Mean and median measures of central tendency would be affected if the outlier 11 was added to the data set.
As per the given data, the data set is 27, 20, 34, 37, 21, 42, and 39.
Mean of the data is the sum of all observations divided by the total number of observations.
Mean = [tex]$\frac{27+20+ 34+ 37+ 21+ 42+ 39}{7}[/tex]
Mean = [tex]$\frac{220}{7}[/tex]
Mean = 31.42
The median of the data for an odd number of observations is the middlemost term.
First, arrange the data in ascending order.
20, 21, 27, 34, 37, 39, 42
Middlemost term = 34.
The mode of the data is the most repeated data.
As no number is repeated there will be no mode.
As given 11 is added to the data set.
Mean = [tex]$\frac{27+20+ 34+ 37+ 21+ 42+ 39+11}{8}[/tex]
Mean = [tex]$\frac{231}{8}[/tex]
Mean = 28.8
The median of the data for an even number of observations is the average of the middle two terms.
First, arrange the data in ascending order.
11, 20, 21, 27, 34, 37, 39, 42
Median = [tex]$\frac{27+34}{2}[/tex]
Median = [tex]$\frac{61}{2}[/tex]
Median = 30.5
For the new data set also there will be no mode as there are no repeated numbers.
Comparing old and new values there is a change in the values of mean and median.
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9. Construct Arguments Katya measured
the growth of a plant seedling. The
seedling grew inch by the end of the
first week and another inch by the end
of the second week. About how much did
6
the seedling grow in the first 2 weeks?
Explain how you made your estimate.
The total growth of the plant in 2 weeks is 7/6 inches.
What are fractions?A fraction is defined as a piece of a whole. The complete could be a single thing or a group of objects. The component reflects the percentage of the cake when we really cut a slice of cake from the whole cake. Latin is where the word "fraction" originates.
Given plant grew in the first week = 1/3 inch
the plant grew in the second week = 5/6 inch
total growth in 2 weeks = 1/3 + 5/6
1/3 is equivalent to 2/6 with same diameter,
total growth in 2 weeks = 2/6 + 5/6
total growth in 2 weeks = 7/6 inches
Hence the total growth is 7/6 inches.
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The correct question is,
Katya measured the growth of a plant seedling. The seedling grew 1/3 inch by the end of the first week and another 5 / 6 inch by the end of the second week. About how much did the seedling grow in the first 2 weeks? Explain how you made your estimate.
What is the mass in grams of 0. 450 moles of magnesium sulfate, MgSO4?
grams
Your answer should be rounded to three significant figures. Do not include units in your answer.
The mass in grams of 0. 450 moles of magnesium sulfate, MgSO4 in grams is 54.2.
The mole, which is 6.0221023 molecular entities, is the basic unit of a substance. One mole of a substance is equivalent to that substance's molecular weight.
The link between moles and molar mass means that the quantity of moles in a material is equal to the product of its mass and molecular mass.
The molar mass of magnesium sulphate is:
Magnesium = 24
Oxygen = 16 x 4 = 64
Sulphate = 32
Thus, the mass of magnesium sulphate is = 24 + 64 + 32 = 120 grams.
Now, moles is equal to:
Moles = given mass/molecular mass
Putting the values:
moles = given mass / 120
0.450 x 120 = given mass
Given mass = 54g.
Thus, the given mass of the magnesium sulphate is 54 g.
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What is the derivative of the natural log of y?
The derivative of the natural log of y is (1/y)(dy/dx). The derivative is performed with respect to x.
What is a natural logarithm?
A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equal to 2.718281828459.
Given function is log y.
The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's fundamental tool is the derivative.
Generally derivative or the changes of the function is found with respect to x.
Assume that
z = log y
Differentiate with respect to x:
dz/dx = d(log y)/dx
Applying the formula of drivative d(ogx)/dx = 1/x:
dz/dx = (1/y)(dy/dx)
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Determine whether an observational study or an experimental study is used.A survey of high school students was conducted to see if students who take advanced classes are offered more scholarship money than students who do not take advanced classes
It is used the observational study. A survey of high school students was conducted to see if students who take advanced classes are offered more scholarship money than students who do not take advanced classes
Now, According to the question:
"Information available from the question"
A survey of high school students was conducted to see if students who take advanced classes are offered more scholarship money than students who do not take advanced classes
Statisticians often refer to the "levels of measurement" of a variable, a measure, or a scale to distinguish between measured variables that have different properties. There are four basic levels: nominal, ordinal, interval, and ratio.
In an observational study, we measure or survey members of a sample without trying to affect them. In a controlled experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive the treatment.
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it is known that the average number of pushups a u.s marine does daily is 300 with standard deviation of 50. a random sample of 49 marines is selected. a) the population of interest is [ select ] the parameter of interest is [ select ] the value of the parameter is [ select ] b) if is the sample mean number of pushups a u.s. marine does, since [ select ] , the central limit theorem holds and [ select ] , [ select ] ) c) the probability that the sample mean is less than 292 is [ select ] .
To solve we need to calculate the z-score, but since we are given the sample size then we shall begin as follows:
The z-score is calculated as (320 - 300)/(50/6) = 2.4, which means that the value of 320 is 2.4 standard deviations above the population mean of 300. Using a standard normal table or calculator, we can find the probability that a standard normal random variable is less than 2.4, which is approximately 0.9918.
This means that the probability that the sample mean is greater than 320 is approximately 0.9918. In other words, there is a 99.18% chance that a randomly selected sample of 36 U.S. Marines will have a mean number of pushups greater than 320.
μ=300, σ=50, n=36, x=320
So,
σ/√n
= 50/√36
= 8.33333
z=(320-300)/8.33333
z=2.4
Therefore,
P(x>320)=P(z<2.4)=0.9918.
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21.1.4 Quiz: Thinking Chronologically
Question 5 of 5
Which timeline correctly organizes the founding of important world religions?
O A
B.
О с.
O D.
World Religions
Christianity was founded about 2,000 years ago.
• Islam was founded about 1,400 years ago.
.
Hinduism was founded about 3,500 years ago.
.
• Buddhism was founded about 2,500 years ago.
• Judaism was founded about 4,000 years ago.
·
← PREVIOUS
Buddhism
Judaism
Christianity
Hinduism
Judaism
Buddhism
Judaism
Islam
Christianity
Christianity
Islam
Christianity
Islam
Islam
Hinduism
Judaism
The timeline which correctly organizes the founding of important world religions are;
Judaism, Buddhism, Christianity, and Islam
The correct answer choice is option B.
Which timeline correctly organizes important world religion?Chronological order is the order of events from the first to the last.
Christianity was founded about 2,000 years ago.
Islam was founded about 1,400 years ago.
Hinduism was founded about 3,500 years ago.
Buddhism was founded about 2,500 years ago.
Judaism was founded about 4,000 years ago
Arrangements from the first to the last;
JudaismHinduismBuddhismChristianityIslamTherefore, the important world religions are in the order; Judaism, Hinduism, Buddhism, Christianity and Islam.
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45°
11√2
11
y
45°
(11√2)/2
022
Find y.
11√2
Answer:
Step-by-step explanation:
it is the pink one
Find the length of the third side. If necessary, round to the nearest tenth.
Answer: 10
Step-by-step explanation:
a2 + b2 =c2
(5 x 5) + (9 x 9) = c2
25 + 81 = 106
Root of 106 = 10.295630141
Round to the nearest tenth
a jar contains three red, five green, two blue, and six yellow marbles. what is the ratio of red to green to blue to yellow marbles?
The ratio of red to green to blue to yellow marbles is, 3 : 5 : 2 : 6
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Give that,
A jar contains,
three red, five green, two blue, and six yellow marbles
the ratio of red to green to blue to yellow marbles = ?
The ratio can be written as,
⇒ 3 : 5 : 2 : 6
Hence, the ratio of balls is 3 : 5 : 2 : 6
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there are 7 people from the computer science (cs) department and 5 people from the math (m) department that could serve on a 4-person committee. a. find the number of different combinations if there are no restrictions on whom could serve on the committee. b. find the probability that the only people serving on the committee are from the cs department.
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The probability is equal to the variety of possible outcomes. the total number of outcomes that could occur. For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.Given data :
a )
There are 7 people from the CS department and 5 people from the math (M) department who could serve on the committee, so there are a total of 12 people.
department that could serve on a 4-person committee
b) probability that the only people serving on the committee are from the cs department :
The general probability formula can be expressed as: Probability = Number of Favorable Outcomes / Total Number of Outcomes. or. P(A) = f / N
= 5 / 7
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An object travels along a horizontal path at a constant rate. The object travels 1/20 of the length of the path in 3/4 seconds. At that rate, how many seconds does it take the object to travel the entire length of the path?
Number of seconds it takes the object to travel the entire length of the path is 15 seconds.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Given that, the object travels 1/20 of the length of the path in 3/4 seconds.
1/20 is a tiny portion of the length that needs to be traveled.
20/20 is the whole length.
If 1/20 gets traveled in 3/4 of a second, multiply 3/4 by 20.
That is, 20(3/4) = 15 seconds
Therefore, number of seconds it takes the object to travel the entire length of the path is 15 seconds.
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factorise 3y^2+10y-8
Answer:
(3y-2)(y+4)Ω
Step-by-step explanation:
real simple
a factory produces plate glass with a mean thickness of 4 mm and a standard deviation of 1.1 mm. a simple random sample of 100 sheets of glass is to be measured, and the sample mean thickness of the 100 sheets x is to be computed. we know the random variable x has approximately a normal distribution because of the group of answer choices law of large numbers. central limit theorem. law of proportions. fact that probability is the long run proportion of times an event occurs. normality of the population distribution.
Using a standard normal distribution table or a z-table gives us
P(¯Z≤0.8181)≈0.20662
Let us write down some of the parameters and statistics that are given in the question.
Population mean thickness
μ=4mm.
Population standard deviation
σ=1.1mm.
Random sample size
n=100.
Let the random normal variable
¯X denote the average thickness of the sample.
Then according to the Central Limit Theorem,
¯X
follows a normal distribution with mean
μ¯X=μ=4
and standard deviation
σ¯X=σ√n=1.1√100=1.110=0.11.
Then we can convert ¯X
into its standard normal form ¯Z
using the following transformation:
¯Z=¯X−μ¯Xσ¯X=¯X−40.11(1)
Now the question reads that we need the probability that the average thickness of the 100 sheets is less than 3.91 mm. In other words, we need
P(¯X<3.91).
Using (2) we get
P(¯X<3.91)=P(¯Z<3.91−40.11)=P(¯Z≤0.8181)(3)
Using a standard normal distribution table or a z-table gives us
P(¯Z≤0.8181)≈0.20662
which is our answer.
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Using a standard normal distribution table or a z-table gives us
P(¯Z≤0.8181)≈0.20662
Let us write down some of the parameters and statistics that are given in the question.
Population mean thickness
μ=4mm.
Population standard deviation
σ=1.1mm.
Random sample size
n=100.
Let the random normal variable
¯X denotes the average thickness of the sample.
Then according to the Central Limit Theorem,
¯X
follows a normal distribution with mean
μ¯X=μ=4
and standard deviation
σ¯X=σ√n=1.1√100=1.110=0.11.
Then we can convert ¯X
into its standard normal form ¯Z
using the following transformation:
¯Z=¯X−μ¯Xσ¯X=¯X−40.11(1)
Now the question reads that we need the probability that the average thickness of the 100 sheets is less than 3.91 mm. In other words, we need
P(¯X<3.91).
Using (2) we get
P(¯X<3.91)=P(¯Z<3.91−40.11)=P(¯Z≤0.8181)(3)
Using a standard normal distribution table or a z-table gives us
P(¯Z≤0.8181)≈0.20662
which is our answer.
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What is 45 divided by 3 using long division?
45 divided by 3 is 15. The solution has been obtained by using long division.
What is long division?
When splitting huge numbers, the task is divided into several sequential steps using the long division approach. The dividend is divided by the divisor, just like in conventional division problems, and the result is known as the quotient; occasionally, it also produces a remainder.
Using long division, we get
1 5
3 | 45
- 3 (Multiplying 3 by 1, we get 3)
1 5 (Bringing down the next number of the dividend)
- 1 5 (Multiplying 3 by 5, we get 15)
0
Hence, 45 divided by 3 is 15.
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Consider a random sample of size 32 from a distribution with mean 40 and variance 8. find the (approximate) probability that the sample mean is between 39.75 and 41.25.
The probability that the sample mean is between 39.75 and 41.25 is approximately 0.5987.
The probability that the sample mean is between 39.75 and 41.25 can be calculated using the Central Limit Theorem. This theorem states that the distribution of the sample means will be normally distributed with a mean equal to the population mean (μ = 40) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (σ = 8/√32).
Using this information, we can calculate the probability that the sample mean is between 39.75 and 41.25, which will be the area under the normal curve between those two points. This area can be calculated using the z-score formula, which is (x-μ)/σ = (41.25-40)/(8/√32). This gives us a z-score of 0.25. The probability can then be calculated using a z-table, which is approximately 0.5987. Therefore, the probability that the sample mean is between 39.75 and 41.25 is approximately 0.5987.
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[tex]z^{9} x z^{6} / z^{7}[/tex]
Step-by-step explanation:
when multiplying factors of the same base, we can simply add the exponents.
when dividing, we subtract.
so,
z⁹xz⁶/z⁷ = xz^(9+6-7) = xz⁸
The shortest side of a right triangle is 7.2 centimeters long and the longest side is 15.5 centimeters long.
What is the length, to the nearest tenth of a centimeter, of the third side? (1 point)
Answer: 15.5^2 - 7.2^2 = 240.25 - 51.84= 188.41
188.41 square root is 13.7262522197 or 13.7
Step-by-step explanation: Hope this helps!! :))
A package containing 12 electrical locks, each with a unique key, must be delivered to 16 job
site superintendents. How many unique keys will result from the distribution?
180
The total number of unique keys after the distribution will be 48.
When the package containing 12 electrical locks is delivered to 16 job site superintendents, each superintendent will receive 3 locks. This means that the total number of locks will be 16 * 3 = 48
When the locks are distributed, each superintendent will receive 12/16 = 3/4 of a lock. This means that each superintendent will receive 3 locks.
Since each lock comes with a unique key, the total number of unique keys after the distribution will also be 48.
It is important to note that each lock is unique and comes with its own key, so even though the locks are being distributed among 16 superintendents, the number of unique keys will remain the same, which is 48.
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Calculate the measures of spread for Mrs. Hampton’s class data. Justify your response by describing the process used to find each measure. 20 points for who ever answers
To calculate the measures of spread for Mrs. Hampton's class data, you need to calculate the range, interquartile range (IQR), variance, and standard deviation.
The range is the difference between the highest and lowest values. To calculate the IQR, you must first find the quartiles of the data set.
The variance is the sum of the squared difference between each data value and the mean, divided by the number of data values. Finally, the standard deviation is the square root of the variance. To justify your response, you can explain how each of these measures of spread can provide insight into the data set, such as showing the spread of values or the degree of variation.
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determine the value of s , the arc length (measured in inches) cut off in a circle with a radius of 8 inches by an angle with a measure of 2.4 radians.
Answer:
19.2 inches
Step-by-step explanation:
The arc length,s, can be calculated using the formula s=r*c, where r is the radius of the circle and c is the central angle in radians. So, for a circle with a radius of 8 inches and a central angle of 2.4 radians, the arc length would be s=8 inches*2.4 radians =19.2 inches
The arc length s cut off by an angle with a measure of 2.4 radians in a circle with a radius of 8 inches is 19.2 inches.
What is the arc length?
Arc length is a measure of the distance along a curved line segment of a circle or a curve. It represents the length of a portion of the circumference of a circle, or the distance between two points on a curved line. In mathematical terms, it is defined as the integral of the magnitude of the velocity vector along the curve. The formula for the arc length of a circle depends on the radius r and the central angle θ (measured in radians) that cuts off the arc. It is given by
s = r * θ
In this case, the radius r is 8 inches, and the central angle θ is 2.4 radians. Plugging in these values, we get:
s = 8 * 2.4 = 19.2 inches
Hence, the arc length s cut off by an angle with a measure of 2.4 radians in a circle with a radius of 8 inches is 19.2 inches.
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To bake a cake, 750g of flour i added to 250 of butter and 300g of ugar. F
ind the ratio of (a) butter to flour (b) flour to ugar (c) butter to ugar
If 500 grams of flour are used, 166.66666 grams of sugar must be added, followed by 200 grams of sugar.
What is meant by ratios?When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage.
A ratio is a tool for comparing like-kind quantities or illustrating relationships between them. To compare similar items, we employ ratios.
Two numbers or measurements are compared to form a ratio. The quantities being compared are referred to as the terms of the ratio. A ratio divides two amounts into equal parts, with the dividend or antecedent serving as the unit of comparison and the divisor or unit of comparison serving as the unit of comparison.
To make a cake, I combined 750g of flour, 250g of butter, and 300g of sugar.
a) 250/750 = 1/3 = 1 : 3
b) 750/300 = 15/6 = 5/2 = 5 : 2
c) 250/300 = 5/6 = 5 : 6
If 500 grams of flour are used, 166.66666 grams of sugar must be added, followed by 200 grams of sugar.
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A survey of 225 students showed the mean number of hours spent studying per week was 20. 6 and the standard deviation was 2. 7. Assuming a 90% confidence level, the margin of error is approximately a 4-column table has 2 rows. The first column has entries confidence level (percentage), z-score. The second column has entries 90, 1. 645. The third column has entries 96, 1. 96. The fourth column has entries 99, 2. 58.
The true mean study time is likely between 19.6 and 21.6 hours per week .The higher the confidence level, meaning that we can be more sure that the true mean study time is within the given range.
The margin of error is an important statistic that helps measure the accuracy of a survey. It is calculated by multiplying the standard deviation by the z-score for the given confidence level. A 90% confidence level has a z-score of 1.645, a 96% confidence level has a z-score of 1.96, and a 99% confidence level has a z-score of 2.58. Using this information, the margin of error for a survey of 225 students with a mean study time of 20.6 and a standard deviation of 2.7 is approximately 1.0. This means that the true mean study time is likely between 19.6 and 21.6 hours per week. The higher the confidence level, the higher the margin of error, meaning that we can be more sure that the true mean study time is within the given range.
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-36 = 3/4n and 2/3h + 14 = 18 I don’t know how to solve
Answer: n= -48 and h=6
Step-by-step explanation:
For the first one,
-36=3/4 n.
So, divide both sides by 3/4.
-36/(3/4)= -48.
Plug into original equation to double check the answer is -48.
3/4(-48)= -36
For the second one, 2/3h +14= 18
subtract 14 from both sides.
2/3h= 4
Now, divide both sides by 2/3 to get you h=6.
Same as the first one, plug into the original equation. h is in fact 6! yay!
A buhel of apple weight about 42 pound there are four pack in a buhel it take 2 lb of apple to make one pie how many pie can you make with one pack of apple
The number of pies made by 1 peck of apples is 5.25.
What is the Unitary method?
A quantity's unit value must first be determined in order to solve a problem for two different quantities of the quantity. The unitary approach is the name of this technique.
Due to that,
One bushel of apples weighs 42 pounds.
There are four pecks in a bushel.
Additionally, two pounds of apples are needed to produce one pie.
The following unitary method can be used to tackle the provided problem:
One peck weighs 42/4, or 10.5 pounds.
Since one pie only requires two pounds.
Pie can be made from 1 pound.
Therefore, 10.5 pounds or one peck can yield 5.25 pies (10.5 0.5).
Thus, 5.25 pies can be made from one peck of apples.
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A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance traveled is 75.897 miles.
Part A: How many miles did the hiker travel on the first day? Round your answer to the nearest mile and show all necessary math work. (4 points)
Part B: What is the equation for Sn? Show all necessary math work. (3 points)
Part C: If this pattern continues, what is the total number of miles the hiker will travel in 10 days? Round your answer to the hundredths place and show all necessary math work. (3 points)
a) The hiked 8 miles on first day.
b) The Equation is [tex]S_7 = a_1(r^7 -1)[/tex]/(r -1)
c) 127.49 miles the hiker will travel in 10 days
What is Sequence?A sequence is defined as an arrangement of numbers in a particular order. On the other hand, a series is defined as the sum of the elements of a sequence.
Given:
The sequence of distances is a geometric sequence with first term a1 and common ratio (1 +10%) = 1.10.
and, The sum of 7 terms of the sequence is ...
So,
[tex]S_7 = a_1(r^7 -1)[/tex]/(r -1)
75.897= [tex]a_1(1.1^7 -1)[/tex]/(1.1 -1)
[tex]a_1[/tex]= 7.99999
[tex]a_1[/tex]= 8
So, hiker hiked 8 miles on first day.
b) The Equation is of the form of Geometric Sequence
[tex]S_7 = a_1(r^7 -1)[/tex]/(r -1)
c) For n= 10 days
[tex]S_{10}= a_1(r^{10} -1)[/tex]/(r -1)
= [tex]8(1.1^{10} -1)[/tex]/(1.1 -1)
= 127.49 miles
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6 1/2 divided by 2 1/4
Answer:
26/9 or 2 8/9
How do you use the mean absolute deviation to compare data sets?
When comparing sets, a higher mean absolute deviation denotes a greater degree of dispersion of the data points from the mean and vice-versa.
What is mean absolute deviation?
The ratio of the sum of all absolute values of deviation from the central measure to the total number of observations is known as the mean absolute deviation.
We find the mean of the data set first, then use that value to calculate the mean absolute deviation of the data.
The mean absolute deviation reveals how dispersed or concentrated a group of data is around the mean. This is the data's variation.
When comparing sets, a higher mean absolute deviation denotes a greater degree of dispersion of the data points from the mean. Data points are more closely packed around the mean when the mean absolute deviation is lower.
Hence, this way the mean absolute deviation is used to compare data sets.
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Please help trying to answer it can be with or without step with step
How do you write 37% as a decimal?
Answer:
0.37
Step-by-step explanation:
37% = 37/100 = 0.37
Solve this trigonometry problem