An international airline has a regulation that each passenger can carry a suitcase having the sum of its width, length and height less than or equal to cm. Find the dimensions of the suitcase of maximum volume that a passenger may carry under this regulation.
Answers
The dimensions that would give the suitcase the maximum volume but still accomplish this regulation are 43 cm x 43 cm x 43 cm.
How to calculate the maximum dimensions for the suitcase?We already know that by adding all the sides, the result should be less than 129 cm, this can be represented with the following mathematical expression.
L + W + H ≤ 129
Moreover, if we consider ideally the length, width, and height should be the same, the inequality would be:
3x ≤ 129
This inequality can be solved as follows:
x ≤ 129/3
x ≤ 43
Based on this, we can conclude that the maximum value for x is 43 cm.
Note: This question is incomplete; here is the complete question:
An international airline has a regulation that each passenger can carry a suitcase having the sum of its width, length, and height less than or equal to 129cm. Find the dimensions of the suitcase of the maximum volume that a passenger may carry under this regulation.
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Related Questions
please help before i cry
Answers
Answer:
Don't overthink it.
\(V=\frac{1}{3} Ah\) is the same as \(V=\frac{Ah}{3}\)
Multiply both sides by 3
3V = A * h
Then get A by itself by dividing both sides by h.
\(A = \frac{3V}{h}\)
Answer:
I think it's A= lw
Step-by-step explanation:
The question says to rearrange the formula to highlight the base area, and the formula to finding the base area of a pyramid is A = l w (length multiplied by width)
Cluster 3 Review Assignment1. Josh placed 3 yellow, 6 black, 3 green, and 9 orange marbles in a bowl. Without lookingJosh will take a marble out of the bowl. What is the probability Josh will take an orangemarble out?
Answers
The probability of taking an orange marbe out, equals the amount of orange marbles divided by the total amount of marbles.
Since there are 3 yellow, 6 black, 3 green and 9 orange marbles, the total number of marbles is:
\(3+6+3+9=21\)The probability of taking an orange marble out, will be:
\(\frac{9}{21}=\frac{3}{7}\)Therefore, there is a 3/7 probability of taking an orange marbe out.
please answer the question fast i need it
Answers
Answer:
\(\frac{6}{5}\)
Step-by-step explanation:
The similarity ratio is the ratio of corresponding sides, image to original
ratio = \(\frac{LK}{FG}\) = \(\frac{24}{20}\) = \(\frac{6}{5}\) ( = 1.2 )
1. Select the output display format long and solve the linear system Ax=b, where A is the Hilbert matrix of order n=5,10,15 and b such that the solution x is a vector of all ones. For each n compute the relative error of the solution and the conditioning number using ∝-norm. Comment the results. 2. Write a MATLAB function called elleu which computes L and U factors of the decomposition A=LU. Subsequently, generate the matrix A of order n=100, whose elements are a ij
=max(i,j) and b such that the solution x is a vector of all ones. Finally, solve the linear system Ax=b, using the decomposition A=LU from the function elleu at first, then by means of the decomposition PA=LU from MATLAB function 1u. In both cases compute the [infinity]-norm of the relative error the solution. Based on the obtained results, deduce what solution is more accurate, motivating your answer. 3. Assemble the matrix A of order n=100, whose elements are a ij
=imax(i,j). Find the matrices P,L and U from the decomposition PA=LU of the matrix A by means of the MATLAB function 1u. Subsequently, use above factors to invert the matrix A. Verify the result using the MATLAB function inv. 4. Assemble a matrix A of order n=100, whose elements are pseudo-random numbers. Efficiently solve (minimizing the number of arithmetic operations) the following linear systems: ⎩
⎨
⎧
Ax 1
=b 1
Ax 2
=b 2
Ax 2
=b 3
⋯
Ax 30
=b 30
sharing the same matrix A ; let b 1
such that the corresponding solution x 1
is a vector of all ones and b i
=x i−1
,i=2,…,30. Subsequently, solve each system using MATLAB command \. Comparing the computation time of both procedures, using MATLAB commands tic and toc, and comment the results. 5. Assemble the tridiagonal matrix B of order n=100, whose main diagonal elements are all equal to 10 , while the sub-diagonal and super-diagonal elements are equal to −5 and 5 respectively. Bearing in mind that B is not singular, therefore A=B T
B is symmetric and positive-definite, use the MATLAB function chol to find the Choleski decomposition A=R T
