The supply curve for steel is 90x−y=−50. The demand curve is 10x+y=200. x is quantity in thousands of metric tons y is price in dollars per metric ton What are the values for quantity and price at the intersection point of the two curves? To find the values, first use addition to combine the left sides and to combine the right sides of the two equations.
Answers
Answer:
The intersection point of the two curves is \((x,y) = \left(\frac{3}{2}\,kton.m, 185\,USD \right)\).
Step-by-step explanation:
From statement we get the following equations:
Supply curve
\(90\cdot x - y = -50\) (1)
Demand curve
\(10\cdot x + y = 200\) (2)
Where:
\(x\) - Quantity, measured in thousands of metric tons.
\(y\) - Price, measured in US dollars per metric tons.
If we add both equations, then we find that quantity is:
\((90\cdot x -y )+(10\cdot x +y) = -50+200\)
\(100\cdot x = 150\)
\(x = \frac{3}{2}\,kton.m\)
Then, we finally find the price by substituting on (2):
\(y = 200-10\cdot \left(\frac{3}{2} \right)\)
\(y = 200-15\)
\(y = 185\,USD\)
The intersection point of the two curves is \((x,y) = \left(\frac{3}{2}\,kton.m, 185\,USD \right)\).
Related Questions
the median of
102 43 100 22
Answers
Answer:
32.5
Brainiest plz
Answer:
median is 71.5
Step-by-step explanation:
arrange from smallest to greatest: 22 43 100 102
since there is no number in the middle will do the average of the two numbers that are in the middle (43+100)/2 = 71.5
Find the positive solution, to the nearest tenth, of f(x)
g(x) = -2x + 25.
X≈
Submit
= g(x), where f(x) = 3* - 2 and
Answers
The result will be the x value when the difference between the values of f(x) and g(x) is less than 0.1, which will be the positive solution to the nearest tenth of f(x)=g(x).
To find the positive solution, to the nearest tenth, of f(x)=g(x) using Cora's process, the steps are as follows:
Input the initial value of x,if x=0.
Calculate f(x) and g(x):
f(x) = x² - 8 = 0 - 8 = -8
g(x) = 2x - 4 = 0 - 4 = -4
If f(x) is less than g(x), then x should be increased and vice versa.
Increase or decrease x accordingly and calculate the new values of f(x) and g(x).
Keep repeating steps 3 and 4 until the difference between the values of f(x) and g(x) is less than 0.1.
Hence, the result will be the x value when the difference between the values of f(x) and g(x) is less than 0.1, which will be the positive solution to the nearest tenth of f(x)=g(x).
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Cora is using successive approximations to estimate a positive solution to f(x) = g(x), where f(x)=x2 - 8 and g(x)=2x - 4. The table shows her results for different input values of x. Use Cora's process to find the positive solution, to the nearest tenth, of f(x) = g(x)
A person is looking from a car to the top of a building. The angle of elevation to the top of the building from the car is 32°. The building is 200 feet away. How tall is the building? Round to the nearest foot.
Answers
Common information for 3 and 4 The probability of contracting a stomach virus while visiting Mexico is 23%. Find the probability that amongst 12 students visiting Mexico 3. Exactly five students contract a stomach virus:
Answers
Answer:
The probability that exactly five students out of 12 contract a stomach virus while visiting Mexico is approximately 0.2707 or 27.07%.
Step-by-step explanation:
To find the probability that exactly five students out of 12 contract a stomach virus while visiting Mexico, we can use the binomial probability formula.
The formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where X is the number of students who contract the virus, k is the specific number we're interested in (in this case, 5), n is the total number of students (12), p is the probability of one student contracting the virus (0.23), and "n choose k" is the binomial coefficient - the number of ways to choose k objects out of n, which can be calculated using the formula n!/(k!(n-k)!).
Using these values, we get:
P(X=5) = (12 choose 5) * 0.23^5 * (1-0.23)^(12-5)
= 792 * 0.0009765625 * 0.3457171406
= 0.2706918748
Therefore, the probability that exactly five students out of 12 contract a stomach virus while visiting Mexico is approximately 0.2707 or 27.07%.
ahmed has AED 180 . He gives his brother 0.7 with bar notation of what he has , how much money did ahmed give his brother ??
Answers
The amount of money that Ahmed gave to his brother is AED 140.
It is given in the question that Ahmed has AED 180. He gives his brother 0.7 with bar notation of the amount he has.
We have to find the amount given by Ahmed to his brother.
Here, we have to convert a non-terminating but recurring rational number into fraction form.
Let 0.7 bar = x
Multiplying the equation by 10, we get
7.7 bar = 10x
10x - x = 7.7 bar - 0.7 bar
9x = 7
x = 7/9
Hence, Ahmed gave 7/9 of the amount he had to his brother.
Hence, we can write,
Amount given to Ahmed's brother by Ahmed = (7/9)*180 = AED 140.
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The graph shows the function f(x) = 2*
What is the value of x when f(x) = 8?
Ay
10-
A. 3
B. 2
C. 0
D. 1
Answers
Answer:
A
Step-by-step explanation:
Equate f(x) to 8 , that is
\(2^{x}\) = 8 = 2³
Since bases on both sides are equal, both 2, then equate exponents
x = 3
The value of the x when the exponential function shown in the graph f(x) = 2ˣ is 8 is when x = 3, which is option A.
Here, given the graph of the function,
f(x) = 2ˣ
We have to find the value of x when f(x) = 8.
In order to find the value of x, when f(x) = 8, we have to write as,
f(x) = 8
2ˣ = 8
Now write 8 as an exponent with base 2.
2ˣ = 2³
Hence the value of x = 3
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Use basic trigonometric identities to simplify the expression: tan^3(x) + tan (x)=?
Answers
Step 1
Simplify the expression.
\(\tan (x)(\tan ^2(x)\text{ +1)}\)Step 2
Find a trigonometric identity that can be used to simplify the expression in step 1
\(\tan ^2(x)+1=sec^2(x)\)Step 3
Get the final answer after substitution.
\(\tan (x)sec^2(x)\)Hence the right answer is option B
If you want to construct a circle that touched each of the corners of a triangle, what should you construct?
Answers
Answer:
Perpendicular bisectors.
Step-by-step explanation:
This is called a circumscribed circle.
First you construct the perpendicular bisector of one side, then repeat with a second side. Where these lines cross is the center of the circle.
Solve the rational equation
and check for extraneous solutions
5 = 4x+1
— ——-
x x^2
(1) x= 1; x = 0 is an extraneous solution
(2) x=0; x = 1 is an extraneous solution
(3) x= -1; x = 0 is an extraneous solution
(4) x=0; x = -1 is an extraneous solution
Answers
Answer:
1) x=1; x= 0 is an extraneous solution
Step-by-step explanation:
5 = 4x + 1
5 = 4 x 1 + 1
5 = 5
x = 1
______________________
x x^2
0 x 0^2
0 x 0 = 0
x = 0
:)
indifference curves cannot be concave to the origin because:
Answers
Indifference curves cannot be concave to the origin because they violate the assumption of diminishing marginal rate of substitution (MRS).
Indifference curves represent the different combinations of two goods that yield the same level of satisfaction for an individual. The slope of an indifference curve represents the marginal rate of substitution (MRS), which is the rate at which the individual is willing to trade one good for another while remaining equally satisfied.
If indifference curves were concave to the origin, it would imply that the MRS is increasing as the individual consumes more of both goods. Mathematically, this would mean that the absolute value of the slope of the indifference curve is increasing. However, this contradicts the assumption of diminishing marginal rate of substitution, which states that as an individual consumes more of one good, they are willing to trade less of it for an additional unit of the other good.
To illustrate this, let's consider two goods, X and Y, and assume the individual has a diminishing MRS. Suppose the slope of the indifference curve at a particular point is given by the absolute value of the change in quantity of Y divided by the change in quantity of X (∆Y/∆X). If the indifference curve were concave to the origin, as we move along the curve from left to right, the slope would increase. However, the assumption of diminishing MRS suggests that as we consume more of both goods, the slope should decrease.
In summary, indifference curves cannot be concave to the origin because it would violate the assumption of diminishing marginal rate of substitution. The concavity of indifference curves is inconsistent with the notion that individuals generally exhibit a decreasing willingness to trade one good for another as they consume more of both goods.
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i am stuck on this question and i’m not sure how to graph it
Answers
Given the function:
\(f\left(t\right)=e^{0.4t}\)For t = -4,
\(f\left(t\right)=e^{0.4(-4)}=e^{-1.6}=0.2\)For t = -2,
\(f(t)=e^{0.4(-2)}=e^{-0.8}=0.4\)For t = 0,
\(f(t)=e^{0.4(0)}=e^0=1\)For t = 2;
\(f(t)=e^{0.4(2)}=e^{0.8}=2.2\)For t = 4,
\(f(t)=e^{0.4(4)}=e^{1.6}=5\)Then we graph the points
(-4,0.2) (-2, 0.4) (0,1) (2, 2.2) and (4,5)
and we get the graph:
Antoine owes $684. He can make six monthly automatic payments with a $2.50 fee for each
payment, or he can pay using a credit card. If he uses his credit card, he will pay $30 in
interest. How much money does he save by using automatic payments?
Answers
Answer:
honestly i got 273.6 so i'm thinking that he would have to pay about 273 times........
Step-by-step explanation:
Answer:
15$
Step-by-step explanation:
How to do u substitution with indefinite integrals.
Answers
The corresponding differential element, rewrite the integral in terms of the new variable, integrate with respect to the new variable, replace the new variable with the original variable, and simplify the expression to find the solution.
To perform u-substitution with indefinite integrals, follow these steps:
Identify a suitable substitution: Look for a part of the integrand that resembles the derivative of a function. Choose a variable u to substitute for that part.
Calculate du: Take the derivative of u with respect to the original variable. This will help us express du in terms of the original variable.
Rewrite the integral: Substitute the chosen variable and du in the original integral, replacing the part to be substituted with u and the corresponding differential element du.
Integrate with respect to u: Treat the integral as a new integral with respect to u. Evaluate the integral using the rules of integration.
Replace u with the original variable: Rewrite the result of the integration in terms of the original variable.
Simplify and solve: If necessary, simplify the expression further or perform additional algebraic manipulations to obtain the final result.
Let's illustrate these steps with an example:
Consider the integral ∫(2x + 3)² dx.
Identify a suitable substitution: Let u = 2x + 3.
Calculate du: Take the derivative of u with respect to x: du/dx = 2. Rearrange the equation to solve for du: du = 2 dx.
Rewrite the integral: In terms of u and du, the integral becomes ∫u² (du/2).
Integrate with respect to u: Treat the integral as a new integral with respect to u: (1/2) ∫u² du = (1/2) * (u³/3) + C, where C is the constant of integration.
Replace u with the original variable: Substitute back u = 2x + 3 in the result: (1/2) * ((2x + 3)³/3) + C.
Simplify and solve: Further simplify the expression if necessary to obtain the final result.
In summary, to perform u-substitution with indefinite integrals, identify a suitable substitution, calculate the corresponding differential element, rewrite the integral in terms of the new variable, integrate with respect to the new variable, replace the new variable with the original variable, and simplify the expression to find the solution.
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use the intermediate value theorem to show that the polynomial has a real zero between the given integers? f(x)= x^3-x-4; between 1 and 7.
Answers
We have demonstrated using the Intermediate Value Theorem that the polynomial function has a real zero between 1 and 7.
To apply the Intermediate Value Theorem to the polynomial function f(x) = x^3 - x - 4 and show that it has a real zero between the integers 1 and 7, we need to verify that f(1) and f(7) have opposite signs.
Let's evaluate f(1) and f(7) to determine their signs:
f(1) = (1)^3 - (1) - 4 = 1 - 1 - 4 = -4
f(7) = (7)^3 - (7) - 4 = 343 - 7 - 4 = 332
From the calculations, we can see that f(1) = -4 and f(7) = 332.
Since f(1) is negative (-4) and f(7) is positive (332), they have opposite signs.
According to the Intermediate Value Theorem, if a continuous function changes sign between two points, then it must have at least one real zero between those points.
Since f(1) = -4 (negative) and f(7) = 332 (positive), the polynomial function f(x) = x^3 - x - 4 must have a real zero between the integers 1 and 7.
Therefore, we have demonstrated using the Intermediate Value Theorem that the polynomial function has a real zero between 1 and 7.
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What is the equation of this line?
y=−2x
y=1/2x
y=−1/2x
y = 2x
Answers
Equation of the given graph is y = 2x
Please show work! thank you :)
Answers
Answer:
c = 18
d = 36
Step-by-step explanation:
2c = d (equation 1)
c + d = 54 (equation 2)
Use substitution by putting 2c in the place of d on the second equation.
c + 2c = 54
3c = 54
Then divide both sides by 3 to get c (18).
Then use equation 1 to find d. Do this by putting 18 in the place of c.
2(18) = d
Solve, and the answer is d = 36
please help me :) Which expression is equivalent to 2 × 2 × 2 × 2 × 2? A.) 10 B.) 2 to the 5 power C.) 4 to the 2 power D.) 5 to the 2 power
Answers
Answer: ITS B
Step-by-step explanation:
(2)(2)(2)(2)(2)
=32
2^5
=32
Hey there! I'm happy to help!
We are talking about exponents here, which is the power to which a number is raised. What does it mean to raise a number to a power? It means to multiply it a certain number times.
For example, 3 to the the 3rd power is 27 because you multiply 3 three times (3×3×3), giving you 27.
We have 2×2×2×2×2. We see that we have the number 2 and need to raise it to a certain power. Since there are 5 2s, we are raising to the 5th power.
Therefore, the answer is B.) 2 to the 5 power.
Have a wonderful day! :D
find the zeros for 2x^2-24=26. what id the positive value of x?
Answers
Answer:
x=5
Step-by-step explanation:
move the constant to the right
calculate
devide both sides
simplify the equation
seperate the solution
(x=5)
What is the longest increasing subsequence problem in dynamic programming?
Answers
The Longest Increasing Subsequence (LIS) problem is a classic problem in dynamic programming. Given a sequence of numbers, the problem is to find the longest subsequence in which the numbers are in increasing order. For example, given the sequence {3, 1, 5, 2, 4}, the longest increasing subsequence is {1, 2, 4}, which has length 3.
The LIS problem can be solved using dynamic programming by defining an array to store the length of the longest increasing subsequence that ends at each position in the sequence. The array is initialized to 1, and then for each position i in the sequence, the length of the longest increasing subsequence that ends at i is calculated by finding the maximum length of any subsequence that ends at a position j < i and has a smaller value than the value at i. The final solution is the maximum length of any subsequence in the array.
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Find the area of a regular hexagon with an apothem length of 12.1 and a side length of 14
Answers
Answer:
area = 520 units²
Step-by-step explanation:
divide the hexagon into 6 equal triangles.
each triangle has a base of 14 and a height of 12.1 so:
the area of one triangles = 1/2BH = 1/2(14)(12.1) = 86.8 units ²
86.8 x 6 triangles = 520.8 units²
A student solves the problem to the left as shown. Which statements describe the solution? Check all of the boxes that apply
Answers
Answer:
The stated solution is correct (lengths of 16 feet and 8 feet).
Based on the way the variable is defined, the equation should be x + 2x = 24.
The way the variable is defined, and because x=16, the longer piece of rope would be 32 feet, which is not possible.
Step-by-step explanation:
Answer: a, b & d !
Step-by-step explanation:
Z'hkiya works as a waitress at her family's restaurant. She works 1 hour every moming during the breakfast shift and
returns to work each evening for the dinner shift. In the last four days, she worked 18 hours. If Z'hkiya works the
same number of hours every evening, how many hours did she work during each dinner shift?
I need help so bad
Answers
Answer:
3 and a half hours every dinner shift
Answer:
the other guy is right I'm pretty sure
$420 is divided between A, B and C. B receives $20 less than A, and C receives half as much as A and B together. how much does each receive?
Also could you explain the answer?
Answers
Answer:
A = $150
B = $130
C = $140
Step-by-step explanation:
Let the amount received by a be $x
b receives $20 less than a;
we have that;
b = x - 20
c receives half of Sum A and B
c = (x + x-20)/2
c = (2x-20)/2
c = x - 10
Add all and it gives 420
x - 10 + x -20 + x = 420
3x -30 = 420
3x = 420 + 30
3x = 450
x = 450/3
x =$150
a = 150
b = x - 20; 150 - 20 = 130
c = x-10
c = 150-10
c = $140
find a b, 9a 7b, |a|, and |a − b|. (simplify your vectors completely.) a = 9i − 8j 7k, b = 7i − 9k a b = 9a 7b = |a| = |a − b| =
Answers
Vectors
a + b = 16i - 8j - 2k
|a + b| = 18
|a| = 13.928
|a - b| = 18
Given:
a = 9i - 8j + 7k
b = 7i - 9k
Let's calculate the required values:
a + b = (9i - 8j + 7k) + (7i - 9k)
= 9i - 8j + 7k + 7i - 9k
= 16i - 8j - 2K
|a + b| = \(\sqrt{ ((16)^2 + (-8)^2 + (-2)^2)\)
= √(256 + 64 + 4)
= √324
= 18
|a| = \(\sqrt{ ((9)^2 + (-8)^2 + (7)^2)\)
= √(81 + 64 + 49)
= √194
≈ 13.928
|a - b| = \(\sqrt{((9 - 7)^2 + (-8)^2 + (7 - (-9))^2)\)
= √(2^2 + 64 + 16^2)
= √(4 + 64 + 256)
= √324
= 18
Therefore:
a + b = 16i - 8j - 2k
|a + b| = 18
|a| ≈ 13.928
|a - b| = 18
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If a wall is built in a room at a 36 degree angle. The angle formed in the other room by the wall is 144 degrees. What kind of angles are formed when they are added together
Answers
They form supplementary angles when they are added together.
Reason for Being Called Supplementary Angles
It is given that the angle made by the wall in one room is 36° and the angle formed by the same wall in the other room is 144°.
This implies that,
∠1 = 36°
∠2 = 144°
∠1 and ∠2 are adjacent angles and,
∠1 + ∠2 = 36° + 144°
⇒ ∠1 + ∠2 = 180°
Hence, these two adjacent angles make a straight-line angle. Hence, they are supplementary angles.
What are supplementary angles?
Two angles that form a straight line angle, that is, angle equal to 180°, when they are added together are said to be a pair of supplementary angles.
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What is the surface area of the right prism?
92 ft2
46 ft2
48 ft2
70 ft2
(will mark brainliest <3)
Answers
=========================================================
Work Shown:
L = 8 ft = lengthW = 3 ft = widthH = 1 ft = heightSA = surface area of the rectangular prism (aka block or box)
SA = 2*(LW + LH + WH)
SA = 2*(8*3 + 8*1 + 3*1)
SA = 2*(24 + 8 + 3)
SA = 2*(35)
SA = 70 square feet
This is the amount of wrapping paper you would need to cover all six sides of the box. This assumes that there are no gaps or overlaps.
Parabolas in Standard Form Please Help
Also please include work.
Find the vertex: y=x²+2x+1
Answers
Answer:
vertex = (- 1, 0 )
Step-by-step explanation:
given a parabola in standard form
ax² + bx + c ( a ≠ 0 )
then the x- coordinate of the vertex is
\(x_{vertex}\) = - \(\frac{b}{2a}\)
y = x² + 2x + 1 ← is in standard form
with a = 1 and b = 2 , then
\(x_{vertex}\) = - \(\frac{2}{2}\) = - 1
substitute x = - 1 into y for corresponding y- coordinate
y = (- 1)² + 2(- 1) + 1 = 1 - 2 + 1 = 0
vertex = (- 1, 0 )
The probability that a health nurse will find a client at home on a particular day is 0.7. what is the probability that on two home visits made by the nurse in a day, she will find each client at home?
Answers
The probability that the nurse will find the two patients is P = 0.49.
How to find the probability?
We know that the probability that the nurse finds the client on a particular day is 0.7
So, each time that the nurse goes that a home, that probability is the same and is independent of what happened before.
So if the nurse goes to two houses, the probability that she will find the client on the first home is 0.7
And the probability that she will find the client on the second home is 0.7
Then the joint probability (the product of the two individual ones) is:
P = 0.7*0.7 = 0.49
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Urgent!! Will give brainliest :)
Answers
The better statistics to compare the distribution are given as follows:
A. Mean and standard deviation.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the cardinality of the data-set, which represents the number of observations in the data-set.
The standard deviation of a data-set is calculated as square root of the sum of the differences squared between each observation and the mean of the data-set, divided by the cardinality of the data-set.
These two measures should be used as both distributions in this problem are symmetric, meaning that they do not contain outliers.
If the distribution contained outliers, then the median and the IQR should have been used.
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Angles J X M, M X N, and N X P form a straight line. Angle M X N is a right angle.
Complete the sentence:
Complete the sentence:
If Angle J X M has a value of 57 degrees, then Angle N X P has a value of
degrees.
Answers
Answer:
123 degrees
Step-by-step explanation:
180 - 57 = 123
Answer:
33
Step-by-step explanation:
123 is not the answer, on edge