If the demand for tomato juice falls, it means that consumers are buying less of it at any given price. This will result in a leftward shift in the demand curve, showing a decrease in quantity demanded at each price level.
As a result, the equilibrium price of tomato juice will decrease, and the equilibrium quantity of tomato juice sold in the market will also decrease. This shift in demand will also affect the producers of tomato juice, who may need to adjust their prices and output levels to match the reduced demand. Overall, a decrease in demand for tomato juice will lead to lower prices and lower quantities sold in the market.
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Let f: R→R be a continuous function such that f(R) ⊂ Q. Show that f is constant.
[tex]$f(x) = q_a$[/tex] for all [tex]$x \in (a-1, a+1)$[/tex]. Since a was arbitrary, it follows that f is constant on any open interval. Since f is continuous, it follows that f is constant on [tex]$\mathbb{R}$[/tex].
Let a be any real number in R. Since f is continuous, the intermediate value theorem implies that the image of any closed interval under f is also an interval. Therefore, [tex]$f([a-1, a+1])$[/tex] is an interval in [tex]$\mathbb{Q}$[/tex]. Since the only intervals in [tex]$\mathbb{Q}$[/tex] are single points, [tex]$f([a-1, a+1]) = {q_a}$[/tex] for some rational number [tex]$q_a$[/tex].
Now let b be any real number with [tex]$b > a+1$[/tex]. By the intermediate value theorem, there exists some [tex]$x \in [a, b]$[/tex] such that [tex]$f(x) = \frac{q_a+q_b}{2}$[/tex]. But since f takes only rational values, [tex]$f(x) = q_a$[/tex]. This argument applies to all real numbers b with [tex]$b > a+1$[/tex], so [tex]$f(x) = q_a$[/tex] for all [tex]$x > a+1$[/tex]. Similarly, we can show that [tex]$f(x) = q_a$[/tex] for all [tex]$x < a-1$[/tex].
Therefore, [tex]$f(x) = q_a$[/tex] for all [tex]$x \in (a-1, a+1)$[/tex]. Since a was arbitrary, it follows that f is constant on any open interval. Since f is continuous, it follows that f is constant on [tex]$\mathbb{R}$[/tex].
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Adeline had a box full of notebooks. If she gives 13 notebooks to each
Adeline has 60 notebooks and 4 children in the given case.
Let's assume that Adeline has x notebooks and y children.
According to the problem, if she gives 13 notebooks to each child, she will have 8 left. This can be expressed as:
x - 13y = 8 --- equation 1
Also, if she gives 15 notebooks to each child, she will have zero left. This can be expressed as:
x - 15y = 0 --- equation 2
We can solve these equations simultaneously to find the values of x and y.
Multiplying equation 1 by 15 and equation 2 by 13, we get:
15x - 195y = 120 --- equation 3
13x - 195y = 0 --- equation 4
Subtracting equation 4 from equation 3, we get:
2x = 120
x = 60
Substituting the value of x in equation 2, we get:
60 - 15y = 0
y = 4
Therefore, Adeline has 60 notebooks and 4 children.
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Adeline has a box full of notebooks. If she gives 13 notebooks to each child, she will have 8 left. If she gives 15 notebooks to each child, she will have zero left. How many notebooks and how many children does Adeline have?
For the following exercises, determine a. Intervals where f is increasing or decreasing, b. Local minima and maxima of f, c. Intervals where f is concave up and concave down, and d. The inflection points of f.
f(x) = x² - 6x
f(x) = x³ - 6x²
f(x) = x⁴ - 6x³
a. (-∞,3) - f(x) is decreasing
(3,∞) - f(x) is rising.
b. Local minima at x=3. No local Minima
c. The function f(x)=x²-6x is always concave upwards.
d. Concave up and does not change concavity, so, No Inflection points.
f(x)= x²-6x
f'(x) = 2x-6
f"(x) = 2
Critical point f'(x)=0
2x-6=0
x=3
Thus, we have two sub intervals over the entire number line. (-∞,3) , (3,∞)
a) sub-interval x-value f'(x) verdict
(-∞,3) 1 2(1)-6=-4<0 f(x) is decreasing
(3,∞) 4 2(4)-6=2>0 f(x) is increasing
b) At x=3; Before x=3, f(x) decreasing and after x=3, f(x)
is increasing, thus Local minima at x=3.