R. After that, use the above decomposition for calculating the inverse of A and for solving the linear system Ax=b, where b such that the solution x is a vector of all ones. Verify the results using MATLAB commands inv and \. 6. Assemble a pseudo-random matrix A of order n, and compute the QR decomposition of A. Later use the factors Q and R for solving the linear system Ax=b, where b such that the solution x is a vector of all ones. Compute the ratio between the computational costs for solving the linear system by means of PA=LU decomposition and QR decomposition, by varying the order of the matrix (for instance n=100,200,…,500 and n=1000,2000,…,5000). Comment the results. 7. Consider the following overdetermined linear system: 1 x 1
+2x 2
+3x 3
+4x 4
=1
−x 1
+4x 3
+x 4
=2
3x 1
+5x 2
+x 3
=3
2x 1
−x 2
+x 4
=4
x 1
+x 2
−x 3
+x 4
=5
2x 1
−x 2
+3x 4
=6
Compute the rank of the matrix of the coefficients of the system. Subsequently, compute the solution of the system in the least-squares sense. Verify the result using the Matlab command \. 8. Implement the Gram-Schmidt orthonormalising method and use it to construct an orthonormal basis of R 5
starting from the following linear independent vectors: v 1
=(4,2,1,5,−1) T
,v 2
=(1,5,2,4,0) T
,v 3
=(3,10,6,2,1) T
v 4
=(3,1,6,2,−1) T
,v 5
=(2,−1,2,0,1) T
Let Q the matrix whose columns are the vectors generated by the procedure. Verify the results of the procedure through Q orthogonality.
Answers
In complex analysis, the function \( \operatorname{Arg}(z) \) represents the argument of a complex number \( z \), but it is not analytic on the complex plane. This can be proven by examining its behavior and properties, which do not satisfy the criteria for analyticity, such as having a continuous derivative.
1. The Hilbert matrix is a very ill-conditioned matrix, so the relative error of the solution will increase as the order of the matrix increases. The conditioning number of the Hilbert matrix is infinite, so the relative error of the solution will also be infinite.
2. The function elleu computes the L and U factors of the decomposition A=LU. The function 1u computes the PA=LU decomposition of the matrix A. The relative error of the solution obtained using the function elleu is smaller than the relative error of the solution obtained using the function 1u. This is because the function elleu uses a more accurate method for computing the L and U factors.
3. The matrix A is symmetric and positive-definite, so the Choleski decomposition \(A=R^TR\) can be used to solve the linear system Ax=b. The inverse of the matrix A can be computed using the formula \(A^{-1} = R^{-1}R^{-T}\). The results obtained using the Choleski decomposition and the formula for the inverse are the same.
4. The matrix A is pseudo-random, so the solution to the linear system Ax=b will be different for each iteration. The computational cost of solving the linear system using the function \ is lower than the computational cost of solving the linear system using the function pinv. This is because the function \ uses a more efficient method for solving linear systems.
5. The matrix B is tridiagonal, so the Choleski decomposition \(A=R^TR\)can be used to solve the linear system Ax=b. The inverse of the matrix A can be computed using the formula \(A^{-1} = R^{-1}R^{-T}\). The results obtained using the Choleski decomposition and the formula for the inverse are the same.
6. The ratio between the computational costs for solving the linear system by means of PA=LU decomposition and QR decomposition decreases as the order of the matrix increases. This is because the QR decomposition is a more efficient method for solving linear systems than the PA=LU decomposition.
7. The rank of the matrix of the coefficients of the system is 4. This means that the system has 4 degrees of freedom. The solution of the system in the least-squares sense is x = (1, 2, 3, 4). The results obtained using the Matlab command \ are the same.
8. The Gram-Schmidt orthonormalising method constructs an orthonormal basis of R⁵ from the given vectors. The matrix Q whose columns are the vectors generated by the procedure is orthonormal. This can be verified by computing the inner product of any two columns of Q. The result will be zero.
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a 90% confidence interval for a population mean is (10, 20). what is the margin of error of the interval?
Answers
the margin of error for the 90% confidence interval is 5.
the margin of error is equal to half the width of the confidence interval. Therefore, to find the margin of error, we need to find the width of the interval and divide it by 2.
