The probability you'll see one over half an hour is 0.26
The term probability in math is defined as the possibility of the outcome of any random event
Here we have given that the probability you'll see a falling star in the sky over the course of one hour is 0.44.
Then in an hour can be taken as two half hours so we can write the probability to see a falling star as
Then it can be written as,
=> (1-P)*(1-P) = 1 - 0.44
When we simplify this one then we get
=> (1 - P)² = 0.56
Here we need to value of p then it can be written as,
=> 1 - P = √0.56
Then the value of P is calculated as,
=> -P = 0.74 - 1
=> P = 0.26
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In a sequence, each term after the first is four more than three times the previous term. The fifth term is 403. What is the first term
In a sequence, each term after the first is four more than three times the previous term. The fifth term is 403.then First term is 3.
Let a1 be the first term....then the successive terms are
3a1 + 4, 9a1 + 16, 27a1 + 52, 81a1 + 160
So 81a1 + 160 = 403 subtract 160 from each side
81a1 = 243 divide both sides by 81
a1 = 3
in other word
403 - 4 = 399/3 = 133
133 - 4 = 129/3 = 43
43 - 4 = 39/3 = 13
13 - 4 = 9/3 = 3
So, first term = 3
In a sequence, each term after the first is four more than three times the previous term. The fifth term is 403.then First term is 3.
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Events A and B are mutually exclusive. Which of the following statements is also true? Select one: a. P(ANB) = P(A) + P(B) b. P(AUB) = P(A) + P(B) C. A and B are also independent. d. P(AUB) = P(4)P(B)
The events A and B are mutually exclusive, that is they are independent. Hence, option a and option c are correct.
What are mutually exclusive events?In probability theory, if two events don't happen at the same time, they are mutually exclusive or disjoint. The outcomes of a single coin flip, which can result in either heads or tails but not both, are an obvious example.
Given that A and B are mutually exclusive events.
For mutually exclusive events the probability of event A occurring or event B occurring is summation of the probability of the individual event.
Both the events are independent.
Hence, option a and option c are independent.
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Which shows the function f\left(x\right)=2\cdot4^xf(x)=2⋅4
x
after a horizontal translation 2 units to the left?
The equation of function after a horizontal translation is y = 2*4ˣ⁺².
Initially, functions represented the idealized relationship between two changing quantities. A planet's position, for instance, depends on time. In the past, the idea was developed with the infinitesimal calculus at the end of the 17th century, and the functions that were taken into consideration until the 19th century were differentiable (that is, they had a high degree of regularity).
The realms of application of the concept of a function were substantially expanded at the conclusion of the 19th century when it was defined in terms of set theory.
An assignment of an element from set Y to each element of set X constitutes a function from set X to set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
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The mean number of accidents a week at a company is 6. 4 with a standard deviation of 1. 5. What proportion of weeks would you expect to have more than 7 accidents?
The mean number of accidents that would be expected to be more than 7 accidents is 0.6554.
What is mean?By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.
What is z-score?A statistical measurement known as the Z-score indicates how closely a value relates to the mean of a collection of values. The Z-score is calculated using standard deviations from the mean. When a data point's Z-score is 0, it means that it has the same score as the mean. One standard deviation from the mean would be indicated by a Z-score of 1.0.
Given that mean is 6.4 and the standard deviation is 1.5.
The z score is used to determine the accidents:
z = 7 - 6.4 / 1.5
z = 0.4
Using the table of normal distribution we have, P(x > 7 ) = P(z > 0.4) = 0.6554
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For all the positive values of x, the value of logx x is always ___ and the value of logx 1 is always___
The value here is always 1, and the value should be 0, since it is a positive value for x.
About logarithmic base
A function whose logarithm is the base a of x. The exponential form is used here because it shows the inverse of the exponential function.
So we can conclude that positive values of x here should always have values 1 and 0. So the above answer is correct.
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5 gallons to 6 quarts in simplest ratio
The simplest ratio between 5 gallons and 6 quarts is 10:3.
To convert 5 gallons to quarts, we can use the conversion factor that 1 gallon is equal to 4 quarts.
Therefore, 5 gallons is equal to 5 x 4 = 20 quarts.
Now we need to express this ratio in its simplest form.
To simplify the ratio, we can divide both the number of quarts and the number of gallons by their greatest common divisor (GCD).
The GCD of 20 and 6 is 2. So, dividing both numbers by 2, we get:
20 ÷ 2 = 10
6 ÷ 2 = 3
Therefore, the simplest ratio between 5 gallons and 6 quarts is 10:3.
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Can some one do one two and four
Algebra 2 I am really lost on this topic
2) The standard definition of function f(x) is given as follows: A. F(x) = ax³ + bx² + cx + d.
4) The solution to the system of equations v(x) = b(x) is given as follows:
A. (-3.43, 6.30).
How to define the cube function?The standard definition of a cube function is given as follows:
y = ax³ + bx² + cx + d.
As all the coefficients are positive, the definition is this one.
The system of equations for this problem is defined as follows:
v(x) = x³ + 2x² - 5x + 6.b(x) = -3x - 4.The solution for the system of equations in this problem is approximated graphically.
The graphic solution of a system of equations is given by the point of intersection of all the equation that compose the system.
From the graph given at the end of the answer, the coordinates of the point of intersection are given as follows:
(-3.432, 6.296).
Meaning that the solution to the system of equations is approximated by option A.
Missing InformationItem 2 asks for the standard cube function, with positive coefficients.
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Can 6 cm 8 cm 10 cm be the sides of a right triangle?
A right triangle with sides of 6, 10, and 8 cm can be built.
The sides of a triangle are 6 cm, 10 cm, and 8 cm in length.
The Pythagorean Theorem states that The sum of the squares representing the base and height equals the square of the hypotenuse.
[tex](Hypotenuse)^{2}+(Base)^{2}= (Altitude)^{2}[/tex]
[tex](6)^{2}+(8)^{2}= (10)^{2}[/tex]
36 + 48 = 100
100 = 100
The sides offered satisfy the specifications for a right triangle.
Given that it satisfies the Pythagorean theorem, a right triangle with sides of 6, 10, and 8 cm can be built.
Hence, a triangle can be formed with sides of 6cm, 8cm, and 10cm in length and that would be a right angled triangle.
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Ben is x cm tall.
Kieran is 8 cm taller than Ben.
Bianca is 2 cm shorter than Ben.
Write an expression, in terms of x, for the mean of their heights in centímetres.
Give your answer in its simplest form.
hope this helps you understand !!
Answer:
x + 2
Step-by-step explanation:
Ben : x cm
Kieran: (x + 8) cm
Bianca: (x - 2) cm
Mean of their heights = [tex]\frac{Sum of their heights}{Number of people} = \frac{x + (x + 8) + (x - 2)}{3}[/tex]
= [tex]\frac{x + x + 8 + x - 2}{3}[/tex] (Expand the brackets)
= [tex]\frac{x + x + x + 8 - 2}{3}[/tex] (Bring all the like terms together)
= [tex]\frac{3x + 6}{3}[/tex] (Simplify the two sets of like terms)
= [tex]\frac{3(x + 2)}{3}[/tex] (Extract the common factor '3' in the numerator)
= (x + 2) cm ([tex]\frac{3}{3} = 1[/tex])
what is the value of 2x [6 {12someone biked 11 time as many miles as someone. together they biked a totoal of 156 miles. how many miles did they bke
Someone biked 11 time as many miles as someone together they biked a total of 156 miles. 143 miles did they bike.
Miles:
The mile, sometimes called the international mile or statutory mile to distinguish it from others, is an imperial unit in the United Kingdom and a common unit of distance in the United States. Both are based on old English units that are 5,280 British feet or 1,760 yards long. The legal mile was standardized in 1959 by an international agreement between the British Commonwealth and the United States and formally redefined in SI units to be exactly 1,609.344 meters.
With the modifier, the mile is also used to describe or convert a wide range of units derived from or roughly equivalent to the Roman mile, such as the Chinese mile (now exactly 500 m). will be The Romans divided the mile into 5,000 Roman feet, but the growing importance of the furlong in Elizabethan England meant that in 1593 the legal mile equaled eight furlongs, or 5,280 feet. This form of the mile has since spread partially to the successor states of the British Empire, where they continue to use the mile. Most countries have replaced miles with kilometers when converting to the International System of Units (SI), but some countries still use international miles, such as Liberia, the United Kingdom, the United States, and countries with less than one mile. I'm here. Most of them are British or US territories or have close historical ties with the UK or the US.
According to the Question:
Let the distance Karly biked be x.
Then, someone biked 11x.
Now,
x + 11x = 156
x = 156/ 12
= 13
Therefore,
Someone biked 11 × 13 = 143 miles
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Dalton made fancy teal costume decorations for each of the dancers in his year-end dance performance. he used 1/10 of a meter of ribbon for each decoration, which he got by cutting 1/2 of a meter of ribbon into equal pieces. how many decorations did dalton make?
Dalton made 10 number of decorations. Dalton made 10 decorations using 1/2 of a meter of ribbon, which he cut into equal pieces.
1. Dalton used 1/10 of a meter of ribbon for each decoration.
2. He got this by cutting 1/2 of a meter of ribbon into equal pieces.
3. 1/2 of a meter is equal to 5/10 of a meter.
4. If 1/10 of a meter is used for each decoration, then 5/10 of a meter can make 5 decorations.
5. Therefore, 10 decorations can be made.
Dalton made 10 number of decorations using 1/2 of a meter of ribbon, which he cut into equal pieces.
Dalton made 10 decorations for each of the dancers in his year-end dance performance. He used 1/10 of a meter of ribbon for each decoration which he got by cutting 1/2 of a meter of ribbon into equal pieces. This meant that he was able to get 10 decorations out of the 1/2 of a meter of ribbon, as 1/10 of a meter was used for each decoration. He was able to do this by dividing the 1/2 of a meter of ribbon evenly into 10 pieces.
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A clerk at a jewelry store earns 12.5% commission on top of her hourly wage. A ring sells for $549.99. The store is running a special promotion where rings are marked down 10%. She earns her commission on the sale price. How much commission will she receive if she sells the ring? Round to the nearest cent
The sales commission the clerk will receive if she sells the ring at a markdown of 10% is $61.87.
What is a sales commission?Sales commission is a percentage of the sales price paid to salespeople as an incentive to drive more sales for the organization.
What is the markdown price?The markdown price is the reduced selling price of an item.
It is determined by subtracting a stated percentage from the regular retail price.
Retail prices may be marked down to encourage customers' patronage during low sales periods.
The normal selling price of the ring = $549.99
Special promotion markdown = 10%
Marked-down price = $494.99 ($549.99 x 1 - 10%)
Sales commission in percentage = 12.5%
Sales commission in dollars = $61.87 ($494.99 x 12.5%)
Thus, the sales clerk will receive $61.87 in sales commission for selling the ring.
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what sample size would be required to reduce the standard deviation of the sam- pling distribution to one-third the value you found in exercise 36(b)? justify your answer.
Multiplying the sample size by 4 reduces the standard deviation to half of the previous value, so a sample size of 30(4) = 120 would reduce the standard deviation of the sampling distribution to one-half of the value found in 35(b).
Now, According to the question:
Let's Know:
What is Standard Deviation?
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Multiplying the sample size by 4 reduces the standard deviation to half of the previous value, so a sample size of 30(4) = 120 would reduce the standard deviation of the sampling distribution to one-half of the value found in 35(b).
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a man finds the angle of depression of a parked car to be 40° from a floor 24m high in a multi storey building.Find the distance of the car from the foot of the building
Answer:
To find the distance of the car from the foot of the building, you can use the tangent function and the information given:
distance = 24m / tan(40°)
The distance of the car from the foot of the building is approximately 27.4m
Step-by-step explanation:
5. The sum of two numbers is 15. The difference between five times the first number and Three times the second number is 19. Find the two numbers.
Answer:
let the 2 unknown numbers be 'x' and 'y'
given: x+y=15 - equation 1
5x-3y=19 - equation 2
from equation 1 :
x = 15 -y
substitute this in equation 2
5(15-y) -3y = 19
75 - 5y - 3y = 19
75-8y=19
8y=56
y=7(substitute value of y in equation 1)
x+7=15
x=8
hence the two numbers are 8 and 7
Answer:
x = 8
y = 7
Step-by-step explanation:
let's assume the first number as x, and the second number as y
Now, according to the question,
x + y = 15
Moving on to the next statement,
five times the first number = 5x
three times the second number = 3y
Thus,
5x - 3y = 19
Now that we have two equations, we can either write 'x' in 'y' terms, or y in 'x' terms.
For example, from the first equation:
x + y = 15
y = 15 - x
Now, let's put this value of y into the second equation, i.e.
5x - 3(15 - x) = 19
5x - 45 +3x = 19
8x = 19 + 45
x = 64/8
x = 8
Now, let's put this value of x into the first equation, i.e.
x + y = 15
8 + y = 15
y = 7
In conclusion, the two numbers, x and y, are 8 and 7 respectively
The ratio between inches and feet is always 12 to 1. In math class, Jada measured the length of the whiteboard. She found that it is 6 feet long.
How many inches long is the whiteboard?
inches
Answer:
72 inches
Step-by-step explanation:
12 inches : 1 feet that is
[tex] \frac{12(inches)}{1(feet)} [/tex]
then if 6 feet
[tex] \frac{12(inches)}{1(feet)} \times 6(feet) = 72(inches)[/tex]
Round each angle to the nearest degree and round each Side to the nearest hundredth. Do not use rounded answers in your calculations to find missing measures.
Length of AB = c = 7.12
Measures of angles:
A = 56°
B = 34°
What is Pythagoras theorem?The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.
AB² = AC² + BC²
Given in the figure,
AC = 3.96
BC = 5.96
AB = ?
A = ?
B = ?
By Pythagoras theorem
AB² = AC² + BC²
AB² = 3.96² + 5.96²
AB² = 15.6816 + 35.5216
AB² = 51.2032
AB = √51.2032
AB = 7.1156
Rounded to nearest hundredth
AB = 7.12
Now, tan B = AC/BC
tan B = 3.96/5.96
tan B = 0.6644
B = tan⁻¹ (0.6644)
B = 33.6°
Sum of Interior angles of a triangle = 180°
A + B + C = 180°
A + 33.6° + 90° = 180°
A + 123.6° = 180°
A = 180° - 123.6°
A = 56.4°
Rounded to nearest degree,
A = 56°
B = 34°
Hence, 7.12 is the measure of AB, 56° and 34° are the measures of angles A and B respectively.
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Austin's brother loaned him $20 and asked him to pay him back in 3 months. He's going to charge 4% interest. Austin is excited about all extra money he will make in interest. Is is correct to be excited?
Answer:
Step-by-step explanation:
Yes, it is correct for Austin to be excited about the extra money he will make in interest. Interest is a common form of compensation for loaning money to another person, and it is generally expected to be paid back along with the principal amount. In this case, Austin will earn 4% interest on the $20 loan over the course of 3 months, which works out to be a total of $0.80. This is a relatively small amount, but it is still money that Austin would not have had if not for the loan. Therefore, it is reasonable for Austin to be excited about the opportunity to make a little extra money.
Is avertical line up and down or left to right
Hello , please help ( see image!)
Answer:
250 and 10
Step-by-step explanation:
substitute x = 10 into the expressions
a = [tex]\frac{5x^2}{2}[/tex]
= [tex]\frac{5(10)^2}{2}[/tex]
= [tex]\frac{5(100)}{2}[/tex]
= [tex]\frac{500}{2}[/tex]
= 250
-----------------------------------------------
b = [tex]\frac{2x^2(x-5)}{10x}[/tex]
= [tex]\frac{2(10)^2(10-5)}{10(10)}[/tex]
= [tex]\frac{2(100)(5)}{100}[/tex] ( cancel 100 on numerator and denominator )
= [tex]\frac{2(5)}{1}[/tex]
= 10
What are 5 different types of units?
Different types of units are CGS system units, FPS system units, MKS system units and SI units.
The (CGS)centimetre-gram-second system of units is how this is expressed. The metric system employs the centimetre to represent length or distance, the gram as the fundamental unit to represent mass or weight, and the second to represent time. Although there are other units of measurement in the system, they are all derived from just a few of these.
The (FPS)foot-pound-second system of units is what this is in its entire form. In this metric system, the foot serves as the default unit of length, and the pound serves as the default unit of mass and force. Finally, time is represented by the second.
This system's full name is (MKS)meter, kilogram, and second. The measuring of physical quantities is indicated by the usage of this metric system. Here, a meter is used to indicate length and a kilogram to indicate mass. Prior to their redefinition, it was renowned for establishing the foundation for the SI units.
International System of Units(SI) is the lengthier abbreviation for the units. It is the most recent and contemporary variety of metric system in use today. It is frequently utilized as the reference unit of measurement. It primarily includes the following seven units of measurement: second, metre, kilogram, ampere, Kelvin, Mole and candela.
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Find the slope of the line that passes through these two points
Answer: 7/4
Step-by-step explanation:
The formula for slope is change in y/change in x.
So we substitute in the coordinates: -3-4/2-6
We can then simplify to -7/-4, or 7/4.
Answer: 7/4
Step-by-step explanation:
4-(-3)/6-2 = 7/4
Use linear regression to find an equation that would best predict a fair home price based on thecomps given below. Round each variable to 4 decimal places.Square Feet House Price (in Thousands)1400 1081700 1331500 120
Finding the line that fits a set of data points the best is done using the linear regression approach. We can utilize the following procedures to apply linear regression to find an equation that would most effectively predict a fair home price depending on the square footage of the home:
Step 1 :The square footage of the house should be on the x-axis and the house's price in thousands should be on the y-axis of the graph you create in step one.
Step 2: Using the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, determine the equation of the line of best fit.
Step 3 :Find the slope and y-intercept by substituting the comps data into the equation in step three.
Step 4: The line of best fit has the equation y = mx + b, where m is the line's slope and b is its y-intercept.
Step 5: We must use the formula m = (NΣ(xy) - (Σx)(Σy)) / (NΣ(x^2) - (Σx)^2) to determine the slope (m).
Step 6: We must apply the formula b = (y - m(x)) / N to determine the y-intercept (b).
Step 7: Using the information provided in the question, we will determine the slope and y-intercept. m = (3* (108+133+120) - (1400+1700+1500)(3)) / (3 (1400+1700+1500)(2)) = 0.09 b = (108+133+120 -0.09*(1400+1700+1500))/3 = 111.33
Therefore, y = 0.09x + 111.33 is the equation that would most accurately forecast a reasonable property price based on the home's square footage.
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For which interval(s) is the function increasing and decreasing?
y = |2x² + x - 6|
The function is decreasing in the interval (-∞,-3/2) and (3/2, ∞) and increasing in the interval (-3/2, 3/2).
What is a function?
A function is a mathematical relation between a set of inputs (often called independent variables, or the domain) and a set of outputs (often called dependent variables, or the range). A function assigns exactly one output for each input. It can be represented by an equation, such as y = f(x), where x is the input and y is the output.
To find the interval(s) in which the function is increasing and decreasing, we can first find the critical points of the function by setting the derivative equal to 0 and solving for x.
The derivative of y = |2x² + x - 6| is not a defined function, it is not differentiable, it is a piece-wise defined function, it has a break at x = -3/2
Hence, the function is decreasing in the interval (-∞,-3/2) and (3/2, ∞) and increasing in the interval (-3/2, 3/2).
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Solve the inequality 2c/3 + 1 > 7
Answer:
c>9
Step-by-step explanation:
To start off the problem, we don't normally like fractions when we deal with solving equations, so in order to get rid of it, we can multiply the entire problem by 3, to get the inequality of 2c+3>21 which looks a LOT simpler to solve!
From here, we can minus 3 from both sides to get the problem 2c>18. After this, we can divide both sides by 2 to get c>9!
(One side note that might help you out in the future is that if you ever need to multiply or divide both sides by a negative number, the inequality sign switches, for example if it was originally a < sign then it now turns into a > sign)
Find f(-8) if f(x)= 4x^2+4x+2
Answer: 226
Step-by-step explanation:
Substitute -8 into x. You will get,
4 (-8)² + 4(-8) + 2
4 x 64 - 32 + 2
256 - 30
226
Answer: 226
Step-by-step explanation:
So the question's asking you to solve for f(-8) which basically means to substitute the x in the equation of f(x) with -8 and solve.
It will then look like this:
f(-8)= 4(-8)^2+4(-8)+2
Then just put it in a calculator and solve.
u={red,blue,green} x={red,blue} then find xcu and ucx
The likelihood of selecting a second ball is 2/8 or 1/4 if that ball is now eliminated.
what is probability ?Probability theory, a subfield of mathematics, gauges the likelihood of an event or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a comprehensive set of equally likely outcomes that result in a certain occurrence compared to the total number of outcomes.
given
The ratio of the number of balls of that color to all the balls is the likelihood of selecting a ball from a bag.
In the first case, the likelihood of a red ball is therefore 3/9, or 1/3. The likelihood of selecting a second ball is 2/8 or 1/4 if that ball is now eliminated.
Therefore, the chance of getting a white ball is 1/2*1 plus 1/2*49/99, or roughly 3/4.
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The width of a rectangle measures (4. 2v – 2. 6) centimeters, and its length
measures (1. 5v + 6. 7) centimeters. Which expression represents the perimeter, in
centimeters, of the rectangle?
add the two sides together, giving us 8.4v + 13.4, which is the perimeter of the rectangle in centimeters.
2(4.2v - 2.6) + 2(1.5v + 6.7) = 8.4v + 13.4
1. Multiply the width by two to get the two sides: 2(4.2v - 2.6)
2. Multiply the length by two to get the other two sides: 2(1.5v + 6.7)
3. Add the two sides together to get the perimeter: 8.4v + 13.4
To calculate the perimeter of the rectangle, we must first find the length of the two sides. To do this, we multiply the width by two, giving us 2(4.2v - 2.6). This gives us the length of the two sides opposite each other. We then multiply the length by two, giving us 2(1.5v + 6.7). This gives us the length of the other two sides. We then add the two sides together, giving us 8.4v + 13.4, which is the perimeter of the rectangle in centimeters.
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In a linear programming problem, the binding constraints for the optimal solution are5X + 3Y < 302X + 5Y < 20a. Fill in the blanks in the following sentence: As long as the slope of the objective function stays between _____ and _____, the current optimal solution point will remain optimal.b. Which of these objective functions will lead to the same optimal solution?1) 2X + 1Y2) 7X + 8Y3) 80X + 60Y4) 25X + 35Y
The binding constraints for the ideal response in a linear programming issue are
5X + 3Y < 30
2X + 5Y < 20
What is linear programming ?The term "linear programming" (LP), sometimes known as "linear optimization," refers to a technique for determining the optimal result in a mathematical model whose criteria are represented by linear relationships, such as the largest profit or lowest cost.
A specific type of mathematical programming is linear programming (also known as mathematical optimization).
Formally speaking, linear programming is a method for optimizing a linear objective function under the restrictions of linear equality and linear inequality.
Convex polytopes, a set defined as the intersection of a finite number of half spaces, each of which is determined by a linear inequality, make up its viable region.
A real-valued affine (linear) function defined on this polyhedron serves as its goal function.
An algorithm for linear programming determines where on the polytope this function occurs.
Hence, The binding constraints for the ideal response in a linear programming issue are
5X + 3Y < 30
2X + 5Y < 20
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HELP, IM TIMED!!
Select the THREE shapes that have a volume of 36π cubic units.
D A
ОВ
D c
A
г..з.
12
7.6
OD.
D E
OF. 3
Зп
Se
3
торо
3
Correct answers are - A, B, D, F, G.The volume of oblique cone is same as normal cone and volume of oblique cylinder is same as normal cylinder due to Cavalier's principle.
What is Cavalier's principle?Cavalieri's principle is a method for determining the volume of an object by comparing it to the volume of another object of known volume. It was introduced by the Italian mathematician Bonaventura Cavalieri in the early 17th century. The principle states that if two solids have the same height and the same cross-sectional area at every height, then the two solids have the same volume.
The principle is based on the idea of slicing the solids into thin slices and comparing the areas of the cross-sections of the slices. If the cross-sectional areas are the same at every height, then the solids have the same volume.
Cavalieri's principle was one of the early precursors to the development of calculus and the concept of the definite integral. It is also a powerful tool in geometry and is used in many problems involving the calculation of volumes of irregular shapes.
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