No local Minima
c) Since f"(x)=2 Always, the function f(x)=x²-6x is always concave upwards
d) Inflection points
Since graph of function f(x)=x²-6x have only been concave up and does not change concavity,
No Inflection points.
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I NEED ANSWERS
b=10m с a=7m
Answer:
c = 12.2
Step-by-step explanation:
a squared + b squared = c sqared
7 squared + 10 squared = 49+ 100 = 149 = [tex]\sqrt{x} 149[/tex] = 12.2
Which ratio is always equivalent to the sine of angle A?
Answer: 4 Which ratio represents the cosine of angle A in the right triangle below? ... Which ratio is always equivalent to the sine of ∠A?
Step-by-step explanation:
Solve the equation 16. 5 + 2. 75h = 9h + 7. 5 − 4. 25h find what h is
Answer:
h = -1.25
Step-by-step explanation:
isolate the variable by dividing each side by factors that don't contain the variable.
Find the slope of the line through points (4,6) and (-6,2).
044
OB. 215
OD. 52
Beses Selection
A car manufacturer provider information about two different car models. The graph and table each show a proportional relationship between the number of miles traveled and the advertised number of gallons of gas used for two car models.
Car A can travel 1.25 times the distance car B can travel when both cars use 1 gallons of gas.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the distance.x represents the gas (gallons).k is the constant of proportionality.Next, we would determine the constant of proportionality (k) for car A by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 50/2
Constant of proportionality, k = 25.
y = 25x = 25(1) = 25 miles.
For car B, the constant of proportionality (k) is given by;
Constant of proportionality, k = 60/3
Constant of proportionality, k = 20.
y = 20x = 20(1) = 20 miles.
Difference = 25/20 = 1.25.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Let X1, ... , Xn be iid ~ Poisson(1), where l E (0,00) is an unknown parameter. Find the MLE for based on the observations x1 = 2, X2 = 5, X3 = 2, X4 = 1, X5 = 1. =
Based on the observations, the maximum likelihood estimate of λ is 11/5.
What is probability?Probability is a field of mathematics that calculates the likelihood of an experiment occurring. We can know everything from the chance of getting heads or tails in a coin to the possibility of inaccuracy in study by using probability.
The probability mass function (PMF) of a Poisson distribution with parameter λ is given by:
P(X = k) = [tex](e^{(-\lambda)} * \lambda^k)[/tex] / k!
The likelihood function for a sample of size n from a is given by:
L(λ) = P(X1 = x1, X2 = x2, ..., Xn = xn) = ∏[i=1 to n] [tex]( e^{(-\lambda)} * \lambda^{xi})[/tex] / xi!
The log-likelihood function is then:
ln L(λ) = ln ∏[i=1 to n] [tex](e^{(-\lambda)} * \lambda^{xi})[/tex] / xi! = ∑[i=1 to n] [tex](ln e^{(-\lambda)} * \lambda^{xi})[/tex] - ∑[i=1 to n] ln(xi!)
Simplifying further, we get:
ln L(λ) = (-nλ) + (∑[i=1 to n] xi)ln(λ) - ∑[i=1 to n] ln(xi!)
To find the maximum likelihood estimate (MLE) of λ, we need to differentiate the log-likelihood function with respect to λ, set the derivative to zero, and solve for λ.
d/dλ ln L(λ) = -n + (∑[i=1 to n] xi)/λ = 0
Solving for λ, we get:
λ = (∑[i=1 to n] xi) / n
Substituting the given values, we get:
λ = (2 + 5 + 2 + 1 + 1) / 5 = 11 / 5
Therefore, the maximum likelihood estimate of λ, based on the given observations, is 11/5.
