The viewing angle a of a person sitting a distance x from the front wall of a classroom with a blackboard that is 12 ft long and starts 3 ft from the wall they are sitting next to can be calculated as: a = cot-1(x/15) - cot-1(x/3)
To understand this calculation, let's consider a diagram of the classroom.
We can see from the diagram that the blackboard has length 12 ft, starting 3 ft from the wall the student is sitting next to. The student is sitting a distance x from the front wall.
The viewing angle a is the angle between the wall the student is sitting next to and the line from the student to the front wall. This angle can be calculated using the tangent of the opposite side (front wall) and adjacent side (wall the student is sitting next to).
We can therefore write: a = tan-1(12/3) - tan-1(x/3)
Simplifying this equation, we can rewrite it as: a = cot-1(x/15) - cot-1(x/3).
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Identify three points that are solutions to
each system.
The solutions for the systems of inequalities are:
a) (0, -100), (0, -150), (0, -1000)
b) (0, 50), (0, 55) , (0, 1,204).
How to identify 3 solutions of each system?When we have a system of inequalities, a solution is a point that solves both ienqualities at the same time.
The first one is:
y ≤ x - 8
y < -3x - 9
Here y must be smaller than x, then we can define x like x = 0, and really small values for y, like y = -100, replacing that we will get:
-100 ≤ 0 - 8 = -8
-100 < - 3*0 - 9 = -9
Both of these are true, so (0, -100) is a solution, and trivially, (0, -150) and (0, -1000) are other two solutions.
For the second system:
y > 5x + 1
y > 3
Let's do the same thing, x = 0 and y gets really large values, like y = 50
50 > 5*0 + 1 = 1 this is true.
50 > 3 this is true.
so (0, 50) is a solution, and also are (0, 55) and (0, 1,204).
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Divide. 8 /52.08 baba boy
Answer:
To divide 8 by 52.08, we can use long division as follows:
0.15 (quotient)
__________
52.08 | 8.00
7.81 (subtract 7.81 from 8.00 to get 0.19)
----
1.19 (bring down the next digit 0, and add a decimal point)
1.04 (subtract 1.04 from 1.19 to get 0.15)
----
0.15 (no more digits to bring down, and the remainder is 0)
Therefore, 8 divided by 52.08 is approximately 0.15.
I need some help with this
the solid is really just a right-cylinder missing a chunk.
so a full circle is 360°, now from the one in the picture above we're missing 90°, that means the cylinder is only using 270°, 360-90=270.
Well, 270° is just 3/4 of a full circle, and since the circle extends all the way down the solid cylinder, we can also say that's 3/4 of the volume of the cylinder, so hmmm let's just get the full volume of the cylinder with a radius of 6 and a height of 12 and then only grab 3/4 of it.
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=6\\ h=12 \end{cases}\implies V=\pi (6)^2(12)\implies V=432\pi \\\\\\ \stackrel{\textit{now let's just grab }\frac{3}{4}}{432\pi \cdot \cfrac{3}{4}}\implies 324\pi ~~ \approx ~~ \text{\LARGE 1017.88}[/tex]
Each side of a sandbox is 4 feet long. It will cost $2.00 per square foot to replace the sand in the sandbox. What would be the total cost to replace the sand?
Answer:
It would cost $32.00
Step-by-step explanation:
Total square feet:
length * width
4 * 4 = 16 sq ft.
Cost per square foot: $2.00
And so...
16 sq ft. * $2.00 = $32.00
What are the zeros of g(x) = x3 + 6x2 − 9x − 54?
Answer:
Solution: Given, the equation is x3 + 6x2 - 9x - 54. We have to find the real zeroes of the given equation. Therefore, the roots of the equation are +3, -3 and -6.
Help Me Find Y
Show Work
Answer:
y = 12
Step-by-step explanation:
if a tangent and a secant are drawn from an external point to a circle, then the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant , that is
y² = 8(8 + 6 + 4) = 8 × 18 = 144 ( take square root of both sides )
y = [tex]\sqrt{144}[/tex] = 12
refer to exercise 7.11. suppose that in the forest fertilization problem the population standard deviation of basal areas is not known and must be estimated from the sample. if a random sample of n = 9 basal areas is to be measured, find two statistics g1 and g2 such that p (g1 ≤ ( y - u ) ≤ g2 ) = 90
A sample of n = 9 basal areas, the two statistics, g1 and g2, such that the probability of the difference between the sample mean and population mean being between them is 90% are g1 = y - u - (1.64 * (s/sqrt(n))) and g2 = y - u + (1.64 * (s/sqrt(n))).
