The original dimension of the metal is width = 21 and length = 41 before cutting off the squares.
What is volume?The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry.
Let us suppose the width of the rectangular metal = w.
Then the length of the rectangular metal is = 20 + w
Given that squares of 4in are cut from the four corners, then the new width and length will be:
width = w - 8
length = 20 + w - 8
The height of the rectangular metal when the flaps are folded are 4 in.
The volume of the rectangular prism is:
V = (l)(w)(h)
Substituting the value of V = 1716, width = w - 8, length = 20 + w - 8, and h = 4 we have:
1716 = (w - 8)(20 + w - 8)(4)
1716 = 80w + 4w^2 - 32w - 640 - 32w + 256
1716 = 4w^2 + 16 w - 384
4w^2 + 16w -384 - 1716 = 0
4w^2 + 16w - 2100 = 0
w^2 + 4w - 525 = 0
w^2 + 25w - 21w - 525 = 0
w(w + 25) - 21 (w + 25) = 0
(w - 21) (w + 25) = 0
w = 21
w = -25
The dimensions of the box cannot be negative hence, the width is 21.
length = 20 + 21
length = 41
The original dimensions of the metal is width = 21 and length = 41 before cutting off the squares.
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P=I^2xR what does I=?
Answer:
[tex]\sqrt{\frac{P}{R} }[/tex]
Step-by-step explanation:
[tex]P=I^2*R\\[/tex]
Divide both sides by R
[tex]\frac{P}{R} =I^2[/tex]
Remove the exponent by finding the square root of each side
[tex]\frac{\sqrt{P} }{\sqrt{R} } = I[/tex]
[tex]I=\sqrt{\frac{P}{R} }[/tex]
before opening a new restaurant, a chef wants to gather information about the eating habits of the local residents. he randomly selects 1000 households from all households in the area and mails a questionnaire to them. of the 1000 surveys mailed, he receives 150 back. which of the following is the most obvious concern with how this information is gathered?
The most obvious concern is those who chose to respond to the survey may have different eating habits from those who did not respond.
One of the major worries when conducting a survey is that people who choose to reply can differ from those who choose not to. The term for this is nonresponse bias. The representativeness of the sample may be impacted by the traits, opinions, or actions of respondents that differ from those of non-respondents.
In this given case, the chef issued a survey to 1000 families, but only 150 of them responded, or 15% of the households. It's probable that those who are very interested in food or cooking will respond to the poll more frequently than others who aren't. Due to the possibility that the eating patterns of individuals who replied may not be typical of the total population, this could cause the sample to be skewed. Thus, the chef would need to consider the nonresponse bias when interpreting the results of the survey.
Complete Question:
Before opening a new restaurant, a chef wants to gather information about the eating habits of the local residents. He randomly selects 1000 households from all households in the area and mails a questionnaire to them. Of the 1000 surveys mailed, 150 are returned. Which of the following is the most obvious concern with how this information is gathered?
(A)Mailing questionnaires instead of conducting in-person interviews produce a convenience sample.
(B)Those who chose to respond to the survey may have different eating habits from those who did not respond.
(C)Only residents from the local area were polled.
(D)The chef must conduct a census in order to avoid all sources of bias.
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Convert the unit as shown below.
2772 cu in. =
gal
2772 cu in. =
gal
(Type a whole number or a decimal. Type your answer using the appropriate number of significant digits.)
Find the Volume for the following cylinder.
a. 527.5 ft2
b. 342.7 ft2
c. 373.7 ft2
d. 307.7 ft2
The volume of the cylinder is 769.3 cubic feet.
What is volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Given a cylinder,
radius = 7 feet
height = 5 feet
volume of cylinder = πr²h
V = πr²h
V = 3.14*(7²)*5
V = 769.3 cubic feet
Hence the volume of a cylinder is 769.3 cubic feet.
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7 milimeter = 5 meter scale factor
The scale factor for 7 millimeters to 5 meters is 0.0014.
What is the scale factor?The scale factor is the ratio between the scale of an original object, drawing, map, model, or blueprint compared to its representation as a larger or smaller object.