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Determine whether the following are subspaces of P4. If so, prove it. If not, show orexplain why. (a. ) The set of all polynomials in P4 of even degree. (b. ) The set of all polynomials of degree 3. (c. ) The set of all polynomials p 2 P4 such that p(0) = 0. (d. ) The set of all polynomials in P4 having at least one real root
The zero vector in P4 is the polynomial 0(x) = 0, which has even degree. The set of all polynomials in P4 of even degree is closed under addition.
The set of all polynomials in P4 of even degree satisfies all three conditions, it is a subspace of P4.
(a) The set of all polynomials in P4 of even degree is a subspace of P4.
To prove this, we need to show that it satisfies the three conditions for a subspace:
i) It contains the zero vector: The zero vector in P4 is the polynomial 0(x) = 0, which has even degree, so it is contained in the set of all polynomials in P4 of even degree.
ii) It is closed under addition: Let p(x) and q(x) be two polynomials in P4 of even degree. Then, p(x) + q(x) is also a polynomial of even degree, since the sum of two even numbers is even. Therefore, the set of all polynomials in P4 of even degree is closed under addition.
iii) It is closed under scalar multiplication: Let p(x) be a polynomial in P4 of even degree, and let c be a scalar. Then, cp(x) is also a polynomial of even degree, since multiplying an even number by a scalar yields an even number. Therefore, the set of all polynomials in P4 of even degree is closed under scalar multiplication.
Since the set of all polynomials in P4 of even degree satisfies all three conditions, it is a subspace of P4.
(b) The set of all polynomials of degree 3 is not a subspace of P4.
To prove this, we only need to show that it does not satisfy the first condition for a subspace:
i) It contains the zero vector: The zero vector in P4 is the polynomial 0(x) = 0, which has degree 0, not degree 3. Therefore, the set of all polynomials of degree 3 does not contain the zero vector and is not a subspace of P4.
(c) The set of all polynomials p in P4 such that p(0) = 0 is a subspace of P4.
To prove this, we need to show that it satisfies the three conditions for a subspace:
i) It contains the zero vector: The zero vector in P4 is the polynomial 0(x) = 0, which satisfies 0(0) = 0, so it is contained in the set of all polynomials p in P4 such that p(0) = 0.
ii) It is closed under addition: Let p(x) and q(x) be two polynomials in P4 such that p(0) = 0 and q(0) = 0. Then, (p+q)(0) = p(0) + q(0) = 0, so p+q is also a polynomial in P4 such that (p+q)(0) = 0. Therefore, the set of all polynomials p in P4 such that p(0) = 0 is closed under addition.
iii) It is closed under scalar multiplication: Let p(x) be a polynomial in P4 such that p(0) = 0, and let c be a scalar. Then, (cp)(0) = c(p(0)) = c(0) = 0, so cp is also a polynomial in P4 such that (cp)(0) = 0. Therefore, the set of all polynomials p in P4 such that p(0) = 0 is closed under scalar multiplication.
Since the set of all polynomials p in P4 such that p(0) = 0 satisfies all three conditions, it is a subspace of P4.
(d) The set of all polynomials in P4 having at least one real root is not a subspace of P4.
To prove this, we only need
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One Lump Sum:
Calculate the APR for a $2000 loan that is paid off in one lump sum at the end of the year. The stated annual interest rate is 8%. Show your work.
The APR for this loan is 8%.
We have,
The formula for calculating APR is:
APR = (r/n) x m
where r is the stated annual interest rate, n is the number of times the interest is compounded in a year, and m is the number of payments made in a year.
In this case,
The loan is paid off in one lump sum at the end of the year, so there is only one payment made in a year (m = 1).
The stated annual interest rate is 8%, so r = 0.08.
We need to determine the value of n.
Since the loan is paid off in one lump sum at the end of the year, we can assume that the interest is compounded annually (n = 1).
Using the formula, we get:
APR = (0.08/1) x 1
APR = 0.08
Therefore,
The APR for this loan is 8%.
