Answer: 4 hours and 10 minutes per week
Step-by-step explanation:
She exercises for 5 days per week (week days only).
(5/6 hr/day) x 5 days = 25/6 = 4.17 hours = 4 hours and 10 minutes per week
A mail-order company charges $5 per order plus $2 per item in the order, up to a maximum of 4 items. write a function rule to describe the situation. find a reasonable domain and range for the function.
The function to describe the order of the mail-order company is given by f(x) = 5 +2x , {x | x ≤ 4 } .
The charge per order = $5 .
Cost of each item = $2
Cost of x items = 2x
Total cost for the order = 5 + 2x
Function to represent this situation : f(x) = 5 + 2x
Now it is given that the maximum of 4 items can be ordered.
Domain: {1,2,3,4}
At x = 1 , f(x) = $7
At x = 2 , f(x) = $9
At x = 3 , f(x) = $11
At x = 4 , f(x) = $13
Range of the function: {7,9,11,13}
A rule is referred to as a function if it produces a distinct result for each input x. In mathematics, a function is represented by a mapping or transformation.
The set of all potential values that can be passed into a function while it is specified is known as the domain. The entire set of values that the function's output is capable of creating is referred to as the "range."
The range of potential values for a function's outputs is known as the co-domain.
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Answer:
Domain: {1, 2, 3, 4}
Range: {7, 9, 11, 13}
Step-by-step explanation:
jill buys a mobile phone that weighs 210g to 2 significant figures. she puts the phone inside a protective case that weighs 15.4g to 1 decimal place. work out the smallest possible total weight, in grams (g) of the phone, and the case combined
The smallest possible total weight of the phone and case combined is 225.4g.
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x.
To find the smallest possible total weight of the phone and case combined, we need to add the weight of the phone and the case.
The weight of the phone is given to 2 significant figures, so we can assume that it has an uncertainty of +/- 0.05g. The weight of the case is given to 1 decimal place, so we can assume that it has an uncertainty of +/- 0.05g as well.
Adding the two weights together, we get:
210g + 15.4g = 225.4g
To find the smallest possible total weight, we need to round this to the nearest 0.1g, since the weight of the case is given to 1 decimal place. Rounding to the nearest 0.1g gives us:
225.4g rounded to 1 decimal place = 225.4g
Therefore, the smallest possible total weight of the phone and case combined is 225.4g.
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The lowest overall weight that may be achieved is [tex]220.35g[/tex].
What does weight actually mean?The amount and quantity of bulk or heaviness; the weight of something. Physics. In an area with constant gravitational acceleration, mass is typically defined as the force of gravity, which is equal to the body's mass times the local velocity of gravity.
What does weight vs. weigh mean?With a few exceptions like statistics, grades, and blankets, we can generally keep weigh or weight distinct through using weight as a verbs and mass as a noun.
As the weight of the smartphone is stated to be [tex]210g[/tex] to two significant numbers, we may conclude that its true weight is between [tex]205g[/tex] & [tex]215g[/tex].
We may estimate that the case weighs between [tex]15.35g[/tex] to [tex]15.45g[/tex] because it is said to weight [tex]15.4g[/tex] to one decimal point.
So, [tex]205g + 15.35g = 220.35g[/tex] is the absolute minimum weight that the phone and case may weigh together.
Hence, [tex]220.35g[/tex] is the lowest feasible overall weight.
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Bill has lost 40 pounds in 8 weeks. What is his weekly rate?
Answer: 5
Step-by-step explanation:
So all you have to do is divide 40 by 8 and you get the answer
how to graph
[tex]1 \frac{1}{3} [/tex]
and
[tex] \frac{2}{3} [/tex]
on a cartesian plane? please explain how
The point (1 and 1/3, 2/3) on the Cartesian plane is given by the image shown at the end of the answer.
How to graph the points on the Cartesian plane?All the points on the coordinate map have a x-coordinate and an y-coordinate, and the format of the point is given by the relation as follows:
(x,y).
