Center of the sphere would be (-4.5, 1, -6) and radius be 6.086.
Write the equation of the sphere?
A sphere's general equation is (x - a)2 + (y - b)2 + (z - c) 2 = r2, where (a, b, c) represents the sphere's center, r represents the radius, and x, y, and z are the coordinates of points on the sphere's surface.
To complete the square, we need to add and subtract the square of half of the x coefficient and y coefficient, and the square of half of the z coefficient.
The equation will be : [tex](x + 9/2)^2 + (y - 1)^2 + (z + 6)^2 = (9/2)^2 + 1^2 + 6^2[/tex]
So the standard form of the equation of the sphere is,
[tex](x + 4.5)^2 + (y - 1)^2 + (z + 6)^2 = 37[/tex]
The center of the sphere is (x, y, z) = (-4.5, 1, -6) and the radius is √37 ≈ 6.086
Therefore, Center of the sphere would be (-4.5, 1, -6) and radius be 6.086.
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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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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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A study in the state of Georgia was conducted to determine the percentage of all community college students who have taken at least one online class. 1500 community college students were contacted and asked if they had taken at least one online class during their time at their community college. These responses were then used to estimate the percentage of all community college students who have taken at least one online class. Identify the population of interest in this study.
the response (Yes/No) to the question, "Have you taken at least one online class?"
the 1500 community college students contacted
the number of online classes a student has taken
all community college students in the state of Georgia
The correct answer is qualitative data, quantitative data.
Qualitative data is a type of data that describes the characteristics or attributes of a phenomenon but does not involve numbers or measurements. It is used to describe or understand the characteristics of a particular group or phenomenon.
This type of data is often used in the social sciences, such as sociology, anthropology, and psychology, but can also be used in other fields such as marketing and advertising.
Qualitative data can be analyzed in different ways, such as content analysis, thematic analysis, discourse analysis, and interpretive analysis.
Quantitative data is a type of data that involves numbers or measurements. It is used to describe or understand the characteristics of a particular group or phenomenon using numerical values or statistics.
This type of data is often used in the natural sciences, such as physics, chemistry, and biology, but can also be used in other fields such as economics, business, and engineering.
Therefore, The correct answer is qualitative data, quantitative data.
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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?
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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(Please help)Beth loves to ride her bike to go to the grocery store and go shopping. The graph below shows Beth
and her distance away from home as she does her shopping.
Choose the correct statement regarding the graph below.
Between 5:15 pm to 6:30 pm, Beth is decreasing her distance from home. Hence option c is the correct answer.
What is Distance?Distance between two points or objects can sometimes be measured qualitatively and sometimes quantitatively.
In physics, the concept of distance can refer to a physical length or, more commonly, to an approximation based on several other considerations.
The term is frequently used metaphorically to denote a measure of the degree of separation or statistical distance between two similar objects (such as edit distance between strings of text or distance between probability distributions), given that spatial cognition is a rich source of probability metaphors in human thought (as exemplified by distance between people in a social network).
Most of these literal and figurative concepts of distance are defined in terms of a mathematical idea called a metric space.
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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
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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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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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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the quotient of -100 and twice 10 is equal to -5. what is the equation
The equation that represents the quotient of -100 and twice 10 equal to -5 is; -100 ÷ 2(10) = -5
How to solve algebra expressions?The quotient of an algebraic operation is defined as a result that is obtained by dividing one quantity by another.
We are told that the quotient of -100 and twice 10 is equal to -5. Thus, we can express the given expression as;
-100 ÷ 2(10) = -5
This is because quotient means answer that is produced from dividing 2 numbers and since the product is a whole number and not a proper fraction, then it means that the larger number will be the numerator while the smaller number will be the denominator.
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K
Given the following sets, find the set (A UBUC)'.
U= {1, 2, 3, ... ,6}
A = {1, 3, 4, 6}
B={1, 2, 3)
C = {2, 3, 4, 5, 6}
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. (AUBUC)' = {}
(Use a comma to separate answers as needed. Use ascending order.)
