², we simply take the derivative of each term and add them together. The derivative of 14 is 0, the derivative of 4x is 4, and the derivative of -x² is -2x. So:
f'(x) = 4 - 2x
To find any critical numbers of the function, we set the derivative equal to 0 and solve for x:
4 - 2x = 0
2x = 4
x = 2
So the critical number is x = 2.
To find the absolute maximum and absolute minimum values of f on the given interval [0,5], we first evaluate the function at the endpoints and the critical number:
f(0) = 14 + 4(0) - (0)² = 14
f(2) = 14 + 4(2) - (2)² = 14 + 8 - 4 = 18
f(5) = 14 + 4(5) - (5)² = 14 + 20 - 25 = 9
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Select the correct answer from the drop-down menu. Katie is watching a helicopter flying at an altitude of 5 miles. If the angle of elevation is , the distance between katie and the helicopter is approximately miles.
Answers
The distance between Katie and Helicopter will be 5.774 miles approximately.
We will solve this problem with the help of Trignometry. So, what is Trignometry?
A branch of mathematics called trigonometry examines correlations between triangles' side lengths and angles. Three crucial trigonometric functions—sine, cosine, and tangent—are represented by the abbreviations sin, cos, and tan.
In this problem, it is given that Katie is watching a helicopter flying at an altitude of 5 miles and the angle of elevation is π/3.
From Sin Cos Tan, you know that:
Sin = opposite/Hypotenuse
sin(π/3) = (5 miles)/Hypotenuse
Hypotenuse = (5 miles) / Sin(π/3) = 5/ (\(\sqrt[]{3}\)/2) miles = 5.774 miles.
So, the distance between Katie to the Helicopter is about 5.774 miles.
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In this problem, it is given that Katie is watching a helicopter flying at an altitude of 5 miles and the angle of elevation is π/3.
From Sin Cos Tan, you know that:
Sin = opposite/Hypotenuse
sin(π/3) = (5 miles)/Hypotenuse
Hypotenuse = (5 miles) / Sin(π/3) = 5/ (/2) miles = 5.774 miles.
So, the distance between Katie to the Helicopter is about 5.774 miles.
Please Help !! What is the volume of a cylinder with base radius 2 and height 9?
Answers
Answer:
The cylinders volume is 113.04 cubic inches
Step-by-step explanation:
The volume of a cylinder can be represented by the formula : V = π*r^2*h
So, now that we have the formula, we can simply plug in the values, and we have the volume of the cylinder.
V = π * 2^2 * 9
V = π * 4 * 9
It says to use 3.14 as π.
V = 3.14 * 4 * 9
V = 113.04
The cylinders volume is 113.04 cubic inches
What the slope of the line y=-2
Answers
Answer:
0
Step-by-step explanation:
The slope is zero because if you put it on a graph the line looks like this
_______________________________
Hope this helps!
And also if the equation is like x = 4 the slope would be undefined.
Bye!!
The difference between the park and house of a student is 1Km 575m. Every day he walks both ways between the park and his house. Find the total distance covered by him in a week's time?
Answers
The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.
To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.
Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.
In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.
Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.
Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.
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How many liters are there in a tank of volume 7.32m³?
Answers
Answer: 3 liters in a tank of volume 7.32m^3
Step-by-step explanation:
(4^2)^4 simplify the expression in the form 4^n please
Answers
Answer:
It would be \(4^{8}\)
Step-by-step explanation:
\((4^{2})^{4}\) is equivalent to \(4^{2*4}\) or \(4^{8}\).
2. Find the slope of the following equation. Simplify your answer.
y = = -5/2x - 2
Answers
Answer:
-2.5
Step-by-step explanation:
2x-y=4
X and y intercept?
Answers
Answer:
x=2 y=-4
Step-by-step explanation:
2x-y=4 solve for x
2x-0=4
2x=4+0
2x=4 . divide both sides by 2
x=2
2x-y=4 . solve for y
0-y=4
-y=4 . divide both sides by -1
y=-4
Katy invests £14 000 in a savings account for 3 years.
The account pays simple interest at a rate of 1.5% per annum.
Calculate the amount in her savings account Katy will get at the end of the 3 years
Answers
Simple interest formula:
Total = start x ( 1 + rate x time )
Total = 14,000 x ( 1 + (0.015 x3))
Total = 14,000 x 1.045
Total = 14,630
Answer:
£14,630
Step-by-step explanation:
Simple interest formula: A = P(1 + rt)
where:
A = final amountP = principal amountr = annual interest rate (as a decimal)t = time (in years)Given:
P = £14,000r = 1.5% = 0.015t = 3 years⇒ A = 14000(1 + 0.015 · 3)
⇒ A = 14000(1.045)
⇒ A = £14,630
statistics the art and science of learning from data 4th edition
Answers
"Statistics: The Art and Science of Learning from Data" (4th edition) is a valuable resource for understanding and applying statistical principles, providing insights into data analysis and decision-making processes.