The goal of this exercise is to find two statistics, g1 and g2, such that the probability of the difference between the sample mean, y, and population mean, u, being between them is 90%. To do this, we will use the z-score equation to calculate the standard deviations, which we will then use to calculate the two statistics.
Given that we are using a sample of n = 9 basal areas, we can calculate the sample standard deviation s using the following equation: s = sqrt[ (1/8) * Σ (x - y)^2], where x is the individual sample value and y is the sample mean.
Once we have the sample standard deviation, we can calculate the two statistics using the following equations:
g1 = y - u - (1.64 * (s/sqrt(n)))
g2 = y - u + (1.64 * (s/sqrt(n)))
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i need help with this aleks assignment
The correct answer to this question is OU=13.7. This answer can be determined by using the Pythagorean Theorem.
What is Pythagorean Theorem?This states that the sum of the squares of the lengths of the two shorter sides of a right triangle will always equal the square of the length of the longest side, or the hypotenuse.
In this problem, the triangle created by points O, U, and V is a right triangle as OV and UW are tangent to the circle at point O. Therefore, the Pythagorean Theorem can be used to solve for OU.
OV is 6.5 and UW is 7.2. This is done by taking the square of the two legs and adding them together. (6.5)2 + (7.2)2 = OU2. Simplifying this equation, OU2 = 73.04. Taking the square root of both sides of this equation yields OU = 13.7
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The answer can be determined by using the Pythagorean Theorem which is OU=9.7.
What is Pythagorean Theorem?This states that the sum of the squares of the lengths of the two shorter sides of a right triangle will always equal the square of the length of the longest side, or the hypotenuse.
In this problem, the triangle created by points O, U, and V is a right triangle as OV and UW are tangent to the circle at point O.
Therefore, the Pythagorean Theorem can be used to solve for OU.
OV= 6.5
UW= 7.2.
(6.5)² + (7.2)² = OU²
Simplifying this equation,
OU² = 94.09.
Taking the square root of both sides of this equation yields
OU = 9.7
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The mass of a car is 2006 kg rounded to the nearest kilogram. The mass of a person is 62.2 kg rounded to 1 decimal place.. Write the error interval for the combined mass, m, of the car and the person in the form a ≤m
The error interval for the combined mass, m, of the car and the person is: [tex]$$2067.65 kg \leq m \leq 2068.75 kg$$[/tex].
How to find error interval?The mass of the car is given as 2006 kg rounded to the nearest kilogram, which means its actual mass could be as low as 2005.5 kg or as high as 2006.5 kg.
The mass of the person is given as 62.2 kg rounded to one decimal place, which means their actual mass could be as low as 62.15 kg or as high as 62.25 kg.
To find the error interval for the combined mass of the car and the person, we need to add the upper and lower bounds of each mass:
Lower bound of combined mass: 2005.5 kg + 62.15 kg = 2067.65 kg
Upper bound of combined mass: 2006.5 kg + 62.25 kg = 2068.75 kg
Therefore, the error interval for the combined mass, m, of the car and the person is: [tex]$$2067.65 kg \leq m \leq 2068.75 kg$$[/tex].
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#1 Brainlist!
Answer and show steps and I will make you brainlist.
Answer:
Multiplying the second equation by 5, we get:
15x + 20y = 180
Now, we can add this equation to the first equation:
26x = 208
x = 8
Substituting x = 8 in the second equation:
3(8) + 4y = 36
4y = 12
y = 3
Therefore, the solution to the system is (8, 3).
the length of the diagonal of a square is 12 cm what is the length of which side
A company has 6000 arrivals of Internet traffic over a period of 13,710 thousandths of a minute. Let the random variable x represent the number of such Internet traffic arrivals in one thousandth of a minute. It appears that these Internet arrivals have a Poisson distribution. If we want to use the formula P(x)= μx•e−μ x! to find the probability of exactly 3 arrivals in one thousandth of a minute, what are the values of μ, x, and e that would be used in that formula?
