Answers
The maximum value of z = 28. I occurs at (x, y) = 4
How to go about this ?To solve thhis linear programming problem, we can use the graphical method..
Graph the feasible region defined by the constraints.....
x >= 0 and y >= 0 represent the non-negative quadrants.
x + y < = 8 represents the area below the line passing through ( 8, 0) and (0, 8).
x + y >= 2 represents the area above the line passing through ( 2 , 0) and (0 , 2).
Identify the corner points of the feasible region .....
(0, 2)
( 2, 0)
( 4, 4)
( 8, 0 )
Calculate tthe objective function at each corner point....
z(0, 2 ) = 3(0) + 4(2) = 8
z (2, 0 ) = 3(2) + 4(0) = 6
z(4, 4 ) = 3(4) + 4(4) = 28
z ( 8, 0) = 3(8) + 4(0) = 24
Determine the maximum value of the objective function and the values of x and y that give this maximum value
The maximum value of z is 28, which occurs at the corner point (4, 4).
So we c can be stated as follows --
Maximum value of z = 28
x = 4
y = 4
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Related Questions
Here is question 3 of 6. Thank you for the help
Answers
Yes, data provide convincing evident that contest has increased participation.
We have,
H₀: p = 0.12
Hₐ: p > 0.12
So, z = (p' - p)/ (√pq/n)
z = 1/6 - 0.2/ √(0.12 x 0.88) /210
z= 2.08
The test is right tailed.
So, P value = P( z> 2.08) = 0.0188
and, P- value < α, Reject H₀
Yes, data provide convincing evident that contest has increased participation.
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|x| = 9 Solve the equation. Check your solutions. Graph the solution(s) on a piece of paper.
Answers
The equation |x| = 9 has two solutions: x = 9 and x = -9. The shaded region includes all points to the left of -9 and all points to the right of 9.
The equation is given as follows:
|x| = 9
The equation |x| = 9 has two solutions: x = 9 and x = -9.
To check these solutions, we can substitute them back into the original equation and see if they satisfy it:
|x| = 9
|9| = 9 --> True
|-9| = 9 --> True
Therefore, the solutions x = 9 and x = -9 are both valid.
To graph the solution(s), we can draw a number line and mark the points x = 9 and x = -9 with closed circles (since the absolute value of x is equal to 9 at those points).
We can then shade the parts of the number line where the absolute value of x is greater than or equal to 9.
This includes all points to the right of 9 and all points to the left of -9.
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Answer
[tex]\large\textrm{There are two solutions: 9 and -9.}[/tex]
Further explanation
If we have the absolute value of x, that means x could be positive or negative.
This means that, in |x| = 9, x could be 9 or -9.
Checking
Plug the answers into the original equation.
You should get a true statement.
[tex]\rm{\mid 9\mid=9}[/tex]because the absolute value of 9 is 9 so that's a solution
[tex]\rm{\mid-9\mid=9}[/tex]the absolute value of -9 is also 9 so that's also a solution
therefore, the solutions are 9 and -9.
What is the domain of the function y=tan (x/8)
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The domain can be written as follows:
R - {x = n*12pi or m*4pi | n, m ∈ Z}
where pi = 3.14 and R is the set of real numbers.
What is the domain of the function?Here we want to find the domain of the function:
y = tan(x/8)
The tangent is the quotient between the cosine and the sine, then we will get:
sin(x/8)/cos(x/8)
The problems of the tangent are all the values that make the denominator equal to zero, then we need to remove these.
The zeros are:
cos(x/8) = 0
We know that cos(pi/2) = cos(3pi/2) = 0
Then:
x/8 = pi/2
x = 4pi
x/8 = 3pi/2
x = 12pi
So the domain is the set of all real numbers except the ones in the next set:
{x = n*12pi or m*4pi | n, m ∈ Z}
Where Z is the set of integers.
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Simplify. (5 x sqrt 2 - 1)^2
Answers
In circle V, VW = 8 and the area of shaded sector = 167. Find the length of
WY X. Express your answer as a fraction times .
W
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The length of m∠WYX is equal to 12π units.
How to calculate the area of a sector?In Mathematics and Geometry, the area of a sector can be calculated by using the following formula:
Area of sector = θπr²/360
Where:
r represents the radius of a circle.θ represents the central angle.By substituting the given parameters into the area of a sector formula, we have the following;
Area of sector = θπr²/360
16π = θ(π/360) × 8²
Central angle, θ = 0.5π
m∠WYX = 2π - m∠WX
m∠WYX = 2π - 0.5π
m∠WYX = 1.5π
Length of m∠WYX = (1.5π)/2π × 2πr
Length of m∠WYX = (1.5π)/2π × 2π(8)
Length of m∠WYX = 12π units.
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Helppp please it’s due tomorrow
Answers
The total number of cups of grapes and raisins include the following: 5/6 cups of grapes and raisins.
How to determine the total number of cups of grapes and raisins?In Mathematics and Geometry, a fraction is a numerical quantity (number or numeral) that is typically expressed as a quotient (ratio) or not expressed as a whole number. This ultimately implies that, a fraction simply refers to a part of a whole number.
Based on the information provided above, the total number of cups of grapes and raisins can be calculated as follows;
Fraction = 1/2 + 2/3
Fraction = (3 + 2)/6
Fraction = 5/6 cups of grapes and raisins.
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One number is 10 more than fifteen times another. Their sum is 42. Find the numbers.
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From the problem, we know that:
- x = 15y + 10 (since "One number is 10 more than fifteen times another")
- x + y = 42 (since "Their sum is 42")
We can use substitution to solve for one of the variables. Substituting the first equation into the second equation, we get:
(15y + 10) + y = 42
Simplifying the left side, we get:
16y + 10 = 42
Subtracting 10 from both sides, we get:
16y = 32
Dividing both sides by 16, we get:
y = 2
Now that we know y, we can use the first equation to solve for x:
x = 15y + 10
x = 15(2) + 10
x = 40
Therefore, the two numbers are 2 and 40.
Answer:
40, 2
Step-by-step explanation:
x = number 1
y = number 2
x = 15y + 10
x + y = 42
we use the first in the second equation and get
15y + 10 + y = 42
16y = 32
y = 32/16 = 2
x + y = 42
x + 2 = 42
x = 40
Use the relationship given in the right triangle and the inverse sine, cosine, and tangent functions to write 0 as a function of x in three different ways. It is not
necessary to rationalize the denominator.
a
-√√81-x²³.c-9
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The measure of inverse of sinθ is c/√ (c² - a²)..
What is the measure of inverse of sinθ?The measure of inverse of sinθ is calculated by applying trigonometry identities for right triangles.
Mathematically, the trig identities are represented using the following method;
SOH CAN TOA
SOH is for sine θ
CAH is fof cos θ
TOA is for tan θ
From the diagram we need find the value of the opposite side;
b = √ (c² - a²)
Sin θ = b/c
The inverse of b/c = c/b
1/sinθ = c/b = c/√ (c² - a²).
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Let f(t) be the sales of a gaming product, in thousands of units, after t months.
Answers
The sales after 5 months is 36,000 units (since f(t) is given in thousands of units).
The given function f(t) represents the sales of a gaming product in thousands of units after t months. To find the sales after 5 months, we need to substitute t = 5 in the function f(t) and evaluate the expression. f(5) = 5(5) + 11
= 25 + 11
= 36
Therefore, the sales of the gaming product after 5 months is 36 thousand units. This means that the company has sold 36 thousand units of the gaming product within the first 5 months since the launch of the product. It also indicates that the sales are increasing by 5 thousand units every month.
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-- The given question is incomplete, the complete question is
"Let f(t) be the sale of a gaming product in thousand of units after t months f(t)=5t+11. Find the sales after 5 months."
Math Algebra Help needed
Answers
You can use functions to complete the table as follow:
x f(g(x))
4 2
10 4
20 6
34 8
52 10
How to use functions to complete the table?A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
We have:
f(x) = √(x+1)
g(x) = 2x - 5
When x = 4:
f(g(x)) = f(g(4))
f(g(4)) = f(2*4 - 5)
f(g(4)) = f(3)
f(g(4)) = √(3+1) [Remember f(x) = √(x+1)]
f(g(4)) = 2
When x = 10:
f(g(10)) = f(2*10 - 5)
f(g(10)) = f(15)
f(g(10)) = √(15+1)
f(g(10)) = 4
When x = 20:
f(g(20)) = f(2*20 - 5)
f(g(20)) = f(35)
f(g(20)) = √(35+1)
f(g(20)) = 6
When x = 34:
f(g(34)) = f(2*34 - 5)
f(g(34)) = f(63)
f(g(34)) = √(63+1)
f(g(34)) = 8
When x = 52:
f(g(34)) = f(2*52 - 5)
f(g(34)) = f(99)
f(g(34)) = √(99+1)
f(g(34)) = 10
Thus, fill the values into the table to complete it.
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Malick is forming clay blocks in the shape of rectangular prisms.
Two faces of the blocks are squares.
First, find the missing length of the clay block. Then, find the volume.
Answers
The missing length is 4 in.
The volume of a rectangular prism is 32 in³.
We have,
Since the two faces of the blocks are squares.
The face that has the missing length can be considered as a square face.
i.e
The front and back faces are squares.
So,
The missing length is 4 in.
Now,
The volume of a rectangular prism.
= length x width x height
= 4 x 2 x 4
= 32 in³
Thus,
The missing length is 4 in.
The volume of a rectangular prism is 32 in³.
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Lisa is putting 11 colored light bulbs into a string of lights. There are 3 red light bulbs, 2 yellow light bulbs, and 6 pink light bulbs. How many distinct orders of light bulbs are there if two light bulbs of the same color are considered identical (not distinct)?
Answers
We can see here that the distinct orders of light bulbs that are there if two light bulbs of the same color are considered identical is: 4,620.
How we arrived to the solution?We can see here that in order to find the solution, we use the permutation with repetition formula:
n! / (n1! × n2! x ... × nk!)
In order to adjust for overcounting, we divide by 3! because of the 3 red light bulbs we have. For the 2 yellow light bulbs, we divide with 2!. For the 6 pink light bulbs, we divide by 6!. This is because we are treating lights bulbs of the same color which are identical.
Therefore, the total number of distinct orders of bulbs will be:
11! / (3! × 2! × 6!) = 4,620
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on a 28 question test there are 2-point questions, 4-point, and 5- point questions. the test is worth a total of 100 points. there are twice as many 2 point questions as 5point questions on the test how many 2point questions are on the test
Answers
Answer:
Number of 2-point questions on the test as per given condition is equals to 8.
Total number of questions in a test = 28
Total points allotted for test = 100
Questions distribution as per points :
2-point questions, 4-point questions, and 5-point questions
'x' represents the 5-point questions
As per condition given,
Number of 2-point questions = 2x
Number of( 2-point + 4-point + 5-point ) questions = 28
⇒ 2x + 4-point questions + x = 28
⇒ 4-point questions = 28 - 3x
Substitute the value in the given condition of the equation we get,
2(2x)+4(28-3x)+5(x) = 100
4x+112-12x+5x=100
112-3x=100
x=4
Determine if triangle RQP is similar to triangle YXW. If they are similar enter the scale factor from triangle YXW to triangle RQP
Answers
The triangles are similar, and the scale factor is given as follows: k = 0.8.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of the missing angle is given as follows:
x + 114 + 24 = 180
x + 138 = 180
x = 42º.
Which is equals to the measure on the second triangle, hence they are similar.
The scale factor is given as follows:
k = 16/20 = 36/45 = 0.8.
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What is 2 plus 2 please tell me
Answers
Answer:
Step-by-step explanation: The answer is 4 all u do is add 2 to 2
Answer: 2+2=4
Step-by-step explanation: The sum of two and two results in a value of four in a quantitative analysis.
The area of a large parking space is 162 square feet. If the width of the parking space is 9 feet, what is the length?
A 12 feet
B 14 feet
C 16 feet
D 18 feet
Answers
162 divided by 9 would equal 18.
Paola has enough mulch to cover 48 square feet. She wants to use it to make three square vegetable gardens of equal sizes. Solve the equation 3s2 = 48 to find s, the length of each garden side (in feet).
Answers
The length of each garden side is 4 ft.
Given that, Paola has 48 ft² of mulch, she wants to make three square vegetable gardens of equal sizes, we need to find the length of each garden side.
Let s be the length of the side of the gardens,
Since, she need 3 gardens,
So,
3 × side² = 48
3s² = 48
s² = 16
s = 4
Hence, the length of each garden side is 4 ft.
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Larry cut a ribbon into 8 equal pieces. If the ribbon was 26 m long, how many meters long was each piece?
Answers
As per the unitary method, each piece is 3.25 meters long by dividing the total length of the ribbon by the number of pieces.
Larry has cut a ribbon into 8 equal pieces. The total length of the ribbon is 26 m. We need to find out the length of each piece of the ribbon.
To do this, we can use the unitary method. We know that the ribbon is divided into 8 equal pieces, so each piece is 1/8th of the total length of the ribbon.
Therefore, we can find the length of each piece by dividing the total length of the ribbon by 8:
Length of each piece = Total length of ribbon / Number of pieces
Length of each piece = 26 m / 8
Length of each piece = 3.25 m
So, each piece of the ribbon is 3.25 meters long.
We used the unitary method by finding the value of one unit (1/8th of the ribbon) and then using it to calculate the value of other units (the length of each piece).
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A plane takes off at a 10 degree angle. How far away is the plane (ground distance) once it reaches an altitude (height) of 30,000 feet?
We are missing a side or and angle? Regular or Inverse Trig?
Answers
The ground distance of the plane is 170,138.5 ft.
What is the ground distance of the plane?
The ground distance of the plane is calculated by applying trigonometry ratio as shown below;
SOH CAH TOA
SOH = sin θ = opposite /hypothenuse side
TOA = tan θ = opposite side / adjacent side
CAH = cos θ = adjacent side / hypothenuse side
The height attained by the plane is the opposite side, while the ground distance is the adjacent side
tan (10) = 30,000 ft/d
d = 30,000 ft/tan(10)
d = 170,138.5 ft
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Graph the relationship with the greater rate of change on the coordinate grid.
• It takes Jason 2 hours to travel 180 miles to reach his destination.
.
Isaiah travels from Nashville to Atlanta. The equation below shows y as the number of miles traveled and x as the number of
hours he traveled.
y = 80x
SOMONE please tel me where to put the slope !!!‼️‼️
Answers
To graph the relationship between the two scenarios, we can plot the points on a coordinate grid. Jason's journey can be represented by the point (2, 180) and Isaiah's journey can be represented by the line y = 80x.
Since Isaiah's rate of change is greater than Jason's, we can see that the line y = 80x has a steeper slope than the line representing Jason's journey. Therefore, the graph of the relationship with the greater rate of change is the line y = 80x.
find the distance between the two points in simplest radical form (9,2) (4,-7)
Answers
Answer:
√50
Step-by-step explanation:
To solve, use distance formula.
√(9-4)^2 + (2-(-7))^2=
√5^2+5^2=
√50
What is the answer to this question
Answers
Answer:
The height of the kite is 63.40 feet.
Trigonometric ratio is used to show the relationship between the sides of a triangle and its angles.
Let h represent the height of the kite. Hence, using trigonometric ratios:
sin(30) = h / 95
h = 47.5 feet
Therefore the height of the kite is 63.40 feet.
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Answers
The volume of the solid is 1922.7 in³.
How to find the volume of a solid?The volume of a solid can be found by adding the volume of the shapes that make the solid. In this case:
Volume of solid = volume of hemisphere + volume of cylinder
Volume = 2/3πr³ + πr²h
where r = 12/2 = 6 in
height of cylinder (h) = 13 - 6 = 7 in
Volume = (2/3 * π * 6³) + (π * 6² * 13)
Volume = 1922.7 in³
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For the polynomial 11x4 + 8x2 + x which represents how much Patrick won from Michael, find the degree of each term. Then find the degree of the polynomial.
Answers
The degree of the polynomial 11x⁴ + 8x² + x is 4, which is the highest degree among its terms. The degrees of the terms are 4, 2, and 1 for the first, second, and third terms, respectively.
The degree of a term in a polynomial is the exponent of its variable.
In the polynomial 11x⁴ + 8x² + x, the degree of the first term 11x⁴ is 4, the degree of the second term 8x² is 2, and the degree of the third term x is 1.
The degree of the polynomial is the highest degree among its terms. In this case, the highest degree is 4, which is the degree of the first term. Therefore, the degree of the polynomial is 4.
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Find the 15th term of the geometric sequence 9, 18, 36, ...
Answers
Answer: 147,456
Step-by-step explanation: 9, 18, 36, 72, 144, 288, 576, 1,152, 2,304, 4,608, 9,216, 18,432, 36,864, 73,728, 147,456
List at least five combinations of nickels and dimes such that the number of nickels is double the number of dimes.
Answers
2 nickels and 1 dime
4 nickels and 2 dimes
6 nickels and 3 dimes
8 nickels and 4 dimes
10 nickels and 5 dimes
if there are 18 triangles in a polygon how many sides has the polygon
Answers
The number of sides of a polygon that has 18 triangles would be 20 sides.
How to find the number of sides ?To determine the number of sides in a polygon consisting of 18 triangles, we can calculate the sum of the interior angles. Each triangle has total interior angle sum of 180 degrees, and since there are 18 triangles, the sum of those angles would be 18 multiplied by 180, which comes to 3, 240 degrees.
Applying the given formula for calculating the interior angles of a polygon, we obtain that (n - 2) multiplied by 180 stands for the sum of all angles within it, with n being the number of sides.
Hence, rearranging the equation gives n :
n = (sum of interior angles ÷ 180) + 2
n = (3240 ÷ 180) + 2 = 20
There must be precisely 20 sides in that particular polygon.
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PLEASE HELP ( WILL GIVE BRAINLIEST)
Answers
Answer: Option C.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Given that the diameter of the container is 24 ft, the radius (r) would be half of that, which is 12 ft.
The depth of the container (h) is given as 4 ft.
Plugging in these values into the formula, we get:
V = π(12^2)(4)
V = 3.14(144)(4)
V = 1808.6 cubic feet (rounded to the nearest tenth)
So, the storage container can hold approximately 1808.6 cubic feet of wood, rounded to the nearest tenth.
Step-by-step explanation:
Please help me answer this question
Answers
The quadratic polynomial with integer as coefficients that has four real roots including these conjugates is a² + b² - 2ab - 20a - 20b + 88 ≥ 0
Here is how to derive the polynomialOne possible quartic polynomial with integer coefficients that has four real roots, including the conjugates 5+√3 and 5-√3, is:
(x - 5 - √3)(x - 5 + √3)(x - a)(x - b)
where a and b are the remaining two roots.
Expanding the first two factors using the difference of squares formula, we get:
(x - 5)² - 3
Expanding the last two factors, we get:
x² - (a + b)x + ab
Putting it all together, the quartic polynomial is:
a² + b² - 2ab - 20a - 20b + 88 ≥ 0
To ensure that a and b are also real, we can use the fact that the discriminant of a quadratic equation ax² + bx + c = 0 with real coefficients is b² - 4ac ≥ 0. Applying this to the quadratic factor in the above polynomial, we get:
(a + b)² - 4ab ≥ 0
Expanding and simplifying, we get:
a² + b² - 2ab - 20a - 20b + 88 ≥ 0
To simplify the problem, we can set a = b, since the polynomial is symmetric with respect to the roots. Then, the inequality becomes:
2a² - 40a + 88 ≥ 0
Dividing by 2 and factoring, we get:
(a - 10)² - 12 ≥ 0
This inequality is always true for real values of a, so we can choose any real value for a and set b = a to obtain a quartic polynomial with integer coefficients that has four real roots, including the conjugates 5+√3 and 5-√3.
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FOR 20 POINTS!!!
(Look at picture)
Answers
Answer:
Kenyon could make a total of 7 bouquets.
Step-by-step explanation:
To find the greatest number of bouquets we need to find GCF.
We need to find GCF for 21 and 28.
The factors of 21 are: 1,3,7, and 21.
The factors of 28 are: 1,2,4,7,14, and 28
1 and 7 are the common factors between 21 and 28.
From the factors, the greatest common factor is 7.