The required maximum value of C is 16, and it occurs when x = 3 and y = 2.
To find the maximum value of C = 4x + 2y subject to the restraints x > 2, x < 5, y > 1, and y < 6, we can use the method of Lagrange multipliers.
First, we set up the Lagrangian function L as follows:
L = 4x + 2y - λ₁(x - 2) - λ₂(x - 5) - λ₃(y - 1) - λ₄(y - 6)
where λ1, λ2, λ3, and λ4 are Lagrange multipliers.
Next, we take the partial derivatives of L with respect to x, y, λ1, λ2, λ3, and λ4, and set them equal to zero:
∂L/∂x = 4 - λ₁ - λ₂ = 0
∂L/∂y = 2 - λ₃ - λ = 0
∂L/∂λ₁ = x - 2 = 0
∂L/∂λ₁ = 5 - x = 0
∂L/∂λ₃ = y - 1 = 0
∂L/∂λ₄ = 6 - y = 0
Solving these equations simultaneously, we get:
λ₁ = 1, λ₂ = 3, λ₃ = 1, λ₄ = 1, x = 3, y = 2
Therefore, the maximum value of C is:
C = 4x + 2y = 4(3) + 2(2) = 16
So, the maximum value of C is 16, and it occurs when x = 3 and y = 2.
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A company produces two products: A and B. The relative market values at the split-off point are not available. For every $300,000 of joint costs, Product A produces 10,000 pounds, and Product B produces 40,000 pounds. The amount of joint costs allocated to Product B using the physical quantities method is $
The joint costs allocated to Product B is $240,000.
What is amount of joint costs allocated to Product B?We must allocate joint costs based on the relative physical quantities produced by each product.
The total physical quantity produced by both products is:
= Quantity of A + Quantity of B
= 10,000 + 40,000
= 50,000 pounds
We will calculate the proportion of physical quantity produced by product A:
= Quantity of B / Total physical quantity
= 40,000 / 50,000
= 0.8
The amount of joint costs allocated to Product B is will be
= Total joint costs x Proportion of
= $300,000 x 0.8
= $240,000.
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M<2
Answers please the ask is in the picture
Find the values of x and y.
E
25
24
20
D
G
The value of x and y are 32.02 and 13.3 respectively.
What is Pythagoras theorem?Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
If a and b are the legs of the triangle and c is the hypotenuse, then,
c² = a²+b²
Triangle EFG is a right angled triangle so also triangle DEG
Therefore,
x² = 25²+20²
x² = 625 + 400
x² = 1025
x = √1025
x = 32.02
Also,
y² = 24² - 20²
y² = 576 - 400
y² = 176
y = √176
y = 13.3
Therefore the value of x and y is 32.02 and 13.3 respectively.
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what is 2/5 x 1/8 please help
Answer:
1/20
Step-by-step explanation:
To multiply two fractions, you simply multiply their numerators (top numbers) together and multiply their denominators (bottom numbers) together.
So, for 2/5 x 1/8, we have:
(2/5) x (1/8) = (2 x 1) / (5 x 8) = 2/40 = 1/20
Therefore, 2/5 x 1/8 is equal to 1/20.
Multiplying the numerators and denominators directly is the most straightforward method to solve the multiplication of fractions. However, there is another method called cross-multiplication, which you can use to solve this problem as well.
To use cross-multiplication, you multiply the numerator of the first fraction by the denominator of the second fraction, and then multiply the denominator of the first fraction by the numerator of the second fraction.
Then, you simplify the resulting fraction.
So, for 2/5 x 1/8, we have:
(2/5) x (1/8) = (2 x 1) / (5 x 8)
Cross-multiplying, we get:
(2/5) x (1/8) = (2 x 1) / (5 x 8) = (2 x 1) / (5 x 8) = 2/40
Simplifying the fraction 2/40, we can divide both the numerator and denominator by 2, to get:
2/40 = 1/20
Therefore, using cross-multiplication, we get the same answer as before:
2/5 x 1/8 is equal to 1/20.