We can compute the scale factor (scaled-down) using the following formula:
Scale factor = Dimension of the new shape ÷ Dimension of the original shape
1 meter = 1,000 millimeters
5 meters = 5,000 millimeters (1,000 x 5)
The scale-down factor of 7 millimeters to 5,000 millimeters = 0.0014 (7/5,000)
The scale-up factor of 7 millimeters to 5,000 millimeters = 714.286 (5,000/7)
Thus, the scale factor is 0.0014.
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Question Completion:What is the scale factor?
In a residential neighborhood, the median value of a house is $200,000. For which of the following sample sizes is the sample median most likely to be above $250.000? O Impossible to determine without more information. O n = 50 O n=1000 O n=100 O n= 10
A) n = 50, Since the sample size is small, it is more likely that a higher value is selected as the median, and the sample would be skewed to the right tail.
What is the median value?
The median value of a set of data is the middle value when the data is arranged in order. It is the value that separates the higher half of the data from the lower half. In other words, it's the value that has half the observations below it and half the observations above it.
In a residential neighborhood, the median value of a house is $200,000, which means that half the houses in the neighborhood are worth more than $200,000 and half are worth less.
For a sample median most likely to be above $250.000, the sample size would have to be small and skewed to the right tail, where the higher values are. In this case, the answer would be
Hence, A) n = 50, Since the sample size is small, it is more likely that a higher value is selected as the median, and the sample would be skewed to the right tail.
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Which is the graph of f(x) = 3(2-) *?
6
5
4
32
3
4
-3-2-1-1
-2
1 23 4 56
6
5
4
-3
2
4
-3-2-1
1 23
O
4
5 6
4
3
--3-2-1
7777
123 4 5 67
O
We graph points A(0,3) and B(1,2) to find the solution.
What is the intercept?
An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses.
Here, we have
Given: f(x) = 3(2/3)ˣ
We first find the y-intercept
The y-intercept is the value of f(x) when the value of x is equal to zero
For x = 0
f(0) = 3(2/3)⁰ = 3
Point A(0,3)
Now, we find the value of f(x) when x = 1
f(1) = 3(2/3)¹ = 2
Point B(1,2)
Hence, we graph points A(0,3) and B(1,2) to find the solution.
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Please hurry
Which of these graphs best illustrates
how the velocity of the free-falling rock
changes during the first four seconds?
J) Has a box that has a line at an angle. Inside the box from the bottom left corner to the top right corner is the angled line like |_ and inside the box is a line angled like this /
K) Same as “J” except the angle is a curved half circle angled from the bottom left corner going to the top of the box. Therefore the curved/bent line isn’t exactly going to the top right corner.
L) Same as “J” except the line is going from top left corner to bottom right corner.
M) same as “K” except the bent/curved line is going from left bottom corner to right side of box like in the middle.
The graph which represents the velocity of the free-falling rock that changes during the first four seconds is option L: Same as “J” except the line is going from top left corner to bottom right corner.
What is velocity?
The pace at which an object's position changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction.
The velocity of a free-falling rock can depicted by equation of motion.
The first equation of motion, v = u + it is referred to as the velocity-time relation. On the other hand, the second equation of motion is s = ut + 1 / 2at² can be called the position-time relation. Likewise, we call the third equation of motion, v² = u²+ 2as, position – velocity relation.
The laws are: (1) Every object moves in a straight line unless acted upon by a force. (2) The acceleration of an object is directly proportional to the net force exerted and inversely proportional to the object's mass. (3) For every action, there is an equal and opposite reaction.
Since, the rock is falling freely it will form a straight line (first equation of motion) on the graph and not curved.
The rock will start to fall at an increasing speed with respect to time.
Therefore, option L is the correct answer.
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Help me please I don’t know how to do it
The slope equals the rise divided by the run: . You can determine the slope of a line from its graph by looking at the rise and run.
How do you find slope of a line?A line has the property that its slope remains constant throughout. Therefore, you may determine the slope by selecting any two points along the line's graph.
The definition of slope in mathematics is pretty close to how we normally define it. Slope is a mathematical term used to indicate a line's steepness and direction. A line's slope can be inferred from its graph alone, especially in relation to other lines plotted on the same coordinate plane.
slope=rise/run.
