The largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9 has dimensions x = 1.5, y = 1, and z = 2.25, with a maximum volume of 3.375 cubic units.
To find the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9, we can use the method of Lagrange multipliers.
Let the sides of the rectangular box be represented by the variables x, y, and z. We want to maximize the volume V = xyz subject to the constraint x + 3y + 4z = 9.
The Lagrangian function is then given by L = xyz + λ(x + 3y + 4z - 9).
Taking the partial derivatives of L with respect to x, y, z, and λ, and setting them equal to zero, we get:
yz + λ = 0
xz + 3λ = 0
x*y + 4λ = 0
x + 3y + 4z - 9 = 0
Solving these equations simultaneously, we get:
x = 1.5, y = 1, z = 2.25, and λ = -0.5625
Therefore, the maximum volume of the rectangular box is V = 1.512.25 = 3.375 cubic units.
To learn more about coordinate planes
https://brainly.com/question/13611766
#SPJ4
a confidence interval for a population mean was reported to be to . if , what sample size was used in this study? (round your answer up to the next whole number.)
The sample size cannot be determined from this information alone. A confidence interval for a population mean is calculated based on the mean of a sample, the sample size, and the standard deviation.
What is deviation?Deviation is the difference between the expected value or average of a set of data and the actual value. For example, if the average of a set of numbers is 10 and one of the numbers is 15, the deviation of that number is 5. Deviation is a measure of how much variation exists in a set of data. It is an important tool used to measure the accuracy of a data set and identify outliers within that data set. Deviation is also used to measure the volatility of a stock or other investment, which is a measure of how much its price changes over time.
Therefore, to determine the sample size, the mean, standard deviation, and confidence interval of the sample must all be known.
To learn more about deviation
https://brainly.com/question/12402189
#SPJ1
The sample size cannot be determined from this information alone. A confidence interval for a population mean is calculated based on the mean of a sample, the sample size, and the standard deviation.
What is deviation?Deviation is the difference between the expected value or average of a set of data and the actual value. For example, if the average of a set of numbers is 10 and one of the numbers is 15, the deviation of that number is 5. Deviation is a measure of how much variation exists in a set of data. It is an important tool used to measure the accuracy of a data set and identify outliers within that data set. Deviation is also used to measure the volatility of a stock or other investment, which is a measure of how much its price changes over time.
Therefore, to determine the sample size, the mean, standard deviation, and confidence interval of the sample must all be known.
To learn more about deviation
brainly.com/question/12402189
#SPJ1
Complete Question:
A 95% confidence interval for a population mean was reported to be 152 to 160. If s 15, what sample size was used in this study?
Corey is ready to begin the process of producing his final animation. Unfortunately,
his computer does not have the power to render the final scene, so he outsources
the render to a computer that will execute the function. What method allows him to
do this?
(1 point)
O image sequences
Obatch render
O net rendering
O multi-passing
Net rendering is a method of rendering a computer-generated animation or image on multiple computers over a network.
Net rendering is a method of rendering a computer-generated animation or image on multiple computers over a network. This technique allows a user to take advantage of the computing power of multiple computers to render a scene. To do this, the user would divide the scene into several parts, assigning each part to a different computer. The computers would then render each part of the scene independently, and then the results are combined into a single image. This process can significantly reduce the time required to render a scene, as the workload is distributed over multiple computers. For example, if it would normally take a single computer 10 minutes to render a scene, net rendering could reduce that time to 2 minutes.
Learn more about significantly here:
https://brainly.com/question/14789537
#SPJ1
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500
Answer:
The following statements about Josiah's solution are true:
He found the proportion of rock songs to the total number of songs correctly: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction.
He solved the proportion correctly: StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction.
He correctly determined that the number of rock songs on his MP3 player is 300 (x = 300).
Therefore, the statements that are true are:
He found the proportion of rock songs to the total number of songs correctly.
