The probability that the sample mean would differ from the population mean by greater than 3 millimetres is 0.0033 + 0.0033 = 0.0066, rounded to four decimal places.
We are given that the population mean diameter of the steel bolts manufactured by Thompson and Thompson is μ = 137 millimeters and the variance is = 49.
We need to find the probability that the sample mean would differ from the population mean by greater than 3 millimeters.
The standard deviation of the sample means is given by the formula:
[tex]\sigma_{\bar{x}} = \frac{\sigma}{{\sqrt{n}}}[/tex]
Substituting the given values, we have:
[tex]\sigma \bar{x}=\frac{\sqrt{49}}{\sqrt{48}}=1.118[/tex]
To find the probability that the sample mean would differ from the population mean by greater than 3 millimeters,
we need to calculate the z-score:
[tex]z=\frac{(\bar{x}-\mu)}{ \sigma _{\bar{x}}}[/tex]
Substituting the given values, we have:
[tex]z=\frac{\bar{x}-137}{1.118}[/tex]
We want to find the probability that |z| > 3/1.118 = 2.683.
Using a standard normal distribution table, we find that the probability of z > 2.683 is 0.0033.
Since this is a two-tailed test, the probability of z < -2.683 is also 0.0033.
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x^2+3x=0 what is the gcf
Answer:
gcf is 'x'
Step-by-step explanation:
the common factor to the terms 'x²' and '3x' is 'x'
What is the total surface area of the figure shown?
The total surface area of the given figure is 619.2 in², which is not listed in the provided options.
Give a brief account on total surface area.The surface area is known to be measure of the total area occupied by the surface of the object. Defining the surface area mathematically in the presence of a curved surface is better than defining the arc length of a one-dimensional curve, or the surface area of a polyhedron (i.e. an object with flat polygonal faces). Much more complicated. For a smooth surface sphere such as the following, surface area is assigned using representation as a parametric surface. This surface definition is based on calculus and includes partial derivatives and double integrals.
The triangular face of the given figure represent an equilateral triangle of sides 12 in.
Area of the triangle = (√3/4) × a²
Area of the triangular face:
= (√3/4) × 12²
= (√3/4) × 144
= 57.6 in²
Area of the rectangle = Length × width
Area of the rectangular face:
= 12 × 14
= 168 in²
Area of the given figure:
= (2 × 57.6) + (3 × 168)
= 115.2 + 504
= 619.2 in²
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A scale drawing of a famous statue uses a scale factor of 230:1. If the height of the drawing is 1.2 feet, what is the actual height of the statue?
191.7 feet
228.2 feet
231.2 feet
276 feet
The actual height of the statue is option C 231.2 feet.
What is scale factor?A scale factor is a number used in mathematics to scale or multiply a quantity or measurement by another factor in order to establish a proportional relationship between two identical figures or objects.
In other terms, the scale factor is the ratio of the corresponding lengths, widths, or heights of the two figures or objects if they are similar, that is, they have the same shape but may range in size. This implies that you may determine the dimension of the second object by multiplying one dimension of one object by the scale factor.
Given that the scale factor is 230:1.
Thus,
actual height of statue / 230 = height of drawing / 1.2 feet
Now,
actual height of statue = (1.2 feet / 1.2 feet) * 230
actual height of statue = 230 feet
Hence, the actual height of the statue is option C 231.2 feet.
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To the nearest tenth, the solution to the equation
4,300e^0.07x-123=5,000 is
The solution to the equation 4,300e^(0.07x) - 123 = 5,000 for x is 2.5.
Evaluating the equation for xWe can solve the equation 4,300e^(0.07x) - 123 = 5,000 for x by first adding 123 to both sides and then dividing both sides by 4,300 and taking the natural logarithm of both sides:
Using the above as a guide, we have the following:
4,300e^(0.07x) - 123 = 5,000
4,300e^(0.07x) = 5,123
e^(0.07x) = 5,123/4,300
e^(0.07x) = 1.1914
0.07x = ln(1.1914)
x = ln(1.1914)/0.07
Using a calculator, we get:
x ≈ 2.50
Rounding to the nearest tenth, the solution to the equation is approximately 2.5.
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please help and explain and show your work on how you got the answer. I WILL MARK YOU BRAINLIEST
Answer:
Step-by-step explanation:
it is -2
Answer: -2
Step-by-step explanation:
So this is asking for the cube root of -8.
