The probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X) is approximately 2.6092%.
Here,
Since the length of the pipes follows a uniform distribution on the interval [10 feet, 10.57 feet], the probability density function (PDF) for each pipe is:
f(x) = 1 / (10.57 - 10) = 1 / 0.57 ≈ 1.7544 for 10 ≤ x ≤ 10.57
Since the lengths of the pipes are independent, the joint probability density function (PDF) of X and Y is the product of their individual PDFs:
f(x, y) = f(x) * f(y) = 1.7544 * 1.7544 = 3.0805 for 10 ≤ x ≤ 10.57 and 10 ≤ y ≤ 10.57
Now, we want to find the probability that the second pipe (Y) is more than 0.11 feet longer than the first pipe (X).
Mathematically, we want to find P(Y > X + 0.11).
Let's set up the integral to calculate this probability:
P(Y > X + 0.11) = ∬[10 ≤ x ≤ 10.57] [y > x + 0.11] f(x, y) dx dy
We integrate with respect to x first and then with respect to y:
P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] ∫[10 ≤ x ≤ y - 0.11] f(x, y) dx dy
P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [∫[10 ≤ x ≤ y - 0.11] 3.0805 dx] dy
P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [3.0805 * (x)] from x = 10 to x = y - 0.11 dy
P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [3.0805 * (y - (10 - 0.11))] dy
P(Y > X + 0.11) = 3.0805 * ∫[10 ≤ y ≤ 10.57] (y - 9.89) dy
P(Y > X + 0.11) = 3.0805 * [(y² / 2) - 9.89y] from y = 10 to y = 10.57
P(Y > X + 0.11) = 3.0805 * [((10.57)² / 2) - 9.89 * 10.57 - (((10)² / 2) - 9.89 * 10)]
P(Y > X + 0.11) = 3.0805 * [((111.7249 / 2) - 104.9135 - (50 / 2 - 98.9)]
P(Y > X + 0.11) = 3.0805 * [(55.86245 - 104.9135 + 49.9)]
P(Y > X + 0.11) = 3.0805 * [0.84895]
P(Y > X + 0.11) ≈ 2.6092
Therefore, the probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X) is approximately 2.6092%.
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What is the answer to (2k^-3)^-4
Answer:
15=15
Step-by-step explanation:
2x + 3 = 15 x = 6
(2) (6) + 3 = 15
15 = 15
TRUE!
Please help :))
i know some off yall are smart so, it would be amazing.
Answer:
The correct answer is c.
Step-by-step explanation:
Hope I helped.
Select all units that can be used for surface area. Group of answer choices square meters feet centimeters cubic inches square inches square feet (which one are they?)
Answer:
Unit that can be used for surface area is cubic inches.
Step-by-step explanation:
Surface area is the sum of the areas of all faces of a three-dimensional shape.
That is in case of surface area, we talk about three dimensions.
So, unit that can be used for surface area is cubic inches.
square meters, square inches and square feet are used for two dimensional shapes.
feet, centimeters are used for one dimensional shapes.
What is the length of AB?
The answer is B, I just answered this question on my quiz.
Guys Please help me with this question urgent!!
There were 120 people at a meeting. The ratio of men to women was 7 to 3.
24 more people joined the meeting. The ratio of men to women was then 11 : 5. How many women were among those 24?
Answer:
9
Step-by-step explanation:
1.)Find the amount of women within the 120 people in the meeting. So 3/10*120 , you get 36.
2.)Add 24 to 120 to get the new amount of people in the room. So 144.
3.)Using the new ratio 11:5 , find the amount of total women out of 144 people . So 5/16*144 , you get 45.
4.)Now minus the 2 amounts of initial women from the amount of total new women , to get the difference to find out how many women are there in the 24 people. So 45-36 , you get 9
SOMEONE PLEASE HELP ILL GIVE BRAINLIEST
Answer:
A.
Step-by-step explanation:
POSSIBLE POINTS: 3.33
Tracy wants to buy some pies for her sisters and she has a budget of $82 to spend on $5
apple pies, $4.5 banana pies, and $5.5 chocolate pies. She wants to buy 16 pies for her
sisters and must buy as many chocolate pies as apple pies and banana pies combined.
How many of each item should she buy? Write a system of equations to help you solve
this problem.
# of applie pies =
# of banana pies =
# of chocolate piles =
1
2 3
Answer:
From the information given, you can write the following system of equations:
x+y+z=16 (1)
5x+4.5y+5.5z=82 (2)
z=x+y (3)
You can replace (3) in (1) and (2):
x+y+x+y=16
2x+2y=16 (4)
5x+4.5y+5.5(x+y)=82
5x+4.5y+5.5x+5.5y=82
10.5x+10y=82 (5)
Now, you have the following equations:
2x+2y=16 (4)
10.5x+10y=82 (5)
You can isolate x in (4):
2x=16-2y
x=8-y (6)
Then, you have to replace (6) in (5):
10.5(8-y)+10y=82
84-10.5y+10y=82
84-82=10.5y-10y
2=0.5y
y=2/0.5
y=4
Now, you can replace the value of y in (6) to find x:
x=8-4
x=4
Finally, you can replace the vaue of x and y in (3) to find z:
z=4+4
z=8
According to this, she should buy 4 apple pies, 4 banana pies and 8 chocolate pies.
