Answer:
The formation of a linear programming model involves the following steps:
1. Define the objective: Determine what you want to optimize or minimize, such as maximizing profit or minimizing costs.
2. Identify the decision variables: Identify the variables that affect the objective, such as the number of units produced.
3. Formulate the constraints: Establish the limitations that the model needs to operate within, such as production capacity, labor availability, or budget constraints.
4. Write the mathematical equations: Use the identified decision variables, constraints and objective function to write a set of linear equations.
5. Test and solve the model: Test the model by solving the linear equations using mathematical techniques such as simplex method or graphical method.
6. Interpret the results: Analyze the results of the model to gain insights into the optimization of your objective and how changes in variables or constraints can affect the outcome.
Consider the following function.
f(x) = −2x^3 − 6x^2 + 5
(a) Use the Intermediate Value Theorem and a graphing utility to find graphically any intervals of length 1 in which the polynomial function is guaranteed to have a zero. Verify your answers by using the table feature of the graphing utility. (Select all that apply.)
(−4, −3)
(−3, −2)
(−2, −1)
(−1, 0)
(0, 1)
(1, 2)
(2, 3)
(3, 4)
(b) Use the zero or root feature of the graphing utility to approximate the real zeros of the function. (Enter your answers as a comma-separated list. Round your answers to three decimal places.)
x =
, in the presented question, we can conclude that Interval [tex](0, 1): f(0) 5, f(1) -3[/tex], indicating that the function switches signs and has a zero in the interval [tex](0, 1).[/tex]
What are polynomials?Interval [tex](4, 3): f(-4) -41, f(-3) 5,[/tex]therefore, the function reverses its sign and has a zero in the interval [tex](-4, -3).[/tex]
Interval [tex](3, 2): f(-3) 5, f(-2) -9,[/tex] indicating that the function changes sign and has a zero in the interval [tex](-3, -2).[/tex]
Interval [tex](2, 1): f(-2) -9, f(-1) 1[/tex], therefore the function reverses its sign and has a zero in the interval [tex](-€2, -1).[/tex]
Interval [tex](1, 0): f(-1) 1, f(0) 5[/tex], so the function does not change sign and the interval may or may not contain a zero [tex](-1, 0).[/tex]
Interval [tex](0, 1): f(0) 5, f(1) -3,[/tex] indicating that the function switches signs and has a zero in the interval [tex](0, 1).[/tex]
Therefore, in the presented question, we can conclude that Interval [tex](0, 1): f(0) 5, f(1) -3[/tex], indicating that the function switches signs and has a zero in the interval [tex](0, 1).[/tex]
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18.A singer sells a single as a music download and CD, making a total profit of £246.64
She sells 456 CD singles, earning 35p for every single sold.
She earns 17p for each music download of the single.
How many music downloads did she sell?
The singer sold 512 music downloads.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".
Let's use the following variables:
CD = the number of CD singles sold
DL = the number of music downloads sold
From the problem, we know the following:
CD + DL = total number of singles sold
CD = 456
The profit from selling CD singles is 35p = £0.35 per CD single
The profit from selling music downloads is 17p = £0.17 per music download
The total profit is £246.64
Using the information above, we can set up two equations based on the profits earned from selling CD singles and music downloads:
0.35 * CD = profit from CD sales
0.17 * DL = profit from download sales
And we know that the sum of these two profits equals the total profit:
0.35 * CD + 0.17 * DL = 246.64
Substituting CD = 456, we get:
0.35 * 456 + 0.17 * DL = 246.64
Simplifying this equation, we get:
159.6 + 0.17 * DL = 246.64
0.17 * DL = 87.04
DL = 512
Therefore, the singer sold 512 music downloads.
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Question 7 of 10
AFGH is a right triangle.
9
6
G
√45
H
A. True
OB. False
Yes, it is true that Triangle FGH is a right triangle.
How can this be determined?We check whether the Pythagorean theorem holds true for these sides to determine if this triangle is a right triangle. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the right triangle's legs.
a² + b² = c²
If this is a right triangle, the hypotenuse will be the longest side, and the other two sides will be the legs. We have these when we incorporate the Pythagorean theorem.
6²+(√45)² = 9²
36+45 = 81
which implies that right triangle because the assertion is true.
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What is the product of 2.5 and 7.08?
Show your work.
The scatterplot of the data below models what type of correlation?
Answer:
asdfasdfasdf
Step-by-step explanation:
asdf
HELP!!!! IM GOING TO FAIL!!!
Answer10 toooooooooooo the third poewedd
Step-by-step explanation:
Para prepara un pastel Anita tenía un paquete de harina de 1 1/3 si solo uso 3/6 kg del paquete que cantidad de harina le sobró
Para preparar un pastel, Anita tenía un paquete de harina de 1 1/3 kg: 0.83 kg
Primero, debemos convertir 1 1/3 kg a una fracción común. 1 1/3 kg es igual a 4/3 kg o 1.33 kg. Luego, podemos simplificar 3/6 a 1/2.
Ahora podemos restar 1/2 de 1.33 kg para encontrar la cantidad de harina que sobró.
1.33 kg - 1/2 kg = 1.33 kg - 0.5 kg = 0.83 kg
Entonces, Anita le sobró aproximadamente 0.83 kg de harina después de preparar su pastel.
Es importante recordar que la medición y las cantidades de los ingredientes son cruciales al preparar cualquier receta de cocina. Es importante seguir las instrucciones cuidadosamente para obtener resultados exitosos en la cocina.
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16 Triangle ABC is translated to triangle A'B'C' by
the following motion rule.
(x, y)(x+2y-5)
-8 -6
G
A. (4,-4)
B. (2,-5)
C. (0.6)
D. (-2.5)
N
8
6
B
-2
S
-6
-8
2
What will be the coordinates of A'?
6 8
Answer:
To find the coordinates of A' after the translation, we need to apply the motion rule to the coordinates of A:
(x, y) → (x + 2y - 5, y - 6)
Substituting the coordinates of point A, which is (4, -4), into this motion rule, we get:
A' = (4 + 2(-4) - 5, -4 - 6) = (-3, -10)
Therefore, the coordinates of A' after the translation are (-3, -10).
f(x) = x². What is g(x)?
WW
(3, 1)
g(x)
-5
y f(x) = x²
5
Click here for long description
A. g(x) = 3x²
B. g(x) = (x)²
2
C. g(x) = x²
2
D. g(x) = (x)
Finding [tex]g(x)[/tex] given that we know [tex]f(x)[/tex] and the graphs for both functions. The correct option is D:
[tex]g(x) = (x/3)^2[/tex]
How to find g(x)?Looking at the graph on the image, we notice that [tex]f(x)[/tex] and [tex]g(x)[/tex] are two quadratic functions, and [tex]g(x)[/tex] is just a dilation o f[tex]f(x)[/tex].
This means that:
[tex]g(x) = A*f(x)[/tex]
Where A is a real number.
We know that:
[tex]f(x) = x^2[/tex]
By looking at the graph in the image, we know that [tex]g(3) = 1[/tex].
Then we can write:
[tex]g(3) = A*f(3) = A*3^2 = 1[/tex]
We can now solve for A:
[tex]A*3^2 = 1[/tex]
[tex]A*9 = 1[/tex]
[tex]A = 1/9[/tex]
We will have:
[tex]g(x) = (1/9)*f(x) = (1/9)*x^2 = (x/3)^2[/tex]
Therefore, the correct option is D.
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Complete question in image attached.
Calculate the area of a square with sides of 5 inches. a. 20 inches b. 20 square inches c. 25 inches d. 25 square inches
Answer: d. 25 square inches
Step-by-step explanation:
If x ≠ 0 and y ≠ 0, which expression is equivalent to −4x−2 y−3 ? Responses A −4x2y3 − 4 x 2 y 3 B 14x2y3 1 4 x 2 y 3 C −4x2y3 − 4 x 2 y 3 D −4xy − 4 xy
Answer:The expression −4x−2y−3 can be written as −4/x^2y^3.
Multiplying both numerator and denominator by -1, we get 4/x^2y^3.
Hence, option A, −4x^2y^3, is equivalent to −4x−2y−3.
Step-by-step explanation:
What is the volume of this cone?
The volume of the cone is 2119. 5 cubic centimeters
How to determine the volume of the coneThe formula used for calculating the volume of a cone is expressed as;
V = πr² h/3
Given that the parameters are namely;
V is the volume of the cone.π takes the constant value of 3.14h is the height of the cone.r is the radius of the cone.Now, substitute the values, we have;
Volume , V = 3.14 × 15² × 9/3
Divide the values, we have;
Volume = 3.14 × 225 × 3
Multiply the values, we get;
Volume, V = 2119. 5 cubic centimeters
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there are 250 n each has a mass of 5.2x10 to the negative 3 power kilograms.What is the total mass in kilograms in decimal form
Answer:
the total mass of the 250 objects is 1.3 kilograms.
Step-by-step explanation:
To find the total mass of the 250 objects, we need to multiply the mass of each object by the number of objects:
Total mass = mass per object x number of objects
The mass per object is given as 5.2x10^-3 kg, and the number of objects is 250. So, we can calculate the total mass as follows:
Total mass = 5.2x10^-3 kg x 250
Total mass = 1.3 kg
What is the surface area of an ice cube that has 4 cm sides?
TA
4 cm
4 cm
The surface area of an ice cube with 4 cm sides is 96 square centimeters.
What is surface area?It is a measurement of the sum of all the areas of the faces, sides, and any other surfaces of an object. For example, a cube has six square faces, each with the same area.
According to question:To find the surface area of an ice cube with 4 cm sides, we need to add up the areas of all six faces. Each face is a square with side length 4 cm, so the area of each face is:
Area of one face = (side length)² = 4 cm × 4 cm = 16 cm²
Since there are six faces on a cube, the total surface area of the ice cube is:
Total surface area = 6 × (area of one face) = 6 × 16 cm² = 96 cm²
Therefore, the surface area of an ice cube with 4 cm sides is 96 square centimeters.
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type an equation for the following pattern x12345 y-2 -4 -6 -8 -10
Answer: y = -2 - 2 * (x - 1).
Step-by-step explanation: The pattern is a linear function with a slope of -2 and an intercept of -2. The slope of a line is the change in y over the change in x. In this case, the change in y is -2 and the change in x is 1. Therefore, the slope is -2/1 = -2. The intercept is where the line crosses the y-axis, which is at y = -2 when x = 1. Therefore, the equation of the line is y = mx + b where m is the slope and b is the intercept. Substituting m = -2 and b = -2 gives us y = -2 - 2 * (x - 1).
Hope this helps, and have a great day!
The length of the longer leg of a 30 60 90 triangle is 6. The shorter leg is 4.
State the solution in Simple Root Form:
State the solution to the nearest tenth:
Step-by-step explanation:
remember the trigonometric triangle inscribed in a circle (the norm circle with radius = 1).
for a larger system the leg lengths are sine and cosine multiplied by the radius (which is the Hypotenuse of the right-angled triangle).
the longer leg is opposite of the larger angle (60°).
the shorter leg is opposite of the smaller angle (30°).
what is the desired solution ? the length of the Hypotenuse ? or what ?
6 = sin(60)×Hypotenuse
Hypotenuse = 6/sin(60) = 6/(sqrt(3)/2) = 12/sqrt(3) =
= 6.92820323... ≈ 6.9
An air tank of 500 mL is 80% oxygen and 20% nitrogen. What is the amount of oxygen in milliliters in a 200 ml air tank that contains the same ratio?
Hence, 160 mL of oxygen is contained inside a 200 mL air tank using the same ratio as a 500 mL air tank.
How is ratio calculated?Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were trying to compare one piece of data (A) to some other data point (B). We are multiplying information A by data B, as this suggests. In the event that A and B are both 5, for example, your ratio would've been 5/10.
80% of 500 mL of oxygen if indeed the air tank contains 80% oxygen & 20% nitrogen, which is:
0.80 x 500 mL = 400 mL
This means that the air tank contains 400 mL of oxygen and 100 mL of nitrogen.
To find the amount of oxygen in a 200 mL air tank that contains the same ratio, we need to use proportions:
If 500 mL contains 400 mL of oxygen, then 1 mL contains 400/500 = 0.8 mL of oxygen.
Therefore, if 200 mL contains the same ratio of oxygen, it will contain:
0.8 mL x 200 mL = 160 mL
So, the amount of oxygen in a 200 mL air tank with the same ratio as the 500 mL air tank is 160 mL.
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15. MULTIPLE CHOICE Determine which statement is true given that CBX = SML.
The statement that is true, given that ΔCBX ≅ ΔSML, would be G. XC ≅ ML.
How to find the true statement on congruent triangles ?Given that ΔCBX ≅ ΔSML, we can use the properties of congruent triangles to determine which statement is true. The correspondence between the vertices of the two triangles is as follows:
C ↔ S
B ↔ M
X ↔ L
XC ≅ ML is true because XC corresponds to the side connecting vertices X and C in ΔCBX, and ML corresponds to the side connecting vertices M and L in ΔSML. Since the triangles are congruent, their corresponding sides are congruent.
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I need help ASAP.I m really confused with it
Solve the following linear programming problem. Maximize: z = 7x + 2y subject to: 7x-y≤ 16 2x+y≥ 10 X≥2 y≤9 The maximum value is
Answer:
To solve the linear programming problem, we need to first graph the feasible region determined by the constraints, and then evaluate the objective function at each corner point of the feasible region to find the maximum value of z.
Plotting the lines corresponding to the inequalities, we get:
Graph of the feasible region:
The feasible region is the shaded polygon in the graph. We can see that the vertices of the feasible region are (2, 9), (2, 12), (4, 7), and (8, 2).
Next, we evaluate the objective function at each of these vertices to find the maximum value of z.
At (2, 9): z = 7x + 2y = 7(2) + 2(9) = 23
At (2, 12): z = 7x + 2y = 7(2) + 2(12) = 31
At (4, 7): z = 7x + 2y = 7(4) + 2(7) = 35
At (8, 2): z = 7x + 2y = 7(8) + 2(2) = 58
Therefore, the maximum value of z is 58, which occurs at the point (8, 2).
Hence, the answer is: the maximum value of z is 58.
Greg covered the back of the picture with a piece of felt. The picture is 1 1/4 inches shorter than the fram and 1 inch less in width what is the area of the felt
The area of the felt is (5L - 4W - 5) / 4 (inches)².
What is an area?
To find the area of the felt, we need to know the dimensions of the picture and the frame.
Let's say the length of the frame is L and the width of the frame is W.
Then, according to the problem:
The length of the picture is 1 1/4 inches shorter than the frame, so its length is L - 1 1/4 = (4L - 5) / 4 inches.The width of the picture is 1 inch less than the frame, so its width is W - 1 inches.To find the area of the felt, we need to subtract the area of the picture from the area of the frame. The area of the frame is L x W, and the area of the picture is (4L - 5) / 4 x (W - 1). So the area of the felt is:
Felt area = Frame area - Picture area
= L x W - (4L - 5) / 4 x (W - 1)
= (4LW - 4W) / 4 - (4LW - 5L - 4W + 5) / 4
= (5L - 4W - 5) / 4
Therefore, the area of the felt is (5L - 4W - 5) / 4 (inches)². Note that we can't simplify this expression further without knowing the specific values of L and W.
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Complete question is: Greg covered the back of the picture with a piece of felt. The picture is 1 1/4 inches shorter than the fram and 1 inch less in width the area of the felt is (5L - 4W - 5) / 4 (inches)².
Alia has 36 1/4 inches shares of silver chain to make some braces if she needs 7 1/4 inches of the chain to make one bracelet how many bracelets can Alia
make
Answer:
To find the number of bracelets Alia can make, we need to divide the total length of the silver chain she has by the length of each bracelet.
Total length of silver chain = 36 1/4 inches
Length of each bracelet = 7 1/4 inches
To divide fractions, we need to invert the second fraction and multiply:
(36 1/4) ÷ (7 1/4) = (145/4) ÷ (29/4) = (145/4) x (4/29) = 5
Therefore, Alia can make 5 bracelets with the given amount of silver chain.
Answer:
5 bracelets
Step-by-step explanation:
Given Information:
Amount of chain needed for 1 bracelet: 7 1/4 inchesTotal chain length: 36 1/4 inchesClearly, the number of bracelets possible (say x) multiplied by the amount of chain required for 1 bracelet will result in the total chain length (36 1/4).
⇒ 7 1/4 × x = 36 1/4Now, we can divide 7 1/4 on both sides to find value of x (total bracelets).
⇒ (7 1/4 × x)/(7 1/4) = (36 1/4)/(7 1/4)⇒ x = (36 1/4)/(7 1/4) = 5Therefore, Alia can make 5 bracelets.
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Do you guys know the answer to this please help?
Answer:37
Step-by-step explanation:
<UYW=<UYV+<VYW=36+2x=110
2x=110-36=74
x=74/2=37
Find the foci of the hyperbola 4y2-x2=16
The foci of the hyperbola is (0,2[tex]\sqrt5[/tex]) and ([tex]0,-2\sqrt5)[/tex].
What is foci of the hyperbola?The two fixed points that are located inside each curve of a hyperbola are known as its foci, and they are important for the formal description of the curve.
Here the given equation of the hyperbola is [tex]4y^2-x^2=16[/tex] .
Now writing the given equation into standard form then,
=> [tex]4y^2-x^2=16[/tex]
=> [tex]-x^2+4y^2=16\\[/tex]
=> [tex]\frac{-x^2}{4}+\frac{4y^2}{4}=\frac{16}{4}[/tex]
=> [tex]\frac{-x^2}{4}+y^2=4[/tex]
=> [tex]\frac{-x^2}{4\times4}+\frac{y^2}{4}=1[/tex]
=> [tex]\frac{-x^2}{16}+\frac{y^2}{4}=1[/tex]
Here we know that [tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex] then a=2 and b=4 , (h , k)=(0,0)
Then c=[tex]\sqrt{a^2+b^2}=\sqrt{2^2+4^2}=\sqrt{4+16}=\sqrt{20}=2\sqrt{5}[/tex].
Then foci is (0,0+c) and (0,0-c) then,
=> (0,2[tex]\sqrt5[/tex]) and ([tex]0,-2\sqrt5)[/tex]
Hence the foci of the hyperbola is (0,2[tex]\sqrt5[/tex]) and ([tex]0,-2\sqrt5)[/tex].
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I please need help matching the angles. I cannot seem to get it right.
The angles and lines that match the angles and lines in the diagram consisting of two lines and their common transversal to the correct description are;
Alternate Interior Angles; 2. ∠4 and ∠8
Consecutive Exterior Angles; 5. ∠1 and ∠6
Alternate Exterior Angles; 3. ∠1 and ∠5
Transversal; line l
Consecutive Interior Angles; 4. ∠3 and ∠4
Corresponding Angles; 1. ∠1 and ∠7
What is a transversal line?A transversal is a line that intersects two or more other lines.
The description of the relationship between the angles in the question are;
Alternate Interior Angles
Alternate interior angles are a pair of angles formed when a transversal intersects two lines. They are located between the two lines on opposite side of the transversal.
Consecutive Exterior Angles
Consecutive Exterior Angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the same side of the transversal
Alternate Exterior Angles
Alternate exterior angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the opposite sides of the transversal.
Consecutive Interior Angles
Consecutive Interior Angles, also known as Same-Side Interior Angles are a pair of angles formed when a transversal intersects two parallel lines. They are located between the two parallel lines on the same side of the transversal.
Corresponding Angles
Corresponding angles are a pair of angles formed when a transversal intersects two lines. They are located on the same relative positions with respect to the transversal and the two lines.
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the opposite of the oppsite of 28,or (-28),is equivalent to which of the following
0
-28
28
The opposite of the oppsite of 28,or (-28), is equivalent to the option (c) 28
How to determine the equivalent expressionThe opposite of a number is the number with the opposite sign.
For example, the opposite of 28 is -28, and the opposite of -28 is 28.
So, the opposite of the opposite of 28, or (-28), is the opposite of -28, which is 28.
This means that the answer is (c) 28.
To explain it further, think of the number line. 28 is a positive number, so its opposite is a negative number, which is -28.
Now, the opposite of -28 is a positive number, which is 28. So, the opposite of the opposite of 28 is 28.
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Which of these points are 5 units away from (-6, -3)? Select all that apply.
(-3, -7)
(-2,-7)
(-2, 0)
(-9, -1)
Answer:(-3, -7)
Step-by-step explanation: (7-3,-) look the middle is (3,-6) and instead on 7 is 6 bec in 7-
If f(x)= 4x/x-3
then determine the value of f^-1 (inverse) (16) Explain or show how you arrived at your answer.
Answer:32+ 1.21
Step-by-step explanation:
if you really want an awser you would take all the nubers and sfhgkjfqipjghwpkrejvhbwptijgbqkejnvwpigtnjuvrepiufgnjwrekjbhartio
PLEASE HELP Area of Cross Sections
Answer:
396 in²
Step-by-step explanation:
To answer this question we need to use pythagorean theorem (a² + b² = c²)
In our case, a would be 14 and b would be 17
14² + 17² = ?²196 + 289 = 485[tex]\sqrt{485}[/tex] = 22.02Now we have to multiply this by 18
22.02 x 18 = 396.36Which rounded would be 396
Hope this helps, have a lovely day! :)
How many quarts of pure antifreeze must be added to 5 quarts of a 10 % antifreeze solution to obtain a 30 % antifreeze solution?
According to the solving this algebra approximately 1.43 quarts of pure antifreeze to the initial 5 quarts of 10% antifreeze solution to obtain a 30% antifreeze solution.
what is algebra?
Mathematical operations are applied to abstract symbols rather than concrete numbers in the field of algebra, which also includes other formal manipulations. The area of mathematics known as geometry is concerned with the qualities of the space that objects are in as well as the shape of the objects themselves.
According to the given information:
Let Q be the number of quarts of pure antifreeze to be added.
Let 0.10(5) be the amount of antifreeze in the initial 5 quarts of the 10% antifreeze solution, which is 0.5 quarts.
To obtain a 30% antifreeze solution, the amount of antifreeze in the final solution should be 0.3(5+Q) quarts.
Since we are only adding pure antifreeze, the amount of antifreeze in the final solution will be the sum of the antifreeze in the initial solution and the antifreeze we add:
0.5 + Q = 0.3(5+Q)
Now we can solve for Q:
0.5 + Q = 1.5 + 0.3Q
0.7Q = 1
Q = 1/0.7
Q ≈ 1.43
Therefore, we need to add approximately 1.43 quarts of pure antifreeze to the initial 5 quarts of 10% antifreeze solution to obtain a 30% antifreeze solution.
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