The ratio of the change in the y-value to the change in the x-value can also be used to determine slope. For instance: Given two points on the line, P = (0, -1) and Q = (4,1), we may compute
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Carmen will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $42 and costs an additional 0.18 per mile driven.The second plan has an initial fee of $51 and costs an additional $0.13 per mile driven.
For what amount of driving/miles do the two plans cost the same?
What is the cost when the two plans cost the same?
The two plans cost the same for 550 miles of driving and $113.5 is the total cost.
What is linear equations?Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts of an equation in this format is rather simple (x and y).A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.This problem is about linear equations. We assume Maya drive X miles, and the total cost is $Y, then we can get like, the first plan has an initial fee of $53 and costs an additional $0.11 per mile driven
For plan 1: Y = 53 + 0.11 X
The second plan has an initial fee of $42 and costs an additional $0.13 per mile driven,
For Plan 2: Y= 42 + 0.13 X
When both plans cost the same, then
Plan 1 = Plan 2
53 + 0.11 X = 42 + 0.13 X
0.13 X - 0.11 X = 53 - 42
0.02 X = 11
[tex]$X=\frac{11}{0.02}=550$[/tex] miles
Put the value of X in equation of Plan 1, we get,
Y = 53 + 0.11(550) = 53 + 60.5= $113.5
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HELP ASAP !! WHATS THE END BEHAVIOR ?
The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.
What is end behaviour ?When referring to a function, "end behaviour" refers to the character of the value as the function parameter becomes closer to +∞ and -∞.
In the given table for f(x), we see that for every value of x, function f(x) is decreasing.
f(-2) = 48
f(0) = 12
f(2) = 3
f(3) = 1.5
In other words as the value of x increases, f(x) is approaching towards 0.
Now we take another function g(x) =
Now we plug in the values of x to get the values of g(x)
g(-1) =2^-1-5
= 1-10/2
= -9/2
= -4.5
g(0) = 2^0-5
= 1 - 5 = -4
g(2) = 2^2-5
= 4 - 5 = -1
g(3) = 2^3-5
= 8 - 5= 3
Now we find that g(x) is increasing with the values of x.
Now we take third function h(x).
By analyzing the given graph we find
h(-4) = 2
h(0) = 3
h(1) = 5
So when we are increasing the value of x function h(x) is increasing.
Finally we conclude by the options given that f(x) is the only function which tends to 0 with the increase in the values of x.
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Como saber cuánto creció
The seedlings grew by 7/6 inches in the first 2 weeks.
What is LCM ?
The abbreviation LCM stands for "Least Common Multiple." The smallest multiple that two or more numbers share is known as the least common multiple.
Let' assume the growth of seedling was 'nil' at the beginning.
According to the situation,
In the first week it grew by 1/3 inches and,
In the next week it grew by 5/6 inches.
So, we can say that the total growth will be the sum of growth in the first and second week.
Hence, total growth would be 7/6 inches (i.e. 1/3 + 5/6).
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-1 2. Solve the pair of equations: 2a-1-3b-¹ = 4; 4a-¹ + b¯¹ = 1 3.
Hope it helps.
If you have any query, feel free to ask.
A building surmounted is in the form of a cylinder by a cone of height 24.m. If the base diameter and total height of the building are 14m and 34 m respectively, find the outer surface area of the building.
Answer: The building is in the form of a cylinder surmounted by a cone. To find the outer surface area of the building, we need to find the total surface area of the cylinder and the cone and add them together.
The total surface area of the cylinder = 2πr^2 + 2πrh = 2π(7^2) + 2π(7)(24) = 2π(49) + 2π(168) = 98π + 336π = 434π square meters
The total surface area of the cone = πr^2 + πr√(r^2 + h^2) = π(7^2) + π(7)(√(7^2 + 24^2)) = 49π + 49π(√(625)) = 49π + 49π(25) = 49π + 1225π = 1274π square meters
The outer surface area of the building is the sum of the total surface area of the cylinder and the cone, which is 434π + 1274π = 1708π square meters.
Step-by-step explanation:
the brigham young university statistics department is conducting a series of randomized comparative experiments to compare teaching methods. response variables include students' final-exam scores and a measure of their attitude toward statistics. one study compares two levels of technology for large-group lectures: standard (overhead projectors and chalk) and multimedia. the experimental units in the study are the 8 lecture sections in a basic statistics course. there are four instructors, each of whom teaches two sections. because the lecturers differ, their lectures form four blocks.