This is the same as asking what is multiplied by itself 3 times to get -8.
-2 * -2 *-2 = -8
You can also use a calculator.
Another way to solve it is to write -8^(1/3).
Hope this helps!!!
The distance between two cities on a map is 17 centimeters. The scale on the map relates 5 centimeters on the map as 30 miles on the road. What is the actual distance, in miles, between the two cities?
Answer: 102 miles.
Step-by-step explanation:
You divide 17 by 5 and then multiply by 30.
A ball is dropped from a height of 32 m.
With each bounce, the ball reaches a
height that is half the height of
the previous bounce. After
which bounce will the ball
rebound to a maximum
height of 25 cm?
4y = -x - 32 (Show work)
Answer: the solution for y in terms of x is y = (-1/4)x - 8.
Step-by-step explanation: In order to obtain a solution for y in the given equation of 4y = -x - 32, it is imperative to achieve the isolation of y on a singular side of the equation. To accomplish this task, it is possible to perform division on both sides of the equation by a factor of 4:
The given equation 4y/4 = (-x - 32)/4 can be expressed in an academic manner as follows: The given equation reveals that the quotient of 4y divided by 4 is equivalent to the quotient of the opposite of x added to negative 32, also divided by 4.
Upon performing simplification, the expression on the right-hand side yields:
The equation y = (-1/4)x - 8 can be expressed in an academic manner as follows: The dependent variable y is equivalent to the product of the constant (-1/4) and the independent variable x, with an additional decrement of eight.
What is the range of f? A coordinate plane. The x- and y-axes both scale by one. The graph of the function f starts at negative six, negative two, which is plotted. Then is decreases at a non linear rate to negative five, negative five, where it increases at a non linear rate to negative two, one and one-half. At two, one and one-half the function decreases at a non linear rate through the origin and to the point two, negative one and one-half. Then the function increases at a non linear rate until five, five, which is plotted.
A coordinate plane. The x- and y-axes both scale by one. The graph of the function f starts at negative six, negative two, which is plotted. Then is decreases at a non linear rate to negative five, negative five, where it increases at a non linear rate to negative two, one and one-half. At two, one and one-half the function decreases at a non linear rate through the origin and to the point two, negative one and one-half. Then the function increases at a non linear rate until five, five, which is plotted.
Choose 1 answer:
(Choice A) The f(x)-values -6, -3, 0, 2, and 5
(Choice B) The f(x)-values -5, -2, 0, 2, and 5
(Choice C) -6 ≤ f(x) ≤ 5
(Choice D) − 5 ≤ f(x) ≤ 5
The range of f include the following: D. -5 ≤ f(x) ≤ 5.
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-6, 5} or -6 ≤ x ≤ 5.
Range = {-5, 5} or -5 ≤ f(x) ≤ 5.
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of the cartons produced by a company, 3% have a puncture, 6% have a smashed corner, and 1.4% have both a puncture and a smashed corner. find the probability that a randomly selected carton has a puncture or a smashed corner.
The probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
To find the probability that a randomly selected carton has a puncture or a smashed corner, we can use the formula:
P(puncture or smashed corner) = P(puncture) + P(smashed corner) - P(puncture and smashed corner)
where P(puncture) is the probability of a carton having a puncture, P(smashed corner) is the probability of a carton having a smashed corner, and P(puncture and smashed corner) is the probability of a carton having both a puncture and a smashed corner.
Substituting the given probabilities into the formula, we get:
P(puncture or smashed corner) = 0.03 + 0.06 - 0.014
P(puncture or smashed corner) = 0.076
Therefore, the probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.
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URGENT!! Will give brainliest :)
What is the equation for the line of best fit for the following data? Round the slope and -intercept of the line to three decimal places.
A. y=-0.580×+ 10.671
B. y=-10.671 x+ 0.580
C. y= 10.671 x-0.580
D. y= 0.580x - 10.671
To find the equation for the line of best fit, we can use linear regression. Based on the given data:
x: 2, 5, 7, 12, 16
y: 9, 10, 5, 3, 2
The equation for the line of best fit would be in the form: y = mx + b, where m is the slope and b is the y-intercept.
Using a calculator or statistical software, we can calculate the slope and y-intercept for the line of best fit.