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PLeASE HELP MEE!! I HAVE TO SUBMIT THIS NOWW
Answer:
I beleive c. i had the same question last year, and i believe i got the answer right. so sorry if its wrong. hope this helps.
Step-by-step explanation:
Algibra 1, unit 1, Math Nation
The area of the rectangle is √32 x √45.
Option A is the correct answer.
We have,
From the figure,
Length = √32
Width = √45
Now,
The area of the rectangle.
= Length x width
= √32 x √45
Thus,
The area of the rectangle is √32 x √45.
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pls help asap will give points
The size of the angle X is calculated to be equal to 47.4° to the nearest tenth of degree using trigonometric ratios cosine
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
Given the triangle STU;
cos X = ST/SU {adjacent/hypotenuse}
cos X = 8.8/13
X = cos⁻¹(8.8/13) {cross multiplication}
X = 47.3963°
Therefore, the measure of the angle X is calculated to be equal to 47.4° to the nearest tenth of degree using trigonometric ratios cosine
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Sherri lives in Canada and is considering buying a new sofa. If the price level in Canada falls and the price level in the United States does not change, Canadian manufactured sofas are relatively A) more expensive, so Sherri will likely purchase a U.S. manufactured sofa. B) more expensive, so Sherri will likely purchase a Canadian manufactured sofa. C) less expensive, so Sherri will likely purchase a U.S. manufactured sofa. D) less expensive, so Sherri will likely purchase a Canadian manufactured sofa. E) Both answers B and D could be correct depending on whether U.S. manufactured sofas were initially more expensive or less expensive than Canadian sofas.
If the price level in Canada falls and the price level in the United States does not change, Canadian-manufactured sofas are relatively less expensive, so Sherri will likely purchase a Canadian manufactured sofa.
This is because the decrease in price level in Canada would make Canadian goods more affordable, including Canadian manufactured sofas. This makes them a more attractive option for Sherri than U.S. manufactured sofas which would still be relatively more expensive even if their price level did not change. Answer D is correct in this scenario. However, if U.S. manufactured sofas were initially more expensive than Canadian sofas, then answer B could also be correct. Overall, Sherri's decision would depend on the initial price difference between Canadian and U.S. manufactured sofas, as well as her personal preferences and any other relevant factors.
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What is the surface area of the entire prism below?
Area of triangle = 1/2bh
Area of rectangle = L*W
5 ft
4 ft
6 ft
5 ft
18 ft
The surface area of the entire prism is 294 ft².
How to find the surface area of the entire prism?The surface area of the entire prism can be found by summing the areas of the triangular and rectangular faces of the prism.
Since we have two triangular faces and 3 rectangular faces. Thus,
surface area of the entire prism = 2*( 1/2bh) + 3*(L*W)
where b = 6, h = 4, L = 18 and W = 5
surface area of the entire prism = 2*( 1/2 * 6*4) + 3*(18*5)
surface area of the entire prism = 24 + 270
surface area of the entire prism = 294 ft²
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A car drives 10.5 miles in 1/6 hour. What is its average speed, in miles per hour?
Answer:
63 mph
Step-by-step explanation:
10.5 × 6 is 63
you multiply by the fraction of the hour so you can get how fast the car is going in miles per an hour
Answer:
The average speed of the car = 63miles per hour
Step-by-step explanation:
Given, the total distance traveled by the car= 10.5 miles
total time is taken by the car to cover 10.5 miles = 1/6 hour
formula to calculate average speed
average speed = total distance/total time
average speed = 10.5/(1/6)
= 10.5×6
= 63 miles per hour
therefore, the average speed of the car is 63 miles per hour
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The point A has coordinates (-3, 4) and the point C has coordinates (5,2). The mid-point of AC is M. The line / is the perpendicular bisector of AC. (a) Find an equation of /. (4) (b) Find the exact length of AC. (2) The point Blies on the line I. The area of triangle ABC is 1772 (c) Find the exact length of BM. (2) (d) Find the exact length of AB. (2) (e) Find the coordinates of each of the two possible positions of B.
a)An equation of / is y = 2x + 1.
b) The exact length of AC is 2√17.
c) The exact length of BM is √17.
d) The coordinates of B are (5, 4).
