Ethan is deciding between two different movie streaming sites to subscribe to. Plan A costs $28 per month plus $2. 50 per movie watched. Plan B costs $37 per month plus $1 per movie watched. Let � A represent the monthly cost of Plan A if Ethan watches � x per month, and let � B represent the monthly cost of Plan B if Ethan watches � x movies per month. Write an equation for each situation, in terms of � , x, and determine the interval of movies watched, � , x, for which Plan A is cheaper than Plan B
If Ethan watches fewer than 6 movies per month, Plan A would be more expensive. If he watches more than 6 movies per month, Plan B would be more expensive.
For Plan A, the monthly cost is composed of a fixed fee of $28 plus a variable fee of $2.50 per movie watched. So, if Ethan watches x movies per month, the monthly cost for Plan A can be represented by the equation:
A = 28 + 2.5x
Here, A represents the monthly cost of Plan A, and x represents the number of movies Ethan watches per month.
For Plan B, the monthly cost is also composed of a fixed fee of $37, but the variable fee per movie watched is only $1. So, if Ethan watches x movies per month, the monthly cost for Plan B can be represented by the equation:
B = 37 + 1x
Again, B represents the monthly cost of Plan B, and x represents the number of movies Ethan watches per month.
To find the number of monthly movies watched, x, that would make the two plans have an equal monthly cost, we need to solve the equation:
A = B
So, we can substitute the equations for A and B to get:
28 + 2.5x = 37 + 1x
Now we can solve for x:
2.5x - 1x = 37 - 28
1.5x = 9
x = 6
So, if Ethan watches 6 movies per month, the monthly cost of Plan A and Plan B would be equal, at $41 per month.
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Which of the following is a valid objective function for a linear programming problem?
A. Max 5xy
B. Min 4x + 3y + (2/3)z
C. Max 5x2+ 6y2
D. Min (x1 + x2)/x3
Option B: Min 4x + 3y + (2/3)z is the valid objective function for a linear programming problem as it is a linear expression involving the decision variables x, y, and z.
Among the options provided, the valid objective function for a linear programming problem is option B: Min 4x + 3y + (2/3)z.
In linear programming, the objective function represents the quantity that needs to be either maximise or minimize. It is a linear expression involving the decision variables of the problem.
Option A: Max 5xy is a valid objective function as it is a linear expression involving the variables x and y. However, it is important to note that an objective function in linear programming must be linear and not involve multiplication between decision variables.
Option C: Max 5x^2 + 6y^2 is not a valid objective function because it includes the square terms (x^2 and y^2). In linear programming, the objective function needs to be linear, meaning it must consist of the variables and their coefficients without any nonlinear terms.
Option D: Min (x1 + x2)/x3 is not a valid objective function because it includes the division between decision variables (x1 + x2) and x3. Similar to multiplication, division between decision variables is not allowed in a linear programming objective function.Therefore, option B: Min 4x + 3y + (2/3)z is the valid objective function for a linear programming problem as it is a linear expression involving the decision variables x, y, and z.
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A car drove 10/45 miles in 0.4 hours. How fast was the car traveling in miles per hour?
Answer:
1.2 hours equal to 30mph
Step-by-step explanation:
Pls mark brainliest
Two sailboats are traveling along the same path away from
a dock, beginning from different locations at the same
time. John's boat begins 15 miles from the dock and is 45
miles from the dock after 5 hours. The distance of
Roberta's boat from the dock is represented by the
function y = 5x + 20, where x represents time, in hours, and
y represents the distance, in miles, from the dock.
Answer:
The answer is B
Step-by-step explanation:
Which equation can be used to solve the problem?
750 is 150 percent of what?
Answer:
it would be 750/500
Step-by-step explanation:
150% of 500 is 750
Carolyn wants to determine the area of her garden. she decided to make a garden in the shape of a parallelogram with a base of 3x2 + 4x + 5 and a height
of 48-9. what is the area of her garden?
Carolyn's garden is in the shape of a parallelogram with a base of 3x^2 + 4x + 5 and a height of 48 - 9. The area of her garden can be calculated by multiplying the base and the height.
To determine the area of Carolyn's garden, we need to use the formula for the area of a parallelogram, which is given by the product of the base and the height. The base of the parallelogram is represented by the expression 3x^2 + 4x + 5, while the height is represented by the expression 48 - 9.
To find the area, we multiply the base and the height:
Area = (3x^2 + 4x + 5) * (48 - 9)
To simplify the expression, we can distribute the values within the parentheses:
Area = 3x^2 * 48 + 3x^2 * (-9) + 4x * 48 + 4x * (-9) + 5 * 48 + 5 * (-9)
Simplifying further, we have:
Area = 144x^2 - 27x^2 + 192x - 36x + 240 - 45
Combining like terms, we get:
Area = 117x^2 + 156x + 195
Therefore, the area of Carolyn's garden is given by the expression 117x^2 + 156x + 195.
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The existence of this relief in the Persian capital city clearly portrays the ________________________ nature of the Persian Empire.
The existence of this relief in the Persian capital city clearly portrays the monumental and artistic nature of the Persian Empire.
The Persian Empire, renowned for its grandeur and opulence, left a rich legacy of architectural and artistic achievements. One of the remarkable features of the Persian Empire was its emphasis on monumental structures and elaborate artistic expressions. The existence of the relief in the Persian capital city stands as a testament to the empire's commitment to showcasing its power, wealth, and cultural sophistication. The relief, with its intricate detailing, impressive scale, and artistic finesse, reflects the grand vision and ambition of the Persian Empire. It serves as a visual representation of the empire's wealth, craftsmanship, and mastery of architectural techniques. The Persian rulers, recognizing the significance of art and architecture in projecting their imperial might, invested considerable resources and talent in creating magnificent structures and artworks. Through the existence of this relief, the Persian Empire conveyed its desire to leave a lasting legacy and demonstrate its dominance in the ancient world. The relief's presence in the capital city symbolizes the empire's cultural and artistic achievements, leaving an enduring impression of the Persian Empire's monumental and artistic nature.
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Approximate the fixed point of the function to two decimal places. [A fixed point of a function f is a real number c such that c) = c.] f(x) = cos x c=______
The approximate fixed point of the function f(x) = cos x to two decimal places is c = 0.74.
How we approximate the fixed point of the function to two decimal places?The terms "approximate," "function," and "real number" are relevant to your question.
A fixed point of a function f is a real number c such that f(c) = c.
We want to find an approximate value of c for the function f(x) = cos x to two decimal places.
To do this, we'll iterate the function and check when the input and output values are approximately equal.
After a few iterations, we find that the fixed point c is approximately 0.74.
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*15 points* any help would be appreciated plz
Answer:
70 degrees because all of the angles in a triangle add up to 180 degrees150 degrees because the adjacent angle is 30 degrees110 degrees because the adjacent angle is 70 degrees50 degrees because angle 5 would also have to be 50 in order for all of the angles on that line to be 180 degreesStep-by-step explanation:
I hope this helps!!!!
64 + {40 ÷(4 - 7 + 8)} - 10 solve this clearly
Answer:
62
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition SubtractionStep-by-step explanation:
Step 1: Define expression
64 + [40 ÷ (4 - 7 + 8)] - 10
Step 2: Evaluate
Brackets - Parenthesis - Subtract: 64 + [40 ÷ (-3 + 8)] - 10Brackets - Parenthesis - Add: 64 + [40 ÷ 5] - 10Brackets - Divide: 64 + 8 - 10Add: 72 - 10Subtract: 62And we have our final answer!
write the coordinates of each point
1). The given coordinate is (4,0,3).
To determine the location of the given coordinate move 4 units in positive x-direction, then move 3 units in the positive z-direction.
Thus, the P point gives the requried location of the given point.
Christopher's car can drive 230 miles on a full tank of gas. He plans to drive with a full tank from Austin to Dallas, which is 195 miles. How many miles will be left once he arrives in Dallas?
Answer:
35 miles
Step-by-step explanation:
Total Miles driven at full tank = 230 miles
Miles drive at full tank from Austin to Dallas = 195 miles
How many miles will be left once he arrives in Dallas?
Number of miles remaining at full tank = Total Miles driven at full tank - Miles drive at full tank from Austin to Dallas
= 230 miles - 195 miles
= 35 miles
A 5 foot tall student casts a shadow that is 8 feet long. A 12.5 foot flag pole close by casts a shadow with an unknown length, s. What is the length of the flag pole’s shadow, s?
Answer:
15.5
Step-by-step explanation:
Let A= ⎣
⎡
1
0
1
1
1
1
1
1
1
1
1
0
⎦
⎤
. (a) Find a basis for nullA. Clearly label the basis that you find. (b) Let b∈R 3
such that b
=0. How many solutions exist for the non-homogeneous linear system Ax=b ? Justify your answer.
(a) The basis for the nullspace of matrix A is {[-1, 1, 0]}. This basis represents the vectors that satisfy Ax = 0.
(b) For the non-homogeneous linear system Ax = b, the number of solutions depends on whether the vector b is in the column space of A. If b is in the column space, there is a unique solution. If b is not in the column space, there are no solutions.
(a)To find a basis for the null space (also known as the kernel) of matrix A, we need to solve the homogeneous equation Ax = 0, where x is a vector.
Let's proceed with the calculations:
Step 1: Set up the augmented matrix [A | 0]:
⎡
⎣
1 0 1 | 0
1 1 1 | 0
1 1 1 | 0
1 1 0 | 0
⎤
⎦
Step 2: Apply row reduction operations to obtain row-echelon form:
R2 = R2 - R1
R3 = R3 - R1
R4 = R4 - R1
⎡
⎣
1 0 1 | 0
0 1 0 | 0
0 1 0 | 0
0 1 -1 | 0
⎤
⎦
Step 3: Continue row reduction:
R3 = R3 - R2
R4 = R4 - R2
⎡
⎣
1 0 1 | 0
0 1 0 | 0
0 0 0 | 0
0 0 -1 | 0
⎤
⎦
Step 4: Rearrange rows:
R3 ↔ R4
⎡
⎣
1 0 1 | 0
0 1 0 | 0
0 0 -1 | 0
0 0 0 | 0
⎤
⎦
Step 5: Solve for the leading variables in terms of the free variables:
x₁ + x₃ = 0
x₂ = 0
-x₃ = 0
Step 6: Express the solution in vector form:
x = [x₁, x₂, x₃] = [0, 0, 0] + x₃[0, 0, -1]
Therefore, the basis for the null space of A is { [0, 0, -1] }.
(b) For the non-homogeneous linear system Ax = b, where b ≠ 0, the number of solutions depends on the consistency of the system.
If the vector b is not in the column space of A, then the system is inconsistent, and there are no solutions.
If the vector b is in the column space of A, then the system is consistent, and there will be infinitely many solutions.
To determine whether b is in the column space of A, we can check if A is invertible by calculating its determinant. If det(A) = 0, then A is not invertible, indicating that b is in the column space of A.
Let's calculate the determinant of A:
det(A) = (1)((1)(1) - (1)(1)) - (0)((1)(1) - (1)(1)) + (1)((1)(1) - (1)(1))
= 0 - 0 + 0
= 0
Since the determinant of A is 0, A is not invertible. Therefore, if b ≠ 0, there are infinitely many solutions to the non-homogeneous linear system Ax = b.
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A dirt bike rider jumps off a ramp and makes a smooth landing on the ground. The ramp is 5 feet tall. The
rider reaches a maximum height of 18 feet and is in the air for 4 seconds.
A dirt bike rider is an individual who rides and operates a dirt bike, which is a type of motorcycle designed for off-road riding. The rider leaves the ramp at a speed of 2.5 feet per second and lands on the ground at a speed of 4.5 feet per second.
To calculate the time it takes for the rider to reach the maximum height, we can divide the total time in the air by 2. In this case, since the rider is in the air for 4 seconds, it would take 2 seconds to reach the maximum height.
To calculate the speed at which the rider leaves the ramp, we can use the formula:
speed = distance/time.
The distance is the height of the ramp, which is 5 feet, and the time is the time it takes for the rider to reach the maximum height, which is 2 seconds.
Therefore, the speed at which the rider leaves the ramp is 5 feet/2 seconds, or 2.5 feet per second.
To calculate the speed at which the rider lands on the ground, we can use the same formula.
The distance is the height the rider reaches, which is 18 feet, and the time is the total time in the air, which is 4 seconds.
Therefore, the speed at which the rider lands on the ground is 18 feet/4 seconds, or 4.5 feet per second.
In summary, the rider leaves the ramp at a speed of 2.5 feet per second and lands on the ground at a speed of 4.5 feet per second.
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How do I do? What is the answer and why
Answer:
Step-by-step explanation:
∠ADE = 74 {Vertically opposite angles are equal}
∠AED + 127 = 180 {Straight line }
∠AED = 180 - 127
∠AED = 53
In ΔADE,
∠DAE + ∠AED + ∠ADE = 180 {angle sum property of triangle}
∠DAE + 53 + 74 = 180
∠DAE + 127 = 180
∠DAE = 180 -127
∠DAE = 53
Please answer the question and explain how to do it step by step.
Parker is wrong, as the volume of the cube container is obtained as \(\frac{1}{512} t^9u^{12}\).
What is volume?
Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
The volume of a cube is given by the formula V = s³, where s is the length of one side of the cube.
In this case, the length of the container is given as \(\frac{1}{8} t^3u^4\).
To find the volume of the cube, we need to cube this length -
\(V=\big(\frac{1}{8} t^3u^4\big)^3\)
Simplifying this expression using the rules of exponents, we get -
\(V=\big(\frac{1}{8}\big)^3 \times (t^3)^3 \times (u^4)^3\)
\(V =\frac{1}{512} t^9u^{12}\)
So, the actual volume of the container is \(\frac{1}{512} t^9u^{12}\), not \(\frac{1}{12} t^9u^{12}\) as Parker said.
Therefore, Parker is incorrect.
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lawnco produces three grades of commercial fertilizers. a 100-lb bag of grade a fertilizer contains 16 lb of nitrogen, 6 lb of phosphate, and 7 lb of potassium. a 100-lb bag of grade b fertilizer contains 20 lb of nitrogen and 4 lb each of phosphate and potassium. a 100-lb bag of grade c fertilizer contains 24 lb of nitrogen, 3 lb of phosphate, and 6 lb of potassium. how many 100-lb bags of each of the three grades of fertilizers should lawnco produce if 26,200 lb of nitrogen, 4,700 lb of phosphate, and 6,600 lb of potassium are available and all the nutrients are used? (let a, b, and c denote the number of bags of grade a, b, and c fertilizer, respectively.)
Lawnco should produce 300 bags of grade a, 400 bags of grade b, and 200 bags of grade c fertilizer in order to meet the given nutrient requirements.
Let x, y, and z denote the number of 100-lb bags of grade a, b, and c fertilizer respectively.
Then, we can create the following system of equations based on the given information:
16x + 20y + 24z = 26200 (total nitrogen)
6x + 4y + 3z = 4700 (total phosphate)
7x + 4y + 6z = 6600 (total potassium)
Solving this system of equations, we get:
x = 300 (number of bags of grade a)
y = 400 (number of bags of grade b)
z = 200 (number of bags of grade c)
To find out how many 100-lb bags of each of the three grades of fertilizers Lawnco should produce, we need to set up a system of linear equations using the given information and solve for a, b, and c.
Equation 1 (nitrogen): 16a + 20b + 24c = 26,200
Equation 2 (phosphate): 6a + 4b + 3c = 4,700
Equation 3 (potassium): 7a + 4b + 6c = 6,600
Solving this system of linear equations will give you the number of bags of grade A, B, and C fertilizers Lawnco should produce to use all available nutrients.
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!!!!!PLEASE HELP MEEEEE!!!!!
Answer:
c hehhe
Step-by-step explanation:
centers of adjacent faces of a unit cube are connected to form a regular octahedron. what is the volume of this octahedron?
The volume of octahedron when centers of adjacent faces of a unit cube are connected to form a regular octahedron is 1/16 unit ³.
Let the side length of a cube is 1unit.
Therefore length of all edges of the regular octahedron =2√2 unit .
Now the base of the pyramids is a square are will be (2√2)² =12 unit.
Now clearly the height of the pyramid is half the height of the cube, i.e.,1/2.
So volume of the Pyramid will be ⇒ 1/3× (Base area) × (height) = 1/3×1/2×1/2 = 1/12.
Therefore, the volume of the octahedron= 2 × volume of Pyramid= 2 ×1/12=1/6 unit³.
Hence, the volume of octahedron when centers of adjacent faces of a unit cube are connected to form a regular octahedron is 1/16 unit ³.
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HELP ASAP!!!!!!!!!!!! PLS PLS PLS
Answer:
A.10
Step-by-step explanation:
add all of them =48
48/5= 9.6
imagine you are performing a two-way anova test, and you find a p-value for interaction of 0.07. what is the correct interpretation of this p-value with an alpha level of 0.05?
The correct interpretation of this p-value with an alpha level of 0.05 is explain below.
What is the correct interpretation of this p-value with an alpha level of 0.05?P-value is the margin of error importance inside a factual speculation test, addressing the likelihood of the event of a given occasion.
According to question:We have, P-value =0.07
Level of significance = 0.05
We know that,
P-value is less than level of significance, then H® is rejected,smaller the p-value longer the evidence that you should reject the null hypothesis.
Now P-value is greater than 0.05.
With a p-value greater than 0.05, fail to reject the H®.Look at multiple comparison of each Level of significance.
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HELP PLEASE!!!!
WILL GIVE BRAINLIEST
ANY LINKS OR WRONG ANSWERS WILL BE REPORTED!!!!
Answer:
A is the answer
.................
What is the area ? To this ?
Answer:
9 square feet
Step-by-step explanation:
A = bh / 2
b = 3
h = 6
A = 6 * 3 / 2 = 9
In a system of N gas molecules, the individual speeds are v7, V2, ..., VN. The rms speed of these molecules is: ov + 12 + ... + x)2/N (v + v + ... + v)/N ovv+ v + - + vx O V[(v + V2 + ... + vx)/N]" i vì + vị++ v
Here we have to find the root mean square (rms) speed of a system of N gas molecules, where the individual speeds are represented by v1, v2, ..., vN.
The rms speed is calculated as the square root of the average of the squared speeds. To compute the rms speed, we need to sum the squares of the individual speeds and divide it by the total number of molecules, N. Then, we take the square root of the resulting value. In equation form, the rms speed is given by: v(rms) = \(\sqrt{\frac{(v1^2 + v2^2 + ... + vN^2)}{N} }\). Here, we square each individual speed, sum them together, divide by N, and take the square root of the resulting value. The rms speed is a measure of the average speed of gas molecules in a system. It is commonly used in physics and thermodynamics to describe the kinetic energy of gas particles and their behavior in various systems.
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the product of w and h
Answer:
wh
Step-by-step explanation:
Product mean multiply.
w × h = wh
calculate E, the amount of euros that has the same value as D U.S. dollars, using the equation E=17/20D=
The given equation is: E=17/20 D , where E=amount of Euros and D= amount of U.S dollar.
Now for 1 U.S dollar, we need to plug D=1 into the above equation. So, we will get.........
E=17/20(1)
E=1/20=0.85
0.85 Euros have the same amount as 1 U.S dollar.
HOPE IT HELPS (◕‿◕✿) SMILE!!
if no digit may be used more than once, how many 5-digit numbers can be formed using only the digits 3, 8, 1, 2, 5, and 7? (1 point)
To solve this problem, we need to use the formula for permutations, which is nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects we are choosing. In this case, we are choosing 5 digits from a set of 6 digits (since we can't repeat any digit), so we have:
6P5 = 6! / (6 - 5)! = 6 x 5 x 4 x 3 x 2 = 720
Therefore, there are 720 5-digit numbers that can be formed using only the digits 3, 8, 1, 2, 5, and 7, where no digit is used more than once.
To form a 5-digit number using the digits 3, 8, 1, 2, 5, and 7 without repetition, follow these steps:
1. Choose a digit for the first position: You have 6 options (3, 8, 1, 2, 5, or 7).
2. Choose a digit for the second position: You now have 5 remaining options (since you cannot repeat the digit chosen in step 1).
3. Choose a digit for the third position: You have 4 remaining options (excluding the digits chosen in steps 1 and 2).
4. Choose a digit for the fourth position: You have 3 remaining options (excluding the digits chosen in steps 1, 2, and 3).
5. Choose a digit for the fifth position: You have 2 remaining options (excluding the digits chosen in steps 1, 2, 3, and 4).
Now, multiply the number of options for each position: 6 × 5 × 4 × 3 × 2 = 720
So, there are 720 different 5-digit numbers that can be formed using the digits 3, 8, 1, 2, 5, and 7 without repetition.
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Marco is driving to the Grand Canyon. His distance from the Grand Canyon decreases 150 mi every 3 h. After 4 h, his distance from the Grand Canyon is 200 mi. Marco's distance from the Grand Canyon in miles, y, is a function of the number of hours he drives, z. The rate of change is -50, what is the initial value? I NEED HELP ASAP.
Answer: 400 miles
Step-by-step explanation: every hour, his distance decreases by 50 miles. After 4 hours, his distance is 200 miles, so 50 miles times 4 hours = 200 miles+the original 200 miles =400 miles.
A wedding reception venue advertises all inclusive venue hire and catering cost of 6950 for 50 guests and 11950 for 100 guests assume the cost of the venue hire and catering for n guests form an arithmetic sequence: write a formula for the general term of the sequence
It says 1950+100n as the answer but Im not sure how to get there
The correct formula for the general term of the arithmetic sequence representing the cost of the venue hire and catering for n guests is 1950 + 100n.
To find the formula for the general term of the arithmetic sequence representing the cost of the venue hire and catering for n guests, we can analyze the given information.
We are given two data points: the cost for 50 guests, which is $6,950, and the cost for 100 guests, which is $11,950. We can observe that the difference between these two costs is $11,950 - $6,950 = $5,000.
Since the cost forms an arithmetic sequence, the difference between consecutive terms will remain constant. In this case, the difference is $5,000.
Now, we need to find the initial term of the sequence. By examining the cost for 50 guests, we notice that the difference between the cost for 50 guests and the initial term is $6,950 - $5,000 = $1,950.
Putting it all together, we have the formula for the general term of the arithmetic sequence: initial term + (difference × (n - 1)).
Plugging in the values, the formula becomes: 1,950 + (5,000 × (n - 1)) = 1,950 + 5,000n - 5,000 = 5,000n - 3,050. Simplifying further, we get the final formula: 5,000n - 3,050.
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