Using the Central Limit Theorem, it is found that the correct option is: C
For all samples of size 400 from this population, the mean of all resulting sample proportions of cell phone screens with a screen defect is 0.05.
By the Central Limit Theorem, for a proportion p in a sample of size n, the mean of the sampling distribution of sample proportions is u=5, while the standard error is [tex]SE=\sqrt{\frac{p*(1-p)}{n} }[/tex]
In this problem, the mean of the sampling distribution of sample proportions is 0.05, that is, the mean proportion of all samples, hence, the correct option is C.
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d 8, write the equation of the plane passing through p with normal vector n in (a) normal form and (b) general form.
The equation of the plane passing through point P with normal vector n A(x-2) + B(y-3) + C(z-4) = 0
(a) Normal Form:
The equation of the plane passing through point P with normal vector n can be written in normal form as:
n • (r - p) = 0
where r is a position vector in three-dimensional space and n is the normal vector of the plane.
Given n = (1,2,3) and p = (2,3,4).
Therefore, n • (r - p) = (1,2,3) • (r - (2,3,4)) = r1 + 2r2 + 3r3 -2 - 3 - 4 = 0
=> r1 + 2r2 + 3r3 - 8 = 0
=> Plane equation in normal form: 1x + 2y + 3z - 8 = 0
(b) General Form:
The equation of the plane passing through point P with normal vector n can also be written in general form as:
A(x-x0) + B(y-y0) + C(z-z0) = 0
where A, B and C are the components of the normal vector n and (x0,y0,z0) are the coordinates of the point p.
Given n = (1,2,3) and p = (2,3,4).
Therefore, A(x-2) + B(y-3) + C(z-4) = 0
=> 1(x-2) + 2(y-3) + 3(z-4) = 0
=> Plane equation in general form: x - 2y + 3z - 8 = 0
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Provide complete question here:Write the equation of the plane passing through p with normal vector n in (a) normal form and (b) general form.
a survey was conducted of 130 purchasers of new bmw 3 series cars, 130 purchasers of new bmw 5 series cars, and 130 purchasers of new bmw 7 series cars. in it, people were asked the age they were when they purchased their car. the following box plots display the results. which group is most likely to have an outlier?
a) The bigger the value, each box plot is spread out. The ages of the top 50% of customers are more varied than 50% of lower consumers. Hence, each plot is slanted to the right.
b) The BMW 3 series is likely to have an outlier. It has the longest whisker.
c) When comparing median age, younger people are likely to purchase the BMW 3 series and while older people are more likely to purchase the BMW 7 series. However, because each data set is so dissimilar, this is not a rule.
d) The spread is the smallest in the second quarter of the box. The difference between the first quartile and the median seems to be barely three years.
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The complete question is:
A survey was conducted of 130 purchasers of new BMW 3 series cars, 130 purchasers of new BMW 5 series cars, and 130 purchasers of new BMW 7 series cars. In it, people were asked the age they were when they purchased their car. The following box plots display the results.
a. In complete sentences, describe what the shape of each box plot implies about the distribution of the data collected for that car series.
b. Which group is most likely to have an outlier? Explain how you determined that.
c. Compare the three box plots. What do they imply about the age of purchasing a BMW from the series when compared to each other?
d. Look at the BMW 5 series. Which quarter has the smallest spread of data? What is the spread?
Marty buys 12 ounces of granola what fraction of a pound did Marty buy?
The fraction of a pound of granola that Marty bought is 3/4 pounds.
How many pounds of granola did Marty buy?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 3/4.
The unit of conversion of ounces to pounds is :
1 pound = 16
12 ounces of granola = 12/16 pounds = 3 /4 pounds
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Which of the following are multiplied by the monthly interest rate when calculating finance charges? Select all that apply.
adjusted balance
daily balance
transaction
previous balance
average daily balance
When calculating the finance charges, the monthly interest rate (MPR) is multiplied by the D. average daily balance.
How is the finance charge for credit cards determined?The finance charge refers to the interest and other fees a borrower pays on a credit card.
To compute the finance charge, the annual percentage rate (APR) or the monthly percentage rate (MPR) is multiplied by the balance owed.
The balance commonly used for this calculation is the average daily balance.
Thus, Option D is multiplied by the MPR to compute the finance charges.
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A student traveled a distance of 68 miles in 136 minutes. Which graph has a slope that best represents this rate?
The given circumstance is represented by the linear equation 2y = x, and the graph is included below.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, A student traveled a distance of 68 miles in 136 minutes.
From the general formula of a linear equation:
y = mx + c
where,
m = slope
c = y-intercept
Since At 0 minutes, he started traveling so at 0 minutes total distance he traveled is 0. So the graph will pass through origin.
Thus, the y-intercept will be zero
And Slope of the graph that passes through the origin is always the ratio of the y and x values at any point of the line.
Thu, m = 68/136
m = 1/2
Therefore, a linear equation that represents the given situation is 2y = x, and the graph is attached below.
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Complete question:
1. What’s the percentile of someone who earns $78 thousand dollars ?
2. How did you find the percentile ?
3. What does this value mean in the context of the problem ?
To find the percentile, we need to calculate what percentage of the data falls below the $78 thousand dollars wage.
What is percentile?
A percentile is a value that separates a data set into 100 equal parts.It represents the value below which a certain percentage of observations in a data set falls.For example, if a person's wage is in the 80th percentile, it means that 80% of the people in the data set earn less than that person, and 20% earn more.Percentiles can be used to summarize and describe the distribution of a set of data.They are often used in statistics and data analysis to compare values and measure the spread of data.
To find the percentile, we sort the data in ascending order and find the percentage of the data that falls below $78 thousand dollars. Here's one way to do this:
69 58 43 43 43 51 57 57 62 68 69 75 76 78 78 80 91 97 102 124 130 135 144 157 185 217
Out of 28 observations, 22 of them are below $78 thousand dollars. So, the percentile for someone who earns $78 thousand dollars is 22/28 * 100 = 78.5714.
In this context, the value of the percentile represents the percentage of the population of full-time employed people who hold at least a Bachelor's degree and earn less than $78 thousand dollars. So, someone who earns $78 thousand dollars is in the 78.5714th percentile of this population.
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Please answer this question for me
The student is trying to construct a bisector of a given Angle i.e. A.
what is a bisector?
In Geometry, a “Bisector” is a line that divides the line into two different or equal parts. It is applied to the line segments and angles. A line that passes through the midpoint of the line segment is known as the line segment bisector, whereas the line that passes through the apex of an angle is known as the angle bisector. The bisector of a segment always contains the midpoint of the segment. There are two types of bisectors based on what geometrical shape it bisects.
Line Segment Bisector (Perpendicular Bisector Theorem)
Angle Bisector (Triangle Bisector Theorem)
Now,
As we can see from the figure given that the bisector is dividing the angle in two equal segments.
Hence,
The student is trying to construct a bisector of a given Angle.
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I need help solving answer
The probability hat 1st winner lives in Guston and the 2nd living in Pikes = 3/25
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, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
1. P(E) = [Number of favorable outcomes of E]/[Total number of potential outcomes of E] is the formula for calculating an event's probability.
2. The likelihood of a given occurrence or a sure thing happening is 1.
3. There is no chance that an impossible occurrence will occur.
4. A number P(E) that has the formula 0 P(E) 1) represents the probability of an occurrence E. The probability scale is always positive.
5. If events A and B are two occurrences that can never occur together, then P(AB) = P(A) + P (B).
6. An basic event is one that has just one result. The total likelihood of such outcomes in an experiment is 1, or 1.
7. The probability of an event plus the probability of its complementary occurrence equals one. P(A) + P(A').
Total number of Customers = 10
Customers lives in Guston = 6
Customers living in Pikes = 2
Customers living in Wells = 2
Probability that 1st winner lives in Guston and the 2nd living in Pikes = 6/10 * 2/10 = 3/25
The probability hat 1st winner lives in Guston and the 2nd living in Pikes = 3/25
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report error suppose the ratio of lev's age to mina's age is $1 : 2$ and the ratio of mina's age to naomi's age is $3 : 4$. if the sum of all three ages is between $30$ and $50$, then how old is mina? note: all ages are calculated to the nearest whole year.
As per the given ratio Mina's age is 12 years old.
Ratio in math is defined as shows how many times one number contains another.
Here we have given ratio information as written as
=> Lev's age : Mina's age = 1 : 2
And the ratio between is written as
=> Mina's age : Naomi's age = 3 : 4
Here we have given the condition that the sum of all three ages is written as,
=> Lev + Mina + Naomi = 30 to 50
Here let us consider Lev's age as L, Mina's age as M and Naomi's age as N
Then the ratio is calculated as,
=> L = 1/2M
=> N = 4/3M
And the sum of all value is written as
=> L + M + N = 30 to 50
When we apply the values on it, then we get,
1/2M + M + 4/3M = 30 to 50
When we simplify it by multiply all by 6, then we get
=> 3M + 6M + 8M = 180 to 300
=> 17M = 180 to 300
Therefore, here we have to find a number between 180 and 300 that divisible by 17 and 6.
So let us consider that that number is 204.
Then the value of M is calculated as,
=> 17M = 204
=> M = 12
Complete question:
Let us consider that suppose the ratio of lev's age to mina's age is 1 : 2 and the ratio of mina's age to Naomi's age is 3 : 4. if the sum of all three ages is between 30 and 50, then how old is mina?
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Question content area top Part 1 Compare A and B in three ways, where A=52093 is the number of deaths due to a deadly disease in the United States in 2005 and B=17821 is the number of deaths due to the same disease in the United States in 2009.
In the below we have compared deaths in A and B in terms of ratio, percentage and in terms of proportion.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
The first comparison is in terms of rato.
The ratio of deaths due to a deadly disease in the United States at A and B is A : B = 17821 : 52093.
The second comparison in terms of percentage,
The percentage of people died in A is (52093/17821)×100 = 292.31% more than people died in B.
The third comparison is in terms of fractions.
The fraction of people died in A is (52093/17821) = 2.92 times more than people died in B.
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a company has offices in 3 different cities and a total of 480 workers. there are 90 workers in new york and 130 workers are in san diego. which number line represents the numbe line represents the number of workers in san diego
Using the arithmetic operation, the number of worker in San Diego is obtained as 260, and the number line which represents the same is option 1.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The number of offices are = 3
The number of workers in the company is = 480
The number of workers in New York city = 90
The number of workers in Denver city = 130
The number of workers in San Diego city = x
To find the number of workers in San Diego use the formula -
Number of workers in San Diego = Total Number of Workers - (Number of workers in New York + Number of workers in Denver)
The arithmetic operation of addition and subtraction is used.
Substitute the values into the equation -
Number of workers in San Diego = 480 - (90 + 130)
Number of workers in San Diego = 480 - 220
Number of workers in San Diego = 260
The number line which represents the number of workers in San Diego is option 1.
Therefore, the number of workers in 260.
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A company has offices in 3 different cities and a total of 480 workers. There are 90 workers in New York and 130 workers are in Denver. Which number line represents the number line represents the number of workers in San Diego?
At a grocery store, a sign says that if you buy three bottles of water, you will pay 1/4 of the regular price per bottle. Which expression shows the amount of money saved on 3 bottles of water at the regular price of d dollars? Select three correct expressions.
Answer:
Step-by-step explanation:
the fourth one
Answer:
first three answers.
Step-by-step explanation:
each bottle is 1/4d. so all three are 3*1/4d
to see if the cartons have a significantly different mean weight from 46 pounds, what would the value of the z-test statistic be? answer choices are rounded to the hundredths place.
The value of the z-test statistic = 1.16667
When told the question that a random number of samples is tested
z test statistic formula = x - x bar(x with bar above it) /Standard error
From the question
x = raw score = 46 pounds
x bar (x with bar above it)= sample mean = 45.5 pounds
Standard Error = σ/√n
Standard deviation = σ = 3
n = random number of samples = 49
z = 46 - 45.5/3/√49
z = 0.5/ 3/7
z =0.5/ 0.4285714286
z = 1.16667
Therefore, the value of the z-test statistic = 1.16667
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How do I do this I am stuck on this question please and thank you
The area of a circle is 4/pi cm. What is the circumference in centimeters express your answers in terms of pi
Answer:
4 cm.
Step-by-step explanation:
Area = pi r^2, so:
pi r^2 = 4 / pi
(pi)^2 r^2 = 4
r^2 = 4/ (pi^2)
r = 2/pi
Therefore, the circumference
= 2 pi r
= 2* pi * 2/pi
= 4
Please help me out. I Need it today
The absolute values of inequality equations totally depend on the symbols.
x+1 = 3, x = 2x+1 > 3 , x > 2 x+1 < 3 , x< 2x+1 ≥ 3 , x ≥ 2 x+1 ≤ 3, x ≤ 2What is inequality?An inequality in mathematics is a relationship that compares two numbers or other mathematical expressions in unequal absolute values. By comparing the absolute valuesof two numbers on the number line, inequality is most frequently utilized. Different types of inequality are represented by a variety of different notations, including:
The symbol a b indicates that an is less than b.
A bigger value for a than a lesser value for b is indicated by the notation a > b.
a is not equal to b in either situation. These relationships are referred to be stringent inequalities since an is either strictly less than or strictly greater than b. Equivalence is not included.
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Can someone show the steps please and thank you
y=ax+3
y=3x+5
A solution to the given system of equations include the following:
x = -2.
y = -1.
How to solve this system of equations?In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:
y = 2x + 3 .......equation 1.
y = 3x + 5 .......equation 2.
By using the substitution method to substitute equation 1 into equation 2, we have the following:
2x + 3 = 3x + 5
By re-arranging and collecting like terms, we have the following:
3x - 2x = 3 - 5
x = -2.
For the value of y, we have the following:
y = 2x + 3
y = 2(-2) + 3
y = -4 + 3
y = -1.
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3. One hundred million copper atoms are arranged in a line. Which is a reasonable estimate for the length of this line?
O
1 nanometer
1 kilometer
1 meter
1 centimeter
Answer:
D. I centimeter
Step-by-step explanation:
Since it is only 0.128 nm wide
0.128 nm x 100,000,000 =
1.28 centi meters
Answer:
D) 1 centimeter
Step-by-step explanation:
The SI base unit for length is meters (m).
The radius of a copper atom is 128 pm.
Picometer (pm) is a unit of length equal to 1 × 10⁻¹² meters.
Therefore, the radius of a copper atom in the SI base unit for length is:
[tex]\implies \sf 128 \times 10^{-12} = 1.28 \times 10^{-10}\;m[/tex]
One hundred million = 100,000,000 = 1 × 10⁸
Therefore, the length of a line of one hundred million copper atoms in meters is:
[tex]\implies \sf 1 \times 10^{8} \times 1.28 \times 10^{-10}[/tex]
[tex]\implies \sf 1.28 \times 10^{-10} \times 10^{8}[/tex]
[tex]\implies \sf 1.28 \times 10^{-10+8}[/tex]
[tex]\implies \sf 1.28 \times 10^{-2}\;\;m[/tex]
Centimeter (cm) is a unit of length equal to 1 × 10⁻² meters.
To convert meters to centimeters, divide by 1 × 10⁻²:
[tex]\implies \sf \dfrac{1.28 \times 10^{-2}}{1 \times 10^{-2}}=1.28\;cm[/tex]
Therefore, a reasonable estimate for the length of one hundred million copper atoms arranged in a line is 1 centimeter.
Find the solutions to the equation:
2x² - 10x + 15 = x
5/2 and 3 are the solutions to the equation 2x² - 10x + 15 = x.
What is equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.
Here,
2x² - 10x + 15 = x
2x² - 11x + 15 = 0
2x² -6x -5x + 15 = 0
2x(x-3)-5(x-3)=0
x=5/2, 3
The solutions to the equation 2x² - 10x + 15 = x is 5/2 and 3.
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If y varies inversely as x^2, and y=11/9 when x=9, what is y when x=3
The value of y is 11/3 when the value of x = 3
What is inverse function?
A function that returns the initial value for which a function has produced output is called an inverse function. If f(x) is a function that produces the value y, then f-1(y), which is the inverse function of y, will produce the value x. Inverse and reciprocal functions should not be confused. The output's original value is returned by the function's inverse, which is represented by the symbol f-1 (x). While the reciprocal of a function is represented by 1/f(x) or f(x)-1
Those that do are referred to as invertible. For a function f: X Y to have an inverse, it must possess the characteristic that there is exactly one x in X such that f(x) = y for every y in Y. This characteristic guarantees the existence of a function g: Y X that has the required connection to f.
If y varies inversely as x^2, and y=11/9 when x=9
when x =3,
y = 11/9 *x²
y = 11/3
Hence, the value of y is 11/3 when the value of x = 3
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The eight grade class is planning a trip to Washington, D.C. this spring. They need a minimum of 75 people to attend in order to reserve busses. If 1/3 of the 8th grade class plus 17 parent chaperones have signed up and this is enough to satisfy the requirement, how many students must be in the 8th grade class. You will need to set up an inequality and solve the inequality
174 number of students must be in the 8th grade class.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that The eight grade class is planning a trip to Washington, D.C. this spring.
They need a minimum of 75 people to attend in order to reserve busses.
1/3 of the 8th grade class plus 17 parent chaperones have signed up and this is enough to satisfy the requirement,
We need to find the number of students must be in the 8th grade class
1/3x+17≤75
Subtract 17 on both sides
1/3x≤58
x≤174
Hence, 174 number of students must be in the 8th grade class.
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Diya earned a 36 out of a possible 80 on a test. Her teacher offered extra credit that would allow Diya to double her score. What score could she earn if she completes the extra credit?
Inez finds that the area of this
figure is 9 square units. Draw unit squares to
cover this figure.
The unit square that covers the figure is attached
What is unit square?The quantity of unit squares necessary to completely cover a shape is its area.
Consequently, area is represented and measured in square units.
The attached figure shows the 9 squares that makes up the figure
Each side has 3 squares and hence
= 3 squares * 3 squares
= 9 squares
The image is attached
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Jessica makes $10 an hour babysitting. She babysat 4 hours on Friday
and 7 hours on Saturday. Write an expression and use the distributive
property to find how much Jessica made.
Equivalent Expression =
Evaluate =
An expression using the distributive property to find the earnings Jessica made on Friday and Saturday is 10(4 + 7).
What is distributive property?The distributive property postulates that multiplying the sum of two or more addends by a number gives the same result as multiplying each addend by the number and then adding the products together.
The distributive property helps to solve mathematical expressions written in the form of a(b + c).
The amount Jessica makes per hour babysitting = $10
The number of hours of babysitting on Friday = 4 hours
The number of hours of babysitting on Saturday = 7 hours
According to the distributive property, the results from 'a' and 'b' below are the same.
a) 10(4 + 7) = 40 + 70 = 110
b) 10(4 + 7) = 10 x 11 = 110
Thus, using the distributive property, Jessica will make $110 for babysitting on Friday and Saturday, notwithstanding whether process A or B was followed.
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USING SIMULATIONS TO CALCULATE ESTIMATED PROBABILITIES
3. A scientist wants to estimate the probability that a drought will happen in an area at least once over the next 4 years. The chances of a drought happening in a given year is 12%. She has generated 20 sets of 8 random numbers to help estimate the probability.
Part A: Before doing any calculations, use your intuition to predict the probability of a drought within the next 4 years if the probability of a drought in any one year is 12%. (1 point)
Scoring Notes: 1 point for any reasonable answer.
Part B: Which pairs of digits, starting at 00, represent a drought happening? Which pairs of digits, ending at 99, represent a drought not happening? (2 points)
Part C: Use the random numbers to estimate the probability that a drought happens at least once over the next 4 years. (7 points)
Part D: Is the probability that you calculated greater than or less than you predicted? Explain. (2 points)
Part E: If you change the pairs of digits that represent a drought happening so that they start at 10 instead of 00, does the estimated probability change? Calculate the estimated probability using the new ranges of numbers. (8 points)
Estimated probabilities are predictions made based on past data, trends, and patterns. They provide an idea of the likelihood that an event will occur in the future.
Calculate estimated probabilitiesPart A:
Answer: The probability of a drought within the next 4 years if the probability of a drought in any one year is 12% is approximately 48%.
Part B:
Answer: Pairs of digits starting at 00 and ending at 11 represent a drought happening. Pairs of digits starting at 88 and ending at 99 represent a drought not happening.
Part C:
Answer: Using the random numbers, the estimated probability that a drought happens at least once over the next 4 years is 68%.
Part D:
Answer: The probability that was calculated is greater than the probability predicted. This is because the sample size of 20 sets of 8 random numbers provided a more accurate and precise estimate than the intuition-based prediction.
Part E:
Answer: Yes, the estimated probability changes when the pairs of digits that represent a drought happening are changed so that they start at 10 instead of 00. Using the new ranges of numbers, the estimated probability that a drought happens at least once over the next 4 years is 64%.
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Estimated probabilities are predictions made based on past data, trends, and patterns. They provide an idea of the likelihood that an event will occur in the future.
Calculate estimated probabilitiesPredictions based on historical data, patterns, and trends are known as estimated probability. They give a sense of how likely it is that a certain occurrence will take place in the future.
Estimated probabilities calculation Part A:
If the likelihood of a drought in any given year is 12%, the likelihood that one will occur within the next four years is roughly 48%.
Part B:
Answer: The drought is represented by pairs of numerals beginning at 00 and ending at 11. A drought that is not occurring is represented by pairs of digits that begin at 88 and terminate at 99.
Part C:
According to the random numbers, there is a 68% chance that a drought will occur at least once over the next four years.
Part D:
Answer: The calculated probability is higher than the expected probability. This is due to the fact that the estimate produced by the sample size of 20 sets of 8 random numbers was more precise and accurate than the intuition-based prediction.
Part E:
Answer: When the pairs of digits that represent the occurrence of a drought are modified so that they begin at 10 instead of 00, the predicted likelihood does indeed change. According to the revised ranges of figures, there is a 64% chance that a drought will occur at least once over the next four years.
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Order the correlation coefficients from least to greatest -0.50,0.60, .98,-0.10,0.68
Answer:
-0.50, -0.10, 0.60, 0.68, 0.98
The base radius and height of a circular cone are measured as 10cm
and 25cm respectively, with a possible error in measurement of as much as 0.1cm in
each. Using linear approximation, estimate the magnitude of maximum error in the
calculated volume of the cone.
The maximum error in the volume of the cone is approximately 20π cubic centimeters.
How to determine the magnitude of maximum error in the volume of the cone
In this problem we must estimate the maximum error in the volume of the cone, based on uncertainties in radius and height of a circular cone. The volume formula for a circular cone is:
V = (π / 3) · R² · h
Where:
R - Base radius, in centimeters. h - Height, in centimeters.V - Volume, in cubic centimeters.And the maximum error formula (ΔV), in cubic centimeters, is found by total differentials:
ΔV = (dV / dR) · ΔR + (dV / dh) · Δh
Where:
(dV / dR) - First derivative of function volume respect radius, in square centimeters.(dV / dh) - First derivative of function volume respect height, in square centimeters.ΔR - Maximum uncertainty for radius, in centimeters. Δh - Maximum uncertainty for height, in centimeters.All first derivatives are shown below:
dV / dR = (2π / 3) · R · h
dV / dh = (π / 3) · R²
If we know that R = 10 cm, h = 25 cm, ΔR = 0.1 cm and Δh = 0.1 cm, then the maximum error in volume of circular cylinder is:
dV / dR = (2π / 3) · (10 cm) · (25 cm)
dV / dR = 500π / 3 cm²
dV / dh = (π / 3) · (10 cm)²
dV / dh = 100π / 3 cm²
ΔV = (500π / 3 cm²) · (0.1 cm) + (100π / 3 cm²) · (0.1 cm)
ΔV = 20π cm³
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What is the answer to this?
The distance across a circle through its center
Provide an appropriate response. From a group of 496 students, every 49th student starting with the 3rd student is selected. Identify the type of sampling used in this example, Select one: A. Cluster sampling B. Systematic random sampling C. Stratified sampling D. Simple random sampling
Systematic random sampling is used when selecting every nth item from a list of items. In this example, every 49th student starting with the 3rd student is selected.
Option B. Systematic random samplingSystematic Random Sampling of 496 StudentsIn systematic random sampling, a list of items is created and every nth item is selected for the sample. This technique is useful when selecting a representative sample from a large population of items. In the example given, 496 students were listed and every 49th student starting from the 3rd student was selected. This is a systematic random sampling technique because the items were selected in a systematic and random fashion. The selection of every 49th student starting from the 3rd student ensures that the sample is representative of the population while also randomizing it so that all students have an equal chance of being selected.
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I need help with this question please
The probability that the mean height of a random sample of 56 ten-year-old males will be greater than 53 inches is approximately 0.9991, or 99.91% when rounded to three decimal places.
What is the central limit theorem?
The central limit theorem, which states that the sample means of large samples (n > 30) from a population with any distribution approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
We can solve this problem by using the central limit theorem,
In this case, the sample size is n = 56, which is larger than 30, so we can assume that the sample means are normally distributed. The mean of the sample means is equal to the population mean, which is 55.5 inches, and the standard deviation of the sample means is equal to the population standard deviation divided by the square root of the sample size:
standard deviation = 6 / √(56) = 0.801
To find the probability that the mean height of the sample will be greater than 53 inches, we can standardize the sample mean using the standard deviation calculated above:
z = (sample mean - population mean) / (standard deviation)
= (53 - 55.5) / 0.801
= -3.12
Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is greater than -3.12:
P(Z > -3.12) = 0.9991 (rounded to four decimal places)
Therefore, the probability that the mean height of a random sample of 56 ten-year-old males will be greater than 53 inches is approximately 0.9991, or 99.91% when rounded to three decimal places.
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