The parameters to the Poisson distribution, to find the probability of exactly 3 arrivals in one thousandth of a minute, are given as follows:
μ = 6000/13719.x = 3.e = 2.71828.What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are listed and explained as follows:
x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval or range of values of the input parameter.A company has 6000 arrivals of Internet traffic over a period of 13,710 thousandths of a minute, hence the mean of the distribution is given as follows:
μ = 6000/13719.
The parameter x represents the number of arrivals in each thousandth of a minute, hence it is given as follows:
x = 3.
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hich of the these are steps for a proof by mathematical induction that P(n) is true for all positive integers n? a. Verify that P(1) is true. b. Demonstrate that the conditional statement Plk) implies Plk+1) is true for all positive integers k. c. Verify that P(1), P(2), P(3), ..., P(k) are all true, where k is a specific large, positive integer. d. Demonstrate that if P(k) is false, then Plk+1) is false for all positive integers k. e. Demonstrate that P(k+1) implies plk) is true for all integers k.
The steps for proof by mathematical induction that P(n) is true for all positive integers n, All options are true.
The steps for a proof by mathematical induction that P(n) is true for all positive integers n are as follows:
a. Verify that P(1) is true.
b. Demonstrate that the conditional statement Plk) implies Plk+1) is true for all positive integers k.
c. Verify that P(1), P(2), P(3), ..., P(k) is all true, where k is a specific large, positive integer.
d. Demonstrate that if P(k) is false, then Plk+1) is false for all positive integers k.
e. Demonstrate that P(k+1) implies Plk) is true for all integers k.
Therefore, option (a), option (b), option (c), option (d), and option (e) are the steps for proof by mathematical induction that P(n) is true for all positive integers n.
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All the students in the sixth grade either purchased their lunch or brought their lunch from home on Monday.
• 24% of the students purchased their lunch.
• 190 students brought their lunch from home.
How many students are in the sixth grade?
The number of students that are in the sixth grade is given as follows:
250 students.
How to obtain the number of students?The number of students is obtained applying the proportions in the context of the problem.
We know that all students in the sixth grade either purchased their lunch or brought their lunch from home on Monday, and 24% of the students purchased their lunch, hence 76% of the students brought their lunch from home.
190 students brought their lunch from home, which is equivalent to 76% of the number of students, hence the number of students is given as follows:
0.76n = 190
n = 190/0.76
n = 250 students.
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The owner of a sports complex wants to carpet a hallway connecting two buildings. The carpet costs $2.50 per square foot. How much does it cost to carpet the hallway?
Therefore, it will cost $510 to carpet the hallway.
What is area?Area is a mathematical concept that describes the size of a two-dimensional surface. It is a measure of the amount of space inside a closed shape, such as a rectangle, circle, or triangle, and is typically expressed in square units, such as square feet or square meters. The area of a shape is calculated by multiplying the length of one side or dimension by the length of another side or dimension. For example, the area of a rectangle can be found by multiplying its length by its width. The concept of area is used in many fields, including mathematics, geometry, engineering, and architecture. It is an important measure for determining the amount of material needed to cover a surface, such as carpet or paint, and is used in a wide variety of real-world applications.
Here,
To find the cost of carpeting the hallway, we need to know the total area of both trapezoids in square feet. Let's assume that the trapezoids have parallel sides of length 16 and 18 feet, and a height of 6 feet.
The area of each trapezoid is given by the formula:
Area = (1/2) x (sum of parallel sides) x height
For the first trapezoid, the sum of parallel sides is 16 + 18 = 34 feet. Therefore, the area of the first trapezoid is:
Area1 = (1/2) x (16 + 18) x 6
Area1 = 102 square feet
For the second trapezoid, the sum of parallel sides is also 16 + 18 = 34 feet. Therefore, the area of the second trapezoid is:
Area2 = (1/2) x (16 + 18) x 6
Area2 = 102 square feet
The total area of both trapezoids is:
Total Area = Area1 + Area2
Total Area = 102 square feet + 102 square feet
Total Area = 204 square feet
Now that we know the area of the hallway, we can calculate the cost of carpeting it. We're told that the carpet costs $2.50 per square foot, so we can multiply the area of the hallway by the cost per square foot to find the total cost:
Total Cost = Area x Cost per square foot
Total Cost = 204 square feet x $2.50 per square foot
Total Cost = $510
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A veterinarian has an annual income of $128,610. The income tax the veterinarian has to pay is 8%. What is the amount of income tax in dollar and cents the veterinarian has to pay?
the veterinarian has to pay $10,288.80 in income tax. To calculate the amount of income tax that the veterinarian has to pay, we can multiply their annual income by the tax rate. In this case, the tax rate is 8%, so we can calculate the income tax as follows:
Income tax = Annual income x Tax rate
Income tax = $128,610 x 0.08
Income tax = $10,288.80
Therefore, the veterinarian has to pay $10,288.80 in income tax.