Statistics is the art and science of learning from data. It involves collecting, organizing, analyzing, interpreting, and presenting data to gain insights and make informed decisions. In the 4th edition of the book "Statistics: The Art and Science of Learning from Data," you can expect to find a comprehensive exploration of these topics.
This edition may cover important concepts such as descriptive statistics, which involve summarizing and displaying data using measures like mean, median, and standard deviation. It may also delve into inferential statistics, which involve making inferences and drawing conclusions about a population based on a sample.
Additionally, the book may discuss various statistical techniques such as hypothesis testing, regression analysis, and analysis of variance (ANOVA). It may also provide real-world examples and case studies to illustrate the application of statistical methods.
When using information from the book, it is important to properly cite and reference it to avoid plagiarism. Be sure to consult the specific edition and follow the guidelines provided by your instructor or institution.
In summary, "Statistics: The Art and Science of Learning from Data" (4th edition) is a valuable resource for understanding and applying statistical principles, providing insights into data analysis and decision-making processes.
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1. Identify all pairs of parallel segments.
C
A
F
B
E
D
** This is a 2-pag
a)_
b)_
c)
Answers
All pairs of parallel segments are AC II FD, AB II FD and AC II FD.
What are parallel lines?Parallel lines in a plane are those that are regularly spaced apart. No parallel lines cross one another.
From the diagram,
B is the middle point of AC.
That means,
AB = AC.
And FA = CD
And line AC and FD are not intersecting each other.
So, AB and AC have the same relation with FD.
That means,
Parallel lines are AC II FD, AB II FD and AC II FD.
Therefore, AC II FD, AB II FD and AC II FD are all pairs of parallel segments.
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If the midpoints of two sides of a triangle are connected with a segment then
Answers
Answer:
Step-by-step explanation:
A midsegment connecting two sides of a triangle is parallel to the third side and is half as long.
PLEASE HELP AND EXPLAIN
Answers
See below for the interpretation of the graph
How to interpret the graph?From the graph, the initial values of x and y are 0
As x increases, y decreases.
This means that the first statement is
Initially, as x increases, y decreases.Slope is calculated as:
\(m = \frac{y_2 - y_1}{x_2 -x_1}\)
Using the graph values at the interval x =0 to x = 3, we have:
\(m = \frac{-3 - 0}{3 - 0}\)
m = -1
This means that the second statement is
The slope of the graph is equal to -1 for all x between x = 0 and x = 3From the graph, y = -3, when x = 3
As x increases at this point, y increases.
This means that the third statement is
Starting at x = 3, the function value y increases as x increasesUsing the graph values at the interval x = 3 to x = 5, we have:
\(m = \frac{3 + 3}{5 - 3}\)
m = 3
This means that the fourth statement is
The slope of the graph is equal to 3 for x between x = 3 and x = 5All y values at x = 0 to x = 4 are less than 0, while all y values at x = 4 to x = 8 are greater than 0
So, the last two statements are
For x between x = 0 and x = 4, the function value y is less than 0For x between x = 4 and x = 8, the function value y is greater than 0Read more about functions at:
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THIS IS URGENT PLEASE GAW DAMMIT ;-;
Using the graph, determine the coordinates of the x-intercepts of the parabola.
Answers
Answer:
i believe the answer would be -1 and 6
Answer:
Coordinates are (5,0) & (7,0)
Just refer to the point where the graph intersects the x-axis I think.
Write in standard form:
v^2 = 81
Answers
This should be it, correct me if I’m wrong.
V=9,/9678
Troy puts $200.00 into an account to use for school expenses. The account earns 7% interest, compounded annually. How much will be in the account after 5 years? Use the formula A=P1+ r n nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.
Answers
Answer:
the final amount is = $280.51
Step-by-step explanation:
The standard formula for compound interest is given as;
A = P(1+r/n)^(nt) .....1
Given that;
Principal P = $200
Interest rate r = 7% = 0.07
Time t = 5 years
Final amount = A
Number of time compounded per year n = 1
Substituting the values;
A = 200(1+0.07/1)^(1×5)
A = 280.51
Therefore, the final amount is = $280.51
What percent of 513 is 248
Answers
Answer:
48.34%
Step-by-step explanation:
Answer:
48%
Step-by-step explanation:
248/513 is .483430799, so rounded is 48%
heather, age 12, lives in the same household and her mother, uncle, and grandmother. who can qualify to claim heather as a dependent? who takes precedence?
Answers
Heather, age 12, lives in the same household as her mother, uncle, and grandmother. The mother can qualify to claim Heather as a dependent and takes precedence.
A dependent is an individual who is unable to support themselves financially and needs the support of another person or family. Dependents can be children under the age of 19 or full-time students under the age of 24 or adults who are unable to take care of themselves. Heather is 12 years old and does not support herself financially.
Therefore, her mother can qualify to claim Heather as a dependent since they live in the same household. The mother is responsible for providing a home for Heather, making sure she has food and clothing, and taking care of her. Heather's uncle and grandmother can also claim her as a dependent if they provide more than half of her financial support or pay for her expenses.
Heather's mother takes precedence over her uncle and grandmother in claiming Heather as a dependent. When more than one person is eligible to claim the same dependent, the person with the higher adjusted gross income (AGI) takes precedence.
Since Heather lives with her mother, her mother has the first right to claim her as a dependent.
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please pick right answer (show work) :( number 19
Answers
Answer:
2 cups
Step-by-step explanation:
5/8 + 11/ 8 = 16/8 = 2
Pls help I’ll give brainliest
Answers
Answer:
5
Step-by-step explanation:
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer: 9.7 seconds
Step-by-step explanation:
\(16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7\)
Change the function f(x) = 2x ^ 2 + 8x + 5 into vertex form.
Answers
Answer:
\(f(x)=2(x+4)^2-27\)
Step-by-step explanation:
Complete the square
\(f(x)=2x^2+8x+5\\f(x)=2(x^2+8x+\frac{5}{2})\\f(x)+2(\frac{27}{2})=2(x^2+8x+\frac{5}{2}+\frac{27}{2})\\f(x)+27=2(x^2+8x+16)\\f(x)+27=2(x+4)^2\\f(x)=2(x+4)^2-27\)
This tells us that the vertex of the parabola is \((-4,-27)\).
forestry ranger is in a stand 200 feet in the air. There is an angle of
depression of 35 degrees to a campfire. How far is it from the base of the
stand to the campfire?
Hunter ic a deer stand 10 feet above the ground. There is an angle c
Answers
The distance from the base of the stand to the campfire is 285.6 feet.
The angle of depression of 35 degrees.
Let's denote the distance from the base of the stand to the campfire as "x."
Since we know that,
The values of all trigonometric functions depending on the ratio of sides in a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.
Using the tangent function, we have:
tan(35 degrees) = opposite/adjacent
tan(35 degrees) = 200/x
To find the value of x, we can rearrange the equation:
x = 200 / tan(35 degrees)
x ≈ 200 / 0.7002
x ≈ 285.6 feet
Therefore, the distance from the base of the stand to the campfire is 285.6 feet.
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How do you write this number using digits?
four hundred twenty-one thousand eight hundred forty
Answers
Answer:421,840
Step-by-step explanation: All you have to do is write the number out.
I need help on this question
Answers
Answer:
I think you need to combine the equations, which would end with 26x - 2, and to solve for x just isolate it by adding to the other side which would look like 26x = 2
Then divide 26 on both sides, 26x/26 = 2/26
You should end with x = 1/13
HELPPP DRIVERS ED HANDBOOK QUESTIONS
!!
Answers
Answer:
B. limited learner permit, limited provisional license, full provisional license
Step-by-step explanation:
3) 18 mm
4mm
4) 11 in
19 in
5) 5 mi
11 m
Answers
Answer:
3= perimeter=44 area=73
4= perimeter=60 area=209
5= perimeter=32 area=55
Step-by-step explanation:
18x4=72
18+18+4+4=44
11+11+19+19=60
11x19=209
5x11=55
5+5+11+11=32
HURRY I NEED THIS PLEASE WORTH 60 points
Triangle ABC has been reflected over the x-axis to create triangle A'B'C'. Which of the following statements is true?
Answers
Answer: choose Answer B
Step-by-step explanation:
because if you flip the triangle back to what it was previously A B lines up with answer B so it’s B
Find the sum of 3 square root of 5 and 2 square root of 2 in simplest form. Also, determine whether the result is rational or irrational and explain your answer
Answers
The simplest form by adding two number is \(3\sqrt{5}+2\sqrt{2}\) and it is irrational number.
What is the square root of a number?The square root of any number is equal to a number, which when squared gives the original number. Let us say n is a positive integer, such that \(\sqrt{n.n}=\sqrt{(n)}^2=n\)
Given that, the two numbers,
3 square root of 5= \(3\sqrt{5 }\)
2 square root of 2 = \(2\sqrt{2}\)
Sum of these two numbers = \(3\sqrt{5}+2\sqrt{2}\)
We cannot simplify this term further.
The simplest form by adding two numbers is \(3\sqrt{5}+2\sqrt{2}\)
As it is clear, it is a irrational number.
Because, \(\sqrt{2}\) and \(\sqrt{5}\) is a irrational number.
Hence, the simplest form by adding two number is \(3\sqrt{5}+2\sqrt{2}\) and it is irrational number.
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