He solved the proportion correctly.
He correctly determined that the number of rock songs on his MP3 player is 300 (x = 300).
a study was conducted on students from a particular high school over the last 8 years. the following information was found regarding standardized tests used for college admitance. scores on the sat test are normally distributed with a mean of 990 and a standard deviation of 201. scores on the act test are normally distributed with a mean of 21.6 and a standard deviation of 4.1. it is assumed that the two tests measure the same aptitude, but use different scales.If a student gets an SAT score that is the 70-percentile, find the actual SAT score. SAT score = _____ Round answer to a whole number. What would be the equivalent ACT score for this student? ACT score = ____Round answer to 1 decimal place.If a student gets an SAT score of 1536, find the equivalent ACT score. ACT score = ____ Round answer to 1 decimal place.
We are given that the SAT and ACT measure the same aptitude but use different scales. To find the equivalent ACT score for a given SAT score, we can use the conversion chart.
SAT 1100 = ACT 23
Therefore, the equivalent ACT score for a student with an SAT score of 1104 is 23.
3. If a student gets an SAT score of 1536, find the equivalent ACT score.
Solution:
To find the equivalent ACT score for a given SAT score, we can use the conversion chart.
SAT 1536 = ACT 35
Therefore, the equivalent ACT score for a student with an SAT score of 1536 is 35.
Therefore, the SAT score = 1536 and the ACT score = 35.
1. If a student gets an SAT score that is the 70th percentile, find the actual SAT score.
Solution:
We are given that SAT scores are normally distributed with a mean of 990 and a standard deviation of 201. We are asked to find the SAT score for the 70th percentile.
P( SAT score < X) = 0.70
We can use the standard normal table to find the corresponding z-score for the 70th percentile.
z = 0.52
We can use the z-score formula to find the SAT score:
z = (X - μ) / σ
0.52 = (X - 990) / 201
X = 1103.72
Therefore, the actual SAT score for the 70th percentile is 1104.
2. What would be the equivalent ACT score for this student?
for such more questions in standard normal
https://brainly.com/question/30492671
#SPJ11
what is the surface area of a cube if all sides are equal to 2
(EMERGENCY) I need to know how exponents work
Answer:
Exponents are a mathematical notation used to represent repeated multiplication. An exponent, also known as a power, consists of a base number and a small superscript number, which indicates how many times the base number should be multiplied by itself.
For example, in the expression 2^3, the base number is 2 and the exponent (or power) is 3. This means that 2 should be multiplied by itself three times: 2 x 2 x 2 = 8. So, 2^3 is equal to 8.
Exponents can also be negative or fractions. In these cases, the negative exponent indicates division and the fraction exponent indicates taking a root.
For instance, in the expression 2^-3, the negative exponent means that 2 is in the denominator of a fraction: 1/2 x 1/2 x 1/2 = 1/8. So, 2^-3 is equal to 1/8.
In the expression 4^(1/2), the fraction exponent means that we take the square root of 4: 2 x 2 = 4. So, 4^(1/2) is equal to 2.
Exponents have many practical applications in science, engineering, and other fields. They can be used to represent large or small quantities, as well as to simplify complex mathematical expressions.
Step-by-step explanation:
Will give brainlest to first correct answer!!!
Evelyn has a bag that contains 3 red marbles and 2 blue marbles.
Evelyn randomly pulls a marble from the bag and then puts it back in the bag. She repeats this 20 times. How many times should she expect to draw a red marble from the bag?
27y/y^2-1• y^2+y/36y^2 state the product in simplest form
The product of the two expressions can be simplified to -1/2(y-1).