Income tax is a tax imposed on income earned by individuals or businesses. The tax rate may vary depending on the income level, the type of income, and the tax laws of the country. In this case, the tax rate is 8%, which means that the veterinarian has to pay 8% of their annual income as income tax.
It's important to note that income tax is usually paid on a regular basis, such as monthly or quarterly, throughout the year. The amount of income tax paid is based on the estimated income for the year, and at the end of the year, the actual income and tax liability are calculated, and any overpayments or underpayments are reconciled.
In conclusion, the veterinarian has to pay $10,288.80 in income tax based on their annual income of $128,610 and a tax rate of 8%.
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10) When Perry Person got a paycheck, Perry went shopping. He spent $26 on a shirt and twice as much on jeans. Then he spent half of what he had left on a snack. On his way home, he found $10 and ended up with $ 24. How much was Perry's paycheck ?
Perry's paycheck was $100. To find Perry's paycheck, we can work backward from the final amount he had after finding $10 and ending up with $24.
Let's denote Perry's paycheck as "x". After buying the shirt and jeans, he spent a total of $26 + $52 = $78. So he had "x" - $78 left. He then spent half of what he had left on a snack, leaving him with 1/2 * ("x" - $78) = 1/2*x - $39.
When he found $10, he ended up with $24, so we can set up the equation:
1/2*x - $39 + $10 = $24
Simplifying this equation gives us:
1/2*x = $53
Multiplying both sides by 2, we get:
x = $106
Therefore, Perry's paycheck was $100.
In summary, we used a series of calculations to work backward from the final amount Perry had to determine his original paycheck. We accounted for the amount he spent on a shirt, jeans, and a snack, as well as the amount he found on his way home.
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PLS HELP GEOMETRY 15 POINTS
polygon ABCD is similar to polygon ZYXW list the relationship between angles and sides
Answer:
Step-by-step explanation:
sorry I don't know
A chemist has 20% and 50% solutions of acid available. How many liters of each solution should be mixed to obtain 600 liters of 21% acid solution?
[tex]x=\textit{Liters of solution at 20\%}\\\\ ~~~~~~ 20\%~of~x\implies \cfrac{20}{100}(x)\implies 0.2 (x) \\\\\\ y=\textit{Liters of solution at 50\%}\\\\ ~~~~~~ 50\%~of~y\implies \cfrac{50}{100}(y)\implies 0.5 (y) \\\\\\ \textit{600 Liters of solution at 21\%}\\\\ ~~~~~~ 21\%~of~600\implies \cfrac{21}{100}(600)\implies 126 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{lcccl} &\stackrel{Liters}{quantity}&\stackrel{\textit{\% of Liters that is}}{\textit{acid only}}&\stackrel{\textit{Liters of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&x&0.2&0.2x\\ \textit{2nd Sol'n}&y&0.5&0.5y\\ \cline{2-4}&\\ mixture&600&0.21&126 \end{array}~\hfill \begin{cases} x + y = 600\\\\ 0.2x+0.5y=126 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=600}\implies x=600-y \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.2(600-y)+0.5y=126}\implies 120-0.2y+0.5y=126 \\\\\\ 120+0.3y=126\implies 0.3y=6\implies y=\cfrac{6}{0.3}\implies \boxed{y=20} \\\\\\ \stackrel{\textit{since we know that}}{x=600-y}\implies \boxed{x=580}[/tex]
The equation and graph show the distance traveled by a covertible and a limousine in miles, y, as a function of time in hours, x.
The rate of change of the distance for limousine is less than the rate of change of the convertible.
What is rate of change?How much a quantity changes over a specific time period or interval is the subject of the mathematical notion of rate of change. Several real-world occurrences are described using this basic calculus notion.
In mathematics, the ratio of a quantity change to a time change or other independent variable is used to indicate the rate of change. For instance, the rate at which a location changes in relation to time is called velocity, and the rate at which a velocity changes in relation to time is called acceleration.
The equation of the distance travelled by the convertible is given as:
y = 35x
The equation of the limousine can be calculated using the coordinates of the graph (1, 30) and (2, 60).
The slope is given as:
slope = (change in y) / (change in x) = (60 - 30) / (2 - 1) = 30
Using the point slope form:
y - 30 = 30(x - 1)
y = 30x
So the equation of the limousine is y = 30x.
Comparing the rates, that is the slope we observe that, the rate of change of the limousine is lower than the rate of change of the convertible.
Hence, the rate of change of the limousine is less than the rate of change of the convertible.
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The probability that Mary will win a game is 0.03, so the probability that she will not win is 0.97. If Mary wins, she will be given $60; if she loses, she must pay $3. If X = amount of money Mary wins (or loses), what is the expected value of X? (Round your answer to the nearest cent.)
The expected value of X is -$1.11. This means that on average, Mary can expect to lose $1.11 per game.
The probability that Mary will not win is 0.97; hence, the probability that she will win is 0.03.
Probability:Probability is the likelihood of an event happening. It is a way of measuring the chance or the likelihood of an event occurring. Probability is measured on a scale from 0 to 1, where 0 is impossible and 1 is certain.
Probability = (number of favorable outcomes) / (total number of outcomes)
Expected value:The expected value is the sum of the products of each outcome and its probability. It represents the average value that one can expect to win from a game by placing a bet on that game.
In a game where the probability of winning is 0.03 and the probability of losing is 0.97,
Mary will win $60 if she wins and lose $3 if she loses.
Then, the expected value of X (the amount of money Mary wins or loses) can be calculated as:
E(X) = (0.03)($60) + (0.97)($-3)
E(X) = $1.80 - $2.91E(X) ⇒ $-1.11
The expected value of X is -$1.11 (a negative value).
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After randomly selecting 1,009 adults and surveying each of them, 545 of them indicated that they were not comfortable with a drone delivering packages to them. The pollster concluded from the data that precisely 54 percent of all American adults are therefore not comfortable having drones make deliveries to them.
Determine whether the pollster’s conclusion makes sense. Address whether the pollster is correct in drawing this conclusion based upon the given information. In preparing your answer, include the following terms:
statistics and parameters,
estimation,
margin of error,
and any other concepts from the assigned readings and/or class sessions you deem helpful and appropriate.
Based on the information, the pollster's conclusion makes sense.
How do you know if the pollster is right with his conclusion?To know if the pollster is right with his conclusion we must perform the following operation.
1,009 / 100 = 10.0910.09 * 54 = 544.86In accordance with the above, we can infer that the pollster concludes that 54% of the people surveyed are equivalent to 545 people correctly because 0.86 is a minimum margin of error for this type of statistics. In addition, it can be inferred that the pollster correctly uses the statistics and study parameters of a sample to establish a correct conclusion.
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which of the following is true about the regression line? o it's an estimation of a linear relationship between dependent and independent variables by assuming the minimum error term it's just a straight line drawn through the data points between x and y axis.o it provides the actual value of a dependent variable for a given value of the independent variable(s)o it indicates a linear relationship between dependent variable and independent variable(s) o it provides the estimation of the value of a dependent variable for a given value of the independent variable(s)
The statement about regression line that is true is "it indicates a linear relationship between dependent variable and independent variable(s)."
In statistics, regression is a method of modeling the connection between a dependent variable (also known as a response variable) and one or more independent variables (also known as explanatory variables or predictors). It's also known as a linear regression model.
A regression model is established in order to identify the linear relationship between the dependent variable and one or more independent variables. The line of best fit is represented by the regression line in a simple linear regression model, which represents the relationship between the dependent variable and independent variable(s).
The line of best fit is determined by minimizing the sum of the squares of the residuals (errors). The objective of the regression model is to obtain a relationship between the dependent variable and the independent variable that explains the variance of the dependent variable based on the independent variable(s).
Hence, the correct option is: it indicates a linear relationship between dependent variable and independent variable(s).
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Mr Hall's salary increases from £25,000 to £28,000 a year. Find the percentage increase in his salary.
Answer:
Step-by-step explanation:
To find the percentage increase in Mr Hall's salary, we can use the following formula:
percentage increase = (new value - old value) / old value x 100%
Substituting the given values, we get:
percentage increase = (28000 - 25000) / 25000 x 100%
Simplifying the expression, we get:
percentage increase = 0.12 x 100%
percentage increase = 12%
Therefore, Mr Hall's salary increased by 12%.
Help I need help fast.
The new points A', B', and C' after rotating triangle ABC 90 degrees counterclockwise about the origin and reflecting it over the x-axis are (-3,1), (0,3), and (2,4) respectively.
How rotate and reflect a point?
To rotate a point in a two-dimensional plane counterclockwise about the origin by a certain angle θ, we can use the rotation matrix. This matrix has the values of sine and cosine of the angle θ and can be used to multiply with the original point's coordinate vector to get the new coordinate vector after rotation. To reflect a point over the x-axis, we negate its y-coordinate.
Calculation the coordinates of the new points :
To rotate triangle ABC 90 degrees counterclockwise about the origin, we can use the rotation matrix:
[ cosθ -sinθ ]
[ sinθ cosθ ]
where θ is the angle of rotation, in this case 90 degrees, so we have:
[ 0 -1 ]
[ 1 0 ]
We can apply this matrix to each of the points of the triangle ABC to obtain their new coordinates after the rotation.
Then, to reflect the triangle over the x-axis, we simply negate the y-coordinate of each point.
So, to find the new points A', B', and C', we perform the following operations:
A' = (1, -3) * [ 0 -1 ] = [ (-3) (-1) ] -> reflect over x-axis -> [ (-3) 1 ]
[ 1 0 ]
B' = (3, 0) * [ 0 -1 ] = [ 0 (-3) ] -> reflect over x-axis -> [ 0 3 ]
[ 1 0 ]
C' = (4, -2) * [ 0 -1 ] = [ 2 (-4) ] -> reflect over x-axis -> [ 2 4 ]
[ 1 0 ]
Therefore, the new points are (-3,1), (0,3), (2,4).
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Answer: give proper question
Step-by-step explanation:
Caris has a carton of 12 eggs, two of which have brown shells while the rest have white shells. Caris randomly chooses a brown egg from the carton. Which of the following statements is true? If she rejects this egg, returns it to the carton, and randomly picks again, these will be dependent events. If she uses this egg in a recipe and picks another one from the carton, these will be dependent events. Whether or not these are dependent or independent events depends on what color egg Caris chooses next. If she uses this egg in a recipe and picks another one from the carton, these will be independent events.
Answer:
Step-by-step explanation:
i think you have to times it
Pablo's is a popular Mexican restaurant, known especially for its homemade salsa. During dinner last night at Pablo's, 7 tables of people ordered chips and salsa for every 2 tables that did not.
Answer: =84
Step-by-step explanation:
I need help please help me
Answer:
54 sq in.
Step-by-step explanation:
For a cube, try using the rectangular prism formula. (there's an easier way but I prefer this one)
2lw + 2hw + 2lh
(2 × 3 × 3) + (2 × 3 × 3) + (2 × 3 × 3)
18 + 18 + 18 + 18
SA = 54 sq in
hope i explained it (you can search up the formula for a cube but i like this one)
A pharmaceutical company produces caffeine pills that are each supposed to contain 200mg of caffeine. A plant that produces thousands of these pills per batch took an SRS of 15 pills from their latest batch to see if they contained the proper amount of caffeine. The sample data had a mean of 200.4mg of caffeine per pill with a standard deviation of 0.8mg. The amounts were roughly symmetric with no outliers. Based on this sample, which of the following is a 95% confidence interval for the mean amount of caffeine (in mg) per pill in this batch?
options
200.4±1.96(0.8)
200±1.96(0.8/sqrt(15))
200.4±1.96(0.8/sqrt(15))
200.4±2.145(0.8/sqrt(15))
200±2.145(0.8/sqrt(15))
The correct answer is 200.4 + 2.145(0.8/sqrt(15)).
We may use the following calculation to determine the confidence interval for the average caffeine content per tablet in this batch:
Confidence interval = sample mean + (critical value) x (standard error)
The crucial number in this situation is 1.96 since we want a 95% confidence interval. Since the sample size is 15, and the standard deviation is 0.8, the standard error is 0.8/sqrt(15). Here is what we get after entering these values:
Confidence interval = 200.4 + 1.96(0.8/sqrt(15))
The result of computing this expression is:
Confidence interval = 200.4 + 0.347
We achieve by simplifying:
Confidence interval = 200.4 + 2.145(0.8/sqrt(15))
As a result, the right response is 200.4 + 2.145(0.8/sqrt(15)).
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Answer:
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