The result is:
Slope (m): -0.580 (rounded to three decimal places) Y-intercept (b): 10.671 (rounded to three decimal places)
So, the correct answer is:
A. y = -0.580x + 10.671
flip a coin three times. you will win $2 for each heads. what is the expected winning (expec- tation of your winning)? a
The expected winning is $2.
To calculate the expected winning, we need to find the probability of each outcome and multiply it by the amount we will win in that outcome.
There are 2 possible outcomes for each coin flip: heads or tails. Therefore, there are 2x2x2=8 possible outcomes for flipping a coin three times.
Here are all the possible outcomes with the number of heads in each outcome:
HHH (3 heads)HHT (2 heads)HTH (2 heads)THH (2 heads)HTT (1 head)THT (1 head)TTH (1 head)TTT (0 heads)The probability of each outcome can be calculated using the formula: probability = (number of favorable outcomes) / (total number of possible outcomes)
For example, the probability of getting 3 heads (HHH) is 1/8 because there is only one favorable outcome out of 8 possible outcomes.
Using this formula, we can calculate the probability and expected winning for each outcome:
HHH: probability = 1/8, expected winning = $6HHT: probability = 1/4, expected winning = $4HTH: probability = 1/4, expected winning = $4THH: probability = 1/4, expected winning = $4HTT: probability = 3/8, expected winning = $2THT: probability = 3/8, expected winning = $2TTH: probability = 3/8, expected winning = $2TTT: probability = 1/8, expected winning = $0To calculate the overall expected winning, we need to add up the expected winning for each outcome multiplied by its probability:
(1/8) x $6 + (1/4) x $4 + (1/4) x $4 + (1/4) x $4 + (3/8) x $2 + (3/8) x $2 + (3/8) x $2 + (1/8) x $0 = $2
Therefore, the expected winning is $2.
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Chad drinks 64. 88 fluid ounces of water per day. How much water does he drink in 6 days
Chad drinks 389.28 fluid ounces of water in 6 days.
What is ounces?A unit of weight equal to ¹/₁₂ troy pound see Weights and Measures Table. : a unit of weight equal to ¹/₁₆ avoirdupois pound. : a small amount. an ounce of sense.
An ounce (oz) is a unit of weight that is equal to one-sixteenth of a pound. Items that weigh approximately one ounce include a slice of bread and a pencil. A fluid ounce is a unit of liquid volume that is equal to one-eighth of a cup. A medicine cup has a volume of approximately one fluid ounce.
given that,
chad drinks 64.88 fluid ounces of water per day,
so in 6 days
he will drink = 6 x water drink per day
= 6 x 64.88
= 389.28
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Choose the algebraic description that maps abc onto abc in the given figure.
So the transformation is: (x, y) → (x + -8, y - 4) which is equivalent to option B.
What is transformation?In mathematics, a transformation is a process that manipulates the position, size, or shape of a geometric object. Transformations can include translations, rotations, reflections, and dilations. They are used to study geometric properties and relationships and are often used in fields such as geometry, algebra, and computer graphics. Transformations are important in understanding symmetry and congruence, as well as in solving problems involving geometric figures.
Here,
We can see that the transformation takes each point of the form (x, y) in ABC to a corresponding point of the form (x', y') in A'B'C'. To find the correct transformation, we need to determine how the coordinates of the points in ABC are related to the coordinates of the corresponding points in A'B'C'. One way to do this is to use the fact that the transformation should preserve the relative distances and angles between the points. Another way is to use the known coordinates of three corresponding points to determine the transformation directly.
In this case, we can see that the transformation maps (-3,-2) to (5,2), (-1,-4) to (7,0), and (-6,-5) to (2,-1). We can use these points to find the transformation:
(x, y) → (x', y')
To map (-3,-2) to (5,2), we need to add 8 to the x-coordinate and add 4 to the y-coordinate:
x' = x + 8
y' = y + 4
To map (-1,-4) to (7,0), we again add 8 to the x-coordinate, but this time we only add 4 to the y-coordinate:
x' = x + 8
y' = y + 4
To map (-6,-5) to (2,-1), we subtract 4 from the x-coordinate and subtract 4 from the y-coordinate:
x' = x - 4
y' = y - 4
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Find a degrees. a 12 13 5
In the given triangle, α is equal to 67.36°.
What is a triangle's definition?