Let's first focus on the expression 27y/(y²-1). This expression has a denominator that is a difference of squares, which we can factor as (y+1)x(y-1). We can then use partial fraction decomposition to rewrite the expression as follows:
27y/(y²-1) = (A/(y+1)) + (B/(y-1))
Multiplying both sides by (y+1)x(y-1), we get:
27y = Ax(y-1) + Bx(y+1)
We can then solve for A and B by setting y = 1 and y = -1, respectively. This gives us:
A = -9 B = 9
Substituting these values back into our partial fraction decomposition, we get:
27y/(y²-1) = (-9/(y+1)) + (9/(y-1))
Now let's focus on the expression (y²+y)/(36y²). We can factor out a y from the numerator and denominator to get:
y(y+1)/(36yxy)
We can then simplify this expression by cancelling out the y's:
(y+1)/36
Now that we have simplified each expression separately, we can multiply them together.
(27y/(y²-1)) x ((y²+y)/(36y²)) = ((-9/(y+1)) + (9/(y-1))) x ((y+1)/36)
We can distribute the second expression and simplify:
=> ((-9y)/(y+1) + (9y)/(y-1)) x ((y+1)/36) = ((-9y)(y-1) + (9y)(y+1)) / (36x(y²-1))
=> (-9y² + 9y - 9y² - 9y) / (36x(y²-1)) = (-18y² - 18y) / (36x(y²-1))
=> (-1/2)x(y+1)/(y-1)(y+1) = -1/2(y-1)
To know more about expression here
https://brainly.com/question/14083225
#SPJ4
What is an equation of the line that passes through the point (5,1) and is parallel to
the line x +y = 9?
The line x + y = 9 is y = -x + 6 is keeps through the point (5,1).
To find the equation of the line that passes through the point (5,1) and is parallel to the line x + y = 9, we need to first find the slope of the line x + y = 9.
Rearranging the equation in slope-intercept form, we get y = -x + 9
The slope of this line is -1, since the coefficient of x is -1.
Since the line we want to find is parallel to this line, it will have the same slope of -1.
Using the point-slope form of a line, the equation of the line passing through the point (5,1) and with a slope of -1 is: y - 1 = -1(x - 5)
Simplifying and rearranging the equation, we get:
y - 1 = -x + 5
y = -x + 6
To know more about equation of line:
https://brainly.com/question/29453867
#SPJ4
5 points on a graph for the equation 2^x+5 +1
I already know the asymptote is 1.
Answer:
When x = 0, y = 2^0 + 6 = 7. So the first point is (0, 7).
When x = 1, y = 2^1 + 6 = 8. So the second point is (1, 8).
When x = 2, y = 2^2 + 6 = 10. So the third point is (2, 10).
When x = -1, y = 2^-1 + 6 = 6.5. So the fourth point is (-1, 6.5).
When x = -2, y = 2^-2 + 6 = 6.25. So the fifth point is (-2, 6.25)
help please and fast due today
Therefore, the area of the whole figure is 60170 square centimeters.
What is area?Area is a measurement of the amount of space inside a 2-dimensional shape, such as a rectangle, triangle, circle, or any other polygon. It is usually measured in square units, such as square inches, square feet, square meters, etc. The formula for finding the area of a shape depends on the type of shape. For example, the area of a rectangle is calculated by multiplying its length by its width, while the area of a circle is calculated by multiplying the square of its radius by pi (3.14).
Here,
To find the area of the whole figure, we need to find the area of the triangle and the area of the rectangle, and then add them together.
The area of the triangle can be found using the formula:
Area of triangle = (1/2) x base x height
where base is the length of one side of the triangle (2 cm) and height is the altitude (1.7 m). We need to convert the altitude to centimeters to match the units of the base:
1.7 m = 170 cm
So, the area of the triangle is:
Area of triangle = (1/2) x 2 cm x 170 cm = 170 cm²
The area of the rectangle is simply:
Area of rectangle = length x width = 2 m x 3 m = 6 m²
Now, we can add the two areas together to get the total area of the figure:
Total area = Area of triangle + Area of rectangle
= 170 cm² + 6 m²
Since the units are different, we need to convert one of them to match the other. Let's convert the area of the rectangle from meters to centimeters:
6 m² = 60000 cm²
Now, we can add the two areas together:
Total area = 170 cm² + 60000 cm²
= 60170 cm²
To know more about area,
https://brainly.com/question/13194650
#SPJ1
find the number of outcomes in the complement of the given event. out of 344 high school students in their senior year, 175 are left-handed.