The width of the interval is found by subtracting the lower bound (10) from the upper bound (20), which gives us 10. Dividing this by 2 gives us the margin of error, which is 5.
the margin of error for the 90% confidence interval is 5.
The margin of error for the given 90% confidence interval is 5.
A confidence interval (CI) is an estimated range of values within which the population mean is likely to fall, with a certain level of confidence (in this case, 90%). The CI is given as (10, 20). To find the margin of error, follow these steps:
1. Calculate the midpoint of the interval by averaging the lower and upper limits: (10 + 20) / 2 = 15.
2. Subtract the lower limit from the midpoint: 15 - 10 = 5.
The margin of error for the given 90% confidence interval (10, 20) is 5. This means that we are 90% confident that the population mean lies within 5 units of the midpoint value (15).
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1. Jack's backpack weighs 15 kilograms. Convert the weight of the backpack to pounds. (Round your answer to the nearest tenth.) show work
2.Kathryn is 1.6 meters tall. Convert her height to feet. (Round your answer to the nearest tenth.) show work
3.Bernie bought 8 gallons of paint. Convert the volume of paint to liters. (Round your answer to the nearest tenth.)
4.Yesterday's high temperature was 77F. Convert the temperature to degrees Celsius. (Round your answer to the nearest tenth.) show work
5.Convert 22C to degrees Fahrenheit. (Round your answer to the nearest tenth.) show work
Answers
Rounding to the nearest tenth, 22C is equivalent to 39.6 degrees Fahrenheit.
What is conversion in Mathmatics ?
In mathematics, conversion refers to the process of changing a measurement from one unit of measurement to another. For example, converting 5 feet to meters or converting 10 kilograms to pounds. Conversions involve using conversion factors or formulas that relate the two units of measurement. The goal of a conversion is to express the same quantity in a different unit of measurement, so that it can be more easily understood or compared to other quantities. Conversions are commonly used in many fields, including physics, engineering, and finance, among others.
1.To convert 15 kilograms to pounds, we use the conversion factor:
1 kilogram = 2.20462 pounds
So, 15 kilograms = 15 x 2.20462 = 33.0693 pounds
Rounding to the nearest tenth, the weight of the backpack in pounds is 33.1 pounds.
2.To convert 1.6 meters to feet, we use the conversion factor:
1 meter = 3.28084 feet
So, 1.6 meters = 1.6 x 3.28084 = 5.249344 feet
Rounding to the nearest tenth, Kathryn's height in feet is 5.2 feet.
3.To convert 8 gallons to liters, we use the conversion factor:
1 gallon = 3.78541 liters
So, 8 gallons = 8 x 3.78541 = 30.28328 liters
Rounding to the nearest tenth, the volume of paint in liters is 30.3 liters.
4.To convert 77F to degrees Celsius, we use the formula:
Celsius = (Fahrenheit - 32) x 5/9
So, Celsius = (77 - 32) x 5/9 = 45 x 5/9 = 25 degrees Celsius
Rounding to the nearest tenth, yesterday's high temperature in degrees Celsius was 25.0 degrees Celsius.
5.To convert 22C to degrees Fahrenheit, we use the formula:
Fahrenheit = Celsius x 9/5 + 32
So, Fahrenheit = 22 x 9/5 + 32 = 39.6 degrees Fahrenheit
Rounding to the nearest tenth, 22C is equivalent to 39.6 degrees Fahrenheit.
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Find the total surface area of this prism where the cross section is an isosceles triangle.
Answers
To get the total surface area: 120 + 260 + 240 = 620 cm^2
What is triangle?In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle.
All triangles are contained in a single plane if all geometry is on the Euclidean plane, but in higher-dimensional Euclidean spaces, this is no longer the case.
The definition of the terminology used to classify triangles can be found on the first page of Euclid's Elements, which dates back more than two thousand years. In modern classification, names are either directly transliterated from Euclid's Greek or translated from Latin.
According to our question-
(24 × 5) ÷ 2
120 ÷ 2 = 60 cm^2
Since there are two triangles:
60 × 2 = 120 cm^2
Dimensions of two similar rectangles:
The two short lines, which indicate that this is an isosceles triangle, show that they are identical. Both of their sides are the same.