The local furniture store pays $300 for a dining room table and sells it with a 40% markup. What is the selling price of the dining room table? \
Selling Price = ?, Cost + Markup = ?
Answer:
$420
Step-by-step explanation:
Cost to the furniture store: $300
Markup: 40%
40% * $300 = $120
The markup is $120
Selling price = cost + markup = $300 + $120 = $420
Answer: $420
Two bowlers bruce and donald want to find out who has the higher three-game series when compared to each of their leagues. Bruce has a score of 500, and his league has a mean score of 620 and a standard deviation of 20. Donald has a score of 520, and his league has a mean of 625 and a standard deviation of 25. Who has the higher three-game series score when compared to each of their leagues?
A. Bruce.
B. Donald.
C. The scores are equal when compared to each of their leagues.
Answer:
Donald
Step-by-step explanation:
Given that :
BRUCE :
score (x) = 500
League average (m) = 620
Standard deviation (σ) = 20
DONALD:
score (x) = 520
League average (m) = 625
Standard deviation (σ) = 25
Take standardized score of both Bruce and Donald
BRUCE:
Zscore = (x - m) / σ
Zscore = (500 - 620) / 20
Zscore = - 120 / 20
Zscore = - 6
DONALD:
Zscore = (x - m) / σ
Zscore = (520 - 625) / 25
Zscore = - 105 / 25
Zscore = - 4.2
Bruce's standardized score is lesser Than Donald's. Hence,
Donald has a higher three-game series score ;
What law is being modeled
Answer:
Step-by-step explanation:
In population genetics, the Hardy–Weinberg principle, also known as the Hardy–Weinberg equilibrium, model, theorem, or law, ... Males, A (p), AA (p2), Aa (pq) ... The sum of the entries is p2 + 2pq + q2 = 1, as the genotype frequencies must sum to ... Suppose that Aa is a pair of Mendelian characters, A being dominant, and
What is the slope intercept form of 9x+7y=14?
Answer:
y = -9/7x + 2 is the slope intercept form.
Step-by-step explanation:
One integer is 3 more than another. Their product is 70. Find the integers.
Answer:
(7, 10) or (-7, -10)
Step-by-step explanation:
If you need an explanation with this lmk but it's most likely answer choice.
You spend 4/5 of an hour on your homework. You spend 1/2 of that time working on your science homework. How many minutes do you spend working on science homework?
Answer:
4/5 of an hour is 48 minutes so 48 minutes divided by 2 is 28 minutes
Step-by-step explanation:
Answer:
24 minutes.
Step-by-step explanation
4/5 = ?/60
4/5 = 48/60
half of 48 = 24
Mason made 3/4 of a pound of trail mix. If he puts 3/8 of a pound into each bag, how many bags can Mason fill?
A. half of a bag
B. 3 bags
C. 4 bags
D. 2 bags
Answer:
3/4^ 8/3= 24/12= 2 so d.2bags
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Forty discrete math students are to be divided into eight discussion groups, each consisting of five students. In how many ways can this be done?
There are 65,800,850,944,000 ways to divide the 40 students into 8 discussion groups, each consisting of 5 students.
To find the number of ways to divide 40 students into 8 discussion groups of 5 students each, we'll use a combination formula.
The number of ways to choose 5 students out of 40 for the first group is given by C(40, 5).
After choosing 5 students for the first group, there will be 35 students left for the second group.
The number of ways to choose 5 students out of these 35 for the second group is C(35, 5).
We continue this process until all 8 groups are formed.
The total number of ways to divide the students into groups is the product of the combinations for each group. So, the total number of ways is:
Total ways [tex]=^{40}C_5 \times ^{35}C_5 \times^{30}C_5 \times ^{25}C_5 \times ^{20}C_5 \times ^{15}C_5 \times ^{10}C_5 \times ^{5}C_5[/tex]
Total ways = 65800850944000
Hence, there are 65,800,850,944,000 ways to divide the 40 students into 8 discussion groups, each consisting of 5 students.
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Which ex press ion shows the perimeter of the quadrilateral below?
A: 6x+4
B: 7x +11
C: -7x+11
D: -7x +12
option B. 7x+11 is the correct answer
Answer:
ur answer is c) -7x+12
Step-by-step explanation:
2x+3+x-1+3x+5+x+4=perimeter
2x+x+3x+x+3-1+5+4=perimeter
7x+11=perimeter
did u got what i had done message on this ans
To write the polynomial 3x3 + x2 − 8x5 + 2x3 − 4x in standard form, which terms should be combined? A. 3x3 and 2x3 B. 3x3, 2x3, and x2 C. x2 and −4x D. x2 and 2x3
Answer:
Option A. is correct
Step-by-step explanation:
Like terms are those terms that have same variables of same powers. Terms that are not like terms are said to be unlike terms.
For example [tex]2x^3,7x^3[/tex] are like terms and [tex]5x^2,9x^5[/tex] are unlike terms.
