To find the marginal cost at the given production level x, differentiate the cost function C(x) and substitute the value of x. The units of measurement for the marginal cost are dollars per unit (x).
Explanation:To find the marginal cost at the given production level x, we need to find the derivative of the cost function C(x) with respect to x. Let's differentiate the function:
C'(x) = 70 - 1,000/x^2
Now, substitute x = 100 into the derivative:
C'(100) = 70 - 1,000/100^2 = 70 - 1 = 69
The units of measurement for the marginal cost are dollars per unit (x).
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The polynomial 6x2 + 37x – 60 represents an integer. Which expressions represent integer factors of 6x2 + 37x – 60 for all values of x?
3x – 4 and 2x + 15
3x + 4 and 2x – 15
2(x – 2) and 3(x + 5)
2(x + 2) and 3(x – 5)
Answer:
[tex]\text{The integral factors are }(3x-4)(2x+15)[/tex]
Step-by-step explanation:
Given the quadratic polynomial
[tex]6x^2+37x-60[/tex]
we have to find the integral factors of the above polynomial.
[tex]\text{The polynomial is }6x^2+37x-60[/tex]
By splitting middle-term, the polynomial can be written as
[tex]6x^2+37x-60[/tex]
[tex]6x^2-8x+45x-60[/tex]
Taking 2x common from first two terms and 15 from last two terms.
[tex]2x(3x-4)+15(3x-4)[/tex]
Taking (3x-4) common
[tex](3x-4)(2x+15)[/tex]
which are required factors of given polynomial.
Hence, option 1 is correct.
The seventh term of the sequence -2, -6, -10, -14, ... is _____.
-26
-24
-22
-20
please help...
The product of (1/2 3/4i) and(1/2-3/4i) divided by (2-3i)
Select one of the factors of x3y2 + 8xy2 - 5x2 - 40.
Can someone help me figure this out?
answer choices
(xy2 + 5)
(x2 + 4)
(xy2 - 5)
(x2 - 8)
Answer:
[tex](xy^2-5)\text{ is one factor of above polynomial}[/tex]
Step-by-step explanation:
Given the polynomial
[tex]x^3y^2+8xy^2-5x^2-40[/tex]
we have to select the option which is one of the factor of above polynomial.
[tex]x^3y^2+8xy^2-5x^2-40[/tex]
[tex]xy^2(x^2+8)-5(x^2+8)[/tex]
[tex](xy^2-5)(x^2+8)[/tex]
[tex]\text{Hence, }(xy^2-5)\text{ is one factor of above polynomial}[/tex]
∴ Option 3 is correct
Find all solutions in the interval [0, 2π).
7 tan^3x - 21 tan x = 0
A) pi/3, 2pi/3, 4pi/3, 5pi/3
B) 0, pi/5, π, 6pi/5
C) 0, pi/3, 2pi/3, π, 4pi/3, 5pi/3
D) 0, pi/3, π, 4pi/3
Solve this problem
13=24+c
A student faculty government committee of 4 people is to be formed from 20 student volunteers and 5 faculty volunteers. Find the probability that the committee will consist of the following, assuming the selection is made at random: a. two students and two faculty members and b. one faculty member and three students. ...?
To solve the question, calculate the total possible ways to form a committee and the ways for each specific case. The probability can be determined by dividing the specific event by the total outcomes. This involves the mathematical principles of combinatorics and probability.
Explanation:
The question is dealing with the concept of combinatorics and probability. In such cases, we look at the total possible outcomes and the outcomes of our specific event of interest.
For the first case, we need to select 2 students and 2 faculty members from respective pools of 20 and 5. The total ways to form a committee are combinations of 4 from 25 (20 students + 5 faculty). So, we have:
Total outcomes = C(25,4)
The event of interest (2 students and 2 faculty) can be calculated as the product of combinations of selecting 2 from each pool:
Specific event outcomes = C(20,2)*C(5,2)
To get the probability, we divide the outcomes of our event of interest by the total outcomes.
The second scenario works similarly. You want one faculty and three students:
Specific event outcomes = C(20,3)*C(5,1)
You'd again divide this result by the total possible outcomes (determined the same as the first scenario) to obtain the desired probability.
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The probability of forming a committee with two students and two faculty members is 15%, while the probability of forming a committee with one faculty member and three students is 45%.
Explanation:a. Two students and two faculty members:
To find the probability of selecting two students and two faculty members, we need to calculate the number of ways this combination can occur and then divide it by the total number of possible combinations.
The number of ways to select two students from 20 is C(20, 2) = 190.
The number of ways to select two faculty members from 5 is C(5, 2) = 10.
The total number of ways to form a committee of 4 from 25 volunteers is C(25, 4) = 12,650.
So the probability is (190 * 10) / 12,650 = 1900 / 12,650 = 0.15, or 15%
b. One faculty member and three students:
Similarly, the number of ways to select one faculty member from 5 is C(5, 1) = 5, and the number of ways to select three students from 20 is C(20, 3) = 1,140.
The total number of ways to form a committee of 4 from 25 volunteers is still C(25, 4) = 12,650.
So the probability is (5 * 1,140) / 12,650 = 5,700 / 12,650 = 0.45, or 45%
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What form of a quadratic function would be graphed if the vertex at the same point as the y-intercept?
PLZZZ HELP ME!!
Edward’s recipe for salad uses a ratio of 2 1/4 cups of lettuce to 1/2 lb of tomatoes.
(a) Use a complex fraction to compare the amount of lettuce to the amount of tomatoes.
(b) Determine how many cups of lettuce Edward needs to mix with 1 lb of tomatoes. Show your work.
Answer:
4.5 cups of lettuce for 1 cup of tomatoes
Step-by-step explanation:
A snake is slithering toward you at 1.5 m/s. If you start walking when it is 5.0 m away, how fast must you go in order that the snake not overtake you when you have gone 40.0 m?
Holly made fruit punch for an office party a few months ago; she used 1 gallon of strawberry juice and 3 gallons of watermelon juice, which cost her a total of $8. For today’s party, she used 3 gallons of strawberry juice and 2 gallons of watermelon juice, spending a total of $10. How much does a gallon of each type of juice cost?
Write a system of equations to describe the situation and solve using elimination. (use x for strawberry juice and y for watermelon juice)
what is the sum of the square roots of 16i?
The sum of the square roots of 16i is zero, as the positive and negative square roots cancel each other out when summed up.
Explanation:The sum of the square roots of 16i is found by first determining the square roots of the given complex number. The complex number 16i can be expressed in terms of its polar form, which then allows us to apply De Moivre's Theorem in order to find the square roots.
First, 16i is purely imaginary, with a magnitude of 16 and an argument that is π/2 or -3π/2 radians. By taking the square root of its magnitude and halving the argument, we find the two square roots, which are in fact ±4√i. Therefore, if we consider both the positive and negative square roots, the sum of the square roots of 16i would be 4√i + (-4√i), which simplifies to 0.
The sum of the square roots of 16i is 4 + 4i * cos (π/8) + 4i * sin(π/8).
Explanation:To find the sum of the square roots of 16i, we first need to find the square root of 16i. To do this, we can write 16i in polar form.
16i = 16(cos (π/2) + isin(π/2))
Then, we can find the square root of 16i by taking the square root of the magnitude and halving the argument.
√16i = √16(cos (π/4) + isin(π/4))
√16i = √16 * cos (π/8) + √16 * isin(π/8)
√16i = 4(cos (π/8) + isin(π/8))
Therefore, the sum of the square roots of 16i is 4 + 4i * cos (π/8) + 4i * sin(π/8).
A graph thAt has a finite or limited number of data points is
The correct answer is:
Discrete graph.
Explanation:
A discrete graph is a graph of disconnected points.
Since they are disconnected, this means the graph only has values at the points drawn, not between.
The opposite of a discrete graph is a continuous graph; it is a graph of connected points. Since the points are connected, the graph has values between all of the points. This is similar to what we learned in geometry about a line; a line has an infinite number of points. This is true of the connections between points in a continuous graph.
Since a discrete graph is the opposite of a continuous graph, this means it does not have an infinite number of points; a discrete graph has a finite number of points.
Why isn't there work when carrying something horizontally at a constant speed?
Which answer describes the type of sequence?
200, 40, 8, 1.6, ...
geometric
neither arithmetic nor geometric
arithmetic
Answer:
it is geometric
Step-by-step explanation
We have been given with the series
200,40,8,1.6
Arithmetic sequence is the sequence in which difference between consecutive terms is same that is common difference d
d=a_2-a_1
d=40-200=-160 herea_2=40,a_1=200
d=8-40=-32 herea_2=8,a_1=40
We can see the difference is not same
Hence, the given sequence is not arithmetic sequence.
Geometric sequence is the sequence in which ratio of consecutive terms is same that is common ratio r
r=\frac{a_2}{a_1}
r=\frac{40}{200}=\frac{1}{5} herea_2=40,a_1=200
r=\frac{8}{40}=\frac{1}{5} herea_2=8,a_1=40
r=\frac{1.6}{8}=\frac{1}{5} herea_2=1.6,a_1=8
We can see the ratio is same.
Hence, given sequence is geometric
Therefore, Option 1 is correct given sequence is geometric.
Answer:
The correct answer is A. geometric
Step-by-step explanation:
The maximum value of f(x) = 2x^3 - 18x^2 + 48x - 1 on the interval [0, 3] is (4 points)
-1
39
35
71
A function assigns the values. The maximum value of f(x) = 2x^3 - 18x^2 + 48x - 1 on the interval [0, 3] is 39. thus, the correct option is B.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
To find the point at which the function has the maximum value we need to differentiate the function. Therefore, the function can be written as,
[tex]f(x) = 2x^3 - 18x^2 + 48x - 1 \\\\\dfrac{d}{dx}f(x) = \dfrac{d}{dx}(2x^3 - 18x^2 + 48x - 1)\\\\f' = 6x^2-36x+48[/tex]
Equate the function with zero to know at what value of x the function returns a maximum value.
6x² - 36x + 48 = 0
x² - 6x + 8 = 0
x² -2x -4x +8 = 0
(x-2)(x-4)=0
Since we want to the value in the interval of 0 to 3, therefore, 2 is the value at which the function will have its maximum value.
f(2) = 2(2)³ - 18(2)² + 48(2) - 1
f(2) = 39
Hence, The maximum value of f(x) = 2x^3 - 18x^2 + 48x - 1 on the interval [0, 3] is 39. thus, the correct option is B.
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To find the maximum value of the function f(x) = 2x^3 - 18x^2 + 48x - 1 on the interval [0, 3], locate the critical points and evaluate the function at the critical points and endpoints. The maximum value is 71.
Explanation:To find the maximum value of the function f(x) = 2x^3 - 18x^2 + 48x - 1 on the interval [0, 3], we need to locate the critical points and the endpoints of the interval. First, find the derivative of the function: f'(x) = 6x^2 - 36x + 48. Set the derivative equal to zero and solve for x to find the critical points. Then evaluate the function at the critical points and the endpoints to find the maximum value.
The critical points are x = 1 and x = 4. Evaluating the function at these points: f(1) = -7 and f(4) = 71. Evaluating the function at the endpoints of the interval: f(0) = -1 and f(3) = 35. The largest value is 71, so the maximum value of f(x) on the interval [0, 3] is 71.
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Solve this 7(3x-4)=56
A^2 + 4^2 = 5^2
A = __
Translate the algebraic expression 3x+5 into a word phrase
Mary baked 21 cookies on Saturday and twice that many on Sunday for a school fundraiser. 4 cookies fell on the ground and had to be thrown out. If she packaged 3 cookies to a bag, how many cookies were left over?
A) 0
B) 1
C) 2
D) 3
a 6 feet tall boy cast a shadow of 9 feet at the same time of the day if the shadow of a tree measures 21 feet what is the height of the tree
5. If p || q, which pair of angles must be congruent?
1 and 8
2 and 5
4 and 6
7 and 8
Answer:
1 and 8.
Step-by-step explanation:
Two angles will be congruent if both measure the same. Then, as p is parallel to q we have that the alternate external angles (pair of angles out of the parallel lines, one on the right of the transversal line and the other on the left of the transversal line) has the same measure. In this case, 1 and 8 are alternate external angles.
A motorist traveled 311 miles on 12 gallons of gas. To the nearest tenth, how many miles can the motorist travel on one gallon of gas?
A) 0.03 miles
B) 23.8 miles
C) 24.6 miles
D) 25.9 miles
Paper cost $49 for 10 reams. How much for 1 ream?
To calculate the cost of 1 ream of paper from the total cost of 10 reams, divide $49 by 10 to get $4.90 per ream.
To find out how much it costs for 1 ream of paper when 10 reams cost $49, we simply divide the total cost by the number of reams. In this case:
Cost per ream = Total cost / Number of reams
Cost per ream = $49 / 10
Cost per ream = $4.90
Therefore, the cost for 1 ream of paper is $4.90.
use benchmarks to estimate 2.81+3.73
I need to know 0.98 as a percent
Answer:
98% hope this helped
Step-by-step explanation:
how do you solve (x3 + 6x2 + 3x + 1 ) ÷ (x - 2)
Line 1
x y
−1 1
0 3
Line 2
x y
1 5
3 3
(a) Write the equation for Line1 in slope-intercept form.
(b) Write the equation for Line 2 in slope-intercept form.
Answer:
im cool
Step-by-step explanation:
Nathan cut 3 pieces of rope. Each was between 1.1 m and 1.2 m. Write down how long each piece might be.
Order the numbers from least to greatest.
0.21,1/5 , 0.18, 24%
The arrangement from least to greatest is 0.18 < 0.20< 0.21< 0.24.
What is Ascending Order?Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right. Increasing order is another name for ascending order.
Given:
0.21,1/5 , 0.18, 24%
Now, writing each fraction in decimal form
1/5 = 0.2
24% = 24/100 = 0.24
So, we have the following numbers
0.21, 0.20, 0.18, 0.24
Hence, the arrangement from least to greatest is 0.18 < 0.20< 0.21< 0.24.
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