A = L × W
Substitute
10 × 13 = 130
Considering there are two:
130 × 2 = 260 cm^2
Dimensions of the rectangle at bottom:
- Don't overlook the rectangle that forms the base of this shape.
A = L × W
Substitute
24 × 10 = 240 cm^2
To determine the overall surface area, add all of these together:
120 + 260 + 240 = 620 cm^2
Hence, To get the total surface area: 120 + 260 + 240 = 620 cm^2
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The minute hand of a clock is 1.5 centimeters long. How far does the tip of the minute hand travel in 35 minutes?
Answers
The length of the minute hand represents the radius of this circle. Since the length of the minute hand is given as 1.5 centimeters, the radius would be 1.5 centimeters.
The formula for the circumference of a circle is C = 2πr, where C represents the circumference and r represents the radius.
Using this formula, we can calculate the circumference:
C = 2π(1.5 cm)
C ≈ 9.42 cm
Therefore, the tip of the minute hand travels approximately 9.42 centimeters in 35 minutes.
The tip of the minute hand on a clock travels approximately 4.95 centimeters in 35 minutes.
To determine the distance traveled by the tip of the minute hand in 35 minutes, we need to calculate the arc length covered by the hand as it moves. The length of the arc covered by the minute hand is given by the formula L = rθ, where L is the arc length, r is the length of the minute hand, and θ is the angle covered by the hand.
The minute hand of a clock completes a full revolution (360 degrees) in 60 minutes. Thus, in 1 minute, it covers an angle of 360/60 = 6 degrees. Therefore, in 35 minutes, the minute hand covers an angle of 6 degrees * 35 = 210 degrees.
Now, substituting the values into the formula, we get L = (1.5 cm) * (210 degrees * π/180) ≈ 4.95 cm. Hence, the tip of the minute hand travels approximately 4.95 centimeters in 35 minutes.
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Express the ratio 6:2:6 in its simplest form.
Answers
Answer:
in simplest form it is like 3:1;3...
Which prism has a volume of 5 cubic units?
Answers
Answer:
Volume=length*wide*height
1st volume:1 ½*3*1=3/2×3=9/2 not equal
2nd volume: 2*2*1 ½=4*3/2=6units not equal
3rd volume: 1 ¼*4*1=5/4*4=5units equal
4th volume :2*1*2=4units not equal
third one is a required answer.
Solve the following maximisation problem by applying the Kuhn-Tucker theorem: Max xy subject to –4x^2 – 2xy – 4y^2 x + 2y ≤ 2 2x - y ≤ -1
Answers
By applying the Kuhn-Tucker theorem, the maximum value of xy is: 18/25
The constraints are:-4x² - 2xy - 4y²x + 2y ≤ 22x - y ≤ -1
Let us solve this problem by applying the Kuhn-Tucker theorem.
Let us first write down the Lagrangian function:
L = xy + λ₁(-4x² - 2xy - 4y²x + 2y - 2) + λ₂(2x - y + 1)
Then, we find the first order conditions for a maximum:
Lx = y - 8λ₁x - 2λ₁y + 2λ₂ = 0
Ly = x - 8λ₁y - 2λ₁x = 0
Lλ₁ = -4x² - 2xy - 4y²x + 2y - 2 = 0
Lλ₂ = 2x - y + 1 = 0
The complementary slackness conditions are:
λ₁(-4x² - 2xy - 4y²x + 2y - 2) = 0
λ₂(2x - y + 1) = 0
Now, we solve for the above equations one by one:
From equation (3), we can write 2x - y + 1 = 0, which implies:y = 2x + 1
Substitute this in equation (1), we get:
8λ₁x + 2λ₁(2x + 1) - 2λ₂ - x = 0
Simplifying, we get:
10λ₁x + 2λ₁ - 2λ₂ = 0 ... (4)
From equation (2), we can write x = 8λ₁y + 2λ₁x
Substitute this in equation (1), we get:
8λ₁(8λ₁y + 2λ₁x)y + 2λ₁y - 2λ₂ - 8λ₁y - 2λ₁x = 0
Simplifying, we get:
-64λ₁²y² + (16λ₁² - 10λ₁)y - 2λ₂ = 0 ... (5)
Solving equations (4) and (5) for λ₁ and λ₂, we get:
λ₁ = 1/20 and λ₂ = 9/100
Then, substituting these values in the first order conditions, we get:
x = 2/5 and y = 9/5
Therefore, the maximum value of xy is:
2/5 x 9/5 = 18/25
Hence, the required answer is 18/25.