The meaning of each coordinate is given as follows:
x-coordinate: horizontal position relative to the origin, that is, relative to x = 0.y-coordinate: vertical position relative to the origin, that is, relative to y = 0.The x-coordinate of the point in this problem is:
x = 1 and 1/3.
It is a mixed number, hence the decimal equivalent is of:
x = 1 + 1/3 = 1 + 0.33 = 1.33.
Meaning that the point is at an horizontal position that 1.33 units from the origin zero, that is, one point plus one third of the distance from one to two.
The y-coordinate is of:
y = 2/3.
Meaning that the vertical position of the point is 2/3 of the way from y = 0 to y = 1.
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look at the 2 boxes and the 4 probability histograms below. each box has 2 probability histograms associated with it. one is the probability histogram for the sum of 2 draws made at random with replacement and the other is the probability histogram for the sum of 20 draws made at random with replacement from the box.
Explaining a bar graph
A bar graph graphically displays information. It uses bars that extend to various heights to symbolize value. Bar graphs can be created using any of the following: vertical bars, horizontal bars, grouped bars (several bars that compare values in a category), and stacked bars (bars containing multiple types of information).
Two sketches are shown in Histogram I for Box A.
20 drawings from Box B are represented in Histogram II.
20 drawings from Box A are represented in Histogram III.
Two draws are shown in Histogram IV for Box B.
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) find the number of ways to distribute 10 identical cards into 3 boxes, where each box has at least one card.
Numbers of ways to distribute 10 identical cards into 3 boxes is 36
Combination is is a way of selecting items from a collection where the order of selection does not matter.
Formula of combination:
Let a x-combination of a set is a subset of x distinct elements of S. If the set has n elements, the number of x-combinations is equal to the binomial coefficient.
ⁿCₓ = n(n-1)(n-2)(n-3). . . (n-x+1) / (x-1)(x-2)(x-3) . . . .(1)
which can be written as ⁿCₓ = n! / (n-x)! x! , when n > x
ⁿCₓ = 0 , when n < x
Where n = distinct object to choose from
C = Combination
x = spaces to fill
According to the question,
Number of identical cards : n =10
Number of box cards are being distributed : x = 3
Number of ways to distribute when no condition is given : ⁿ⁺ˣ⁻¹Cₓ₋₁
If we place one one card in each box then
Number of cards left with us = 10 - 3
= 7
Now, condition of at least one cards in each box is satisfied ,
Then total number of ways to distribute 7 cards into 3 = ⁷⁺³⁻¹C₃₋₁
=> ⁹C₂ = 9! / (9 - 2)! 2!
=> 9×8×7! / 7!2!
=> 9×8/2
=> 9×4
=>36 ways
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yolanda is planning a 778-mile trip to visit her daughter in maryland. she plans to average 50 miles per hour. at that speed, approximately how long will the trip take? express your answer to the nearest tenth of an hour.
A cla vote for their cla preident. Candidate
A
receive 21
21
vote, which i 60%
60
%
of the vote. What i the total number of tudent who voted?
There were 35 students that cast ballots in total.
How much is a percentage?
In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. Frequently, it is denoted with the percent sign ("%")
We possess
60% of the vote, or 21 votes, are cast in favor of Candidate A.
The answer to the query is
Formulate the following given the conditions: 21 /60%
Use the same number to multiply the numerator and denominator: 210/6
Remove the connecting element: 35
Consequently, 35 students in all cast ballots.
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Is it important to solve or address the problem why or why not?.
A jacket normally costs £79.50.
In a sale there is 30% off the normal price.
What is the sale price of the jacket?
Answer:
£55.56
Step-by-step explanation:
30% off means you pay 70% of the full price.
70% = 0.7
£79.50 * 0.7 = £55.56
please answer asap (15 points)
only write down what I gotta put in the box and explanation
Answer:
b=-14
Step-by-step explanation:
slope intercept form is y=mx+b
m- slope
b- y intercept
So just fill in what we know
-2=2(6)+b
-2=12+b
-12 -12
-14=b
Hopes this helps please mark brainliest
Which congruence theorem can be used to prove triangle ABC is congruent to triangle DEC?.
Because the corresponding sections of congruent triangles are congruent, you may use the Vertical Angles Congruence Theorem to demonstrate that ABC DEC. b. CAB CDE.
Which congruence theorem can be used to demonstrate that triangles ABC and DEF are congruent?Triangle ABC is congruent to triangle DEF if in triangles ABC and DEF, AB = DE, AC = DF, and angle A = angle D. In other words, if a triangle's third side matches the third side of another triangle's third side, the triangles are said to be congruent.
The SAS Theorem is what?The side-angle-side (SAS) theorem is the first such theorem. The triangles are congruent if two sides and the included angle of one triangle are equivalent to two sides and the included angle of another triangle.
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how many different 4 card hands can be dealt from a deck of 52 cards? the order of the cards does not matter in this case.
Answer:
270,725 hands.
Step-by-step explanation:
(52 x 51 x 50 x 49)/(4 x 3 x 2) = 13 x 17 x 25 x 49 = 270,725
A computer programming team has 17 members. (a) How many ways can a group of nine be chosen to work on a project? As in Example 9.5.4, since the set of people in a group is a subset of the set of people on the team, the answer is (b) Suppose nine team members are women and eight are men. (1) How many groups of nine can be chosen that contain five women and four men? As in Example 9.5.7a, think of forming the group as a two-step process, where step 1 is to choose the women and step 2 is to choose the men. The answer is (ii) How many groups of nine can be chosen that contain at least one man? As in Example 9.5.7b, consider the relationship between the set of groups that consist entirely of women and the set of groups with at least one man. This thinking leads to the conclusion that the number of groups with at least on man is (iii) How many groups of nine can be chosen that contain at most three women? A group of nine that contains at most three women can contain no women, one woman, two women, or three women. So, the number of groups of nine that contain at most three women is (c) Suppose two team members refuse to work together on projects. How many groups of nine can be chosen to work on a project? In a similar way as in Example 9.5.6, let A and B be the two team members who refuse to work together in a group. Thinking about the number of groups that contain A and not B, B and not A, and neither A nor B leads to the conclusion that the total number of groups of that can be chosen to work on the project is (d) Suppose two team members insist on either working together or not at all on projects. How many groups of nine can be chosen to work on a project? As in Example 9.5.5, let A and B be the two team members who insist on working in a group together or not at all. How many groups contain both A and B? How many groups contain neither A nor B?
The number of groups that can be chosen from the team of 17 depends on the given conditions of the selection.
The correct responses are;
(a) The number of ways of choosing groups of 9 from the 17 members are 24,310 ways.
(b) (i) The number of groups of 9 containing 5 women and 4 men are 8,820 groups.
(ii) The number of groups of 9 that contain at least one man is 24,309 groups.
(iii) The number of groups of 9 that contain at most 3 women are 2,649 groups.
(c) If two team members refuse to work together on projects, the number of groups of 9 that can be chosen are 17,875 groups.
(d) If two team members must work together or not at all the number of groups of 9 that can be chosen are 1,430 groups.
Given,
The combination of n objects taking r at a time is given as follows
ₙCr = (ⁿr)
(a) The number of ways of choosing groups of 9 from the 17 members is given as follows;
Number of ways of choosing groups of 9 = (17, 9) = 24,310 ways.
(b) (i) Number of women = 9
Number of men = 8
Number of groups of 9 containing 5 women and 4 men = (9, 5) x (8, 4)
(9, 5) x (8, 4) = 126 x 70 = 8820
Number of groups of 9 containing 5 women and 4 men = 8,820 groups.
(ii) The number of groups that contain at least one man is (17, 9) - (9, 9)
(17, 9) - (9, 9) = 24,310 - 1 = 24,309
The number of groups that contain at least one man are 24,309 groups.
(iii) The number of groups of 9 that contain at most 3 women if given as follows;
(8, 8) × (9, 1) + (8, 7) × (9, 2) + (8, 6) × (9, 3) = 2649
The number of groups of 9 that contain at most 3 women are 2,649 groups.
(c) Given that two team members refuse to work together on projects, the number of groups of 9 that can be chosen are (15, 9) + 2 × (15, 8)
(15, 9) + 2 × (15, 8) = 5,005 + 2 × 6,435 = 17,875
(d) Two team members must work together or not at all is (15, 7) - (15, 9)
(15, 7) - (15, 9) = 6,435 - 5,005 = 1,430
The number of groups of 9 that can be chosen two team members must work together or not at all are 1,430 groups.
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A polygon has vertices at (-1, 3), (−1, 6), (2, 10), (5, 6), and (5, 3).
What is the area of the polygon? Enter your answer in the box.
The perimeter of the polygon is 22 units.
What is the area of the polygon?
The area of a polygon is defined as the area enclosed by the polygon's boundary. In other words, the region occupied by any polygon determines its area. In this lesson, we will learn how to calculate polygon area and the difference between polygon perimeter and area in detail.
we know that
the perimeter of a polygon is the sum of the length sides
in this problem, we have five vertices
so the polygon has five sides
Let,
A(-1, 3)
B(−1, 6)
C(2, 10)
D(5, 6)
E(5, 3).
the perimeter is equal to
P = AB + BC + CD + DE + AE
The formula to calculate the distance between two points is equal to
d = √(y₂ - y₁)² + (x₂ - x₁)²
The distance of AB:
A(-1, 3)
B(−1, 6)
d = √(6 - 3)² + (-1 - (-1))²
d = √(3)² + (0)²
d = 3
The distance of BC:
B(−1, 6)
C(2, 10)
d = √(10 - 6)² + (2 - (-1))²
d = √(4)² + (3)²
d = 5
The distance of CD:
C(2, 10)
D(5, 6)
d = √(6 - 10)² + (5 - 2)²
d = 5
The distance of DE:
D(5, 6)
E(5, 3).
d = √(3 - 6)² + (5 - 5)²
d = 3
The distance of AE:
A(-1, 3)
E(5, 3)
d = √(3 - 3)² + (5 - (-1))²
d = 6
Find the perimeter
the perimeter is equal to
P = AB + BC + CD + DE + AE
P = 3+5+5+3+6
P = 22 units.
Hence, the perimeter of the polygon is 22 units.
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You have solved equations containing square roots by squaring each side. You were
using the property that if a = b then a²-b². Show that the following statements are
NOT true for all real numbers.
a) if a² = b² then a = b
b) if a s b then a² sb²
These statements are not always true for all real numbers
What is a real number ?
A real number is a number that can be used to represent a continuous one-dimensional quantity in mathematics, such as a temperature, duration, or distance. Continuous in this context suggests that values may vary by arbitrary little amounts. An infinite decimal expansion can nearly always represent any real number.
a. If a² = b² and a = b is not always true because (-3)² = (3)² is true but
-3 = 3 is not true
Hence if a² = b² then a = b is not always true
b. if a< b then a²<b² is not always true
because -5<4 is true but (-5)² < (4)² is not true
Hence if a<b then a² < b² is not always true
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can it be concluded at a 0.01 level of significance that there is a linear correlation between the two variables?
The p value is 0.0055 and it can be .concluded at a 0.01 level of significance that there is a linear correlation between the two variables
What is meant by correlation?In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although the term "correlation" can apply to any sort of link, in statistics it usually refers to the degree to which two variables are linearly related. The association between the height of parents and their kids, as illustrated in the so-called demand curve, is an example of a dependent phenomenon.
Dependent variable :Distance
Independent variable :Weight
Distance=10.336482+0.34383484 weight
Sample size=24
Correlation coefficient(R)=0.54872231
Estimation error of standard deviation=8.5738353
Parameter estimates:
Parameter Estimate Std.Err Alternative DF T-Stat P-value
Intercept 10.336482 9.7264272 ≠0 22 1.0627214 0.2994
Slope 0.34383484 0.11168494 ≠0 22 3.0786141 0.0055
From the above values in the table,
p-value=0.0055 which is less than 0.01.
So, the significant linear correlation exists between two variables.
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Work out the perimeter of a semicircle with radius 3 cm.
Give your answer in terms of pi .
The perimeter of a semicircle with radius 3 cm is 6π cm.
What is semi-circle?
When a line travelling through the Centre of a circle reaches its two ends, a semicircle is created. Thus, a circle can be formed by combining two semicircles.Half of the area of a circle is contained within a semicircle. Since r2 is the radius of a circle, A semicircle's area is therefore 1/2(πr2), where r is its radius π has a value of 3.14, or 22/7.Half of the circle's circumference plus its diameter add up to a semicircle's perimeter. Since a circle's circumference is 2πr or πd, A semicircle's perimeter is therefore 1/2 (πd) + d, or πr + 2r, where r is its radius.Given :
Radius = 3cm
Circumference or Perimeter of a circle = 2πr
= 2 * π * 3
= 6π cm
Hence, the perimeter of a semicircle with radius 3 cm is 6π cm.
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Announcements for 84 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum magazines. The mean length of the conferences was 3.94 days, with a standard deviation of 1.28 days. Assume the underlying population is normal.
Margin of error for the given standard deviation is m = 3.77 , 4.21.
What is standard deviation?
Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.
Main body:
Consider the given data, the sample of 84 announcements of upcoming engineering conferences were randomly selected. Here, sample mean = 3.94 days and sample standard deviation s = 1.28 days. The population standard deviation is unknown.
C.I . = 95% = 0.95
value of 0.95 in z-table = 1.96
m(margin of error ) = x - bar ±z*σ/√n
m = 3.94 ± 1.96*1.28/√84
m = 3.94±0.27
m = 3.77 , 4.21
Hence margin of error is m = 3.77 , 4.21
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there are a large number of potential human errors. what are possible counter measures for inexperimence?
The countermeasures to avoid potential human errors are Visual aids & work instructions, education and/or discipline, work standardization and discipline and TPM and skill building etc.
Many major accidents, such as Texas City, Piper Alpha, and Chernobyl, were caused by potential human error. Companies must manage human failure as rigorously as they manage technical and engineering measures to avoid accidents and illness.
There are several countermeasures for amateur or beginner mistakes. Potential human errors can be avoided by some measures including training, skill development, work standardisation, visual aids, and work instructions. Every human being makes mistakes, whether they are professional or not.
Thus, Visual aids and work instructions, education and/or discipline, work standardisation and discipline, TPM and skill building, and other counter measures are used to avoid potential human errors.
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100 grams/day of substance x is filtered, 50 grams/day is reabsorbed, 75 grams/day is secreted and 125 grams/day is excreted. substance x is undergoing in the nephron and would have a clearance value that is .(choose one)
100 grams/day of substance x is filtered, 50 grams/day is reabsorbed, 75 grams/day is secreted and 125 grams/day is excreted. substance x is undergoing in the nephron net secretion and would have a clearance value that is greater than GFR
The formula for calculating clearance is Cx is given in terms of volume per time, where Ax is the quantity of x removed from the plasma, Px is the average plasma concentration, and Cx = Ax /Px.
Ax= 125 grams/day
and Px= 50 grams/day
Cx= 125/ 50
Cx= 2.5 grams/day
Therefore, the creatinine clearance overestimates GFR more severely in patients with a very low GFR than in those with higher GFR values. For a patient with a very low GFR, the secreted component is a relatively larger fraction of the total amount excreted.
Creatinine clearance remains the most popular method for routinely assessing patient GFR and the integrity of renal filtration, despite its low cost and convenience.
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Complete question :
Patient was experiencing respiratory acidosis (the increased hydrogen ion concentration was predominantly activating his peripheral chemoreceptors). 100 grams/day of substance X is filtered, 50 grams/day is reabsorbed, 75 grams/day is secreted and 125 grams/day is excreted. Substance X is undergoing ___________ in the nephron and would have a clearance value that is _________.(choose one)
A)net reabsorption, less than GFR
B)net secretion, greater than GFR
C)neither net reabsorption nor net secretion, equal to GFR
D)net reabsorption, greater than GFR
E) net secretion, less than GFR
4. For all non-zero real numbers x and y such that x - y = xy. What is the value of (1/x)-(1/y)
Answer:
The value is -1-----------------------------
Simplify 1/x - 1/y1/x - 1/y = Common denominator is xyy/(xy) - x/(xy) = Bring to common denominator (y - x)/(xy) = Combine numerators- (x - y)/(xy) = Both numerator and denominator are same- 1 Answeryou are interested in knowing what proportion of college students smoke. in a big university, you take a small random sample of 650 students and find that 25 of them smoke. based on the results of your survey, construct a 99% confidence interval for the proportion of college students who smoke.
A 99% confidence interval for the proportion of college students who smoke for the given standard deviation is (0.021. 0.045).
What is standard deviation?
Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.
Main body:
formula for confidence interval is :
m = p-bar ± z*√p(1-p)/n
given information =
n= 650
p - bar = 25/650 = 1/26
C.I. = 99% = 0.99
we need to find value of 0.99 in z -table
z = 2.33
substituting value ,
0.038 ± 2.33√( 0.038(1-0.038))/650
0.038 ± 2.33 * 0.075
0.038 ± 0.017
(0.021. 0.045)
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How many sides and angles does a circle have?.
The number of sides in a circle is 0.
The number of angles in a circle is 0.
What is the Radius of a circle?
Any circular object's radius is the measurement from the center to its outermost border or boundary. A radius is a dimension that applies to spheres, semispheres, cones with circular bases, and cylinders with circular bases in addition to circles.
It is possible to define a circle as the locus of a point moving in a plane while maintaining a constant distance from a fixed point. The radius of a circle is the distance from any point on the circle to its center. The fixed point is referred to as the center of the circle.
The angle formed by any two-circle radii is known as the central angle. The arc length, or the distance between the two places where the two radii cross the circumference, and the radius length must be determined in order to determine the central angle.
So, we can say that:
Since a circle is made up of arcs, which form a continuous line that joins at both ends, it has no sides. The distance between each circle's component components and its center is equal. A side must have two angles, one on either side of the line, and a line.
Hence,
The number of sides in a circle is 0.
The number of angles in a circle is 0.
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In Chicago, the temperature dropped from 21 degrees to -7 degrees over the course of 6 hours.
Identify a rational number that represents the average temperature change per hour.
The rational number that represents the average temperature change per hour is 28/6.
What is a rational number?Any number that can be represented as the ratio of two integers and where the denominator is not zero is referred to as rational.
Given that, the temperature dropped from 21 degrees to -7 degrees over the course of 6 hours.
The change in temperature is:
21 - (-7)
= 21 + 7
= 28
The average temperature change per hour is:
28/6
Hence, the rational number that represents the average temperature change per hour is 28/6.
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59.303 x 10 to the second power
Since 10 to the power of 2 is 100, we multiply 59.303 by 100, meaning we can just push the decimals two places up with an answer of 5930.3
Hope this helps.
Answer:5930.3
Step-by-step explanation:
10^2=10x10
10x10x59.303=5930.3
What are the steps for using a compass and straightedge to construct a regular hexagon inscribed?.
The steps to construct a regular hexagon inscribed are-Construct a horizontal line I and a point H on this line I, draw a circle having to intersect line I with it's center at point H, label the point of intersection of the circle and the left of point H, point J.
Detailed steps to construct a regular hexagon inscribed using a compass are:
Construct a horizontal line I and a point H on this line I.Construct a circle which will intersect line I with it's center at point H.Name the point of intersection of the circle and the left of point H, point J.Construct a circle by taking center point at point J and with a radius of HJ. Construct a circle by taking center at point K having a radius of HJ.Name the point of intersection of circles H and J that lies above line I, point M, and the point of the intersection that lies below line I, point N. Name the point of intersection of circles H and K that lies above line I, point O, and the point of their intersection that lies below line I, point P. Construct and JM, MO, OK, KP, PN, and NJ to complete regular hexagon JMOKPN.To know more about regular hexagon, visit here:
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Justine started her own landscaping business. she charges $6 an hour for mowing lawns and $11 for pulling weeds. in september she mowed lawns for 13 hours and pulled weeds for 5 hours. how much money did she earn in september?
If she mowed lawns for 13 hours and pulled weeds for 5 hours, then she earn $133 in September
The charges for mowing lawns = $6 per hour
The charges for pulling weeds = $11 per hour
Total number of hours that she mowed the lawn = 13 hours
Total number of hours that she pulled weeds = 5 hours
Total amount that she earned in September = (The charges for mowing lawns × Total number of hours that she mowed the lawn) + (The charges for pulling weeds × Total number of hours that she pulled weeds)
Substitute the values in the equation
6 × 13 + 11 × 5
= 78 + 55
= $133
Hence, the total amount that she earned in September is $133
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According to USA today, customers are not settling for automobiles straight off the production lines. As an ex. , those who purchase a $355,000 Rolls-Royce typically add $25,000 in accessories. One of the affordable automobiles to receive additions is BMWs mini cooper. A sample of 179 recent Mini purchasers yielded a sample mean of $5,000 above the $20,200 base sticker price. Suppose the cost of accessories purchased for all Mini Coopers has a standard deviation of $1,500.
A. Calculate a 95% confidence interval for the average cost of accessories on Mini Cooper.
B. Determine the margin of error in estimating the average cost of accessories on Mini Coopers.
C. What sample size would be required to reduce the margin of error by 50%?
The 95% confidence interval for the average cost of
accessories on Mini Cooper is between $4790.254 and $5219.746
The margin of error in estimating the average cost of accessories on Mini Coopers is $219.7459.
The required sample size should be 34574400 to reduce the
margin of error by 50%
Sample size, n = 179
Sample mean, x = 5,000
Population standard deviation, σ = 1,500
Confidence level, 1-α=0.95
⇒ Level of significance, α = 0.05
From the z-table, the tabulated value is given by
[tex]Z_{\alpha /2}[/tex] / [tex]Z_{0.025}[/tex]
=1.95
95% confidence interval for the average cost of accessories on Mini Cooper is
5,000±1.96×(1,500/√179)
= (5,000 ± 219.7459)
=($4790.254, $5219.746)
Therefore the 95% confidence interval for the average cost of
accessories on Mini Cooper is between $4790.254 and $5219.746.
Margin of error
= 1.96x(1,500/√179)
= 219.7459
Therefore, the margin of error in estimating the average cost of accessories on Mini Coopers is $219.7459.
The margin of error (E) is 0.50
⇒(0.50) √n=1.96(1500)
√n = 1.96(1500) /0.50
= n = (1.96(1500) /0.50)²
= n = (5880)²
= n = 34574400
Therefore, the required sample size should be 34574400 to reduce the
the margin of error by 50%
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why does a post-anova planned comparison use a pooled estimate of more groups than the number of groups whose means you are comparing?
In a post-anova planned comparison additional information increases the likelihood that the data may vary, leading to more degree of freedom.
Define the post-anova plan?The ANOVA test determines whether there is a general difference between the groups, but does not identify the precise groups that varied—only post hoc analyses do that.
Post hoc tests should only be conducted when you have demonstrated an overall statistically significant distinction in group averages since they are used to confirm where the differences between groups occurred (as statistically significant one-way ANOVA result). Similar to how one-way ANOVA was being used instead of numerous t-tests to control the find a different error rate (often alpha = 0.05), post hoc tests aim to do the same. A posteriori tests, or post hoc tests, are those that are carried out after the fact.Thus, the post-anova planned comparison makes use of a pooled estimate of data from more groups than just the number of studies whose means you intend comparing because more data increases the degree of freedom and the possibility that the data may change.
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