Given polynomial is [tex]3x^3+x^2-8x^5+2x^3-4x[/tex]
Like terms need to be combined to write the polynomial in standard form
Here, like terms are [tex]3x^3,2x^3[/tex]
Option A. is correct.
Write 1.96 ...... as a mixed number in simplest form.
What is the solution to the equation? √x - 3 + 1 = 6
A. 64
B. 46
C. 28
D. 22
The solution of the given equation √x - 3 + 1 = 6 will be x = 64 so option (A) will be correct.
What is the equation?An equation can be defined in numerous ways. Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.
For example 8x + 7y = 15.
Given the equation,
√x - 3 + 1 = 6
√x + (-3 + 1) = 6
√x - 2 = 6
√x = 6 + 2 = 8
By squaring
x = 8² = 64.
Hence "The solution of the given equation √x - 3 + 1 = 6 will be x = 64".
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Answer:the correct answer is C.28
Step-by-step explanation:
Salary 8) Devin is a security officer. His annual salary is $18.250. What is his
monthly salary?
Kent earns $12.75 per hour at his part time job. Kent worked 18 hours last week. This week he spent 1/3 of his money on car repairs. How much did the repairs cost?
ANSWERS TO THE WHOLE QUIZ:
1. 13.23
2. 1/2
3. 0.25
4. 31.16
5. 76.50
Your Welcome and have a great day!
( I had to fail the quiz to give the answers)
five ninths minus two sixths equals blank what is the answer
Which of these is a biomorphic shape? Choose the answer.
O a capital letter W
O a microphone
an outline of a pine tree
O a pyramid
Answer:
Option C: an outline of a pine tree
Step-by-step explanation:
Artists usually use two main types of shapes when drawing. One is geometric shape and the other is bimorphic shape.
A geometric shape simply refers to common regular and precise shapes like triangles, rectangles, squares which are commonly found in man made objects. Whereas, a bimorphic shape is one that is basically rounded or irregular and depicts natural things or living organisms.
Now, from the question, the only thing there that refers to a natural occurring object is "an outline of a pine tree".
Thus, it is a bimorphic shape.
Answer:
C. an outline of a pine tree
Step-by-step explanation:
I just took the test!
Find 1.5% of 220 please help
Answer: 3.3
x. = 1.5
220 100
A 5.8-ft-tall person walks away from a 9-ft lamppost at a constant rate of 3.4 ft/sec. What is the rate that the tip of the person's shadow moves away from the lamppost when the person is 11 ft away from the lampost
Answer:
9.56 ft/sec
Step-by-step explanation:
We are told that a 5.8-ft-tall person walks away from a 9-ft lamppost at a constant rate of 3.4 ft/sec.
I've attached an image showing triangle that depicts this;
Thus; dx/dt = 3.4 ft/sec
From the attached image and using principle of similar triangles, we can say that;
9/y = 5.8/(y - x)
9(y - x) = 5.8y
9y - 9x = 5.8y
9y - 5.8y = 9x
3.2y = 9x
y = 9x/3.2
dy/dx = 9/3.2
Now, to find how fast the tip of the shadow is moving away from the lamp post, it is;
dy/dt = dy/dx × dx/dt
dy/dt = (9/3.2) × 3.4
dy/dt = 9.5625 ft/s ≈ 9.56 ft/sec
2. What is the first term of the arithmetic
sequence
41 346, 19
919?
Answer: The first term of the arithmetic sequence= 41,346.
Step-by-step explanation:
The first term in the Arithmetic sequence (generally denoted by 'a') is the beginning term of the sequence.
It helps to find the other terms([tex]a_n[/tex]) as it gives the initial point to start the sequence.
In the given sequence, the sequence starts from the number 41,346.
That means, the first term of the arithmetic sequence= 41,346.
Selina didn't use the distributive property correctly. Where did she go wrong? Explain your thinking.
Answer:
PEMDAS
Step-by-step explanation:
Well, I don't know if there should be a picture of the problem that should go with the question. But a trick for solving distributive property is to use the trick PEMDAS In order.
For Example:
P-Paraenthese
E-Exponent
M-Multiply
D-Divide
A-Add
S-Subtract
NOTE!
Remember to always Multiply and divide BEFORE adding and subtracting.
Hoped this helped!
Which of the following expressions is equal to 4+3(x-2)?
Answer:
i believe it is "3x+2"
Explanation:
first you distribute the 3 to the expression in the parenthesis and you get "3x-6" and add the +4 to the end of that expression and you get "3x-6+4" add "-6+4" and you get "-2" and then you get "3x--2"since a subtraction sign and a negative sign make it be addition you get the expression "3x+2"
One number is five more than another. Their sum is thirteen. Find both numbers.
(smaller value)
(larger value)
Answer:
4 and 9
Step-by-step explanation:
x+(x+5)=13
2x+5=13
2x=8
X=4
Answer:
the smaller value is 2.2
the larger value is 10.8
Step-by-step explanation:
5a + a = 13
6a = 13
a = 2.2
5(2.2) = 10.8
10.8 + 2.2 = 13
Wade picked 4 pints of blackberries. His friend, Matt, picked 6 pints. How
many pints did they pick altogether?