A triangle is a two-dimensional closed geometric form that has three sides, three angles, and three vertices (corners). It is the most basic polygon, produced by joining any three non-collinear points in a plane. The sum all angles of a triangle is always 180°. Triangles are classed according to their side length (equilateral, isosceles, or scalene) and angle measurement (acute, right, or obtuse).
Now,
Using Trigonometric functions
We can use the sine function
So,
Sin α=Perpendicular/Hypotenuse
Sin α = 12/13
α=67.36°
Hence,
The value of α will be 67.36°.
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I need questions 26-31 for 5 STARS
Answer:
26) 1.32
27) 90
28) 0.00845
29) 2.56x10^-1
30) 9.5x10^-3
31) 7.8x10
I NEED HELP ON THIS ASAP!
The exponential function for the new participants is f(x) = 3 * 4^x
Writing the exponential function for the new participantsLet's start with the initial number of participants who sent selfies on Day 0.
We know that Aliyah, Kim, and Reese each sent selfies to 4 friends, so there are 3 x 4 = 12 participants on Day 1.
On Day 2, each of these 12 participants will send selfies to 4 friends, so we will have 12 x 4 = 48 new participants.
We can see that the number of new participants each day is increasing exponentially. In fact, the number of new participants each day is multiplied by 4, since each participant sends selfies to 4 friends.
Therefore, we can write an exponential function of the form:
f(x)=a * 4^x
Where x is the number of days since the challenge started, and $a$ is the initial number of participants who sent selfies on Day 0.
We know that a = 12 from our earlier calculations.
So, we have
f(x) = 3 * 4^x
Hence, the function is f(x) = 3 * 4^x
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What is the value of x in this triangle?
x=47°
The degree of a triangle is equal to 180°.
Since a triange=180°, you would subtract 180 by 102+31 because the other two angles are 102° and 31°.
180-102-31=47°
Therefore the answer would be x=47°
3x + 18 > 54 solve the inequality? pls help?
Answer:
x > 12
Step-by-step explanation:
3x + 18 > 54
please someone help and give answers !!!
16.) Mean average deviation= option C
17.) Range of a data set = option E.
18.) First quartile = opinion AB
19.) Second quartile = option B
20.) Third quartile = option A
21.) Interquartile range = option D
How to determine the measures of the spread?
To determine the measures of the spread is to match their various definitions to the correct measures given such as follows:
16.) Mean average deviation: The average deviation of data from the mean.
17.) Range of a data set : The difference between the highest value and the lowest value in a numerical data set.
18.) First quartile: The median in the lower half.
19.) Second quartile: The median value in a data set.
20.) Third quartile: The median in the upper half.
21.) Interquartile range: The distance between the first and the third quartile.
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Mack's Toy Shop made 600 trains yesterday and found that 30 were defective. They
plan to make 4,500 trains this week.
Using the information given, how many trains are expected to be defective?
225 trains
6,000 trains
15 trains
500 trains
Answer:
225 trains
Step-by-step explanation:
since they are using the same process and materials, we expect them to have the same ratio between trains made and defective trains :
600 / 30 = 20/1
one out of 20 is defect.
so, when they make 4500 trains, we need to divide this by 20 to get the number of expected defective trains :
4500 / 20 = 225
I find the answer option of 6000 defective trains really funny : if that were true, more than the produced trains (4500) would be defective. how ... ?
Madison is reading a book that is 860 pages long. She reads 25 pages in 0.5 hours. At that rate, how long will it take for her to read the entire book
Answer:
17.2 hours, or 17 hours and 12 minutes
Step-by-step explanation:
If she reads 50 pages per hour, then 860/50 = 17.2
-4 ≤ x- 4 ≤ 0 graph the conjuntion ?? can someone help
The inequality is simplified as 0 ≤ x ≤ 4
Define inequalityIn mathematics, inequality refers to a mathematical expression that indicates that two values or quantities are unequal. An inequality is represented by the symbols "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).
For example, the inequality "x > 5" means that the value of x is greater than 5, and the inequality "y ≤ 10" means that the value of y is less than or equal to 10.
To graph the conjunction, we first need to solve for x:
-4 ≤ x - 4 ≤ 0
Add 4 to all parts of the inequality:
0 ≤ x ≤ 4
Image of graph is attached below.
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In an all boys school, the heights of the student body are normally distributed with a mean of 69 inches and a standard deviation of 3.5 inches. What is the probability that a randomly selected student will be taller than 63 inches tall, to the nearest thousandth?