There are 169 outcomes in the complement of the given event.
To find the number of outcomes in the complement of the given event, which is that out of 344 high school students in their senior year, 175 are left-handed, you need to follow a few steps. So, let's get started. To find the number of outcomes in the complement of the given event, you will first find the total number of students that are right-handed, which can be found by subtracting the number of left-handed students from the total number of students:344 - 175 = 169Therefore, there are 169 right-handed students.
Next, to find the number of outcomes in the complement of the given event, you will need to subtract the number of outcomes in the given event from the total number of possible outcomes. Since the number of possible outcomes is equal to the total number of students, the number of outcomes in the complement of the given event can be found by subtracting the number of left-handed students from the total number of students:344 - 175 = 169 Therefore, there are 169 outcomes in the complement of the given event.
Learn more about Complement
brainly.com/question/13058328
#SPJ11
Rob decided to play a card game with his friend, Travis. He told Travis that if he picked a black card with a value of nine or greater, Travis would win. (Jacks, queens, and kings are considered to be greater than nine.) If Rob picked a red card with a value of less than nine, Rob would win. (Aces are considered to have the value of one in this case.)
A. What is the probability that Travis will win?
B. What is the probability that Rob will win?
C. According to the definition in the introduction to this lesson, is this a fair game? Why or why not?
This is not a fair game, because the probabilities of Travis winning and Rob winning are not equal. If the game were fair, the probabilities would be equal.
What is probability?The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability theory is used in various fields, including statistics, economics, engineering, physics, and finance, among others, to analyze and make predictions about uncertain events.
According to question:A. To find the probability that Travis will win, we need to count the number of black cards with a value of nine or greater, and divide that by the total number of cards in the deck. There are 26 black cards in the deck, and 12 of them are worth nine or greater (four each of jacks, queens, and kings). So the probability that Travis will win is 12/52, or 3/13.
B. To find the probability that Rob will win, we need to count the number of red cards with a value of less than nine, and divide that by the total number of cards in the deck. There are 26 red cards in the deck, and 20 of them are worth less than nine (the sixes, sevens, and eights, plus the four aces). So the probability that Rob will win is 20/52, or 5/13.
C. This is not a fair game, because the probabilities of Travis winning and Rob winning are not equal. If the game were fair, the probabilities would be equal.
To know more about probability visit:
https://brainly.com/question/30034780
#SPJ1
Write the expression in complete factored
form.
3p(a - 1) - 2(a - 1)
Help!
Answer:
(a - 1)(3p - 2)
Step-by-step explanation:
3p(a - 1) - 2(a - 1) ← factor out (a - 1) from each term
= (a - 1)(3p - 2)
Algebra help please!
In response to the stated question, we may state that As a result, the function student will have to pay off the debt in 24 weeks.
what is function?In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.v
a. Let L(w) be the monetary amount owing after w weeks.
Because the starting amount owing is $360 and the weekly payment is $15, the equation for the amount owed as a function of time is: L(w) = 360 - 15w
b. The inverse function of L(w) reflects the number of weeks required to repay a certain loan amount. In terms of L, we can solve for w:
L = 360 - 15w
L - 360 = -15w
w = (360 - L)/15
As a result, the inverse function is: L(-1)(w) = (360 - w)/15.
c. 0 = 360 - 15w
15w = 360 = 24
As a result, the student will have to pay off the debt in 24 weeks.
To know more about function visit:
https://brainly.com/question/28193995
#SPJ1
HHHHEEEEELLLPPPPPP
Solve for x. using the tangent lines.