Individuals basically use statistics to make decisions in financial planning and budgeting, while organizations are guided by statistics in financial policy decisions.
What exactly do you mean by statistics?
Statistics is the study of data collection, organisation, analysis, interpretation, and presentation. When applying statistics to a scientific, industrial, or social problem, it is customary to begin with a statistical population or a statistical model to be researched.Populations can refer to a variety of groupings of individuals or things, such as "every individual living in a nation" or "each atom making up a crystal." Every facet of data, including the planning of data collecting in terms of the layout of surveys and experiments, is covered by statistics.The science of statistics focuses on creating and researching strategies for gathering, analyzing, interpreting, and presenting empirical data.Given data :
Step 1 :
The statistics department at Brigham Young University (BYU) is doing research to contrast various teaching strategies.
For lengthy courses, two technological echelons are contrasted: standard and multimedia. Eight lecture parts with students are present. There are four teachers in all.
Step 2 :
Consider that we randomly select two professors to use standard technology and the other two to use multimedia technology. Various professors will have various teaching philosophies, which will eventually influence final grades. We won't be able to tell a teaching method from a piece of technology in this way. Regarding technological disparities, there is no assurance.
Step 3 :
The ideal plan would be to divide each teacher's lectures into two sections, one utilising normal technology and the other multimedia.
There are four blocks as a result, one for each teacher.
Variability would be reduced because they are all being taught by the same person.
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A car dealership can offer a $36,000 car under a special promotion with four years financing at 0%, or can offer a discount off the price of the vehicle if the buyer finances the sale at .5% monthly over the four years. What discount off thepurchase price results in the buyer making the identical monthly payment under either purchase option. Please include excel solution in this using either goal seek or solverA car dealership can offer a $36,000 car under a special promotion with four years financing at 0%, or can offer a discount off the price of the vehicle if the buyer finances the sale at .5% monthly over the four years. What discount off thepurchase price results in the buyer making the identical monthly payment under either purchase option. Please include excel solution in this using either goal seek or solver
The discount of the purchase price results in the buyer making the identical monthly payment under either purchase option, $4064.76.
Financing is the process of providing funds for business activities, making purchases, or investing. Financial institutions, such as banks, are in the business of providing capital to businesses, consumers, and investors to help them achieve their goals. The use of financing is vital in any economic system, as it allows companies to purchase products out of their immediate reach.
the PV=FV÷(1+r)^N,
here, PV is present value, FV is future value and r is the rate of discount or interst.
According to the given conditions,
if car financing at 0% ,
then car price=$36,000.
time period =48 months.
so, monthly payment =36000÷48
=$750.
if financing at regular rate then, monthly interest rate is 0.5%
time=48 month.
monthly payment, if we consider same payment=$750
the discount of the purchase price will be $4064.76.
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Determine the friction force on the 40 kg crate, and the resultant normal force and its position x, measured from point A, if the force P = 300 N. Take μs=0.5 and μk=0.2
The friction force on the 40 kg crate is the product of the coefficient of static friction, μs, and the normal force on the crate. Therefore, the friction force is 40 kg ×0.5 = 20 N.
The resultant normal force on the crate is the sum of the force P and the friction force, which is
300 N + 20 N = 320 N.
The position x, measured from point A, is determined by the direction of the force P. If the force P is acting to the right, then the normal force will have a position x that is to the right of point A. If the force P is acting to the left, then the normal force will have a position x that is to the left of point A.
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For each transformation below, state whether the lengths, angles or both are invariant.
How the transformations below affect length, angles or both?
Translation - shifting same figure, lengths remain as is, angles remain as is;Reflection - mirroring the figure, lengths remain as is, angles remain as is;Rotation - rotation of the figure, lengths remain as is, angles remain as is;Enlargement - resizing the figure, lengths become larger, angles remain as is.match each term with its definition. experimental group dependent variable control group operational definition independent variable
A dependent variable is precisely what it sounds like, just like an independent variable. It is something on which other elements depend.