The 6-inch segment of tape stores 4608 bits of data and it is a portion of a tape reel that is 1200 feet long. How much data can be stored on the entire reel?
The data can be stored on the entire reel is 66,355,200 bits.
What is Unit Conversion?Conversion could appear difficult, but this tip will make it simple for you to convert any unit. The fundamental rule is to multiply when converting from a larger unit to a smaller unit. Divide if you need to go from a smaller to a larger unit.
We have,
The 6-inch segment of tape stores 4608 bits of data.
Now, length of of reel = 1200 feet
= 1200 x 12
= 14,400 inch
So, the data that can be stored in reel
= 14,400 x 4608
= 66,355,200 bits
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Use the order of operations
(-2 + 1)² + 5(12 ÷ 3) - 9.
Answer:
12
Step-by-step explanation:
PEMDAS (Parenthesis, exponents, multiplication/division, addition/subtraction
(-1)² + 5(4) - 9
1 + 5(4) - 9
1 + 20 - 9
=12
Morton made 42 out of 50 free throws last season. What percent of his free throws did Morton make? Morton made % of his free throws.
Answer: morton made 84% of his free throws.
Step-by-step explanation: 50 is half of 100
•multiply 42 by 2 because 50 is half of 100
HELP PLEASEE
Find the value of x to the nearest tenth of a unit.
Check the picture below.
[tex]\tan(18^o )=\cfrac{\stackrel{opposite}{x}}{\underset{adjacent}{18}} \implies 18\tan(18^o)=x \implies 5.8\approx x[/tex]
Make sure your calculator is in Degree mode.
Fill in the missing values to make the equations true.
The missing terms in the logarithmic equation are solved
Given data ,
Let the logarithmic equation be represented as A
Now , the value of A is
a)
log₄ 11 + log₄ 5 = log₄ ( a )
Now , the value of a is
From the logarithmic properties , we get
log A + log B = log AB
So , a = 11 + 5 = 16
b)
log₅ 3 - log₅ ( a ) = log₅( 3/5 )
From the logarithmic properties , we get
log A − log B = log A/B
So , a = 5
c)
log₇ 8 = 3 log₇ ( a )
From the logarithmic properties , we get
log Aⁿ = n log A
8 = 2³
So , a = 3
Hence , the logarithmic equation is solved
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Given the triangle ABC at points A = ( 2, 2 ) B = ( 4, 5 ) C = ( 6, 3 ), and if the triangle is first reflected over the y axis, and then over the x axis, find the new point A''.
To reflect a point over the y-axis, we negate the x-coordinate of the point. To reflect the resulting point over the x-axis, we negate the y-coordinate of the point. So, to find the new point A'', we can perform these operations on the original point A:
1. Reflect A over the y-axis to get A': (-2, 2)
2. Reflect A' over the x-axis to get A'': (-2, -2)
Therefore, the new point A'' is (-2, -2).
URGENT!! ILL GIVE BRAINLIEST! ALONG WITH 100 POINTS!!!!!!!!
Match the given information with the equation for the line
-5x + 3y = -12
y = 3/2 x - 8
2y-x = -4
Y= -3/4x-2
Answer:
1. y = 3/2 x - 8
2. 2y-x = -4
3. y = -3/4x-2
4. -5x + 3y = -12
what is the radius of this shape?
Answer 7/12
Step-by-step explanation:
Answer:
Step-by-step explanation:
The radius is the length from the center dot to the circle.
They gave you the radius
r=6 1/4 in
David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 15 customers buy gasoline at this station. What is the probability that more than 8 and less than 12 customers pay in cash?
The probability that more than 8 and less than 12 customers pay in cash is 0.376 or 37.6%.
What is the probability?The probability that more than 8 and less than 12 customers pay in cash is calculated using the binomial probability formula:
P(x) = (n choose x) * p^x * (1-p)^(n-x)where:
n is the number of trials = 15
x = customers who pay in cash
p = paying in cash, which is 0.4 according to the problem
The probability that more than 8 and less than 12 customers pay in cash. is the sum of the probabilities of 9, 10, and 11 customers paying in cash.
Using the binomial probability formula:
P(x) = (15Cx) * 0.4 * (1 - 0.4)¹⁵⁻ˣP(9) = 15C₉ * 0.4⁹ * 0.6⁶
P(9) = 0.212
P(10) = 15C₁₀ * 0.4¹⁰ * 0.6⁵
P(10) = 0.121
P(11) = 15C₁₁* 0.4¹¹ * 0.6⁴
P(11)= 0.043
Hence;
P(9 or 10 or 11) = 0.212 + 0.121 + 0.043
P(9 or 10 or 11) = 0.376
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The tree diagram shows the sample space for tossing a coin three times. Which of these shows all outcomes with exactly 2 heads?
The probability of tossing exactly 2 tails is 0.375.
We have,
A coin is tossed three times.
So, the outcomes can either be a head or a tail.
The possible outcomes when a coin is tossed three times are:
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Now, the Pr(tossing exactly 2 tails)
= 3/8
= 0.375
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Correct answer gets brainliest!! So please help!!
Answer:
b
Step-by-step explanation:just do it heh
Answer:
The Correct answer is D
the lower whiskers from 10 to 28
folue the √(x-3) ³ - 64 equation √(ac-3)solve the equation
Solving the equation √(x - 3)³ - 64 = 0 for the variable x gives x = 19
Solving the equation for xFrom the question, we have the following parameters that can be used in our computation:
√(x - 3)³ - 64
Express as an equation
So, we have
√(x - 3)³ - 64 = 0
Add 64 to both sides of the equation
√(x - 3)³ = 64
Take the cube roots of both sides
So, we have
√(x - 3) = 4
Square both sides of the equation
This gives
x - 3 = 16
Add 3 to the equation
x = 19
Hence, the solution is x = 19
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A spinner was spun 900 times using Spin Spinner on the TI-84
calculator, with 1 representing blue, 2 representing purple, 3
representing green, and 4 representing red as shown
what was the experimental
probability of landing on green?
a 23.80%
b 26.80%
C 22.80%
d 24.80%
The experimental probability of the spinner landing on green is calculated as follows:
p = Number of times that the number 3 was generated/900 x 100%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
A green result is obtained when the number on the calculator is of 3, hence the experimental probability of the spinner landing on green is calculated as follows:
p = Number of times that the number 3 was generated/900 x 100%.
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Numbers from 1 to 30 are painted on white balls and mixed by a
machine. One ball is selected at random. Write each probability as a
fraction, a decimal, and a percent. Round decimals to the nearest
hundredth and percents to the nearest percent.
7. Plodd)
8. Plone-digit number)
9. P(negative)
11. P(divisible by 6)
13. P(1 or 30)
10. P(ending in 0)
12. P(two-digit number)
14. P(greater than 17 but less than 26)
7. Plodd) = 50%
8. Plone-digit number) = 30 percent
9. . P(negative) = 0
11. P(divisible by 6) = 17%
13. P(1 or 30) = 7%
How to solve the probability7. The probability of selecting an odd number from 1 to 30 can be found by counting the number of odd numbers in that range, which is 15, and dividing it by the total number of balls, which is 30. Therefore,
Fraction: 15/30
Decimal: 0.50
Percent: 50%
8. The probability of selecting a one-digit number from 1 to 30 can be found by counting the number of one-digit numbers in that range, which is 9, and dividing it by the total number of balls, which is 30. Therefore,
Fraction: 9/30
Decimal: 0.30
Percent: 30%
9. There are no negative numbers in the range from 1 to 30, so the probability of selecting a negative number is 0.
Fraction: 0/30
Decimal: 0
Percent: 0%
11. To be divisible by 6, a number must be divisible by both 2 and 3. There are 15 numbers in the range from 1 to 30 that are divisible by 2, and 10 numbers that are divisible by 3. However, there are only 5 numbers that are divisible by both 2 and 3, which are 6, 12, 18, 24, and 30. Therefore,
Fraction: 5/30
Decimal: 0.17
Percent: 17%
13. The probability of selecting either 1 or 30 is the same as the sum of the probability of selecting 1 and the probability of selecting 30. Since there is only one ball with each of these numbers,
Fraction: 1/30 + 1/30 = 2/30
Decimal: 0.07
Percent: 7%
10. To end in 0, a number must be a multiple of 10, which means it must be one of the numbers 10, 20, or 30. Therefore,
Fraction: 3/30
Decimal: 0.10
Percent: 10%
12. A two-digit number can be any number from 10 to 30, except for 10 and 30 themselves. Therefore,
Fraction: 18/30
Decimal: 0.60
Percent: 60%
14 The numbers greater than 17 but less than 26 are 18, 19, 20, 21, 22, 23, 24, and 25. Therefore,
Fraction: 8/30.
Decimal: 0.27
Percent: 27%
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Triangle XYZ is drawn with vertices X(4, −5), Y(6, −1), Z(10, −8). Determine the line of reflection if X′(4, 5).
y-axis
x-axis
y = 1
x = −4
The line of reflection is x-axis.
Given that, the triangle XYZ is drawn with vertices X(4, −5), Y(6, −1), Z(10, −8). we need to determine the line of the reflection if the X′(4, 5).
We know that the rule of the reflection over x-axis is
(x, y) → (x, -y)
Here, the y-intercept is changing its sign so we can say that the line of reflection is x-axis.
Hence, the line of reflection is x-axis.
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A rectangular field is four times as long as it is wideIf the perimeter of the field is 300yards, what are the field's dimensions?
Answer:
Length = 120 yards, width = 30 yards.
Step-by-step explanation:
Lets use [tex]l[/tex] for length and [tex]w[/tex] for width.
The perimeter of a rectangular field is [tex]2l + 2w[/tex]. We can construct the following equations:
[tex]4w = l[/tex].
[tex]2l + 2w = 300.[/tex]
If we plug [tex]4w[/tex] in for [tex]l[/tex] into the second equation, we get:
[tex]2w + 2(4w) = 300.[/tex]
[tex]2w+8w = 300.[/tex]
[tex]10w = 300.[/tex]
[tex]w= 30.[/tex]
Plug 30 in for [tex]w[/tex] into the first equation.
[tex]l = 4*30 = 120.[/tex]
Length = 120 yards, width = 30 yards.
Proba
Find the probability that a randomly
selected point within the circle falls in the
red-shaded square.
7
U
7
7
P = [?]
Enter as a decimal rounded to the nearest hundredth.
Enter
The probability that a randomly
selected point within the circle falls in the
red-shaded square is 63.7%.
How to calculate the probabilityA figure is shown, in which a square is inscribed in a circle. To find the probability that a randomly selected point within the circle falls in the red shaded area (Square).
radius = 7cm
side of square = 7√2 cm
Area of the circle = πr²
= 3.14 * 7²
= 153.86 cm²
Area of the square = side * side
= 7√2 * 7√2
= 98 cm²
= Area of square / Area of the circle
= 98 / 153.86
= 63.7%
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Answer:
63.7
Step-by-step explanation:
I entered that and got it right
En una correctera tiene una longitud 65 millas
¿cuántos metros mide
esa carretera?
If the length of the road in miles is 65, then in meters is approximately 104607.1 meters.
To convert miles to meters, we need to use a conversion factor. There are 1609.34 meters in one mile. So, to convert 65 miles to meters, we can multiply 65 by 1609.34.
65 miles * 1609.34 meters/mile = 104607.1 meters
The units when making conversions. Miles and meters are units of length, but they are not the same. To convert from one unit to another, we need to use a conversion factor that relates the two units. In this case, we used the conversion factor of 1609.34 meters per mile to convert from miles to meters.
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Math, some system by elimination
The elimination method is a technique used to solve linear equations that comprise a system. The fundamental principle behind this methodology involves nullifying one of the variables.
What is the elimination method about?It should be noted that to implement the elimination approach successfully, we must exclude either x or y, which can be accomplished by multiplying the second equation by an amount necessary to make the coefficient of y consistent in both the equations:
With x's value now discerned, we can insert it into any of the original equations to calculate y. This explains the method.
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The RSM geometry Principal test has 8 true-false questions. In how many ways can a student answer these questions?
Thank you :)
Answer:
256 ways-------------------------
Each question can be answered either true or false, giving two possible choices for each of the 8 questions.
Therefore, the total number of ways to answer the questions is the product of the number of choices for each question, which is:
2⁸ = 256The 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. and there is a 20% probability the friend will arrive within how many minutes?
Help solving
5/8 + 11/12 =
Answer:
37/24
Step-by-step explanation:
You have to find the common denominator.
A rectangular prism measures cm by 12 cm by cm. Calculate the number of cubes with edge length cm that fit in this prism. What is the volume of the prism in ? Show your reasoning. If you are stuck, think about how many cubes with -cm edge lengths fit into .
By calculating the volume of both figures, we will see that 11,160 cubes can be fit in the prism.
Now, So we start with a rectangular prism that measures (7 + 1/2)cm by 12cm by (15 + 1/2) cm.
Hence, The volume is just the product of these 3 values,
so we get:
V = (7 + 1/2)cm × 12cm × (15 + 1/2)cm
V = 1,395 cm³
Now, a cube with an edge length of 1/2 cm has a volume of:
V' = (1/2cm)³
V' = 0.125 cm³
To see how many of the small cubes enter in the prism, we just need to take the quotient between these two volumes, this is:
V/V' = ( 1,395 cm³)/(0.125 cm³) = 11,160
This means that, 11,160 of the cubes can be fit in the prism.
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complete question is,
A rectangular prism measure 7 1/2 by 12 by 15 1/2
Calculate the number of cubes with edge length 1/2 cm that fit in this prism.
What is the volume of the prism in cm? If you are stuck, think about how many cubes with 1/2-cm edge lengths fit into 1 cm.
Jake bought 2 packets of bread for 3 dollars. The cost of each packet of bread is _______ dollars.
Answer:
$1.50
Step-by-step explanation:
3÷2=1.50
If A is the set of numbers that are multiples of 8, B is the set of multiples of 4, and C is the set of multiples of 2, which of the following is the set of integers that will be in A but not B and C?
The set of integers that will be in A but not B and C will be 24, 32, 40,
How to explain the integerThe multiples of 8 comprise a set of {8, 16, 24, 32, 40, ...}, while the multiples of 4 correspond to {4, 8, 12, 16, 20, ...} and those of 2 are documented as {2, 4, 6, 8, 10, …}. The intersection of these two sets, B and C (B ∩ C = {4, 8, 12, 16, 20, ...}) remains unchanged.
It should be noted that to obtain the number of integers found in the multples of 8 that aren’t multiples either of 4 or 2, the intersection needs to be excluded from set A. This will yield {24, 32, 40, ...} - thus it is concluded that the integer set of multiples of 8, but not of 4 or 2, is {24, 32, 40, ...}
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In ΔPJK,
help me please on god.
The value of the variable x for the triangle base length is derived as 5.
How to calculate for the variable x of the triangleUsing the proportionality theorem for evaluating x as follows:
JD/DK = PJ/PK
3x/(4x + 1) = 20/28
3x × 28 = 20(4x + 1) {cross multiplication}
84x = 80x + 20
84x - 80x = 20 {collect like terms}
4x = 20
x = 20/4 {divide through by 4}
x = 5
Therefore, the value of the variable x for the triangle base length is derived as 5.
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