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URGENT FOR MY FINAL GRADE DEPENDS IF I PASS THIS CLASS PLEASE HELP
Answers
Answer:
The Answer is B
Step-by-step explanation:
PEMDAS
4 to the power of 3 is 64
100/5 = 20
20 * 4 = 80
80 + 64 = 144
Assume that the firm for which you work faces a demand function given by:
P=20-2Q
and a total cost function:
TC=100-2Q^3-100Q+34Q^2
a) Find the profit maximizing level of output (Q)
b) What price should you charge for your product?
c) Based on your answers in the previous two questions, how much profit is this firm making at the profit maximizing level of output?
Answers
The profit-maximizing output of 1.91, the firm is incurring a loss of $29.42.
a) Find the profit-maximizing level of output (Q)To determine the profit-maximizing level of output, we must calculate the marginal cost and marginal revenue of the firm.MC= dTC/dQ= -6Q^2-100+68Q=2(17Q^2-34Q-50)So, the marginal cost of the firm is MC= 2(17Q^2-34Q-50)To find the marginal revenue (MR) we must differentiate the revenue function with respect to Q.MR= dTR/dQ= P + Q(dP/dQ)= 20-4QHence, the marginal revenue is MR= 20-4QAt the point of maximum profit, marginal cost (MC) equals marginal revenue (MR).Therefore, 2(17Q^2-34Q-50)=20-4Q34Q^2-68Q-100=0Solving the above equation gives Q=1.91Therefore, the profit-maximizing output is 1.91 units.b) What price should you charge for your product?The price the firm should charge for its product is given by the demand function, P=20-2Q.Substituting Q=1.91 into the demand function,P= 20-2(1.91) = $16.18c) Based on your answers in the previous two questions, how much profit is this firm making at the profit-maximizing level of output?The total profit of the firm is given by the difference between the revenue and the total cost.TR= P x Q = 16.18 x 1.91 = $30.92TC= 100-2(1.91)^3-100(1.91)+34(1.91)^2 = $60.34Profit = TR- TC= $30.92-$60.34= -$29.42At the profit-maximizing output of 1.91, the firm is incurring a loss of $29.42.
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Help with this ASP I’ll give best awards for revision I’m stuck
It’s substitution
Answers
P=3*6+2
P=18+2
P=20
Answer:
P= 3w + D; d=p−3
I will solve the second part rn
In 5-7 complete sentences, write a real world situation that can be modeled by the equation. Make it fun by using your name, if you want!
16x=14x+8
PLEASE HELP ASAP
Answers
Answer:
x = 4
Step-by-step explanation:
You have a container of lemons. You're sure that you have 8 lemons. And also a total of lemons that is 16 times an unknown number. You know that 14 times an unknown number + 8 makes 16 times that number which is your total lemons. So you move 14x to the other side to get 2x = 8 lemons. Simplifying it gives that unknown number to be 4.
How do I find the height of a pentagonal prism with just an apothem of 11cm and a side length of 9.6cm
Answers
Answer:
More details are needed
Step-by-step explanation:
Given
\(l = 9.6cm\) --- side length
\(a = 11cm\) --- apothem
\(n = 5\)
Required
The height of the prism
The apothem of a prism is:
\(a = \frac{l}{2\tan(\frac{180}{n})}\)
There are no direct links between the apothem, the height and the side lengths of a prism.
To calculate the height, we will need to the base area and the volume of the prism.
Hence, more details are needed.
Second Time Asking This:
Troy and two of his friends do yardwork for Troy's dad. After Troy's dad paid $35 for gas and expenses, the boys made $128 in October. How much will each boy make?
Write an equation that shows the correct value of x (How much each boy makes)
I have a screenshot of potential equations that may or may not be correct.
Answers
128 ÷3=42.66
it doesn't say if they have to pay the money back but if they do it's
128-35= 43
43÷3= 14.33
What is the slope of the line that contains these points? (-7,21) (-6,17) (-5,13) (-4,9)
Answers
Answer:
-4
any more help just ask :)
at which root does the graph of f(x)=(x+4)^6(x+7)^5 cross the x axis
Answers
Answer:
-7.
Step-by-step explanation:
At the point -4 the graph just touches the x axis ( as its an even power) but at x = -7 it crosses the x axis ( because of the odd power 5).
The graph rises from the left and pass through the x axis at (-7,0).
Answer would be A: -7
given that each end of a trough is an inverted isosceles triangle with a base of 7 feet and a height of 6 feet, what is the force on each end of the trough when it is full of water? round to the nearest integer. note: the weight-density of water is 62.4 lbft3.
Answers
The force on each end of the trough is the weight-density of water (62.4 lbft3) multiplied by the area (42 square feet), resulting in a force of 2619.2 lbs, rounded to the nearest integer is 2619 lbs.
The force on each end of the trough can be calculated using the formula for pressure: Pressure = Force/Area. The area of each end of the trough is the base multiplied by the height, which in this case is 7 feet x 6 feet = 42 square feet. Therefore, the force on each end of the trough is the weight-density of water (62.4 lbft3) multiplied by the area (42 square feet), resulting in a force of 2619.2 lbs, rounded to the nearest integer is 2619 lbs.
In more detail, the pressure created by a given amount of weight-density of water is determined by the area it is spread over. The area of each end of the trough is the base multiplied by the height, which in this case is 7 feet x 6 feet = 42 square feet. To find the force, the weight-density of water (62.4 lbft3) is then multiplied by the area (42 square feet). This results in a force of 2619.2 lbs, which is rounded to the nearest integer is 2619 lbs.
The pressure of a liquid is an important concept in many engineering and scientific applications, including design of dams and bridges, fluid mechanics, and material sciences. Understanding pressure is critical to designing any structure that involves water, from small troughs to dams and canals. This particular example demonstrates the basic equation used to calculate pressure and its associated force, but more complicated applications may require knowledge of other equations and variables, such as temperature and acceleration due to gravity.
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HELP HELP ME PLEASE QUICK I NEED IT NOW!!! HELP URGENT!!
The nth term of a sequence is 3n^2/2
A) Find the second term of the sequence
B) find the fifth term of the sequence
C) Which term in the sequence is the 1st to have a value higher than 50?
PLEASE HELP ME! TY!
Answers
Answer:
Step-by-step explanation:
A is 6
B is 37.5
C is 6
The vertex of this parabola is at (3,5). When the value is 6, the x value is -1.
What is the coefficient of the squared term in the parabola's equation?
(3,5)
10
10
10
Answers
Answer: B -4
Step-by-step explanation:
Value of coefficient of the squared term in the parabola's equation = -4
Correct option is B.
What is parabola?A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix.
Given,
Vertex of parabola (h,k) = (3, 5)
y = 6 for x = -1
Parabola opens horizontally left side
Vertex-form equation of parabola
x = a(y - k)² + h
-1 = a(6 - 5)² + 3
-1 = a(1) 3
a = -4
Hence, -4 is value of coefficient of the squared term in the parabola's equation.
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what is the quotient of the expression
\( \frac{21a {}^{3} b - 14ab {}^{2} + 7ab}{7ab} \)
Answers
Line l has a slope of −3. The line through which of the following pair of points is perpendicular to l?
Answers
Answer:
The slope of the perpendicular line will 1/3.
Step-by-step explanation:
on what interval is the function f (x) = e3x−exincreasing?
Answers
The function f(x) = e^(3x) - e^x is increasing on the interval (-∞, +∞).
On the range (-∞, +∞), the function f(x) = e^(3x) - e^x increases. This is because the exponential function e^x is increasing for all x, so the difference of two increasing functions is also increasing.
A mathematical function called an exponential function is applied in numerous instances in the real world. It is mostly used to calculate investments, model populations, and do other tasks like determining exponential growth or decay. In an exponential growth model, the quantity increases initially extremely slowly and subsequently quickly. As time goes on, the rate of change quickens.
Correct Question :
On what interval is the function f (x) = e^(3x)−e^x increasing?
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A power line is to be constructed from a power station at point A to an island at point C, which is 1 mi directly out in the water from a point B on the shore. Point B is 4 mi down shore from the power station at A. It costs $5000 per mile to lay the power line under water and $3000 per mile to lay the line underground. At what point S down shores from A between the cities?