A test score, for instance, may be a dependent variable because it could vary based on a number of variables, including how much you studied, how much sleep you got the night before the test, and even how hungry you were. Typically, when attempting to establish a connection between two variables, the goal is to determine what causes the dependant variable to vary in the manner that it does.
Many people struggle to recall which variable is the independent variable and which variable is the dependent variable.
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Nineteen immigrants to the U.S were asked how many years, to the nearest year, they have lived in the U.S. The data are as follows: 2; 5; 7; 2; 2; 10; 20; 15; 0; 7; 0; 20; 5; 12; 15; 12; 4; 5; 10.
Table 1.35 was produced.
a. Fix the errors in Table 1.35. Also, explain how someone might have arrived at the incorrect number(s).
b. Explain what is wrong with this statement: "47 percent of the people surveyed have lived in the U.S. for 5 years."
c. Fix the statement in b to make it correct.
d. What fraction of the people surveyed have lived in the U.S. five or seven years?
e. What fraction of the people surveyed have lived in the U.S. at most 12 years?
f. What fraction of the people surveyed have lived in the U.S. fewer than 12 years?
g. What fraction of the people surveyed have lived in the U.S. from five to 20 years, inclusive?
Someone might have arrived at the incorrect number by incorrectly counting frequencies or not accounting for every data point.
Table 1.35 should be as follows:
Number of Years in US | Frequency
2 | 3
5 | 4
7 | 2
10 | 2
12 | 2
15 | 2
20 | 2
b. This statement is incorrect because 47 percent does not equal the total number of people surveyed.
c. This statement can be fixed by saying "Four out of the nineteen people surveyed have lived in the U.S. for 5 years."
d. The fraction of people surveyed who have lived in the U.S. for five or seven years is 6/19, or 31.58%.
e. The fraction of people surveyed who have lived in the U.S. for at most 12 years is 10/19, or 52.63%.
f. The fraction of people surveyed who have lived in the U.S. for fewer than 12 years is 9/19, or 47.37%.
g. The fraction of people surveyed who have lived in the U.S. from five to 20 years, inclusive, is 12/19, or 63.16%. This can be calculated by subtracting the number of people who have lived in the U.S. fewer than five years (3) from the number of people who have lived in the U.S. 20 or more years (2), and dividing the result (12) by the total number of people surveyed (19).
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WHAT IS THE ANSWER FOR THE 2nd ONE?! PLS HELP!!
The total volume of both storages will be 76 cubic ft.
What is volume?A volume is defined as the amount of space occupied by a three-dimensional solid shape. It is difficult to visualize in any shape, but it can be compared between shapes.
A compass box, for example, has a larger volume than an eraser placed inside it. We divide any two-dimensional shape into equal square units to calculate its area.
The volume of the larger box will be calculated as:-
Volume = side³
Volume = (4)³
Volume = 64 cubic ft
The volume of the smaller box = 12 cubic ft
Total volume = 64 + 12 = 76 cubic ft
Hence, the total volume of the boxes is 76 cubic ft.
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write the equation in slope-intercept form
m = -1/2; (0,-5)
problem: you have a box of chocolates that contains 17 pieces of which:
7 are solid chocolate
4 are filled with cashews and
6 are filled with cherries.
all of the candies look exactly alike. you select a piece, eat it, select a second piece eat it and finally eat one last piece.
the question is what is the probability of selecting a solid chocolate and 2 cherry filled in any order
The probability of selecting one solid chocolate and 2 cherries is given as follows:
0.1544 = 15.44%.
How to obtain a probability?A probability is obtained by the division of the number of desired outcomes by the number of total outcomes.
The outcomes resulting in one chocolate and two cherries being taken are given as follows:
Chocolate (7/17 probability), cherry (6/16 probability) and cherry (5/15 probability).Cherry (6/17 probability), chocolate (7/16 probability) and cherry (5/15 probability).Cherry (6/17 probability), cherry (5/16 probability) and chocolate (7/15) probability.Hence the probability is obtained as follows:
p = 7/17 x 6/16 x 5/15 + 6/17 x 7/16 x 5/15 + 6/17 x 5/16 x 7/15
p = 0.1544 = 15.44%.
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Find the vectors u and v whose initial and terminal points are given. Initial Point Terminal Point u: (4,2) (5, 6) v: (2, 4) (3,8) U = V =
The vector is given by (1,4) and (1,4) for the given 2 conditons
what is vector?A vector is a mathematical object that has both magnitude and direction. In physics, vectors are used to represent quantities such as velocity, force, and acceleration. In mathematics, vectors can be represented by an ordered list of numbers (also known as components or coordinates) that specify the magnitudes of the vector in different directions. Vectors can be added, subtracted and multiplied by scalars. They also have properties such as dot and cross product. Vectors can be represented graphically as directed line segments. They are used in various fields like physics, engineering, computer science etc.
Part 1:
The vector is given by (final -initial)
=> (5-4 , 6-2)
=> (1 , 4)
Part : 2
The 2nd vector is given by (final - initial)
=> (3-2 , 8-4)
=> (1 , 4)
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a circle is formed when a plane slices through a cone. which of the following describes the relationship between the plane and the cone? the plane is parallel to the base of the cone. the plane is perpendicular to the base of the cone. the plane is parallel to the slant edge of the cone and intersects the base of the cone. the plane is at a slight angle with respect to the base of the cone, but does not intersect it.
The relationship between the plane and the cone is expressed by the statement that it is parallel to the base of the cone.
Given,
A circle is a closed, curved shape with two dimensions in geometry, alternatively we might say that a circle is a spherical form without borders or edges.
When a cone is cut by a plane that is parallel to the cone's base, a circle is the resultant cross-section.
The form that results from a plane cutting a cone at an angle such that it misses the base or the vertex is called an ellipse. (As in the figure.)
Hence When a plane cuts through a cone and the plane is parallel to the base of the cone, the result is a circle.
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Christmas lights are produced in a large quantity and as a result one-fifth are faulty. If
individual lights are taken out one by one from this large quantity, find the probability
that when the first three lights are taken out
a there is one faulty light
b there are two faulty lights
c there is at least one faulty light.
The probability of there is one faulty light is 0.60%, There are two faulty lights is 0.12% and There is at least one faulty light is 0.60%.
What is probability?The likelihood that an event will occur is measured by probability. It is difficult to make a complete prediction for many events. By using it, we are only able to forecast the likelihood of an event, or how likely it is, to occur. Between 0 and 1, where 1 denotes a certain event and 0 denotes an impossibility, is the range of probability. For students in class 10, probability is a crucial subject because it clarifies all of the fundamental ideas. In a sample space, there is a probability of 1 for each event.
a. Let there be 100 lights, 1/5th are faulty = 20
There is one faulty in first three, P = 3/100 × 20/100
= 0.006
= 0.60%
b. There are two faulty lights, P = 3/100 × 20/100 × 20/100
= 0.0012
= 0.12%
c. There is at least one faulty light = 3/100 ×1/5
= 0.006
= 0.60%
Thus, The probability of there is one faulty light is 0.60%, There are two faulty lights is 0.12% and There is at least one faulty light is 0.60%.
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One side of a right triangle is known to be 25 cm exactly. The angle opposite to this side is measured to be 60 with a possible error +_ 0.5
a. Use differentials to estimate the errors in the adjacent side and the hypothenuse.
b. Estimate the percentage errors in the adjacent side and hypothenuse.
The estimate errors in the adjacent side and the hypothenuse are ≅ ±0.29 cm and ≅ ±0.145 cm respectively. The percentage errors in the adjacent side and hypothenuse are 2.009% & 0.502%.
Hypothenuse y₁ = 25/sin x = 25cosec x
Adjacent y₂ = 25/tan x = 25cot x
Opposite angle is 60° = π/3
Possible error, dx ≅ ±0.5° = 0.5 × π/180 = ±π/360
Differentiating y₁ = 25cosec x
dy₁ = -25(cosec x · cot x)dx
dy₁ = -25(cosec (π/3) · cot (π/3))×±π/360
= -25(2/√3)(1/√3)(±π/360)
= ≅ ±0.145 cm
Similarly
dy₂ = -25 cosec²x .dx
dy₂ = -25 cosec²(π/3) .×±π/360
= -25(2/√3)²×±π/360
≅ ±0.29 cm
So the errors in the hypothenuse = ±0.145 cm
Error in the adjacent side = ±0.29 cm
Percentage error in the adjacent side = 0.29/(25/√3) = 2.009 %
Percentage error in the hypothenuse = 0.145/(25/sin60) = 0.502%
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What are the chances your flight will leave on time? To the right are a histogram and summary statistics for the percentage of flights departing on time each month from 2001 thru 2006. There is no evidence of a trend over time. (The correlation of On Time Departure % with time is r = - 0.006.) Complete parts a) through c) below. Find a 90% confidence interval for the true percentage of flights that depart on time. Interpret this interval for a traveler planning to fly. Choose the correct answer below. There is a 90% chance that the true mean monthly percentage of on-time departures is within the interval. We can be 90% confident that the interval contains the true mean monthly percentage of on-time departures. A randomly selected month has a 90% chance of having an on-time departure percentage within the interval. 90% of all months have on=time departure rates within the interval.
