It has been found that 1 out of every 10 municipal bills is incorrect. If we randomly select a sample of 12 bills, what is the probability that no more than two of the bills will be incorrect? Interpret your answer. 2.2.2 The time taken to complete a half-marathon is normally distributed, with an average time (m) of 3.15 hours and a standard deviation (0) of 0.95 hours. What is the probability that a randomly selected runner will: (5) Q.2.2.1 Take between 2.80 and 3.25 hours to complete the half-marathon? Interpret your answer. 2.2.2.2 Take between 2.35 and 2.85 hours to complete the half-marathon? 151 Interpret your answer. Question (Marks: 101 Give a brief explanation of the central limit theorem. it has been found that 12% of customers at a particular restaurant wait longer than 0.3.2 25 minutes for their order. We assume normal distribution, and randomly select 5 customers 0.3.21 Q3.2.2 Determine the standard error for this sample What is the probability that, for the sample of customers the proportion who wait longer than 25 minutes for the greater than 12.75557
Answers
Taking the given data into consideration we reach the conclusion that
a) the probability that a randomly selected runner will take between 2.35 and 2.85 hours to complete the half-marathon is 0.1974, or about 19.74%.
This means that if we randomly select a runner, there is a 19.74% chance that their completion time will be between 2.35 and 2.85 hours.
b) randomly select 5 customers from the restaurant, there is a 63.68% chance that the proportion of customers who wait longer than 25 minutes for their order will be greater than 0.1276.
a) To solve this problem, we can use the binomial probability formula:
\(P(X \leq 2) = \sum n=0,1,2 (nC_x) * p^n * (1-p)^{(n-x)}\)
where:
X = count of incorrect bills in the sample
n = sample size, which is 12 in this case
p = evaluated probability of an incorrect bill, which is 1/10 or 0.1
\(nC_x\) = count of combinations of n things taken x at a time
Applying this formula, we can calculate the probability of no more than two incorrect bills in the sample:
\(P(X \leq 2) = (0C_0 * 0.1^0 * 0.9^{12} ) + (1C_1 * 0.1^1 * 0.9^{11} ) + (2C_2 * 0.1^2 * 0.9^{10} )\)
\(P(X \leq 2) = (1 * 1 * 0.2824) + (12 * 0.1 * 0.2824) + (66 * 0.01 * 0.3487)\)
\(P(X \leq 2) = 0.2824 + 0.3389 + 0.0229\)
\(P(X \leq 2) = 0.6442\)
Hence , the probability that no more than two of the bills will be incorrect is 0.6442, or about 64.42%. This means that if we randomly select a sample of 12 bills, there is a 64.42% chance that no more than two of them will be incorrect.
The time taken to complete a half-marathon is normally distributed, with an average time (m) of 3.15 hours and a standard deviation (\(\sigma\)) of 0.95 hours.
To solve this problem, we need to standardize the range of times using the z-score formula:
\(z = (x - m) / \sigma\)
where:
x = time taken to complete the half-marathon
m = average time, which is 3.15 hours
\(\sigma\) = standard deviation, which is 0.95 hours
For the lower bound of 2.80 hours:
\(z = (2.80 - 3.15) / 0.95\)
\(z = -0.3684\)
For the upper bound of 3.25 hours:
\(z = (3.25 - 3.15) / 0.95\)
\(z = 0.1053\)
Applying a standard normal distribution table , we can find the area under the curve between these two z-scores:
\(P(-0.3684 \leq z \leq 0.1053) = 0.3557\)
Then, the probability that a randomly selected runner will take between 2.80 and 3.25 hours to complete the half-marathon is 0.3557, or about 35.57%. This means that if we randomly select a runner, there is a 35.57% chance that their completion time will be between 2.80 and 3.25 hours.
To evaluate this problem, we need to standardize the range of times using the z-score formula:
\(z_1 = (2.35 - 3.15) / 0.95\)
\(z_1 = -0.8421\)
\(z_2 = (2.85 - 3.15) / 0.95\)
\(z_2 = -0.3158\)
Applying a standard normal distribution table , we can find the area under the curve between these two z-scores:
\(P(-0.8421 \leq z \leq -0.3158) = 0.1974\)
Now for the second question
b) In the given problem, we are told that 12% of customers at a particular restaurant wait longer than 25 minutes for their order, and we assume normal distribution. We randomly select 5 customers.
