It's better to describe the center of distribution in Bakery A using the mean because the data is symmetric, while for Bakery B, the median is preferred due to asymmetric data.
To determine whether it's better to describe the centers of distribution in terms of the mean or the median for each bakery, we need to consider the shape of the data distribution.
For Bakery A:
- The data appears to be relatively symmetric, with values ranging from 34 to 61.
- There are no extreme outliers that significantly skew the data.
For Bakery B:
- The data is not symmetric; there is a wide range of values from 10 to 57.
- There is a notable outlier (10) that is much lower than the rest of the data.
Given these observations:
- For Bakery A, since the data is symmetric and there are no significant outliers, the mean (average) would be an appropriate measure of the center.
- For Bakery B, because the distribution is not symmetric and there is a significant outlier, the median (middle value) would be a more robust measure of the center.
So, the correct answer is:
C) Mean for Bakery B because the data is symmetric; median for Bakery A because the data is not symmetric.
Complete Question:
The number of bagels sold daily for two bakeries is shown in the table:
Bakery A 45 52 51 48 61 34 55 46
Bakery B 48 42 25 45 57 10 43 46
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.
A) Mean for both bakeries because the data is symmetric
B) Median because the distribution is not symmetric for both bakeries
C) Mean for Bakery B because the data is symmetric; median for Bakery A because the data is not symmetric
D) Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric
The correct answer is B): Median because the distribution is not symmetric for both bakeries.
Let's first calculate the mean and median for each bakery:
Bakery A:
Data: 45, 52, 51, 48, 61, 34, 55, 46
Mean (average):
[tex]\[ \text{Mean} = \frac{45 + 52 + 51 + 48 + 61 + 34 + 55 + 46}{8} = \frac{392}{8} = 49 \][/tex]
Median (middle value):
Arrange the data in ascending order: 34, 45, 46, 48, 51, 52, 55, 61
[tex]\[ \text{Median} = \frac{48 + 51}{2} = 49.5 \][/tex]
For Bakery A, the mean is 49 and the median is 49.5. The median (49.5) is slightly higher than the mean (49), indicating a slight right skew in the data.
Bakery B:
Data: 48, 42, 25, 45, 57, 10, 43, 46
Mean (average):
[tex]\[ \text{Mean} = \frac{48 + 42 + 25 + 45 + 57 + 10 + 43 + 46}{8} = \frac{316}{8} = 39.5 \][/tex]
Median (middle value):
Arrange the data in ascending order: 10, 25, 42, 43, 45, 46, 48, 57
[tex]\[ \text{Median} = \frac{43 + 45}{2} = 44 \][/tex]
For Bakery B, the mean is 39.5 and the median is 44. The mean (39.5) is lower than the median (44), indicating a left skew in the data.
Bakery A: The median (49.5) is slightly higher than the mean (49), suggesting a slight right skew. Given this slight skewness, the median might be a better measure of central tendency for Bakery A.
Bakery B: The mean (39.5) is noticeably lower than the median (44), indicating a left skew. Therefore, the median would likely be a better measure of central tendency for Bakery B.
Based on this analysis, the correct answer is B): Median because the distribution is not symmetric for both bakeries.
Complete Question:
The number of bagels sold daily for two bakeries is shown in the table:
Bakery A 45 52 51 48 61 34 55 46
Bakery B 48 42 25 45 57 10 43 46
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.
A) Mean for both bakeries because the data is symmetric
B) Median because the distribution is not symmetric for both bakeries
C) Mean for Bakery B because the data is symmetric; median for Bakery A because the data is not symmetric
D) Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric
In the figure, if AB ≅ CD, then
A. AB ⊥ CD
B. CE ≅ BE
C. ∠CEA ≅ ∠CEB.
D. arc AB ≅ arc CD.
Answer:
D. arc AB ≅ arc CD.Step-by-step explanation:
To solve this problem, we need to use the Intersecting Chords Theorem which states "when two chords intersect each other inside a circle, the products of their segments are equal".
Applying this theorem, we have
[tex]AE \times EB = CE \times ED[/tex]
Where [tex]AB=AE+EB[/tex] and [tex]CD=CE+ED[/tex], also [tex]AB \cong CD[/tex], which means
[tex]AE+EB=CE+ED[/tex]
However, if both chords are equal, then their arcs are also equal, that's the easiest way to deduct it, that is
[tex]arc(AB) \cong arc(CD)[/tex]
Because an arc is defined by its chord basically, and in this case they are congruent.
How to find the volume of a parallelepiped with 8 vertices?
The volume of parallelepiped with 8 vertices is 75 units.
What is Volume of Parallelepiped?A parallelepiped's volume is determined by multiplying its surface area by its height.
The area of the parallelogram base is the cross product's magnitude, ∥a×b∥ , according to its geometric specification, and the vector a×b direction is perpendicular to the base.
Given:
let the 8 vertices are (0,0,0), (3,0,0), (0,5,1), (3,5,1), (2,0,5), (5,0,5), (2,5,6), and (5,5,6).
so, Volume = det [tex]|\left[\begin{array}{ccc}0&3&2\\5&0&0\\1&0&5\end{array}\right] |[/tex]
= |0( 0- 0) - 3(25- 0) + 2(0 - 0)|
= |0 - 75 + 0|
= |- 75|
= 75 units
Hence, the volume of parallelepiped with 8 vertices is 75 units.
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When constructing a circle circumscribed about a triangle, what is the purpose of constructing perpendicular bisectors?
Find the length of an arc that subtends a central angle of 135° in a circle of radius 2 mi
What is the solution to the system of linear equations graphed below?
A. (3.5, -4)
B. (-4, 3.5)
C. (0,3)
D. (0,-4)
Look at the picture.
Answer: A. (3.5, -4)
Do not use spaces in your answer. If f(x) = (-x)3, then f(-3) =
Give the degree and classify the polynomial by the number of terms- 3
A)degree 1, monomial
B)degree 1, binomial
C)degree 0, monomial
D)degree 0, binomial
Answer:
Step-by-step explanation:
the answer is a
Write the standard form of the equation of the line passing through the point (2,5) and perpendicular to the line 4x - y = 2. The answer key says that the answer is x + 4y = 22, but I'm confused on how to get there
To find the perpendicular line's equation, first find the negative reciprocal of the original line's slope. Next, use the point-slope form with the given point. Lastly, rearrange the equation into standard form, resulting in x + 4y = 22.
To find the equation of a line that is perpendicular to another line and passes through a given point, you need to perform a series of steps. The first line's equation is given as 4x - y = 2. Firstly, solve for y to put it in slope-intercept form, y = mx + b. Here, the equation becomes y = 4x - 2, so the slope (m) is 4. The slope of the perpendicular line will be the negative reciprocal of this, which is -1/4.
The next step is to use the point-slope form of the line, which is y - y1 = m(x - x1), where (x1, y1) is the point through which the line passes. For the point (2,5), the equation of the line is y - 5 = -1/4(x - 2). Multiplying both sides by 4 to clear the fraction gives 4y - 20 = -x + 2.
Finally, rearrange the equation to get it into standard form, Ax + By = C, giving us x + 4y = 22. This is the standard form of the equation we were seeking.
A security fence encloses a rectangular area on one side of a park in a city. three sides of fencing are? used, since the fourth side of the area is formed by a building. the enclosed area measures 392392 square feet. exactly 5656 feet of fencing is used to fence in three sides of this rectangle. what are the possible dimensions that could have been used to construct this? area?
Is the square root of 113 rational or irrational?
Answer:
[tex]\sqrt{113}[/tex] is an irrational number.
Step-by-step explanation:
We are asked to find whether square root of 113 is rational or irrational.
We know that a number is rational number when it can be written as a fraction.
Upon finding the value of [tex]\sqrt{113}[/tex], we will get:
[tex]\sqrt{113}=10.6301458127346[/tex]
We can see that [tex]\sqrt{113}[/tex] has neither non-terminating nor a repeating decimal, therefore, it cannot be written as a fraction and it is an irrational number.
The length of a rectangle is five times its width. if the area of the rectangle is 320 feet, find its perimeter.
Suppose a simple random sample of size n is obtained from a population whose distribution is skewed right. as the sample size nâ increases, what happens to the shape of the distribution of the sampleâ mean?
As the sample size increases, the distribution of the sample mean tends to become more normal regardless of the population distribution due to the Central Limit Theorem. The mean of the sampling distribution approaches the population mean, and the standard error decreases, resulting in more reliable statistical analyses.
Effects of Increasing Sample Size on the Distribution of the Sample Mean
As the sample size n increases, the distribution of the sample mean tends to become more normal, even if the population distribution is not normal. This is a result of the Central Limit Theorem, which states that the sampling distribution of the mean approaches a normal distribution as n, the sample size, increases. According to the law of large numbers, the mean of the sample means will get closer to the population mean as sample size grows.
When the population is skewed right and we take a simple random sample, the original distribution being non-normal requires a larger sample size to make the sample mean distribution resemble a normal distribution. Generally, sample sizes equal to or greater than 30 are considered sufficient for the sampling distribution to be normal; however, if the original population distribution is further from a normal curve, a larger sample size may be needed to achieve normality.
The practical implication of this is that as sample size increases, the variability (as measured by the standard error) of the sample mean decreases, and this results in a sampling distribution that is more tightly clustered around the true population mean. Therefore, statistical analyses and predictions become more reliable with larger samples.
Candis took out a payday loan with an effective interest rate of 15,400%. if she had 220 to invest for a year at this interest rate, how much would make in interest?
A. 3,388,000
B 338,800
C.. 3388
D 33,880
To find the interest Candis would make from a 15,400% interest rate on a $220 investment for one year, we calculate using the simple interest formula, resulting in $33,880.
Explanation:The question asks us to determine how much interest Candis would make from a payday loan with an effective interest rate of 15,400% if she invested $220 for a year. To calculate the interest earned, we can use the formula for simple interest which is I = Prt, where I is interest, P is principal amount (the initial amount of money), r is the annual interest rate (in decimal form), and t is the time in years.
Converting 15,400% to a decimal, we get 154. Then, apply the formula:
I = $220 × 154 × 1
This gives us:
I = $33,880
Therefore, Candis would make $33,880 in interest after one year, which corresponds to option D.
Please help me,I need help understand so I can do my own! Worth 20 points!!
determine the slope of y=3x^2-8 at (x,y)
Human iq scores are approximately normally distributed with mean 100 and standard deviation 15. determine the minimum iq scores for the top 5% of the population.
To solve this problem, we make use of the z statistic. A population of 5% means that we are looking for the population at >95%, P = 0.95. Using the standard distribution tables for z, a value of P = 0.95 indicates a value of z of z = 1.645
Now given the z and standard deviation s and the mean u, we can calculate for the value of IQ of the top 5% (x):
x = z s + u
x = 1.645 (15) + 100
x = 24.675 + 100
x = 124.675
Therefore the minimum iq score for the top 5% of the population is around 124.675
The minimum IQ score for the top 5% of the population, with a normal distribution mean of 100 and a standard deviation of 15, is approximately 124.7. This is found by using the z-score that corresponds to the 95th percentile, which is 1.645, and applying it to the formula for a score in a normal distribution.
To determine the minimum IQ score for the top 5% of the population, given that human IQ scores are approximately normally distributed with a mean of 100 and a standard deviation of 15, we can use the properties of the normal distribution. Typically, the top 5% of values on a normal distribution lie above a certain z-score threshold. This z-score corresponds to the point on the distribution where the cumulative area to the left is 95% (100% - 5%), since we are looking for the score above which the top 5% of scores fall.
To find this z-score, we look up the value in a standard normal distribution table or use a statistical software or calculator. The z-score that corresponds to the 95th percentile is typically around 1.645. To find the actual IQ score, we can then apply the following formula:
IQ Score = Mean + (Z-score * Standard Deviation)
Plugging the values in:
IQ Score = 100 + (1.645 * 15)
IQ Score = 100 + 24.675
IQ Score = 124.675
Therefore, the minimum IQ score for the top 5% of the population is approximately 124.7 (since IQ scores are usually reported to the nearest whole number).
Find the equation of the line specified.
The slope is -7, and it passes through ( 5, -3).
a.
y = -7x - 3
c.
y = -14x + 32
b.
y = -7x + 32
d.
y = -7x - 38
Please select the best answer from the choices provided
Answer:
answer is b
Step-by-step explanation:
Graph y < 1/3x + 1/2
The Russo-Japanese War was a conflict between Russia and Japan that started in the year 1904. Let x represent any year. Write an inequality in terms of x and 1904 that is true only for values of x that represent years before the start of the Russo-Japanese War.
Find the sum of the first 100 terms in the series
[tex] \frac{1}{(1*2)} + \frac{1}{(2*3)} + \frac{1}{(3*4)} + . . . \frac{1}{n*(n+1)} [/tex]
solve for the equation for the interval [0, 2pi). sec x/2 = cos x/2
To solve sec x/2 = cos x/2, we use the identity sec(θ) = 1/cos(θ). After rearranging, we identify the solution as x = 0 and x = 2π, fitting the interval [0, 2π).
Explanation:To solve the equation sec x/2 = cos x/2 for the interval [0, 2π), we first need to understand the relationship between secant and cosine functions. Recall that sec(θ) is the reciprocal of cos(θ), thus sec(θ) = 1/cos(θ). Given the equation sec x/2 = cos x/2, we can substitute sec x/2 with 1/cos x/2 to get 1/cos x/2 = cos x/2.
Next, to solve for x, we multiply both sides by cos x/2 to get rid of the fraction: 1 = cos^2(x/2). We know that the square of the cosine function can also be related to the identity cos^2(x) = (1 + cos(2x))/2. Applying this identity, we have 1 = (1 + cos x)/2. Solving for cos x, we get cos x = 1, which occurs at x = 0, 2π in the interval [0, 2π). Therefore, the solution to the equation is x = 0 and x = 2π.
The equation sec x/2 = cos x/2 is solved by finding angles where the cosine of half the angle is either 1 or -1. This leads to solutions x = 0 and x = 2pi within the interval [0, 2pi).
Explanation:To solve the equation sec x/2 = cos x/2 for the interval [0, 2pi), we can make use of trigonometric identities to simplify and solve for x. The secant function is the reciprocal of the cosine function, so sec(x/2) = 1/cos(x/2). This leads to the equation 1/cos(x/2) = cos(x/2). Solving for cos(x/2), we get cos^2(x/2) = 1, which implies that cos(x/2) = ±1. Therefore, we're looking for angles where the cosine of half the angle is either 1 or -1. This corresponds to angles of 0, pi, and 2pi for cos(x/2) = 1, and pi for cos(x/2) = -1, remembering that we are considering x/2 and need to multiply these results by 2 to solve for x. Accordingly, the solution to the equation within the given interval is x = 0, 2pi, and 4pi (which is equivalent to 0 within one full rotation of the circle), but since we're restricting x to be within [0, 2pi), the accepted solutions are x = 0 and x = 2pi.
Carmen hiked at Yosemite national park for 1.25 hours. Her average speed was 3.9 miles per hour. How many miles did she hike? Give the exact answer- do not round!
(02.03 LC)
Read the following statement:
Line segment AB is congruent to line segment CD.
Which of the following is an equivalent statement?
AB overbar similar to CD overbar
AB overbar congruent to CD overbar
AB overbar equal to CD overbar
AB overbar element to CD overbar
Answer:
AB overbar congruent to CD overbar
Explanation:
The question is asking whether Line segment AB is CONGRUENT to line segment CD.
The meaning of congruent is having the same shape and size.
Congruent ≅
Element ∈
Equal =
Similar ~
In conclusion, you could say:
AB ≅ CD
I cannot type the lines over the top AB and CD but they are there.
(I know this question is probably old, and i am also tying this so I remember as well, but the other answer didn't have a bit bigger explanation so if anyone comes across this i hope this helped. :)
If two or more objects are the same copy in length and shape then that will be said to be congruent thus AB overbar is congruent to CD overbar and AB overbar is equal to CD overbar are the equivalent thus options (B) and (C) is correct.
What is congruence?If two figures are exactly the same in sense of their length side all things then they will be congruent.
In other meaning, if you can copy a figure then that copy and the original figure will be congruent.
All line segments are in the same shape and have degrees as one in the equation therefore only one criterion which is length is needed to prove congruency.
So, congruent lines are lines whose lengths are the same.
The sign of congruency is ≅ so AB ≅ CD.
Hence " AB overbar is congruent to CD overbar and AB overbar is equal to CD overbar are the equivalent to AB ≅ CD".
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please i need help....the question is.........
area = H/2*(b1+b2)
8.1 = 1.5/2*(6.7 +b2)
8.1=0.75*(6.7+b2)
10.8=6.7+b2
b2=10.8-6.7
b2=4.1m
HELP! Will give Brainliest! Using dimensional analysis, convert 293 cm into m. (1 m= 100 cm)
(and this is also a Chemistry Question)
I get how to work out the other question, but I'm confused on this one
The larger of two numbers is 15 less than twice the smaller number. the sum of the two numbers is 39. find the two numbers.
You are typing a paper. At 4:04pm you have typed 275 words. By 4:18pm you have 765 words. Find the rate of change in words per minute. Round your answer to the nearest whole number.
A). None of these
B). 20 words per minute
C). 43 words per minute
D). 35 words per minute
E). 55 words per minute
The rate of change in words per minute will be [tex]35[/tex] words per minute.
What is rate of change ?Rate of change is a rate that tells how one quantity changes in relation to another quantity.
i.e. Rate of change [tex]=\frac{Change\ in\ words}{Change\ in\ time}[/tex]
We have,
At [tex]4:04[/tex] pm typed [tex]275[/tex] words,
By [tex]4:18[/tex] pm you have [tex]765[/tex] words.
So,
Change in type [tex]= 4:18\ PM -4:04\ PM=14[/tex]
So,
Rate of change [tex]=\frac{Change\ in\ words}{Change\ in\ time}[/tex]
[tex]=\frac{765-275}{14}[/tex]
[tex]=\frac{490}{14}[/tex]
Rate of change [tex]=35[/tex] words per minute
So, the rate of change is [tex]35[/tex] words per minute which is given in option [tex](D)[/tex].
Hence, we can say that the rate of change in words per minute will be [tex]35[/tex] words per minute.
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A regular octagon has a radius of 6 ft and a side length of 4.6 ft. what is the approximate area of the octagon? 71 ft2 101 ft2 110 ft2 202 ft2
Answer:
Option B is correct.
The approximate area of regular octagon is, 101 square ft.
Step-by-step explanation:
Given: A regular octagon has a radius of 6 ft and a side length of 4.6 ft.
To find the area of a regular octagon(A) of side length a is given by :
[tex]A=2\cdot(1+\sqrt{2})a^2[/tex]
Given the length of side, a= 4.6 ft
Substitute the value of a=4.6 ft in the given formula of area:
[tex]A=2\cdot(1+\sqrt{2})\cdot(4.6)^2[/tex] or
[tex]A=(2+2\sqrt{2})\cdot (21.16)[/tex] or
[tex]A=(2+2.828)\cdot(21.16)[/tex]
Simplify:
[tex]A=4.828\cdot 21.16 =102.16048[/tex] square ft.
therefore, the approximate area of regular octagon is, 101 square ft
If Matrix A has dimensions 1x4 and Matrix B has dimensions 3x4, can these be multiplied?
the old price for school lunches is $5. The new price is $5.25. What is the percent increase in the cost if school lunches? Write answer as percent. The formula is p=b-a/a. b =new price for lunch. a=old price for lunch. P=percent increase
p=(5.25-5.00)/5.00
p=0.25/5.00
p=0.05
p = 5% increase