B. (A UBUC)' is the empty set.
Answer:
Step-by-step explanation:
A. (AUBUC)' = {}
B. (A UBUC)' is the empty set.
Both options A and B express that the complement of the union of the sets A, B, and C is the empty set. The complement of a set is the set of all elements that are not in that set. The union of sets is the set of all elements that are in at least one of the sets.
When taking the union of A, B, and C all the elements in U are included, so there is no element that is not in the set, making the complement of the union of A,B,C is an empty set.
Need help with question (3)
Answer:
all
Step-by-step explanation:
all of them
What is the answer to this?
The distance across a circle through its center
Which of the following charts would be best to justify focusing on a few large problems and ignoring many smaller ones?
A Pareto diagram assists a team in focusing its efforts on the variables that have the biggest influence by separating the important few from the unimportant many. Additionally, it facilitates the team's ability to explain why specific areas are important.
The following situations call for the use of scatter plots.
In the case of paired numerical data
when more than one value of the dependent variable is associated with a particular value of the independent variable
When determining the relationships between variables, it might be helpful to look for potential problem-solving causes, see if two products that seem connected both have the same root cause, and so on.
A histogram is a graphic depiction of a frequency distribution with continuous classes that has been grouped. A series of rectangles with bases equal to the distances between class boundaries and areas proportional to frequencies in the associated classes make up the area diagram. Since the base in such representations spans the spaces between class boundaries, every rectangle is neighbouring. Rectangle heights are inversely correlated with comparable frequencies for similar classes, and inversely correlated with frequency densities for other class.
A run chart, also known as a run-sequence plot is a graph that displays observed data in a time sequence. Often, the data displayed represent some aspect of the output or performance of a manufacturing or other business process. It is therefore a form of line chart.
The complete question is :-
Which of the following charts would be best to justify focusing on a few large problems and ignoring many smaller ones?
1) run chart (2) pareto diagram
(3) histogram (4) scatter plot
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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:
Is g = 100 a solution to the inequality below? g 5 < 12
Answer:
no solution
Step-by-step explanation:
5(100)<12
500<12 false
has no solution
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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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.
What is the length of the missing side?
The length of missing side is 39.
What is define by Pythagoras theorem?Pythagoras theorem is a mathematical statement that states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the two other sides (the legs).
It can be expressed as a2 + b2 = c2, where a and b are the two legs of the triangle and c is the hypotenuse. The theorem is named after the ancient Greek mathematician Pythagoras, who is believed to have discovered it.
Pythagoras theorem is an important concept in geometry, and is used to calculate the length of the hypotenuse in a right triangle when the lengths of the other two sides are known.
It can also be used to determine the lengths of the other two sides when the length of the hypotenuse is known. In addition, it can be used to find the angles of a right triangle when the lengths of the sides are known.
Pythagoras theorem has many applications in everyday life. For example, it can be used to calculate the height of a building, or the distance between two points.
It can also be used in carpentry, engineering, and architecture to measure distances and angles. In addition, it can be used in trigonometry to find the values of trigonometric functions.
Finally, it can be used in navigation to calculate distances and angles.
Let c be the length of missing side,
According to Pythagoras theorem,
a² + b² = c²
36² + 15² = c²
c = √1521
c = 39
So, the length of missing side is 39.
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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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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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the graphs of f and g are given. use them to evaluate each limit, if it exists. (if an answer does not exist, enter dne.)
The limit will be ,lim x→2 [f(x) + g(x)] = 2 + 0 = 2
In Mathematics, a limit is defined as a value that a function approaches the output for the given input values. Limits are important in calculus and mathematical analysis and used to define integrals, derivatives, and continuity. It is used in the analysis process, and it always concerns about the behaviour of the function at a particular point. The limit of a sequence is further generalized in the concept of the limit of a topological net and related to the limit and direct limit in theory category. Generally, the integrals are classified into two types namely, definite and indefinite integrals. For definite integrals, the upper limit and lower limits are defined properly. Whereas in indefinite the integrals are expressed without limits, and it will have an arbitrary constant while integrating the function.
lim x→2 means what is the value of y as x approaches 2 from the left side and the right side - they must be the same value for the limit to exist. "Approaches" is the operative word - it does not have to exist at that y-value, as in example a. lim x→1 [g(x)] = DNE because (left side of 1) lim x→1- [g(x)] = 2 and (right side of 1) lim x→1+ [g(x)] = 1
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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?
Solve for value of e (3e-7) 101
Answer:
E = 36
Step-by-step explanation:
1. Add 7 to both sides of the equation
3e - 7 = 101
+7 +7
------------------
3e = 108
2. Isolate the variable e by dividing by 3 on both sides
[tex]\frac{3e}{3} = \frac{108}{3}[/tex]
3. Simipfy the equation
[tex]e = 36[/tex]
im completely lost on this
The domain is: a = -4, and b = 1 and the y = mx + b rule that makes the left (red) piece of the graph is given by y = -0.5x - 2.
What is domain and range?The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x).
The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set. They are the values for y.
The domain of the left (red) graph is determined using the x-coordinates of the line. The x-coordinates give the input of the function of the graph, which forms the domain.
The domain is:
a = -4, and
b = 1
Hence, the domain of the function of the graph is: -4 < x <1.
The y = mx + b is the equation of the linear function where, m is the slope and b is the point where the line intersects the y-axis.
The value of m - slope is given by:
m = (y2 - y1) / (x2 - x1)
m = (-2.5 - 0) / (1 - (-4))
m = -2.5/ 5
m = - 0.5
The value of b from the graph is:
b= -2
Substituting the values of m and b in the equation we have:
y = mx + b
y = -0.5x - 2
Hence, the y = mx + b rule that makes the left (red) piece of the graph is given by y = -0.5x - 2.
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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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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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If Darell is going to take music lessons, then he needs a trumpet. If Darell is not going to take music lessons, then he does not need a trumpet. Is the second conditional the contrapositive, converse, or inverse of the first conditional?
The statement given is showing a condition for a contrapositive statement.
What are conditional statements?Conditional statements are those statements where a hypothesis is followed by a conclusion.
Given that, If Darell is going to take music lessons, then he needs a trumpet. If Darell is not going to take music lessons, then he does not need a trumpet.
So, this is a structure of, If A then B ⇒ If not A then not B.
Which is a structure for contrapositive conditional statements.
Hence, the statement given is showing a condition for a contrapositive statement.
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A pen in the shape of an isosceles right triangle with legs of length x feet and hypotenuse of length h feet is to be built. If fencing costs $5 per feet for the legs and $10 per feet for the hypotenuse, write the total cost C of construction as a function of h.
The total cost C of construction as a function of h is:
[tex]C = \frac{10 + 5\sqrt{2}~ h^2}{h}[/tex]
As the pen is in the shape of an isosceles right angle, one of the
angle must be 90 degrees.
Also, the two sides of the triangle are equal and the base angles
are equal.
Here, x represents the length of legs of isosceles right triangle
and h be the length of hypotenuse of isosceles right triangle
Using Pythagoras theorem,
x² + x² = h²
2x² = h²
x² = h² / 2
x = [tex]\sqrt{\frac{h^2}{2} }[/tex]
So, x = [tex]\frac{h}{\sqrt{2} }[/tex]
The fencing costs $5 per feet for the legs and $10 per feet for the hypotenuse.
So, the fencing cost for the legs would be,
= 5 × (2x)
= 10x
= [tex]10\times \frac{h}{\sqrt{2} }[/tex]
= [tex]5\sqrt{2}~ h[/tex]
And the fencing cost for the hypotenuse would be,
= 10/ h
So, the total cost of fencing C would be,
[tex]C = \frac{10}{h} + 5\sqrt{2}~ h\\\\C = \frac{10 + 5\sqrt{2}~ h^2}{h}[/tex]
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