The standard error for a sample proportion is given by the formula:
\(SE = \sqrt(p * (1 - p) / n)\)
where:
p is the sample proportion, which is 0.12 in this case
n is the sample size, which is 5 in this case
Substituting the values, we get:
\(SE = \sqrt(0.12 * (1 - 0.12) / 5)\)
SE = 0.219
Therefore, the standard error for this sample is 0.219.
To evaluate this problem, we need to standardize the sample proportion using the z-score formula:
\(z = (p - P) / SE\)
where:
p = sample proportion, which is 0.12 in this case
P = population proportion, which is 0.1276 in this case
SE = standard error, which we calculated to be 0.219
Staging the values, we get:
\(z = (0.12 - 0.1276) / 0.219\)
\(z = -0.346\)
Applying a standard normal distribution table or calculator, we can find the area under the curve to the right of this z-score:
\(P(z > -0.346) = 0.6368\)
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Related Questions
Suppose f(x, y, z) = x2 + y2 + z2 and W is the solid cylinder with height 5 and base radius 6 that is centered about the z-axis with its base at z : -1. Enter O as theta. - (a) As an iterated integral, F sav = 10% x^2+y^2+z12 dz dr de W with limits of integration A = 0 B = C= 0 D= 6 E = -1 F = (b) Evaluate the integral.
Answers
∫_A^B ∫_B^C ∫_D^E (10%)(x^2 + y^2 + z^12) dz dr dθ.
This represents the full iterated integral for F_sav over the given solid cylinder.
(a) The iterated integral for F_sav with the given limits of integration is as follows:
∫∫∫_W (10%)(x^2 + y^2 + z^12) dz dr dθ,
where the limits of integration are A = 0, B = C = 0, D = 6, and E = -1.
(b) To evaluate the integral, we begin with the innermost integration with respect to z. Since z ranges from -1 to 6, the integral becomes:
∫∫_D^E (10%)(x^2 + y^2 + z^12) dz.
Next, we integrate with respect to r, where r represents the radial distance from the z-axis. As the solid cylinder is centered about the z-axis and has a base radius of 6, r ranges from 0 to 6. Thus, the integral becomes:
∫_B^C ∫_D^E (10%)(x^2 + y^2 + z^12) dz dr.
Finally, we integrate with respect to θ, where θ represents the angle around the z-axis. As the cylinder is symmetric about the z-axis, we integrate over a full circle, so θ ranges from 0 to 2π. Hence, the integral becomes:
∫_A^B ∫_B^C ∫_D^E (10%)(x^2 + y^2 + z^12) dz dr dθ.
This represents the full iterated integral for F_sav over the given solid cylinder.
The problem asks for the iterated integral of F_sav over the solid cylinder W. To evaluate this integral, we use the cylindrical coordinate system (r, θ, z) since the cylinder is centered about the z-axis. The function inside the integral is 10% times the sum of squares of x, y, and z^12. By integrating successively with respect to z, r, and θ, and setting appropriate limits of integration, we obtain the final iterated integral. The integration limits are determined based on the given dimensions of the cylinder.
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can someone please help me find the domain and range
Answers
Answer:
the domains are x axis or intercepts and range is y axis or intercepts
Find the absolute maximum and absolute minimum values of f on the given interval. F(x) = x + 4 x , [0. 2, 8].
Answers
Using Absolute Maximum and Minimum,
the absolute Maximum value of f(x) is 8.5 at x = 8 and absolute minimum value of f (x) is 2.44 at x = 0.2 on given interval [0. 2, 8].
we have given function is
f(x) = x + 4/x ---(1)
and interval [ 0.2 , 8]
firstly, find first order derivative of f(x)
f'(x) = 1 - 4/x²
now, f'(x) = 0 then 1 - 4/x^2 =0
=> 4/x²= 1
=> x² = 4
=> x = 2 or -2
that is 2 and -2 are critical points but only critical number 3 belong to given closed interval.
we evaluate the value of "f" at critical point, x =3 and at ends points of given interval [0.2, 8].
f(3) = 3 + 4/3 = 4.33 , f(0.2) = 0.2 + 4/0.2 = 2.44
, f(8) = 8 + 4/8 = 17/2 = 8.5
Hence, the absolute Maximum value of f on [0.2,8] is 8.5 occuring at x = 8 and absolute minimum value of f on [0.2,8] is 2.44 occuring at x= 0.2 ..
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An airplane flew with the wind for 2. 5 hours and returned the same distance against the wind in 3. 5 hours. If the cruising speed of the plane was a constant 360 mph in air, how fast was the wind blowing? (Hint: If the wind speed is r miles per hour, then the plane travels at (360- + r) mph with the wind and at (360 - r) mph against the wind
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The speed of the wind is 60 mph.
Determine the speedLet's denote the speed of the wind as r. When the plane is flying with the wind, its speed is (360 + r) mph, and when it's flying against the wind, its speed is (360 - r) mph.
According to the question, the plane flew the same distance with and against the wind, so we can set up an equation:
2.5(360 + r) = 3.5(360 - r)
Expanding the equation, we get:
900 + 2.5r = 1260 - 3.5r
Simplifying and rearranging the terms, we get:
6r = 360
Dividing both sides of the equation by 6, we get:
r = 60
Therefore, the speed of the wind is 60 mph.
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Which points are the vertices of the ellipse?
points G and H
points J and K
points L and N
points M and N
Answers
Answer:
Your answer is A) points G and H
Step-by-step explanation:
I took the test on edge 100%
a goalie makes 28 saves in 4 games what is the unit rate saves per game?
Answers
Answer:
7 saves per game
Step-by-step explanation:
The diagonals of a square are 4 meters long. The side of this square is equal to the diagonal of the second square. Find the side of the second square.
Answers
Answer:
bro what is the diagonal of second square.
for which value(s) of x does f(x)=3x3 3x2−11x−1 have a tangent line of slope −3
Answers
Given function:\(f(x) = 3x³ - 3x² - 11x - 1\) We have to find the value of x for which f(x) has a tangent line of slope -3.Tangent to a curve at point P(x₁,y₁) is given by the equation,\(y - y₁ = m(x - x₁)\) where m is the slope of the tangent line.the value of x for which f(x) has a tangent line of slope -3 are\(x = 1 and x = -8/3.\)
So, we have to find the value of x for which the slope\(m = -3, i.e.,f '(x) = 9x² - 6x - 11 = -3\) Let's solve for x using the quadratic formula.\(9x² - 6x - 8 = 0\) Dividing throughout by
\(3,3x² - 2x - 8/3 = 0\)
Using the quadratic formula,\(x = [-(-2) ± √((-2)² - 4(3)(-8/3))]/(2)(3)x = [2 ± 10/3]/6x = 1 or -8/3\)
\(For x = 1,f(x) = 3(1)³ - 3(1)² - 11(1) - 1 = -12For x = -8/3,f(x) = 3(-8/3)³ - 3(-8/3)² - 11(-8/3) - 1 = -14.81\)
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Complete the point-slope equation of the line through (1,3)(1,3)left parenthesis, 1, comma, 3, right parenthesis and (5,1)(5,1)left parenthesis, 5, comma, 1, right parenthesis.
Answers
Answer: dang that's tough but like look it up
Step-by-step explanation: give brainlyiest
Marty's cat weighs 10.4 pounds.This is 24.4 pounds less than the weight of his dog .write and solve a subtraction equation to find the weight of Martys dog
If you answer this I will list you as a brainly recommender
Answers
Answer:
34.8 pounds
Step-by-step explanation:
The cat weighs 10.4. Which is 24.4 pounds less that the dog. So find the weight of the dog, we need to make an equation. This equation would be:
\(dog\)\(-24.4=10.4\)
Solve:
\(dog-24.4=10.4\)
\(+24.4\) \(+24.4\)
\(dog=34.8\)
Hope this helped!
Stay safe and have a great day/night! (:
Given: f(x) = 2x + 5 and g(x) = x2 and h(x) = -2x
h(g(f(x))) = ?x²+ ?x + ?
Answers
Answer:
h(g(f(x))) = (-8)x^2+(-40)x+(-50).
Step-by-step explanation:
We have:
h(x) = -2x
g(x) = x^2
f(x) = 2x + 5
So, we can replace the respective value:
h(g(f(x)))
first substituting the value of f(x) in x of g(x).
h(g(2x + 5))
second, substituting the value of g(x) in x of h(x).
h((2x + 5)^2)
expanding value using the formula (a+b)^2=a^2+2ab+b^2
h(4x^2+20x+25)
Thirdly, substituting the value of h(x) in x of h(x).
-2(4x^2+20x+25)
opening bracket
-8x^2-40x-50
Therefore, h(g(f(x))) = -8x^2-40x-50.
sorry i chose the wrong image
Answers
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i just got some free money off of you kid
pls help if you can asap!!!!
Answers
Answer: A
Step-by-step explanation: I would say A because the angle is greater than 90 degrees
Answer:
We have supplementary angles.
76 + 3x + 2 = 180
3x + 78 = 180
3x = 102
x = 34
SIMPLE COORDINATES!!!! HELP FASTTT
Answers
Answer:
b
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
4. Part A
James has a board that is foot long. He wants to cut the board into pieces
that are each foot long.
How many pieces can James cut from the board? Explain how James can use
the number line diagram to determine the number of pieces he can cut from
the board.
Enter your answer and your explanation in the space provided.
Part B
Write an equation using division that represents how James can find the
number of pieces he can cut from the board.
Answers
The number of pieces that James can cut from the board is 6 pieces.
How to get the number of piecesTo get the number of pieces that James can cut from the board, we will have to determine how many 1/8 divisions there are in a total of 3/4 foot long board. When the division is done, we will have:
3/4 ÷ 1/8
=3/4 × 8/1
= 6
So, James can hope to get 6 pieces of 1/8 foot long board pieces.
An equation using division that represents how James can find the number of pieces is 3/4 ÷ 1/8.
Complete Question:
4. Part A
James has a board that is 3/4 foot long. He wants to cut the board into pieces
that are each 1/8 foot long.
How many pieces can James cut from the board? Explain how James can use
the number line diagram to determine the number of pieces he can cut from
the board.
Enter your answer and your explanation in the space provided.
Part B
Write an equation using division that represents how James can find the
number of pieces he can cut from the board.
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help on math homework
Answers
Answer:
b can I have
Step-by-step explanation:
PLEASE HELP! FIRST ANSWER GETS POINTS AND MARKED BRAINLIEST. If joe has 13 pieces of art but his teacher tells him to make 13 times more, how many does joe have to make?
Answers
Answer: 169 more?
Step-by-step explanation: I multiplied 13x13 and got 169
Find the area of a sector which has an angle of 125∘ and a radius of 5 m.
Answers
Answer:
27.27cm²
Step-by-step explanation:
∅=125° r=5m
A=∅/360×πr²
A=125/360×3.142×5²
A=27.27cm²
does the assumption of normality seem appropriate for the fill volume data
Answers
Based on the information provided in the question, it is not clear what the fill volume data refers to. However, the assumption of normality is generally considered appropriate for data sets that have a large enough sample size and follow a symmetrical, bell-shaped distribution.
If the fill volume data meets these criteria, then the assumption of normality may be appropriate. However, if the data is skewed or has a small sample size, the assumption of normality may not be appropriate and alternative statistical methods may need to be used.
It is important to always check the distribution of the data before making any assumptions about normality. This can be done through visual inspection of the data or by conducting formal tests, such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test.
In conclusion, the assumption of normality may be appropriate for the fill volume data if it meets the criteria of a large sample size and a symmetrical, bell-shaped distribution. However, it is always important to check the distribution of the data before making any assumptions.
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Mike measured the stage where his band was going to play to determine if it is a right triangle. Does the stage with side lengths of 36 feet, 48 feet, and 60 feet form a right triangle
Answers
Answer:
let
hypotenuse[h]=60ft
base[b]=36ft
perpendicular [p]=48ft
by using Pythagoras law
p²+b²=h²
48²+36²=60²
2896≠3600
since p²+b²≠ h²[so the stage is not in a right angled triangle]but it is scalene triangle
Multiply (3x-5)(x+4)
Answers
Answer:
3x^2+7x-20
Step-by-step explanation:
Answer:
expand the brackets
3x^2 + 7x -20
Step-by-step explanation:
(3x-5)(x+4)
= 3x^2 + 12x - 5x + 20
= 3x^2 + 7x + 20
Marjane wants to create a set of data with 6 values. She wants the mode to be as good as the median to represent the data set. Which set of data best represents what Marjane could create?