50 deg
X
x =[?]^
from the given circle having tangents, the value of x is 130°.
What does a tangent line mean?A line that touches a curve at one point, y = f(x), is said to be the curve's tangent line. (x0, y0). The point at which it is drawn is substituted into the derivative f'(x) to find its slope (m), and y - y0 = m is used to find its equation. (x - x0).
In geometry, a tangent is a straight line that touches a curve or a surface at a single point, without intersecting it at that point. In the case of a curve, the tangent line at a point on the curve has the same slope as the curve at that point.
In trigonometry, the tangent is a mathematical function that relates the angles of a right triangle to the ratio of the length of the opposite side to the length of the adjacent side.
From the given figure,
We know that
50 + AB = 180
AB = 180 - 50
AB = 130
The value of x or arc AB is 130°.
To know more about tangent visit:-
brainly.com/question/19064965
#SPJ1
If Jacob spent 45$ on dinner and wanted to top the waitress 15%, which of the following would be a good estimate for the tip?
Answer: 6.75
Step-by-step explanation:
45 x 0.15= 6.75
If the sample space S is an infinite set, does thisnecessarily imply that any random variable X defined from S willhave an infinite set of possible values? If yes, say why. If no,give an example.
No, it does not necessarily imply that any random variable X defined from S will have an infinite set of possible values.
For instance, consider a random variable X that takes values from the set of natural numbers S = {1, 2, 3, ...}. We can define X as follows: X(n) = n for any n ∈ S.
Although S is an infinite set, X can only take values in S, which is also an infinite set, but not a larger one. Therefore, X has a countable (finite or infinite) set of possible values.
In general, the set of possible values of a random variable depends on how the variable is defined and not just on the size of the sample space.
For more questions like Variable click the link below:
https://brainly.com/question/17344045
#SPJ11
17. Find the average rate of change of f(x) over the interval [-2,1]
The rate of change between these two points is 28/3.
What role does the rate of change have in mathematics?A key idea in mathematics is the rate of change, which defines how quickly one variable changes in relation to another. From physics and engineering to economics and social sciences, it is used to explain a broad variety of occurrences. Calculus gives a means to calculate the instantaneous rate of change at any given moment by using the derivative of a function as the rate of change. Several practical applications, such as forecasting population increase, simulating the behaviour of a physical system, or streamlining a production process, depend on an understanding of the rate of change.
The coordinates of the point for the interval [-2, 1] is (-2, 4) and (1, 32).
The rate of change is the slope between the two points. Thus,
m = (y2 - y1) / (x2 - x1)
m = (32 - 4) / (1 - (-2)) = 28 / 3
Therefore, the rate of change between these two points is 28/3.
Learn more about rate of change here:
https://brainly.com/question/12786410
#SPJ1
please me on this two colummn proof.
As a result, the triangles and are similar triangles according to the meaning of similarity. Thus, the Angle-Angle Similarity Principle has been demonstrated.
what is triangle ?Three straight edges and three angles make up a closed, two-dimensional triangle. By joining three non-collinear lines, it is created. One of the most fundamental geometric shapes, triangles are used in many disciplines, including physics, engineering, and construction. According to their edges and angles, triangles can be classified as equilateral, isosceles, scalene, acute, obtuse, or right triangles.
given
Take into account two triangles Z and T such that ZT ZX and ZUZY. We must demonstrate the similarity of these two shapes.
We are aware that if two triangles are similar, their respective sides and angles will be proportional.
Now, let's prove that the respective sides of these two triangles are proportional. Since ZT ZX, the respective sides of similar triangles result in TZ/ZX = TU/ZY. If we simplify this number, we obtain:
TU/ZX Equals TZ/ZY.
This demonstrates that the ratio between the respective sides of these two triangles.
As a result, the triangles and are similar triangles according to the meaning of similarity. Thus, the Angle-Angle Similarity Principle has been demonstrated.
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ1
The complete question is :- Write a proof of the Angle-Angle Similarity Theorem.
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Given: ZT ZX, ZUZY
Prove: Δτυν - ΔΧΥΖ
Dilate XYZ by the scale factor
Andrea took out a loan to start a business. She borrowed $30,000 for 3 years. If the loan has a maturity value of $34, 275, what
interest rate was Andrea charged on the loan? Round the percent to 2 decimal places.
4.75%
4.50%
4.00%
4.25%
The loan's interest rate, which is [tex]0.475[/tex] percent or [tex]4.75[/tex]%, is imposed by Andrea.
What are interest rates on average?An interest rate provides information on how costly lending is or how profitable saving is. Hence, if you are a borrower, an interest rate refers to the total you pay for borrowing money and is expressed as a proportion of the total loan amount.
Is a high interest rate beneficial?Borrowing money is more expensive when rates of interest are elevated and less expensive when rates of interest are low. Be sure you fully understand how the rate of interest will impact the entire amount you have to pay before accepting a loan.
maturity value [tex]=[/tex] principal [tex]+[/tex] (principal [tex]*[/tex] interest rate [tex]*[/tex] time)
maturity value [tex]= 34,275[/tex]
principal [tex]= 30,000[/tex]
time [tex]= 3[/tex] years
So we have:
[tex]34,275 = 30,000 + (30,000 * interest rate * 3)[/tex]
Simplifying this equation, we get:
[tex]34,275 - 30,000 = 9,000 *[/tex] interest rate
[tex]4,275 = 9,000[/tex] [tex]*[/tex] interest rate
interest rate [tex]= 4,275 / 9,000[/tex]
interest rate [tex]= 0.475[/tex]
Therefore, the interest rate charged on the loan is [tex]0.475[/tex] or [tex]4.75[/tex]%.
To know more about interest rate visit:
https://brainly.com/question/14120268
#SPJ1
find the equation of the line with the given properties. express the equation in general form or slope intercept form. perpendicular to the line -4x+y=43 ; contains the point (-8,10)
The equation of the required line in slope-intercept form is y = -1/4x + 8.
Here are the steps to find the equation of the line:
Step 1: Find the slope of the given line in slope-intercept form
y = mx + c
-4x + y = 43 ⇒ y = 4x + 43... (1)
Here, the slope (m1) of the given line is 4.
Step 2: Find the slope of the required line as the two lines are perpendicular to each other.
m1 × m2 = -1
[As the given line and the required line are perpendicular to each other]
4 × m2 = -1 ⇒ m2 = -1/4
So, the slope (m2) of the required line is -1/4.
Step 3: Write the equation of the required line in point-slope form.
y - y1 = m(x - x1)
[Using the point-slope formula]
Let (x1, y1) = (-8, 10)m = -1/4
Putting the values in the above formula, we get
y - 10 = -1/4(x - (-8)) ⇒ y - 10 = -1/4(x + 8)... (2)
Step 4: Simplify the above equation to get the required equation of the line in slope-intercept form.
y - 10 = -1/4x - 2 ⇒ y = -1/4x + 8... (3)
You can learn more about slope and intercept at: brainly.com/question/30216543
#SPJ11
Solve for x and graph the solution on the number line below
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
check 5 greater than or equal to (y-2)
Answer: 5 ≥ y-2 is equivalent to y ≤ 7.
Step-by-step explanation: To check if 5 is greater than or equal to y-2, we need to isolate the variable y on one side of the inequality sign.
5 ≥ y - 2
First, we can add 2 to both sides to get rid of the subtraction of 2 on the right side:
5 + 2 ≥ y - 2 + 2
7 ≥ y
Therefore, we can see that y is less than or equal to 7 for this inequality to hold true.
a quality-conscious disk manufacturer wishes to know the fraction of disks his company makes which are defective. step 2 of 2 : suppose a sample of 1015 1015 floppy disks is drawn. of these disks, 904 904 were not defective. using the data, construct the 95% 95 % confidence interval for the population proportion of disks which are defective. round your answers to three decimal places.
Therefore, the 95% confidence interval for the population proportion of disks that are defective is (0.8357, 0.9475). This means that there is a 95% probability that the true population proportion of disks that are defective is between 0.8357 and 0.9475.
The quality-conscious disk manufacturer can use a 95% confidence interval to estimate the fraction of defective disks made by the company. The 95% confidence interval is calculated using the sample data to construct an interval estimate of the population proportion.
Using the given data, the sample proportion of disks that are not defective is 904/1015 = 0.8915.
The 95% confidence interval for the population proportion of disks that are defective is then given by:
Lower limit = 0.8915 – (1.96 x √(0.8915 x (1- 0.8915)/1015))
= 0.8915 – (1.96 x 0.0285)
= 0.8915 – 0.0558
= 0.8357
Upper limit = 0.8915 + (1.96 x √(0.8915 x (1- 0.8915)/1015))
= 0.8915 + (1.96 x 0.0285)
= 0.8915 + 0.0558
= 0.9475
For such more questions on probability
https://brainly.com/question/24756209
#SPJ11
When the circumference and area of a circle are numerically equal what is the radius numerically equal to?
Answer:
Step-by-step explanation:
If the circumference and area of a circle are numerically equal, then we can write the following equation:
C = A
where C is the circumference and A is the area of the circle.
Using the formulas for the circumference and area of a circle, we can substitute and simplify the equation as follows:
2πr = πr^2
Dividing both sides by πr gives:
2 = r
Therefore, if the circumference and area of a circle are numerically equal, then the radius is numerically equal to 2.
In a right triangle, sin (5x-7) = cos (3x-10). Solve for x.
gamboa, inc. sold 110 selfie sticks for $10 each. if producing the selfie sticks had an average cost of $3 , how much profit did the company make?
The company made a profit of $770
How much profit did the company make?Profit is the difference between revenue and costs. In this scenario, the revenue from selling 110 selfie sticks is $10 × 110 = $1100.
Therefore, the costs of producing the same number of selfie sticks are
110 × $3 = $330
So, the profit that Gamboa, Inc. made is
$1100 - $330 = $770.
As we can see, based on the number of selfie sticks together with their production, we managed to obtain a profit of $770.
Hence, the company made a profit of $770.
See more about profit at: https://brainly.com/question/1078746
#SPJ11
The difference between two numbers is eight.
if the smaller number is n to the third power
what is the greater number?
The greater number is [tex]$n^3+8$[/tex]
Let x be the greater number and y be the smaller number. We know that x-y=8.
We are also given that the smaller number is n³.
So we can set up the equation:
x = y + 8
x = n³ + 8
Therefore, the greater number is [tex]$n^3+8$[/tex].
The greater number is given as n³ + 8. If the smaller number we get is represented by the n³, then by adding 8 to that value gives the greater number. The difference between the two numbers is always going to be 8, regardless of the value of n.
Learn more about numbers
https://brainly.com/question/25734188
#SPJ4
A floor is shaped like a regular pentagon. Each side length is represented by (2×+ 4) inches and (4×-2) inches. Find the length of each side
The length of each side of the regular pentagon is 10 units
Let's use the fact that the floor is a regular pentagon to set up an equation involving the side lengths.
A regular pentagon has five sides of equal length, so we can set the two expressions for the side lengths equal to each other:
2× + 4 = 4 × - 2
Solving for x, we get:
2x = 6
x = 3
Now that we have the value of x, we can substitute it back into either expression for the side length to find the length of each side. Let's use the expression (2× + 4) inches:
2× + 4 = 2(3) + 4
= 6 + 4
= 10 units
Learn more about pentagon here
brainly.com/question/24275169
#SPJ4