We can be 90% confident that the interval [76.4, 79.3] contains the true mean monthly percentage of on-time departures. This means that we are highly confident that the true mean monthly percentage of on-time departures lies within this interval.
To find the 90% confidence interval, we first need to calculate the margin of error. To calculate this, we need to use the standard error, which is calculated by dividing the standard deviation by the square root of the sample size. The standard deviation for the given data is 2.2 and the sample size is 72 (6 years × 12 months). So, the standard error is calculated as 2.2/√72 = 0.44. The margin of error is then calculated by multiplying the standard error by the critical value for 90% confidence, which is 1.645. The margin of error is therefore 0.44 × 1.645 = 0.72. The confidence interval is then calculated by adding and subtracting the margin of error from the sample mean. The sample mean is 77.8, so the 90% confidence interval is 77.8 ± 0.72, or [76.4, 79.3]. This means that we are highly confident that the true mean monthly percentage of on-time departures lies within this interval.
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It seems these days that students have to work more and more each week to be able to afford the costs of college. For a recent labor survey conducted by the
government, there were 78 respondents who were working while attending college. The frequency distribution below summarizes the number of hours worked
per week as reported by the respondents.
Number of hours
worked per week Frequency
(hours per week)
26 to 30
31 to 35
36 to 40
41 to 45
46 to 50
51 to 55
10
24
20
13
7
4
Based on the frequency distribution, using the midpoint of each data class, estimate the mean number of hours worked per week by the respondents. For your
intermediate computations, use four or more decimal places, and round your answer to one decimal place.
hours per week
The mean number of hours worked per week by the respondents will be 37.68.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.
Number of hours worked per week Frequency
26 to 30 10
31 to 35 24
36 to 40 20
41 to 45 13
46 to 50 7
51 to 55 4
The mean is given as,
Mean = [28 x 10 + 33 x 24 + 38 x 20 + 43 x 13 + 48 x 7 + 53 x 4]
(10 + 24 + 20 + 13 + 7 + 4)
Mean = 2939 / 78
Mean = 37.68
The mean number of hours worked per week by the respondents will be 37.68.
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Jeremy has two pieces of wood: one is 90 inches and the other is 72 inches. He wants to cut both pieces into smaller pieces of the same length. What is the longest possible length he can cut and not have any lumber left over?
answer choices
O 9
O 2
O 18
O 72
The longest piece of same size that can be cut from 90 inches and 72 inches pieces of wood using HCF is of length 18 inches.
So, the correct option is (c) 18.
Given that,
Jeremy has two pieces of 90 inches and the other is 72 inches wood. He wants to cut both pieces of wood into smaller pieces of same length and length as long as possible.
Therefore, the Highest Common Factor (H.C.F.) of both the lengths will gives the highest possible length i.e between both the wooden pieces.
To find Highest Common factor,
Prime factorizations of 90 and 72 :
90 = (2 x 3 x 3) x 5
72 = 2 x 2 x (2 x 3 x 3)
2 x 3 x 3 is common factor between 90 and 72
∴ The Highest Common Factor of 90 and 72 = 2 x 3 x 3 = 18
The longest possible length that can be cut out from both the pieces are of length = 18 inches
Number of pieces that can be cut from 90 inches long piece = 90/18 = 5
Number of pieces that can be cut from 72 inches long piece = 72/18 = 4
Therefore, the total number of pieces of lumber = 5+4 = 9 pieces
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