The probability that a randomly selected student will be taller than 63 inches tall is 0.9332, to the nearest thousandth.
a production process is designed to fill 100 soda cans per minute with with 6.8 ounces of soda, on average. overfilling is costly and under-filling risks a large fine. you are the production chief and instruct your staff to take regular random samples to test the process. what is the correct way to set up the hypotheses test?
Answer:
6.8 ounces
To set up a hypothesis test for this production process, we need to define the null and alternative hypotheses. The null hypothesis (H0) is that the average amount of soda in each can is equal to 6.8 ounces, while the alternative hypothesis (Ha) is that the average amount of soda in each can is not equal to 6.8 ounces.
We can then collect data by taking regular random samples from the production process and calculate the sample mean and standard deviation. We can then perform a statistical test such as a t-test or z-test to determine whether we can reject or fail to reject the null hypothesis.
If we reject the null hypothesis, we can conclude that there is evidence that the average amount of soda in each can is different from 6.8 ounces. If we fail to reject the null hypothesis, we cannot conclude that there is evidence that the average amount of soda in each can is different from 6.8 ounces.
I hope this helps! Let me know if you have any other questions.
how can the power series method be used to solve the nonhomogeneous equation, about the ordinary point ? carry out your idea by solving the equation. you can either attach your work or type in your work.
The power series method can be used to solve a nonhomogeneous differential equation about an ordinary point by finding both a homogeneous and particular solution using a series expansion and the method of undetermined coefficients.
The power series method is a technique used to find a series solution of a differential equation. When applied to a nonhomogeneous differential equation, the method involves finding both a homogeneous solution and a particular solution.
Assuming that the nonhomogeneous differential equation has the form
y''(x) + p(x)y'(x) + q(x)y(x) = f(x)
where p(x), q(x), and f(x) are functions of x, we can begin by finding the solution to the associated homogeneous equation
y''(x) + p(x)y'(x) + q(x)y(x) = 0
Using the power series method, we can assume a solution of the form:
y(x) = a0 + a1(x - x0) + a2(x - x0)^2 + ...
where a0, a1, a2, ... are constants to be determined, and x0 is the ordinary point of the differential equation.
Next, we can find the coefficients of the power series by substituting the series solution into the differential equation and equating coefficients of like powers of (x-x0). This leads to a system of equations for the coefficients, which can be solved iteratively.
After finding the homogeneous solution, we can find a particular solution using a similar method. Assuming a particular solution of the form:
y(x) = u(x) + v(x)
where u(x) is a solution to the associated homogeneous equation, and v(x) is a particular solution to the nonhomogeneous equation, we can use the method of undetermined coefficients to find v(x). This involves assuming a form for v(x) based on the form of f(x), and then solving for its coefficients using the same technique as before.
Once we have found both the homogeneous and particular solutions, we can combine them to obtain the general solution to the nonhomogeneous differential equation.
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PLEASE HELP AND EXPLAIN AND SHOW WORK ON HOW YOU GOT THE ANSWER I WILL MARK YOU BRAINLIEST.
Answer:
Step-by-step explanation:
Happy birthday Rainbowww :)
Question: What is the pathagorean therom?
Answer: c=a2+b2
Step-by-step explanation:
true or false? use cases can help with developing quantitative and measurable usability tests. group of answer choices
The given statement about developing quantitative and measurable usability tests is true.
Explain about how this given statement is true?Use cases can help with developing quantitative and measurable usability tests. Use cases are scenarios that describe how a user might interact with a system or product in a specific situation.
By developing use cases, researchers can identify specific tasks that users may need to perform and design usability tests to measure how well users can perform those tasks.
This can help make the usability tests more objective and measurable, as researchers can use metrics such as completion rates, task time, and errors to assess the usability of the system or product.
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what is the proportional relationship between x 2 6 8 10 and y 6 18 24 30
The proportional relationship is y = 3x.
What is the proportional relationship?
If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
Here, we have
Given:
x: 2, 6, 8, 10
y: 6, 18, 24, 30
We have to find the proportional relationship between x and y.
So, we can see from inspection and visual observation that there is a proportional relationship between x and y.
6 = 3 2, 18 = 3 6, 24 = 3 8, 30 = 3 10.
Hence, The proportional relationship is y = 3x.
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