(a) Since / is the perpendicular bisector of AC, it passes through the midpoint M of AC. The coordinates of M can be found by taking the average of the x-coordinates and the average of the y-coordinates of A and C, respectively:
x-coordinate of M = (-3 + 5)/2 = 1
y-coordinate of M = (4 + 2)/2 = 3
Therefore, the coordinates of M are (1, 3). Since / is perpendicular to AC, its slope is the negative reciprocal of the slope of AC:
slope of AC = (2 - 4)/(5 - (-3)) = -1/2
slope of / = 2 (negative reciprocal of -1/2)
Using the point-slope form of the equation of a line with the point M, we get:
y - 3 = 2(x - 1)
Simplifying and rearranging, we get:
y = 2x + 1
Therefore, an equation of / is y = 2x + 1.
(b) The length of AC can be found using the distance formula:
AC = √[(5 - (-3))^2 + (2 - 4)^2] = √64 + 4 = √68 = 2√17
Therefore, the exact length of AC is 2√17.
(c) Since BM is a median of triangle ABC, it divides AC into two equal parts. Therefore, BM has length half of AC:
BM = AC/2 = (1/2)(2√17) = √17
Therefore, the exact length of BM is √17.
(d) Since B lies on line /, its x-coordinate is 5 (since / passes through point (5, 2)). To find the y-coordinate, we can substitute x = 5 into the equation of /:
y = 2x + 1 = 2(5) + 1 = 11
Therefore, the coordinates of B are (5, 11).
Alternatively, we can use the fact that B lies on the circumcircle of triangle ABC (since angle ABC is a right angle) to find its coordinates. The circumcenter of triangle ABC is the midpoint of AC (which is also the intersection of the perpendicular bisectors of AC), so the coordinates of the circumcenter are (1, 3). The radius of the circumcircle is half of AC, so it is √17. Therefore, the equation of the circumcircle is:
(x - 1)^2 + (y - 3)^2 = 17
Since B lies on the circumcircle, its coordinates satisfy this equation. Substituting x = 5, we get:
(5 - 1)^2 + (y - 3)^2 = 17
16 + (y - 3)^2 = 17
(y - 3)^2 = 1
y - 3 = ±1
Solving for y, we get y = 2 or y = 4. Since B lies on line /, its y-coordinate must be greater than 2, so y = 4. Therefore, the coordinates of B are (5, 4).
(e) There are two possible positions of B, which are reflections of each other across the line /. One position has coordinates (5, 11), as found in part (d), and the other has coordinates (-3, 2). To find the coordinates of the second position, we can reflect point A across line / to get the point B':
B' has the same x-coordinate as A, which is -3. To find its y-coordinate, we can use the equation
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What cash payment is equivalent to making payments of $1074.00 at the end of every month for 5 years interest is 11% per annum compounded semi-annually The cash payment is (Round the final answer to the nearest count as needed. Round all intermediate values to sex decimal places as needed
The cash payment equivalent to making monthly payments of $1074 for 5 years with an interest rate of 11% per annum compounded semi-annually is $49,701.
To find the cash payment, we can use the Present Value of the Annuity formula:
PV = PMT * [(1 - (1 + r)⁻ⁿ) / r]
Where:
PV = Present Value (cash payment)
PMT = Monthly payment ($1074)
r = Monthly interest rate
n = Number of payments (5 years * 12 months = 60)
First, we need to find the monthly interest rate. Since the interest is compounded semi-annually, we'll divide the annual interest rate by 2, and then convert it to a monthly rate:
Semi-annual interest rate = 11% / 2 = 5.5% = 0.055
[tex](1 + 0.055)^{(1/6)} - 1[/tex] ≈ 0.008944 (rounded to 6 decimal places)
Now we can plug the values into the Present Value of Annuity formula:
PV = 1074 * [(1 - (1 + 0.008944)⁻⁶⁰) / 0.008944]
PV ≈ 1074 * [1 - (0.5861) / 0.008944]
PV ≈ 1074 * 46.2768
PV ≈ 49,701
The cash payment equivalent is approximately $49,701 (rounded to the nearest dollar).
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Michael goes to a theme park and rides two different roller coasters that both begin on a raised platform. His height while on the first roller coaster, measured in feet from the platform height, can be modeled by this graph, where t is the number of seconds since the ride began.
His height while on the second roller coaster, measured in feet from the platform height, can be modeled by a trigonometric function, shown in this table, where t is the number of seconds since the ride began.
The statement that describe the situation are;
E. While on the first roller coaster, the height switches from positive to negative approximately every 40 seconds,
D.While on the second roller coaster, the height switches every 80 seconds.
Since Function is a type of relation, or rule, that maps one input to specific single output. It is Linear function which is a function whose graph is a straight line
While on the first roller coaster, we can see that the function modeling Michael's height switches from positive to negative approximately every 40 seconds, meaning he changes from being at a height above the platform to below the platform approximately every 40 seconds.
While on the second roller coaster, we can see that this change occurs every 80 seconds.
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Find the value of x in the given
right triangle.
10
7
х
x = [?]°
Enter your answer as a decimal rounded to the
nearest tenth.
Enter
In the given case, x = cos⁻¹ (0.7) ≈ 44.4 ° rounded to the nearest tenth.
To find the value of x in degrees, we can use trigonometric ratios. In a right triangle, the sine of an acute angle is defined as the length of the side opposite the angle divided by the length of the hypotenuse. The cosine of an acute angle is defined as the length of the adjacent side divided by the length of the hypotenuse.
In this case, we have the side opposite to angle x is 7 and the hypotenuse is 10.
Therefore, sin(x) = 7/10. Solving for x, we get x = sin⁻¹ (7/10) ≈ 44.4° rounded to the nearest tenth.
Alternatively, we could use the cosine ratio since we also know the adjacent side. We have the adjacent side as x and the hypotenuse as 10. Therefore, cos(x) = x/10.
Solving for x, we get x = 10cos(x). We also have the opposite side as 7, which means that sin(x) = 7/10. Using the identity sin²(x) + cos²(x) = 1, we can solve for cos(x) as cos(x) = [tex]√(1 - sin²(x)[/tex]). Substituting sin(x) = 7/10, we get cos(x) = √(1 - (7/10)²) ≈ 0.7. Thus, x = cos⁻¹(0.7) ≈ 44.4° rounded to the nearest tenth.
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Find the value of x in the given right triangle.
10⁷х x = [?]°
Enter your answer as a decimal rounded to the nearest tenth.
complete solution pls
thankyou
Solve for the inverse Matrix 1. Using Adjoint of a Matrix A=2 -1 0
0 1 2
1 1 0 2.Using Gauss Jordan A=1 3
2 5
3. Using Equations and Identity Matrix A=1 -2
2 -3
The inverse of matrix A is:
A^-1 = |-3 -2|
|-2 -1|
Using Adjoint of a Matrix A=2 -1 0
0 1 2
1 1 0
The first step is to find the determinant of the matrix A:
|A| = 2(10 - 21) - (-1)(10 - 12) + 0(11 - 10)
= 4 + 2 + 0
= 6
Next, we need to find the adjoint of matrix A, which is the transpose of its cofactor matrix. The cofactor matrix is obtained by taking the determinant of the submatrix obtained by removing each element of the original matrix in turn and multiplying it by (-1)^(i+j), where i and j are the row and column indices of the removed element, respectively.
Cofactor matrix of A is
| 1 2 -1|
|-2 0 2|
|-1 2 1|
Taking the transpose of the cofactor matrix, we get the adjoint matrix of A as follows:
A^T = | 1 -2 -1 |
| 2 0 2 |
|-1 2 1 |
To find the inverse of A, we use the formula:
A^-1 = (1/|A|) A^T
Substituting the values, we get:
A^-1 = (1/6) | 1 -2 -1 |
| 2 0 2 |
|-1 2 1 |
Using Gauss Jordan A= |1 3|
|2 5|
We can find the inverse of a matrix using Gauss-Jordan elimination method as follows:
|1 3|1 0| |1 3|0 1|
|2 5|0 1|-> |0 1|-2/3 -1/3|
Therefore, the inverse of matrix A is:
A^-1 = |-2/3 -1/3|
| 1/3 1/3|
Using Equations and Identity Matrix A= |1 -2|
|2 -3|
We can find the inverse of a matrix A using the equations AX=I, where I is the identity matrix and X is the matrix that represents the inverse of A. The solution is given by:
|1 -2| |x11 x12| |1 0|
|2 -3| |x21 x22| = |0 1|
Multiplying the matrices, we get:
x11 = -3
x12 = -2
x21 = -2
x22 = -1
Therefore, the inverse of matrix A is:
A^-1 = |-3 -2|
|-2 -1|
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Marlon has $600 in his bank account and plans to withdraw $25 each week. Cassandra has $45 in her bank account and plans to deposit $12 each week. Which equation can be used to determine the number of weeks it will take until Marlon and Cassandra have the same balance in their accounts? A)
600−25x=45+12x
cross out
B)
600x−25=45x+12
cross out
C)
25x+12x=600+45
cross out
D)
600x−45x=25+12
Part B
As per the given situation, it will take 15 weeks for Marlon and Cassandra to have the same balance in their accounts is 600−25x=45+12x. The correct option is A.
We can start by setting up an equation that represents the balance of each person after x weeks.
After x weeks, Marlon's balance would be:
600 - 25x
After x weeks, Cassandra's balance would be:
45 + 12x
To find the number of weeks it will take until they have the same balance, we can set these two expressions equal to each other:
600 - 25x = 45 + 12x
Simplifying this equation, we can combine like terms:
600 = 45 + 37x
Subtracting 45 from both sides:
555 = 37x
Dividing both sides by 37:
x = 15
Therefore, it will take 15 weeks for Marlon and Cassandra to have the same balance in their accounts.
Thus, the correct equation is A) 600−25x=45+12x.
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please help
What is the surface area, in square centimeters, of the tissue box shown below?
48
240
264
288
The surface area of the tissue box is 240 cm².
Option B is the correct answer.
We have,
The tissue box can be considered a triangular prism.
The formula for the surface area of the tissue box can be made as:
The perimeter of the triangular base x height of the box.
Now,
Perimeter
= 8 + 6 + 10
= 24 cm
And,
The surface area of the tissue box.
= 24 x 10
= 240 cm²
Thus,
The surface area of the tissue box is240 cm².
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A line passes through the points (3,-2) and (3, 4). Determine the slope of the line.
0 m =
O m = 0
O The slope is undefined.
Om = 3
Since the line passes through the points (3,-2) and (3, 4), the slope of the line is: C. the slope is undefined.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Slope (m) = (4 + 2)/(3 - 3)
Slope (m) = (6)/(0)
Slope (m) = undefined.
Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is undefined.
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Thema deposits 500$ ina savings account with a simple interest rate of 1. 3%. How could you use this information to find the interest she would earn in 4 years and determine the percent change in her savings account
The percent change in her savings account is 5.2%, meaning her savings account has increased by 5.2% due to the interest earned over 4 years.
To find the interest Thema would earn in 4 years, we can use the simple interest formula:
where I is the interest earned, P is the principal (initial deposit), r is the interest rate (as a decimal), and t is the time period in years.
In this case, we have P = $500, r = 0.013, and t = 4. Plugging in these values, we get:
I = [tex]($500) (0.013) (4) = $26[/tex]
So, Thema would earn $26 in interest over 4 years.