24, 24, 25, 29, 29, 29
24, 25, 26, 27, 30, 30
24, 25, 25, 25, 26, 26
24, 24, 25, 26, 26, 27
Answers
As per the median, the set of data that fulfilling Marjane's requirement is 24, 25, 25, 25, 26, 26 (option c).
In statistics, data is a collection of numbers or values that represent a particular phenomenon. One way to measure central tendency, or the typical or representative value of the data, is through the median and the mode.
The median is the middle value when the data is arranged in numerical order, and the mode is the value that appears most frequently.
The third set of data is 24, 25, 25, 25, 26, 26.
The median is the middle value, which is also (25+25)/2 = 25.
The mode is the value that appears most frequently, which is 25.
Therefore, the mode and median are the same, fulfilling Marjane's requirement.
Therefore, the correct option is (c).
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How many kilograms did the elephant
weigh at birth?
Answers
Answer:
The option not listed
Step-by-step explanation:
The other options don't make sense when comparing it to the graph.
U6W3 A1.1.1.5.1 Mastery Check Polynomial Operations April 25 Perform the following operation with the polynomial and pick the correct answer:
(2x-3)(2x+3)
A 4x^2 + 12x - 9
B 4x^2-9
C 4x + 12
d 4x+9
give me an answer asap
Answers
The correct answer of the operation is option B: 4x^2 - 9.
To perform the operation (2x-3)(2x+3), we can use the FOIL method, which stands for First, Outer, Inner, Last. Let's go through the steps:
First: Multiply the first terms of each binomial.
(2x)(2x) = 4x^2
Outer: Multiply the outer terms of each binomial.
(2x)(3) = 6x
Inner: Multiply the inner terms of each binomial.
(-3)(2x) = -6x
Last: Multiply the last terms of each binomial.
(-3)(3) = -9
A binomial is a two-term algebraic expression that contains variable, coefficient, exponents and constant, a binomial is an expression that has two unlike terms connected through an addition or subtraction operator in between.
Now, let's combine the like terms:
4x^2 + 6x - 6x - 9
Notice that the terms 6x and -6x cancel each other out.
Simplifying further, we have:
4x^2 - 9
The correct answer is option B: 4x^2 - 9.
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In a certain lottery, 5 numbers between 1 and 13 inclusive are drawn. These are the winning numbers. How many different selections are possible
Answers
1287 combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter.
How many different lottery combinations are there?You win the jackpot if you match all six numbers. You receive a lesser fixed prize if you partially match some of the numbers.
Divide the number of winning lottery numbers by the total number of available lottery numbers to discover the probability of winning any lottery. Use the formula if the numbers are picked from a set and the order of the numbers is unimportant.
To find the winning combination we use the following formula
n !/ r!( n – r ) !
Where n = total number of to be drawn
r = the number which are drawn
In this question, n = 13, and r = 5
from the formula
13 !/5!( 13 – 5 ) !
= 13! / 5! 8!
= 13*12*11*10*9*8! / 5*4*3*2*1*8!
= 154,440 / 120
= 1287
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PLEASE HELP
WILL GIVE BRAINLIEST AND 5.0 STAR RATING
Answers
You only need to type in the numbers. The parenthesis are already taken care of, and the same applies for the comma as well.
========================================================
Explanation:
The drawing is below.
Start at the bottom left corner of the grid which is the location (0,0) known as the origin.
Move 1 unit to the right and 3 units up to arrive at the location (1,3). Think of it like an address of a house. Imagine each grid line as a street of sorts. Or you can think of it like latitude/longitude.
Once you are at (1,3), move down 2 units to get to (1, 1) which is the answer.
I NEED HELP ASAPPPPPPP
Answers
Answer:
B
Step-by-step explanation:
You can see that the only difference between the two graphs is that the red one is shifted up by 4 units. To accomplish this, simply add 4 to the parent function (which in this case is x²). Thus, the answer is just x²+4
2/3 + 4/5 × 1/2 alguien me puede ayudar porfavor? ._.
Answers
Answer:
16/15 or 1 1/15
Step-by-step explanation:
ANSWER FAST! Which expression is equivalent to 7^3•7-^5
Answers
7^3x7^-5
7x7x7=343
-7x-7x-7x-7x-7=-16807
343x-16807
-5764801
hope it helps!
if not, sorry...
y is greater than two less than the product of x and three.
what would the equation look like?
Answers
Answer:
y > 2 < x · 3
Step-by-step explanation: