The maximum volume of the cylindrical can such that the sum of its height and its circumference is 45 cm is 337.5 cm³
Let's denote the radius of the cylindrical can as r, and its height as h.
The circumference of the base of the can is 2πr, so the sum of the height and the circumference can be written as:
h + 2πr = 45..(1)
We want to find the maximum volume of the can, which is given by:
V = πr²h..(2)
From (1), h = 45 - 2πr
Substitute h value in equation above
V = πr²(45-2r)
V = 45πr² - 2π²r³
To find the maximum volume, we have to find the differentiation of V
dV/dr = 90πr - 6π²r² = 0
Solving for r, we get:
r = 15/π cm
Now plug in r value in h
V = π(15/π)²(15)
= 337.5 cm³
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what are two numbers have a product of 20 and a sum of 9
Answer:
Step-by-step explanation:
A worker fences in a construction site using four pieces of fencing that have lengths of 20, yards 16, yards, 20 yards, and 16 yards. Name all of the possible four-sided shapes that the worker can enclose with the fencing.
The possible shapes of the fencing are a parallelogram and a rectangle.
Given that, a worker fences in a construction site using four pieces of fencing that have lengths of 20, yards 16, yards, 20 yards, and 16 yards.
We need to tell possible four-sided shapes that the worker can enclose with the fencing.
So, we can see that, the pair of sides are equal,
Which is condition in a parallelogram and a rectangle.
Hence, the possible shapes of the fencing are a parallelogram and a rectangle.
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I need help fast!!
It’s past due
The relative frequency of "tails" when the companions coalesce their results is close to 0.524.
How to calculate the relative frequencyIn order to ascertain the relative frequency of "tails" when the friends amalgamate their outcomes, one must accumulate the amount of tails, then divide that sum by the entirety of trials:
Relative frequency of "tails" = total number of tails / cumulative number of trials
= 129 / (117 + 129)
= 129 / 246
≈ 0.524
Consequently, the relative frequency of "tails" when the companions coalesce their results is close to 0.524.
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The solution to a system of two linear equations is x = 3; y = 9.
How could the intersection of the graphs of the two equations be located on a coordinate grid?
What does the solution to a system of two linear equations mean on the graph? The point where
Can you have more than one solution to a Linear system of equations? Yes, because the
Can you have exactly two solutions to a Linear system of equations? The point that th
Can you have no solutions to a Linear system of equations? No, because line
:: From the origin, move 3 units up and 9 units right
The point of inte!
:: From the origin, move 3 units right and 9 units up
:: Yes, if the lines are parallel
:: Yes, if both lines are the same exact line
The lines intercept at the point (3, 9), and:
A system of linear equations can have one solution, no solutions, and infinite solutions, these are the only options.
How could the intersection be located a coordinate grid?If we have an equation system, the solutions are the spots where the graphs of the equations intersect.
We know that the solution of the system of linear equations is (3, 9), which signifies that the linear equations intersect at that location.
Can we have more than one solutions?
Yes, you can have
no solutioninfinite solutionsone solutionThese are the 3 options.
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y≥−
3
1
x+2
y≥3x
Which graph represents the system of inequalities?
Choose 1 answer:
Choose 1 answer:
Both lines will be solid lines and the intersection of the point will be at (1/3, 1).
Given that:
y ≥ −3x + 2
y ≥ 3x
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The region above the line y ≥ −3x + 2 is considered.
The region above the line y ≥ 3x is considered.
And both lines will be solid lines and the intersection of the point will be at (1/3, 1).
The graph is given below.
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NEED HELP ON ALL THE QUESTIONS
a. A translation on a coordinate plane involves moving every point on the plane a certain distance in a particular direction without distrupting their orientation. The shape and size of the figure do not change, only that the position shifts.
What is the effect of the translation,?b. If the translation is moving 3 units to the right, it is affecting the x-coordinate. Basically, the x-coordinate of each point on the plane is increased by 3 units, while the y-coordinate remains the same.
c. If the translation is moving 8 units down, it is affecting the y-coordinate. Basically, the y-coordinate of each point on the plane is decreased by 8 units, while the x-coordinate remains the same.
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h(1) = 23 meters and h(a) = 34.25 meters.
The average rate of change of the height of the rocket is 11.25/(a - 1)
Estimating the average rate of change of the height of the rocketFrom the question, we have the following parameters that can be used in our computation:
h(1) = 23 meters and h(a) = 34.25 meters.
The average rate of change of the height of the rocket is
Rate = Change in height /Time
So, we have
Rate = (34.25 - 23)/(a - 1)
Evaluate
Rate = 11.25/(a - 1)
Hence, the rate = 11.25/(a - 1)
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Complete question
Melissa launches a rocket from a 3-meter-tall platform. The height, h, of the rocket, in meters, can be modeled by the given graph.
Melissa knows that h(1) = 23 meters and h(a) = 34.25 meters.
What is a reasonable estimate of the average rate of change of the height of the rocket, in meters per second
The graph to the right is the uniform probability density function for a friend who is x minutes late. (a) Find the probability that the friend is between 10 and 30 minutes late. (b) It is 10 A.M. There is a 20% probability the friend will arrive within how many minutes? part a) what is the probability that the friend is between 10 and 30 minutes late_?
The probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.
Since the probability density function is uniform, the probability of the friend being between 10 and 30 minutes late is equal to the area of the rectangle that lies between x = 10 and x = 30, and below the curve of the probability density function.
The height of the rectangle is equal to the maximum value of the probability density function, which is 1/30 since the interval of possible values for x is [0, 30] minutes.
The width of the rectangle is equal to the difference between the upper and lower limits of the interval, which is 30 - 10 = 20 minutes.
Therefore, the probability of the friend being between 10 and 30 minutes late is:
P(10 < x < 30) = (height of rectangle) x (width of rectangle)
= (1/30) x 20
= 2/3
≈ 0.6667
So the probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.
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In art class students are mixing In art class students are mixing blue and red paint to make purple paint. Bo mixes 3 cups of blue paint and 4 cups of red paint. Latanya mixes 2 cups of blue paint and 3 cups of red paint. Use Bo and Latanya’s percent of blue paint to determine whose purple paint will be bluer.blue and red paint to make purple paint. Bo mixes 3 cups of blue paint and 4 cups of red paint. Latanya mixes 2 cups of blue paint and 3 cups of red paint. Use Bo and Latanya’s percent of blue paint to determine whose purple paint will be bluer.
Based on the percentage of blue paint to red paint, Bo's purple paint will be bluer.
What is the percentage?The percentage refers to the quotient of one value (proportion of blue paints) compared to another (the sum of blue and red paints).
Percentages are ratios expressed over 100.
Blue Red Ratio (%) of Blue to Red
Bo's paints 3 4 3:4 = 43% (3/7 x 100)
Sum of ratios = 7
Latanya's paints 2 3 2:3 = 40% (2/5 x 100)
Sum of ratios = 5
Thus, based on the ratios or percentages of to red paints, Bo's purple paint will be bluer than Latanya's.
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A small liberal arts college in the Northeast has 200
freshmen. Eighty of the freshmen are education majors. Suppose fifty freshmen are randomly selected (without replacement).
Step 1 of 2 : Find the expected number of education majors in the sample. Round your answer to two decimal places, if necessary.
The expected number of education majors in the sample is 20.
Probability calculationSince 80 out of 200 freshmen are education majors, the probability of randomly selecting an education major from the population is:
P(edu major) = 80/200 = 0.4
To find the expected number of education majors in a sample of 50 freshmen, we can use the formula for the expected value of a discrete random variable:
E(X) = n x p
Substituting the given values, we get:
E(X) = 50 x 0.4 = 20
Therefore, the expected number of education majors in a sample of 50 freshmen is 20.
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The time spent waiting in the line is approximately normally distributed. The mean waiting time is 7
minutes and the standard deviation of the waiting time is 1
minute. Find the probability that a person will wait for less than 9
minutes. Round your answer to four decimal places.
The probability that a person will wait for more than 9 minutes is approximately 0.0912 or 9.12%. This means that out of 100 people, about 9 of them will wait for more than 9 minutes in the line.
We know that,
To solve this problem, we need to use the normal distribution and standardize the variable of interest. We know that the mean waiting time is 5 minutes and the standard deviation is 3 minutes, so we can write: Z = (X - μ) / σ
where X is the waiting time, μ is the mean waiting time (5 minutes), σ is the standard deviation (3 minutes), and Z is the standardized variable.
To find the probability that a person will wait for more than 9 minutes, we need to find the area under the normal curve to the right of 9. We can do this by standardizing 9 using the formula above: Z = (9 - 5) / 3 = 1.33 .
We can use a standard normal table or a calculator to find the probability that Z is greater than 1.33. Using a calculator, we find that this probability is approximately 0.0912.
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Find the arc length of a circle with radius 12 and central measure pi/4 radians.
The length of the arc of a circle of radius 12 is 37.68.
What is an arc?
The arc of a circle is defined as the part or segment of the circumference of a circle.
To calculate the arc of the circle, we the formula below.
Formula:
L = 2πrФ/360Where:
L = Length of the arcr = Radius of the circle∅ = Angle of the arc at the center of the circleFrom the question,
Given:
r = 12∅ = pi/4 radian = π/4π = 3.14Note: 360° = 2π radian
Substitute these values into equation 1
L = (π/4)×12×2×3.14/2πL = 37.68Hence, the length of the arc is 37.68.
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A wild horse runs at a rate of 8 miles an hour for 6 hours. Let y be the distance, in miles, the horse
travels for a given amount of time, x, in hours. This situation can be modeled by a function.
Which of these describes the domain of the function?
A. 0≤x≤6
B. 0≤y≤6
C. 0≤x≤ 48
D. 0≤ y ≤ 48
0≤x≤6 best describes the domain of the function.
The domain of a function describes the set of all possible input values.
In this case, the input variable is x, which represents the time in hours.
Since the horse runs for 6 hours, it is not possible for x to be greater than 6.
Additionally, x cannot be negative or zero, since time cannot be negative or zero.
Therefore, the domain of the function is 0 ≤ x ≤ 6.
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The business checking account for a pottery store had a balance of $7349.44 before checks for $1349.67 and $344.12 were written. The store manager then deposited $956.60. Find the checkbook balance
If he business checking account for a pottery store had a balance of $7349.44 before checks for $1349.67 and $344.12 were written, checkbook balance after checks and deposit are processed is $6613.25.
To find the checkbook balance, we need to add up the initial balance, subtract the amounts of the written checks, and add the deposit made by the store manager.
Starting with the initial balance of $7349.44, we subtract the amount of the first check for $1349.67, leaving a balance of $6000.77. Then we subtract the second check for $344.12, leaving a balance of $5656.65.
Finally, we add the deposit made by the store manager for $956.60, which gives us a final balance of $6613.25.
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The temperature in Toronto one afternoon was 14° F. The temperature that same night fell to -5° F.
What was the difference in temperatures?
Answer: The difference in temperatures was 19°F.
Step-by-step explanation:
Answer:
19F
Step-by-step explanation:
NEED HELP DESPERATELY PLEASE !
solve this triangle. Round to the nearest tenth
The missing measures in the triangle are given as follows:
m < F = 111.4º, m < D = 28.6º, f = 35.1.
What is the law of sines?Suppose we have a triangle in which:
Side with a length of a is opposite to angle A.Side with a length of b is opposite to angle B.Side with a length of c is opposite to angle C.The lengths and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
Considering the triangle in this problem, the relation is given as follows:
sin(D)/18 = sin(40º)/24.2.
Hence the measure of angle D is obtained as follows:
sin(D) = 18 x sine of 40 degrees/24.2
sin(D) = 0.4781
m < D = arcsin(0.4781)
m < D = 28.6º.
The sum of the internal angle measures of a triangle is of 180º, hence the measure of angle F is obtained as follows:
m < F + 40 + 28.6 = 180
m < F = 180 - (40 + 28.6)
m < F = 111.4º
Then the length f is obtained as follows:
sin(111.4º)/f = sin(40º)/24.2
f = 24.2 x sine of 111.4 degrees/sine of 40 degrees
f = 35.1.
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Select the correct answer. How many solutions for x does the following equation have? A. 4 B. 0 C. infinite D. 1
The equation 2 (p+ 7) = 4 - 8p has only one solution that is; -9.
We know that solution of an equation refers usually to the values of the variables involved in that equation that if substituted in place of that variable would give a true mathematical statement.
We need to determine the solutions does the equation 2 (p+ 7) = 4 - 8p have;
Now solving for p,
2 (p+ 7) = 4 - 8
Open the bracket,
2p+ 14 = 4 - 8
Combine the like terms,
2p = -4 - 14
2p = -18
p = -18/2 = -9
Therefore, the equation has only one solution which is -9.
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The world record in the long jump is 29 feet 4 inches. How many inches short of 10 yards is the record long jump?
The record long jump is 8 inches short of 10 yards.
First, we need to convert 10 yards to inches. Since 1 yard = 3 feet and 1 foot = 12 inches, we have:
10 yards = 30 feet
= 30 x 12 inches
= 360 inches
To find how many inches short of 10 yards the long jump is, we can subtract the length of the long jump from 360 inches:
360 inches - 29 feet 4 inches
= 360 inches - (29 x 12 + 4) inches
= 360 inches - 352 inches
= 8 inches
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The product of six and a number is 108. What is the solution to the equation 1822, 102, 648
The value of the number is 18. Option A
How to determine the valueTo determine the product of the expression, we need to consider that;
Algebraic expressions are described as those mathematical expressions that are composed of terms, their coefficients, the variables and the factors and constant values.
These expressions are also made up of mathematical operations. These operations are;
AdditionBracketParenthesesMultiplicationDivisionSubtractionFrom the information given, we have that;
The product of six and a number is 108
Let the number be x, we have;
6x = 108
Divide sides by the coefficient
x = 18
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Problems 17, 20 Please
The summation of the given expression is as follows:
17.) = 5
18.) = 1
19.) = 1/2
How to calculate the summation of the given expressions above?For question 17.)
The summation of 2k+3 when K= 1
= 2(1)+3
= 2+3
= 5
For question 18.)
The summation of (3/2)^k where k = 0 would be = 1
For question 19.)
The summation of 1/2^k+1 where k = 0
= 1/2^0+1
=1/2^1
=1/2
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One hundred fifty bacteria are put into a petri dish, and the culture triples in size every hour. This is modeled by P(h) = 150(3), where P is the num
of bacteria in the population and h is the number of hours that have passed.
Which graph models the function P(h)?
The graph of the population equation is on the image at the end.
Which graph models the function?Here we know that the function p(h) models the population of bacteria as the function of h, the number of hours.
And we can write this as the exponential function:
p(h) = 150*(3)^h
The graph of this will be an exponential that starts at 150 and triples for each increase in the horizontal variable, then the graph of this will be like the one you can see at the end of the answer.
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PLS HELP THIS IS DUE TODAY what is 736 x 21
Answer:
15456
Step-by-step explanation:
My work is attached to this answer
A 1-bedroom apartment costs $850 and increases by $150 for each additional bedroom.ñ
Step-by-step explanation:
dependingon h o w m a n y bedrooms that are added to the
apartment, an additional $150will be added to $850.
Find the arc
length of AB.
3 cm
P 64°
A
B
PLEASE SHOW WORK!
The measure of the arc length AB is 16π/15 centimeters.
Since,
An arc length is simply the distance between two points along a section of a curve.
We know that;
The arc length is expressed as:
s = 2πr × (θ/360°)
Where s is the arc length, r is the radius, θ is the angle and π is constant pi.
Given that:
Radius r = 3cm
Angle θ = 64 degree
Arc length s = ?
Now, Plug the values into the above formula
s = 2πr × (θ/360°)
s = 2 × π × 3cm × ( 64°/360°)
s = 16π/15 cm
Therefore, the arc length is 16π/15 cm.
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Let F= 6(x+y)i + 8 sin(y)j,. Find the line integral of F around the perimeter of the rectangle with corners (3,0),(3,2),(-3,2),(-3,0) traversed in that order.
line integral =
The line integral of F around the perimeter of the rectangle with corners (3,0),(3,2),(-3,2),(-3,0) traversed in that order is -333.06456
How to determine the line integral of F around the perimeter?The F can be rewritten as
F(x,y) = [6(x+y) , 6sin(y)
The path C on which we are going to evaluate the integral is
A manufacturer makes decorative globes out of silver in the shape of a solid sphere. Suppose each sphere has a radius of 4.5 cm. If silver is priced at $5.00 per cm3", how much will the silver cost to make one solid sphere?
Use 3.14 for , and do not round your answer.
Answer:
The silver will cost $1908.5125 to make one solid sphere
Step-by-step explanation:
The formula for the volume of a sphere is:
V = (4/3)πr^3
where r is the radius of the sphere.
Substituting the given value for the radius:
V = (4/3)π(4.5 cm)^3
= (4/3)(3.14)(91.125 cm^3)
= 381.7025 cm^3
The cost of the silver can be calculated by multiplying the volume by the cost per cm^3:
Cost = 381.7025 cm^3 × $5.00/cm^3
= $1908.5125
You are now a competent person monitoring the IETS at your plant. Despite the frustration
of not getting the annual bonus, you know that you cannot simply use extra coagulant
because the additional turbidity might exceed the acceptable level. In that case, determine
the amount of coagulant that gives you the lowest turbidity value. In any relevant method,
use 0.1% as the stopping criterion
A feasible solution to minimizing turbidity value is through the use of an iterative technique, entailing either gradient descent method or simulated annealing method.
How to minimize turbidityThe stopping criterion for this approach would be at 0.1 percent. It involves sequentially determining water turbidity dependent on the coagulant dosages used in adjustment procedures based on preceding calculated values.
By further implementing this process until the specified percentage average is met, ease and accuracy in assessing turbidity levels are achievable.
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A rectangular prism has a length of 7 cm, a width of 4 cm, and a height of 2 1/2cm.
The prism is filled with cubes that have edge lengths of 1/2 cm.
How many cubes are needed to fill the rectangular prism?
Enter your answer in the box.
To fill the rectangular prism,
cubes are needed.
There are 560 cubes with edge lengths of 1/2 cm needed to fill the rectangular prism.
The volume of a rectangular prism is found by multiplying its length by its width by its height.
So, the volume of this rectangular prism is:
Volume = length x width x height
Volume = 7 cm x 4 cm x 2 1/2 cm
Volume = 70 cm³/2
Now, we need to find out how many cubes with edge lengths of 1/2 cm can fit into this volume.
The volume of each cube with an edge length of 1/2 cm is:
Volume of cube = edge length x edge length x edge length
Volume of cube = (1/2 cm)³
Volume of cube = 1/8 cm³
To find no. of cubes are needed, we need to divide the volume of the rectangular prism by the volume of each cube:
Number of cubes = (Volume of rectangular prism) / (Volume of each cube)
Number of cubes = (70 cm³/2) / (1/8 cm³)
Number of cubes = (70 cm³/2) x (8/1 cm³)
Number of cubes = 560 cubes
Therefore, 560 cubes with edge lengths of 1/2 cm are needed.
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A box has four cards numbered , , , and . Kareem will toss a coin once and record the toss as heads () or tails (). Then he will randomly pick a card from the box and record the number chosen. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event that the number chosen is . Use the format to mean that the coin toss is heads and the number chosen is . If there is more than one element in the set, separate them with commas.
Answer:
The sample space describing all possible outcomes is:
{H1, H2, H3, H4, T1, T2, T3, T4}
The outcomes for the event that the coin toss is heads are:
{H1, H2, H3, H4}
Step-by-step explanation:
If it pertains to using the format H1 to mean that the coin toss is heads and the number chosen is 1.
How did concepts related to thermal energy and heat transfe guide your design process
Thermal energy and heat transfer principles guide the design of efficient systems, minimizing heat loss and maximizing performance.
It is crucial to take into account a number of aspects that may impact the functionality and efficiency of systems and objects that include thermal energy and heat transmission. You would need to take into account things like the kind and quantity of heat source, the materials utilized, the insulation, and the processes employed for heat transfer, for instance.
Additionally, you would have to think about ways to increase heat transmission effectiveness and reduce heat loss. High thermal conductivity materials may be used, or the system may be designed to have more heat-transfer surface area.
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