To determine the percent change in her savings account, we need to compare the amount she will have after 4 years to the initial deposit. After 4 years, her savings account will have:
A = P + I = $500 + $26 = $526
The percent change in her savings account can be calculated as:
percent change = (new amount - old amount) / old amount x 100%
Substituting the values, we get:
percent change = ($526 - $500) / $500 x 100% = 5.2%
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prove that in a group of 250 students, the family name of at least ten students must start with the same letter. there are 26 letters in the english alphabet
To prove that in a group of 250 students, the family name of at least ten students must start with the same letter, we can use the Pigeonhole Principle.
The Pigeonhole Principle states that if you have n pigeonholes (in this case, the 26 letters of the English alphabet) and you are placing m > n items (here, 250 students) into the pigeonholes, at least one pigeonhole must contain more than one item.
Here's a step-by-step explanation:
1. We have 26 pigeonholes, representing the 26 letters of the English alphabet.
2. We have 250 students (items) to place into these pigeonholes based on the first letter of their family name.
3. Apply the Pigeonhole Principle: Divide the total number of students (250) by the total number of pigeonholes (26).
250 ÷ 26 ≈ 9.6
4. Since we can't have a fraction of a student, we round up to the nearest whole number.
10 students per pigeonhole
5. By rounding up, we find that at least one pigeonhole (letter of the alphabet) must have 10 or more students with family names starting with that letter.
So, in a group of 250 students, the family name of at least ten students must start with the same letter, as demonstrated by the Pigeonhole Principle.
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Write the general form equation for the circle shown.
Check the picture below.
so the circle has a radius of 3 and a center at (-2 , 1)
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-2}{h}~~,~~\underset{1}{k})}\qquad \stackrel{radius}{\underset{3}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-2) ~~ )^2 ~~ + ~~ ( ~~ y-1 ~~ )^2~~ = ~~3^2\implies (x+2)^2 + (y-1)^2 = 9[/tex]
A boat's heading is E15
∘
∘
N with a speed of 16 knots. The current is moving NW at 5 knots. What is the actual speed of the boat rounded to the nearest tenth?
The real speed of the vessel, adjusted to the closest tenth, is 20.4 hitches.
How to Solve the Problem?To unravel this issue, we got to break down the boat's speed into its components. We will use trigonometry to discover the eastbound and northward components of the boat's speed.
First, let's draw a diagram:
N
|
|
NW 5 | E15
|
--------------|---------------> E
|
|
|
S
From the chart, we will see that the northward component of the boat's speed is:
16 hitches * sin(15°) = 4.16 knots
And the eastbound component of the boat's speed is:
16 ties * cos(15°) = 15.38 knots
Next, we ought to discover the whole northward and eastbound speed of the vessel by including the boat's speed components to the current's speed components. We are able moreover utilize trigonometry to discover the northward and eastbound components of the current's speed:
5 hitches * sin(45°) = 3.54 ties northward
5 hitches * cos(45°) = 3.54 ties eastbound
So, the overall northward speed of the pontoon is:
4.16 ties + 3.54 hitches = 7.7 hitches northward
And the full eastbound speed of the pontoon is:
15.38 ties + 3.54 ties = 18.9 ties eastbound
Presently, we will utilize the Pythagorean hypothesis to discover the greatness of the boat's speed vector:
sqrt((7.7 knots)^2 + (18.9 knots)^2) = 20.4 ties
In this manner, the real speed of the vessel, adjusted to the closest tenth, is 20.4 hitches.
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approximately how many feet tall is the streetlight.
Show all work pls
Answer: 16.8 feet
Note: your teacher may not want you to enter "feet" and instead may just want the number only.
===================================================
Work Shown:
tan(angle) = opposite/adjacent
tan(40) = h/20
20*tan(40) = h
h = 20*tan(40)
h = 16.7819926 which is approximate
h = 16.8
The streetlamp is approximately 16.8 ft tall.
When using your calculator, make sure it's in degree mode. One way to check is to compute something like tan(45) and you should get 1 as a result.
Step-by-step explanation: