Answer:
The pattern is you are subtracting by 8. The subsequent three terms are 51, 43, and 35.
Step-by-step explanation:
First, you can subtract the first value from the second to find the common difference. Then you continue on this pattern. Simple!
4+5x > 19
how to do
Answer:
x>3
Step-by-step explanation:
i assume you're solving for x so,
1) rearrange terms,
5x+4>19
2)subtract 4 from both sides
5x+4-4>19-4
3) Simplify
5x>15
4) divide both sides by 5, because they are same factor
\frac{5x}{5} > \frac{15}{5}
5) Finally, the answer is
x>3
Robert takes out a loan for $7200 at a 4. 3% rate for 2 years. What is the loan future value?
(Round to the nearest cent)
The loan future value is $7726.73.
To find the loan future value, we need to calculate the total amount that Robert will owe at the end of the 2-year loan term, including both the principal (initial loan amount) and the interest.
To begin, we can use the formula for calculating compound interest:
[tex]A = P(1 + r/n)^{(nt)[/tex]
where A is the final amount, P is the principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, we know that the principal is $7200, the interest rate is 4.3% (or 0.043 as a decimal), the loan term is 2 years, and the interest is compounded once per year (n = 1).
Substituting these values into the formula, we get:
A = 7200(1 + 0.043/1)²
A = 7200(1.043)²
A = 7726.73
Therefore, the loan future value is $7726.73. This means that at the end of the 2-year loan term, Robert will owe a total of $7726.73, which includes the original $7200 loan amount and $526.73 in interest.
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Choose the function that the graph represents.
Click on the correct answer.
y = f(x) = log7x
y = f(x)=x7
y = f(x) = 7x
Answer:
y=f(x) = log7x
Just trust me
The graph best represents the function y = f(x) = 7x, an exponential function.
The graph represents the function y = 7x, which is an exponential function. In an exponential function, the variable x is the base, and the exponent is a constant, which in this case is 7. This means that the function grows rapidly as x increases, creating a steep curve on the graph.
The other two options, y = f(x) = log7x and y = f(x) = x7, are not represented by the given graph.
The function y = f(x) = log7x is a logarithmic function, which has a different shape on the graph, with a horizontal asymptote and the x-axis acting as its asymptote.
The function y = f(x) = x7 is a polynomial function, where x is raised to the power of 7, and it would have a different pattern on the graph compared to the exponential function shown.
Thus, the graph best represents the function y = f(x) = 7x, an exponential function.
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gardens a square landscape plan is composed of three indoor gardens and one walkway that are all congruent. the gardens are centered around a square lounging area. if each side of the lounging area is 15 feet long, what is the area of one of the gardens?gardens a square landscape plan is composed of three indoor gardens and one walkway that are all congruent. the gardens are centered around a square lounging area. if each side of the lounging area is 15 feet long, what is the area of one of the gardens?
The area of one garden using each side of the lounging area is 15 feet long is equal to 56.25 square feet.
Shape of the garden landscape is square.
If the lounging area is a square with sides of length 15 feet,
Area of lounging area
= (15 feet) × (15 feet)
= 225 square feet
Four congruent sections of the landscape plan .
Three indoor gardens and one walkway.
Divide the lounging area into four equal square sections.
Each of the congruent sections has an area equal to,
Area of lounging area = 4 × area of one garden
Let's call the area of one garden be x.
⇒225 = 4x
Solving for x, we divide both sides by 4
⇒x = 225/4
⇒x = 56.25 square feet
Therefore, the area of one garden is 56.25 square feet.
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Help!! Will give out brainliest answer :)
Leslie paid $13 for 4 children’s tickets and 1 adult ticket.
Antonio paid $14 for 3 adult’s tickets and 2 children’s tickets.
Write and solve a system of equations to find the unit price for a child ticket and an adult ticket. Explain your steps and show all your work
The unit price for a child ticket is $2.50 and the unit price for an adult ticket is $3.
To find the unit price for a child ticket and an adult ticket, we can set up a system of equations based on the given information. Let x be the unit price for a child ticket and y be the unit price for an adult ticket.
From the first sentence, we know that:
4x + y = 13 ...(1)
From the second sentence, we know that:
3y + 2x = 14 ...(2)
Now we have a system of equations with two variables, which we can solve using either substitution or elimination method. For simplicity, we will use the elimination method.
Multiplying equation (1) by 3, we get:
12x + 3y = 39 ...(3)
Subtracting equation (2) from equation (3), we get:
10x = 25
x = 2.50
Substituting x = 2.50 into equation (1), we get:
4(2.50) + y = 13
y = 3
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A whole wall is split in half and we painted half of the wall 3 colors what fraction of the wall does each color occupy?
The total fraction of the wall that has been painted is 1/2. If a whole wall is split in half and we painted half of the wall 3 colors, each color occupies 1/6 of the painted area.
To answer your question, we need to first determine the total fraction of the wall that has been painted. Since the wall has been split in half, we can say that the painted area covers half of the wall. Therefore, the total fraction of the wall that has been painted is 1/2.
Now, we need to divide this 1/2 fraction among the three colors that were used. Let's say the three colors are red, blue, and green. We can represent the fraction of the wall occupied by each color as follows:
- Red: 1/3 x 1/2 = 1/6
- Blue: 1/3 x 1/2 = 1/6
- Green: 1/3 x 1/2 = 1/6
So each color occupies 1/6 of the painted area, which is equivalent to 1/12 of the whole wall. This means that if the wall was not split in half and we painted the entire wall with the same 3 colors, each color would occupy 1/12 of the total wall area.
In summary, if a whole wall is split in half and we painted half of the wall 3 colors, each color occupies 1/6 of the painted area, which is equivalent to 1/12 of the whole wall.
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Q11
A ball is thrown vertically upward. After t seconds, its height, h (in feet), is given by the function h left parenthesis t right parenthesis equals 76 t minus 16 t squared. After how long will it reach its maximum height?
Round your answer to the nearest hundredth.
Group of answer choices
90 seconds
1.2 seconds
0.17 seconds
2.38 seconds
Answer:
Step-by-step explanation:
To find when the ball reaches its maximum height, we need to find the vertex of the quadratic function h(t) = 76t - 16t^2.
The vertex of a quadratic function of the form y = ax^2 + bx + c is at the point (-b/2a, f(-b/2a)), where f(x) = ax^2 + bx + c.
In this case, a = -16 and b = 76, so the time at which the ball reaches its maximum height is given by:
t = -b/2a = -76/(2*(-16)) = 2.375
Rounded to the nearest hundredth, the ball reaches its maximum height after 2.38 seconds (Option D).
The measurements for a television are 120 cm
wide, 68 cm high, and 14 cm deep. What is the
total surface area of the television?
The total surface area of the television is 21,584 square centimeters.
To find the total surface area of the television, we need to calculate the area of all six sides and add them up.
The front and back sides have the same dimensions and area, so we can find the area of one and multiply it by two. The same goes for the left and right sides.
The area of the front/back sides is:
120 cm x 68 cm = 8160 sq cm
Multiplying by 2 gives us the total area of both front/back sides:
2 x 8160 sq cm = 16,320 sq cm
The area of the left/right sides is:
68 cm x 14 cm = 952 sq cm
Multiplying by 2 gives us the total area of both left/right sides:
2 x 952 sq cm = 1904 sq cm
The area of the top and bottom sides is:
120 cm x 14 cm = 1680 sq cm
Multiplying by 2 gives us the total area of both top/bottom sides:
2 x 1680 sq cm = 3360 sq cm
Adding up all six sides, we get:
16,320 sq cm + 1904 sq cm + 3360 sq cm = 21,584 sq cm
Therefore, the total surface area of the television is 21,584 square centimeters.
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8. If AB and BC are tangent to circle D,
AB = 15 inches, and DB = 17 inches, find
the perimeter of ABCD.
Answer:
46 inches
Step-by-step explanation:
You want the perimeter of ABCD, where AB and BC are tangent to circle D, and AB = 15 inches, BD = 17 inches.
FigureThe attachment shows the figure. Radii DA and DC are perpendicular to the tangens, so each triangle is a right triangle. The hypotenuse BD is given as 17 inches, and the leg AB is given as 15 inches. The other leg is found from the Pythagorean theorem (or from your knowledge of Pythagorean triples). It is ...
AD = √(DB² -AB²)
AD = √(17² -15²) = √(289 -225) = √64
AD = 8
PerimeterThe perimeter is the sum of side lengths. The kite shape is symmetrical, so the perimeter is ...
P = 2(AD +AB) = 2(8 +15) = 46 . . . . inches
The perimeter of ABCD is 46 inches.
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Simplify each of the following and leave answer in standard form to 3 decimal places.
(3. 05 x 10 ^ -7) (8. 67×10 ^ 4)
The simplified standard form of (3.05 x 10⁻⁷) (8.67 x 10⁴) is 2.642 x 10⁻¹.
To simplify (3.05 x 10⁻⁷) (8.67 x 10⁴) and leave the answer in standard form to 3 decimal places:
1: Multiply the decimal numbers:
3.05 * 8.67 = 26.4245
2: Add the exponents:
-7 + 4 = -3
3: Combine the result and exponent in standard form:
26.4245 x 10⁻³
4: Adjust the decimal to have only one non-zero digit to the left of the decimal point and adjust the exponent accordingly:
2.64245 x 10² x 10⁻³
5: Simplify by combining exponents:
2.64245 x 10⁻¹
6: Round to 3 decimal places:
2.642 x 10⁻¹
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Solve this system.
Select one:
a.
No solution
b.
(4,-2)
c.
(5,10)
d.
Infinite solutions
The solution to this system of equations are x =5 and y =10
Calculating the x and y coordinates of the solution to this system of equations.From the question, we have the following parameters that can be used in our computation:
5x - 2y = 5 2x + 2y = 30
Express properly
So, we have
5x - 2y = 5
2x + 2y = 30
Add the equations to eliminate y
7x = 35
Divide both sides by 7
x = 5
Next, we have
2(5) + 2y = 30
So, we have
2y = 20
y = 10
Hence, the value of y is 10
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Please hurry I need it ASAP
Answer:
2[tex]\sqrt{17}[/tex]
Step-by-step explanation:
Use the distance formula to determine the distance between the two points.
Distance = [tex]\sqrt{(7-(-1))^{2} + (4-2)^{2} }[/tex]
Simplify, and you will get the answer
2[tex]\sqrt{17}[/tex]
An ant travels 33cm in walking completely around the edges of a rectangle. If the rectangle is twice as long as it is wide, how long is the shortest side?
Rectangle: w = 5.5cm, l = 11cm. Shortest side is width.
1. Write a function of × that performs the following operations: Raise x to the ninth
power, multiply by 6, and then add 4.
y = f(x) = _____
2. Find the inverse to the function you found in
part (a).
x = g (y) =
A function of x that performs the operations y = f(x) = 6x^9 + 4, the inverse to the function found in part (a). x = g (y) = ((y - 4) / 6)^(1/9)
The function that performs the operations of raising x to the ninth power, multiplying by 6, and adding 4 is
f(x) = 6x^9 + 4
To find the inverse function, we need to solve for x in terms of y
y = 6x^9 + 4
Subtract 4 from both sides
y - 4 = 6x^9
Divide both sides by 6
(x^9) = (y - 4) / 6
Take the ninth root of both sides
x = ((y - 4) / 6)^(1/9)
Therefore, the inverse function is
g(y) = ((y - 4) / 6)^(1/9)
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Insert a monomial so that the trinomial may be represented by the square of a
binomial.
0.0152 +.... +100c2
The trinomial can now be represented by the square of the binomial (0.123 + 10c)²
To insert a monomial so that the trinomial may be represented by the square of a binomial, consider the trinomial 0.0152 + ... + 100c².
1: Identify the square root of the first and last terms, which are √0.0152 and √100c². The square roots are 0.123 and 10c, respectively.
2: Determine the middle term by multiplying the square roots together and doubling the result. (0.123)(10c)(2) = 2.46c.
3: Insert the middle term into the trinomial, forming the complete trinomial: 0.0152 + 2.46c + 100c².
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Evaluate the iterated integral by converting to polar coordinates.∫8−8∫√64−x20(x2+y2) dy dx
To convert to polar coordinates, we need to express x and y in terms of r and θ. We have:
x = r cos θ
y = r sin θ
Also, we need to change the limits of integration. The region of integration is the circle centered at the origin with radius 8, so we have:
-π/2 ≤ θ ≤ π/2 (for the upper half of the circle)
0 ≤ r ≤ 8
Now we can express the integrand in terms of r and θ:
[tex]x^2 + y^2 = r^2[/tex] (by Pythagoras)
[tex]20(x^2 + y^2) = 20r^2[/tex]
So the integral becomes:
∫-π/2π/2∫[tex]08r^3 cos^2 θ sin θ dr dθ[/tex]
We can simplify cos^2 θ sin θ using the identity cos^2 θ sin θ = (1/3)sin^3 θ, so we get:
∫-π/2π/2∫[tex]08r^3 (1/3)sin^3 θ dr dθ[/tex]
The integral with respect to r is easy to evaluate:
∫0^8r^3 dr = (1/4)8^4 = 2048
The integral with respect to θ is also easy to evaluate using the fact that sin^3 θ is an odd function:
∫-π/2π/2(1/3)[tex]sin^3[/tex] θ dθ = 0
Therefore, the value of the iterated integral is:
2048(0) = 0
The volume of the solid is zero. This makes sense because the integrand is an odd function of y (or sin θ) and the region of integration is symmetric with respect to the x-axis.
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Your doing practice 4
Using the compound interest formula, the amount in Russ' account after 4 years is $ 12588.15
How to find the how much will be in Russ' account after 4 years?To find how much will be in Russ' account after 4 years, we use the compound interest formula.
A = P(1 + r)ⁿ where
A = amount after n years,P = principal,r = interest rate andn = number of yearsGiven that
P = $8000r = 6 % compounded semi annually = 6% ÷ 1/2 per year = 12 % per year = 0.12n = 4 yearsSo, substituting the values of the variables into the equation, we have that
A = P(1 + r)ⁿ
A = $8000(1 + 0.12)⁴
A = $8000(1.12)⁴
A= $8000(1.5735)
A= $ 12588.15
So, the amount is $ 12588.15
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The domain of the function is the set of all real numbers, and the range of the function is the set of all real numbers greater than or equal to ------.
The range of the function is the set of all real numbers greater than or equal to -4.
What are the domain and range of a function?The domain of a function is the set that contains all possible input values of the function, that is, all the values assumed by the independent variable x in the function.The range of a function is the set that contains all possible output values of the function, that is, all the values assumed by the dependent variable y in the function.The function assumes values of y = -4 or greater, which represent the range of the graphed function.
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How to find number 3?
Answer:
V=3456, SA= 1008
Step-by-step explanation:
V=b*h*L (Formula)
8*18*24=3456 (sub, alg)
SA=30*8+24*18+24*8+8*18=54*8+32*18=1008 (Formula; sub, alg)
Find an equation of the plane that passes through the given point and is perpendicular to the given vector or line.
Point (0, 9, 0) Perpendicular to
n = -2i ÷ 4k
To find the equation of the plane that passes through the point (0, 9, 0) and is perpendicular to the vector n = -2i ÷ 4k, we first need to find the normal vector of the plane.
Since the plane is perpendicular to the given vector, the normal vector will be parallel to it. So, we can take the given vector and multiply it by -1 to get a vector in the opposite direction, which will be normal to the plane.
n = -2i ÷ 4k = -1/2i ÷ k
Multiplying by -1 gives us:
n = 1/2i ÷ k
Now we can use the point-normal form of the equation of a plane:
r · n = d
where r is the position vector of any point on the plane, n is the normal vector, and d is the distance of the plane from the origin (since the normal vector is normalized, d will be the signed distance of the plane from the origin).
Substituting the given point (0, 9, 0) and the normal vector n = 1/2i ÷ k into the equation, we get:
(0, 9, 0) · (1/2i ÷ k) = d
0 + 9(1/2) + 0 = d
d = 4.5
So the equation of the plane is:
x/2 + z/2 = 4.5
or, multiplying by 2 to eliminate fractions:
x + z = 9
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Solve for the indicated variable. X/y=z-8 for x
Answer: To solve for x in the equation X/y=z-8, we need to isolate x on one side of the equation.
Multiplying both sides by y, we get:
X = y(z-8)
Therefore, the solution for x is:
X = y(z-8)
Step-by-step explanation:
What integer represents ""a credit of $30"" if zero represents the original balance? explain your reasoning.
The integer that represents a credit of $30 if zero represents the original balance is +30.
A credit represents an increase in funds, while a debit represents a decrease. In this case, a credit of $30 means that $30 has been added to the account, increasing the balance. Since zero represents the original balance, adding $30 results in a positive balance of $30, which is represented by the integer +30.
Therefore, +30 represents a credit of $30 if the original balance is zero. The reasoning behind this is that a credit increases the balance, so a positive integer is used to indicate the amount by which the balance has increased. In this case, it is an increase of $30, hence +30.
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The attendance for a week at a local theatre is normally distributed, with a mean of 4000 and a standard
deviation of 500. Draw the normal curve to represent the normally distributed attendance for the week.
What percentage of the attendance figures would be less than 3500? What percentage of the attendance
figures would be greater than
5000? What percentage of the attendance figures would be between 3700
and 4300 each week?
About 15.87% of the attendance figures would be less than 3500.
About 0.62% of the attendance figures would be greater than 5000.
About 34.13% of the attendance figures would be between 3700 and 4300 each week.
The mean is the average of a set of numbers, while the standard deviation measures the spread of the data around the mean. The normal distribution is fully characterized by its mean and standard deviation. In this case, the mean attendance is 4000, and the standard deviation is 500.
To answer the first question, "What percentage of the attendance figures would be less than 3500?" we need to calculate the area under the curve to the left of 3500. We can use a standard normal distribution table or a calculator to find this area. The result is approximately 15.87%.
To answer the second question, "What percentage of the attendance figures would be greater than 5000?" we need to calculate the area under the curve to the right of 5000. Again, we can use a standard normal distribution table or a calculator to find this area. The result is approximately 0.62%.
To answer the third question, "What percentage of the attendance figures would be between 3700 and 4300 each week?" we need to calculate the area under the curve between 3700 and 4300. We can use a standard normal distribution table or a calculator to find this area. The result is approximately 34.13%.
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Consider a piece of wire with uniform density. It is the quarter of a circle in the first quadrant. The circle is centered at the origin and has radius 6. Find the center of GRAVITY (x¯,y¯) of the wire. x¯=
y¯=
the wire has uniform density, the center of gravity is located at the centroid of the quarter-circle, which is (4/3, 4/3).
How to Find the center of GRAVITY (x¯,y¯)The center of gravity (x¯,y¯) of the wire lies on the line of symmetry, which passes through the origin and the centroid of the quarter-circle.
The centroid of a quarter-circle with radius 6 is located at (4/3, 4/3) from the origin (as derived using calculus). Thus, the line of symmetry passes through the origin and (4/3, 4/3).
The equation of the line passing through two points (x1, y1) and (x2, y2) is given by:
(y - y1) / (x - x1) = (y2 - y1) / (x2 - x1)
Substituting (x1, y1) = (0, 0) and (x2, y2) = (4/3, 4/3), we get:
(y - 0) / (x - 0) = (4/3 - 0) / (4/3 - 0)
Simplifying, we get:
y = x
Therefore, the center of gravity (x¯,y¯) is located on the line y = x.
Since the wire has uniform density, the center of gravity is located at the centroid of the quarter-circle, which is (4/3, 4/3).
Hence, x¯=y¯=4/3.
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The Nielsen Company surveyed 371 owners of Android phones and found that 200
of them planned to get another Android as their next phone. What is the lower
bound for the 95% confidence interval for the proportion of Android users who plan
to get another Android?
The lower bound for the 95% confidence interval for the proportion of Android users who plan to get another Android phone is 0.463 .
It can be evaluated applying the formula
Lower Bound = Sample Proportion - Z-Score × Standard Error
Here
Sample Proportion
= 200/371 = 0.539
Z-Score = 1.96 (for a 95% confidence interval)
Standard Error = √[(Sample Proportion * (1 - Sample Proportion)) / Sample Size]
= √[(0.539 × (1 - 0.539)) / 371]
= 0.045
Therefore,
Lower Bound = 0.539 - 1.96 × 0.045 = 0.463
A confidence interval is a known as the specified range of values that is prone to contain an unknown population area with a certain degree of confidence.
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A circular piece of board contains sections numbered 2, 9, 4, 9, 6, 9, 9, 9. If a spinner is attached to the center of the board and spun 10 times, find the probability of spinning fewer than four nines.
The probability of spinning fewer than four nines is 1,626,101,367 / 1073741824, which simplifies to approximately 1.514%.
To find the probability of spinning fewer than four nines, we need to first calculate the total number of possible outcomes. The spinner can land on any of the eight sections on the board, and it is spun 10 times. So, the total number of possible outcomes is 8^10, which is 1073741824.
Next, we need to calculate the number of outcomes where fewer than four nines are spun. We can do this by finding the number of outcomes with 0, 1, 2, or 3 nines, and adding them up.
To find the number of outcomes with 0 nines, we need to find the number of ways to choose from the non-nine sections on the board. There are 5 non-nine sections, and we need to choose 10 of them. This is a combination problem, and the number of outcomes is 252.
To find the number of outcomes with 1, 2, or 3 nines, we need to use a similar approach. We can use combinations to find the number of ways to choose the nines and the non-nines, and then multiply them together. The number of outcomes with 1 nine is 9 x 5^9, with 2 nines is 9 x 9 x 5^8, and with 3 nines is 9 x 9 x 9 x 5^7.
Adding up all these outcomes, we get 252 + 9 x 5^9 + 9 x 9 x 5^8 + 9 x 9 x 9 x 5^7 = 1,626,101,367.
So, the probability of spinning fewer than four nines is 1,626,101,367 / 1073741824, which simplifies to approximately 1.514%.
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2. A triangle has one side that is 5 units long and an adjacent angle that measures 25 The two other angles in the triangle measure 90° and 65°. Complete the two diagrams to create two different triangles with these measurements. 25° 5 25° 5
The diagram to create a similar triangle has been attached.
How to create a similar triangles?Similar triangles are defined as triangles that possess the same shape, but then their sizes will likely vary. We can also say that two triangles are referred to as similar if they possess the same ratio of its' corresponding sides and also an equal pair of corresponding angles
The two different triangles can be formed by placing the 90° angle adjacent to, or opposite the given side.
In the diagram below attached, we see that the two triangles are ABC and ABD. Thus, the right angles are located at vertex C and vertex B, respectively.
Thus, it has been created with the given measurements
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Suppose that the cost, in dollars, for a company to produce x pairs of a new line of jeans is C(x) = 2300 + 5x + 0.01x2 + 0.0002x? (a) Find the marginal cost function 5 + 0.02x + 0.0006r2 (b) Find C'(100) C'(100) = 11 What does this predict? The exact cost of the 100th pair of jeans. The approximate cost of the 101st pair of jeans. The approximate cost of the 100th pair of jeans. The exact cost of the 101st pair of jeans The exact cost of the 99th pair of jeans. (c) Find the difference between C'(100) and the actual cost of manufacturing the 101st pair of jeans (Round your answer to two decimal places.) $ 3100
The exact cost of the 100th pair of jeans. The approximate cost of the 101st pair of jeans. The approximate cost of the 100th pair of jeans. The exact cost of the 101st pair of jeans The exact cost of the 99th pair of jeans.
The marginal cost function of C(x) = 2300 + 5x + 0.01x2 + 0.0002x is $3100
Process of finding marginal cost:
(a) To find the marginal cost function, we need to take the derivative of the cost function C(x) with respect to x. This gives us:
C'(x) = 5 + 0.02x + 0.0006x^2
So the marginal cost function is:
MC(x) = 5 + 0.02x + 0.0006x^2
(b) To find C'(100), we simply plug in x = 100 into the marginal cost function we just found:
C'(100) = 5 + 0.02(100) + 0.0006(100)^2 = 11
This predicts the exact cost of manufacturing the 101st pair of jeans.
The approximate cost of the 101st pair of jeans can be found by plugging in x = 101 into the original cost function C(x):
C(101) = 2300 + 5(101) + 0.01(101)^2 + 0.0002(101) ≈ $3120.02
The approximate cost of the 101st pair of jeans.
The exact cost of the 100th pair of jeans can be found by plugging in x = 100 into the original cost function C(x):
C(100) = 2300 + 5(100) + 0.01(100)^2 + 0.0002(100) = $3100
Hence the marginal cost is $3100
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Greg wants to replace the wooden floor at his gym. The floor is in the shape of a rectangle. Its length is 45 feet and its width is 35 feet. Suppose wood flooring costs $9 for each square foot. How much will the wood flooring cost for the floor?
The wood flooring for the floor will cost $14,175.
To calculate the cost of replacing the wooden floor at Greg's gym, we first need to find the area of the rectangular floor. The area of a rectangle can be found using the formula: area = length × width. In this case, the length is 45 feet and the width is 35 feet.
Area = 45 feet × 35 feet = 1575 square feet
Since the cost of wood flooring is $9 per square foot, we can now calculate the total cost:
Total cost = area × cost per square foot = 1575 square feet × $9/square foot = $14,175
So, the wood flooring will cost Greg $14,175 to replace the floor at his gym.
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Using the substitution method, find the solution to this system of equations. -2x+2y=7 -x+y=4 Be sure to show your work!
Based on your results in Problem 1, what do you know about the two lines in that system (graphically)?
There is no solution to the given system of equations and the lines are parallel which has been obtained by using the substitution method.
What is the substitution method?
When solving simultaneous linear equations in algebra, the substitution approach is a common technique. As the name of the procedure suggests, one variable's value from one equation is switched in the second equation.
We are given equations as -2x + 2y = 7 and -x + y = 4.
Now, using the second equation, we get
⇒ -x + y = 4
⇒ y = 4 + x
Now, on substituting this in the first equation, we get
⇒ -2x + 2y = 7
⇒ -2x + 2 (4 + x) = 7
⇒ -2x + 8 + 2x = 7
⇒ 8 ≠ 7
So, there is no solution to the given system.
This means that the two lines in the system are parallel which means they will never meet.
A graph depicting the same has been attached below.
Hence, there is no solution to the given system.
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