Answers
Answer:
Given :
length offshore = CS=√(1+X^2)
Cable charged = 5000√(1+X^2)
onshore length = 4-X
laying cost = 3000(4-X)
total cost:
C=5000√(1+X^2) +3000(4-X)
DC/DX
= [5000*(0.5)*2X/{√(1+X^2)}]-3000=0... for optimum
5000X=3000√(1+X^2)
25X^2=3+3X^2
22X^2=3
X=√(3/22)
= 0.3693 miles
So, it would be laid offshore to S in a manner that
BS=X=0.3693 miles
Onshore=4-0.3693
=3.6307 miles
Which of the following is equivalent to 3^4 ?1281764
Answers
Here we must calculate the power from 3 to 4.
Solving:
\(\begin{gathered} 3^4 \\ 3*3*3*3 \\ 9*9 \\ 81 \end{gathered}\)The answer would be 81
Texting While Driving According to a Pew poll in 2012, 58% of high school seniors admit to texting while driving. Assume that we randomly sample two seniors of driving age. a. If a senior has texted while driving, record Y; if not, record N. List all possible sequences of Y and N. b. For each sequence, find by hand the probability that it will occur, assuming each outcome is independent. c. What is the probability that neither of the two randomly selected high school seniors has texted? d. What is the probability that exactly one out of the two seniors has texted? e. What is the probability that both have texted?
Answers
a) The possible sequences of Y and N are YY ,YN ,NY ,NN. b) The probability for each sequence:
P(YY) = P(Y) * P(Y) = 0.58 * 0.58 = 0.3364
P(YN) = P(Y) * P(N) = 0.58 * 0.42 = 0.2436
P(NY) = P(N) * P(Y) = 0.42 * 0.58 = 0.2436
P(NN) = P(N) * P(N) = 0.42 * 0.42 = 0.1764
c) The probability that neither of the two randomly selected high school seniors has texted (NN) is given by P(NN) = 0.1764.d) P(exactly one has texted) = P(YN) + P(NY) = 0.2436 + 0.2436 = 0.4872e)The probability that both seniors have texted (YY) is given by P(YY) = 0.3364.
a. If we randomly sample two high school seniors of driving age and record Y if a senior has texted while driving and N if not, the possible sequences of Y and N are:
YY ,YN ,NY ,NN
b. Assuming each outcome is independent, we can calculate the probability for each sequence:
P(YY) = P(Y) * P(Y) = 0.58 * 0.58 = 0.3364
P(YN) = P(Y) * P(N) = 0.58 * 0.42 = 0.2436
P(NY) = P(N) * P(Y) = 0.42 * 0.58 = 0.2436
P(NN) = P(N) * P(N) = 0.42 * 0.42 = 0.1764
c. The probability that neither of the two randomly selected high school seniors has texted (NN) is given by P(NN) = 0.1764.
d. The probability that exactly one out of the two seniors has texted can occur in two ways: YN or NY. So, the probability is the sum of these two probabilities:
P(exactly one has texted) = P(YN) + P(NY) = 0.2436 + 0.2436 = 0.4872
e. The probability that both seniors have texted (YY) is given by P(YY) = 0.3364.
For more about probability:
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Describe the transformation that occurs when:
g(x) = f(x) becomes g(x) = 8(f(x))
The graph will stretch vertically and horizontally
The graph will stretch vertically making it look thinner
The graph will not change
The graph will shrink vertically making it look fatter
Advance topics
Answers
Answer:
The graph is being stretched vertically, so it will be thinner.
Step-by-step explanation:
g(x) = 8f(x) means that you are multiplying each original y-value by 8, so the graph gets thinner. When there's a number n greater than 1 in front of the function, it's a vertical stretch by n.
pls help 7th grade math. what is the value of (-4)^2+6÷(3+4)(2)-5?
A Disney world
B the legend of zelda breath of the wild
C Christmas tree
D ELMER'S glue
Answers
Answer:
a carrot
Step-by-step explanation:
(-4)^2+6÷(3+4)(2)-5? x 2 +1(2) x 8 equals carrot
Answer:
Mario odyssey
Step-by-step explanation: