The inverse of the given matrix [1 -1 0 -4 2 -1 4 3 3] is:
[0 -2 4/3]
[4/3 -1 -4/3]
[-4/3 4/3 2/3]
The inverse of a matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix. To find the inverse of the given matrix [1 -1 0 -4 2 -1 4 3 3], we need to use the following steps:
Step 1: Find the determinant of the matrix. The determinant of a 3x3 matrix is given by:
|A| = a(ei - fh) - b(di - fg) + c(dh - eg)
where a, b, c, d, e, f, g, h, and i are the elements of the matrix. Plugging in the values from the given matrix, we get:
|A| = (1)(2*3 - (-1)*3) - (-1)(-4*3 - 0*4) + (0)(-4*(-1) - 2*4)
|A| = (1)(6 + 3) - (-1)(-12) + (0)(4 - 8)
|A| = 9 - 12 + 0
|A| = -3
Step 2: Find the matrix of minors. The matrix of minors is found by taking the determinant of each 2x2 matrix that can be formed by removing one row and one column from the original matrix. The matrix of minors for the given matrix is:
[(-1)(3) - (-1)(3) (0)(3) - (-1)(4) (0)(3) - (-1)(-4)]
[(-4)(3) - (2)(3) (1)(3) - (0)(4) (1)(-4) - (0)(2) ]
[(-4)(-1) - (2)(0) (1)(0) - (-1)(-4) (1)(2) - (-1)(-4)]
= [0 4 4]
[-6 3 -4]
[4 -4 -2]
Step 3: Find the matrix of cofactors. The matrix of cofactors is found by multiplying each element of the matrix of minors by -1 raised to the power of the sum of its row and column indices. The matrix of cofactors for the given matrix is:
[0 -4 4]
[6 3 -4]
[-4 4 -2]
Step 4: Find the adjugate matrix. The adjugate matrix is found by taking the transpose of the matrix of cofactors. The adjugate matrix for the given matrix is:
[0 6 -4]
[-4 3 4]
[4 -4 -2]
Step 5: Find the inverse matrix. The inverse matrix is found by dividing each element of the adjugate matrix by the determinant of the original matrix. The inverse matrix for the given matrix is:
[0/(-3) 6/(-3) -4/(-3)]
[-4/(-3) 3/(-3) 4/(-3)]
[4/(-3) -4/(-3) -2/(-3)]
= [0 -2 4/3]
[4/3 -1 -4/3]
[-4/3 4/3 2/3]
Therefore, the inverse of the given matrix [1 -1 0 -4 2 -1 4 3 3] is:
[0 -2 4/3]
[4/3 -1 -4/3]
[-4/3 4/3 2/3]
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"Define T : R 2 → R 2 by T(~x) = T x1 x2 = 3x1 − 2x2 2x2 a) Let
~u = u1 u2 and ~v = v1 v2 be two vectors in R 2 and let c be any
scalar. Prove that T is a linear transformation. 2 b) Find the
stand"ard matrix A of T. Answer: c) Is T one-to-one? Prove your answer using the matrix A.
To prove that T is a linear transformation, we need to show that T(c~u + ~v) = cT(~u) + T(~v) for any scalar c and any vectors ~u and ~v in R2.
Let ~u = (u1, u2) and ~v = (v1, v2) be two vectors in R2 and let c be any scalar. Then,
T(c~u + ~v) = T(cu1 + v1, cu2 + v2) = (3(cu1 + v1) - 2(cu2 + v2), 2(cu2 + v2))
= (3cu1 + 3v1 - 2cu2 - 2v2, 2cu2 + 2v2)
= (3cu1 - 2cu2, 2cu2) + (3v1 - 2v2, 2v2)
= c(3u1 - 2u2, 2u2) + (3v1 - 2v2, 2v2)
= cT(~u) + T(~v)
Therefore, T is a linear transformation.
To find the standard matrix A of T, we can use the fact that T(~e1) and T(~e2) are the first and second columns of A, respectively, where ~e1 = (1, 0) and ~e2 = (0, 1) are the standard basis vectors of R2.
T(~e1) = T(1, 0) = (3(1) - 2(0), 2(0)) = (3, 0)
T(~e2) = T(0, 1) = (3(0) - 2(1), 2(1)) = (-2, 2)
Therefore, the standard matrix A of T is:
A = [ 3 -2 ]
[ 0 2 ]
To determine if T is one-to-one, we can use the fact that a linear transformation is one-to-one if and only if its standard matrix A has linearly independent columns. In this case, the columns of A are linearly independent because they are not scalar multiples of each other. Therefore, T is one-to-one. Alternatively, we can use the fact that a linear transformation is one-to-one if and only if its standard matrix A has a nonzero determinant. In this case, the determinant of A is (3)(2) - (0)(-2) = 6, which is nonzero. Therefore, T is one-to-one.
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6. Given a right triangle with leg lengths 19 inches and 17 inches, find the length of the
hypotenuse. Round to the nearest tenths.
In response to the supplied query, we may state that Therefore, the Pythagorean theorem length of the hypotenuse is approximately 25.5 inches.
what is Pythagorean theorem?The Pythagorean Theorem, often known as the Pythagorean Theorem, is the fundamental Euclidean geometry relationship between the three sides of a right triangle. The area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides, according to this rule. The Pythagorean Theorem says that the square that spans a right triangle's hypotenuse opposite the right angle equals the sum of the squares that span its sides. It is sometimes written as the general algebraic notation a2 + b2 = c2.
The Pythagorean theorem may be used to calculate the hypotenuse's length. According to the Pythagorean theorem, the square of the length of the hypotenuse (c) in a right triangle equals the sum of the squares of the lengths of the legs (a and b):
[tex]c^2 = a^2 + b^2[/tex]
[tex]c^2 = 19^2 + 17^2\\c^2 = 361 + 289\\c^2 = 650\\c =\sqrt(650)\\c = 25.5\\c = 25.5 inches[/tex]
Therefore, the length of the hypotenuse is approximately 25.5 inches.
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Which of the following equations represents a linear function?
x = 3
y equals one half times x minus 5
y equals three fourths times x squared
3x − 6 = 4
Answer:
The equation that represents a linear function is:
y equals one half times x minus 5
This is a linear equation because it has a constant rate of change, or slope, of one half. This means that for every increase of 1 in x, y will increase by 1/2. The equation is also in the standard form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
The other equations are not linear functions:
x = 3 is a vertical line, which is not a function because it fails the vertical line test.
y equals three fourths times x squared is a quadratic function because it includes an x-squared term.
3x − 6 = 4 is a linear equation, but it is not in the standard form of y = mx + b. It can be rearranged to y = (3/1)x - 2, which is a linear equation in slope-intercept form.
Power of test related to
A type 1 error
B type 2 error
C type 1 and type 2
D non of sbovr
Answer:
B
Step-by-step explanation:
The correct answer is Option C - Type 1 and Type 2. The power of a test is the probability of rejecting the null hypothesis when it is false; in other words, it is the probability of avoiding a type II error.
The power may also be thought of as the likelihood that a particular study will detect a deviation from the null hypothesis given that one exists. A Type 1 error occurs when a hypothesis test results in rejecting a true null hypothesis, and a Type 2 error occurs when a hypothesis test fails to reject a false null hypothesis.
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The average salary of 36 employee was 4650. Using historical data, we will assume that the population standard deviation is 165. Find the 98% confidence interval for the population mean salary.
Select one:
a. 4650±63.97
b. 4650±67.05
c. 4650±70.84
d. 4650±45.24
e. 4650±74.91
f. 4650±53.90
g. 4650±46.48
h. 4650±55.83
The average salary of 36 employee was 4650. Using historical data, we will assume that the population standard deviation is 165. The 98% confidence interval for the population mean salary is 4650±70.84. The correct answer is option c. 4650±70.84.
To find the 98% confidence interval for the population mean salary, we will use the formula:
CI = X ± Z* (σ/√n)
Where:
CI = Confidence Interval
X = Sample mean
Z = Z-score for the given confidence level
σ = Population standard deviation
n = Sample size
Plugging in the given values, we get:
CI = 4650 ± 2.33* (165/√36)
CI = 4650 ± 70.84
Therefore, the 98% confidence interval for the population mean salary is 4650±70.84. The correct answer is C.
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For the following situation, do the following but do not solve.
1. Define variables x and y.
2. Give a complete list of constraint inequalities.
3. Give a target (objective) equation (concerning profit).
Suppose a coffee company makes two blends, Columbian Supreme and Columbian Treat. Columbian Supreme takes 12 ounces of premium beans and 4 ounces of bargain beans per bag of coffee. Columbian Treat takes 7 ounces of premium beans and 9 ounces of bargain beans per bag of coffee. Suppose that 1600 ounces of premium beans and 800 ounces of bargain beans are available. If the company profits $4 per pound of Columbian Supreme and $3.25 per pound of Columbian Treat, then how can they maximize their profit? What is the maximum profit?
equation is 4x + 3.25y
To maximize their profit, the coffee company needs to define the variables x and y, which represent the number of pounds of Columbian Supreme and Columbian Treat respectively. Then, the complete list of constraint inequalities can be written as:
Finally, the target (objective) equation is 4x + 3.25y, which represents the total profit from selling x pounds of Columbian Supreme and y pounds of Columbian Treat.
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I need help doing the math homework
By algebra properties, the factor form of polynomials are listed below:
(a + b) · (a - b) (a + b) · (a² - a · b + b²) (a - b) · (a² + a · b + b²) (x² + 6) · (x + √6) · (x - √6) (4 · c + 1) · (16 · c² - 4 · c + 1) (k - 3) · (k² + 3 · k + 9) (∛54 · x + ∛250 · y) · [(∛54 · x)² - (∛54 · x) · (∛250 · y) + (∛250 · y)²] 3 · (m - 2 · √n) · (m + 2 · √n) · (m² + 4 · n) a · b² · (a + 1) · (a² - a + 1) · (a - 1) · (a² + a + 1) y² · (x - 7 · y) · (x² + 7 · x · y + 49 · y²) 9 · y · (y - ∛4) · [y² + ∛4 · y + (∛4)²] · (y + ∛4) · [y² - ∛4 · y + (∛4)²] (w - 4) · (w - 9) p · (p + 12) · (p - 7)How to factor polynomials
In this problem we need to factor 13 cases of polynomials, whose results must be derived by algebra properties. The factor form of the polynomial is:
Case 1:
a² - b²
(a + b) · (a - b)
Case 2:
a³ + b³
(a + b) · (a² - a · b + b²)
Case 3:
a³ - b³
(a - b) · (a² + a · b + b²)
Case 4:
x⁴ - 36
(x² + 6) · (x² - 6)
(x² + 6) · (x + √6) · (x - √6)
Case 5:
64 · c³ + 1
(4 · c + 1) · (16 · c² - 4 · c + 1)
Case 6:
k³ - 27
(k - 3) · (k² + 3 · k + 9)
Case 7:
54 · x³ + 250 · y³
(∛54 · x + ∛250 · y) · [(∛54 · x)² - (∛54 · x) · (∛250 · y) + (∛250 · y)²]
Case 8:
3 · m⁴ - 48 · n²
(√3 · m² - 4√3 · n) · (√3 · m² + 4√3 · n)
3 · (m² - 4 · n) · (m² + 4 · n)
3 · (m - 2 · √n) · (m + 2 · √n) · (m² + 4 · n)
Case 9:
a⁷ · b² - a · b²
a · b² · (a⁶ - 1)
a · b² · (a³ + 1) · (a³ - 1)
a · b² · (a + 1) · (a² - a + 1) · (a - 1) · (a² + a + 1)
Case 10:
x³ · y² - 343 · y⁵
y² · (x³ - 343 · y³)
y² · (x - 7 · y) · (x² + 7 · x · y + 49 · y²)
Case 11:
9 · y⁷ - 144 · y
y · (9 · y⁶ - 144)
y · (3 · y³ - 12) · (3 · y³ + 12)
9 · y · (y³ - 4) · (y³ + 4)
9 · y · (y - ∛4) · [y² + ∛4 · y + (∛4)²] · (y + ∛4) · [y² - ∛4 · y + (∛4)²]
Case 12:
w² - 13 · w + 36
(w - 4) · (w - 9)
Case 13:
p³ + 5 · p² - 84 · p
p · (p² + 5 · p - 84)
p · (p + 12) · (p - 7)
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PLEASE HELP :(
Isabella is collecting pledges for a walk-a-thon. Her mother has pledged a flat donation of $20, and her grandmother has pledged $2 per kilometer. If Isabella walks a certain distance, the two donors will end up owing the same amount. What is that distance?
Write a system of equations, graph them.
Answer:
Step-by-step explanation:
25 becuase 3 times 52 is that plus 32 is 73 and isabella with be rivher then ever than muh hahaha
How much of a 40% antifreeze solution must a mechanic mix with an 80% antifreeze solution if 16 gallons of a 50% antifreeze solution are needed?
The mechanic must mix 12 gallons of a 40% antifreeze solution with 4 gallons of an 80% antifreeze solution to create 16 gallons of a 50% antifreeze solution.
To find out how much of a 40% antifreeze solution must be mixed with an 80% antifreeze solution to create 16 gallons of a 50% antifreeze solution, we can use the following equation:
40% x + 80% y = 50% (16)
Where x is the amount of 40% antifreeze solution and y is the amount of 80% antifreeze solution.
We can also use the fact that the total amount of solution must equal 16 gallons:
x + y = 16
Now we can solve for one variable in terms of the other. Let's solve for x in the second equation:
x = 16 - y
And substitute this value of x into the first equation:
40% (16 - y) + 80% y = 50% (16)
Simplifying:
[tex]6.4 - 0.4y + 0.8y = 8[/tex]
0.4y = 1.6
y = 4
Now we can substitute this value of y back into the equation for x:
x = 16 - 4
x = 12
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x^2-8x+5=25 solve by completeing the square
We have the following response after answering the given question: As a result, the following are the answers to the equation: [tex]x = 4 + 6 = 10[/tex] and [tex]x = 4 - 6 = -2[/tex]
What is equation?In a mathematical equation, the equals sign (=), which connects two claims and denotes equality, is utilised. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressions can be used to describe the relationship between the two sentences on either side of a letter. The logo and the particular piece of software frequently correspond. like, for instance, 2x - 4 = 2.
We may use the completing the square method to solve the equation x2 - 8x + 5 = 25 by doing the following steps:
[tex]x^2 - 8x + 5 - 25 = 0\\x^2 - 8x - 20 = 0\\(-8/2)^2 = c\\16 = c\\x^2 - 8x + 16 - 16 - 20 = 0\\(x - 4)^2 - 36 = 0\\(x - 4)^2 = 36\\x - 4 = +6\\x = 4 + 6[/tex]
As a result, the following are the answers to the equation:
[tex]x = 4 + 6 = 10[/tex]
[tex]x = 4 - 6 = -2[/tex]
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Kaleigh binge-watched her favorite 30-minute episodes. Which representation does NOT show the amount of time Kaleigh spent watching TV at this rate?
x
x
A
C
Time (minutes)
4x D
Time Spent Watching TV
180
150
120
90
60
30
0
B y = 30x, where x represents the number of episodes watched and y represents the amount of time in minutes.
2468
Number of Episodes
Kaleigh spent 180 minutes watching 4 episodes.
Time Spent Watching TV
Episodes, x
2
4
6
8
Time (minutes), y
60
120
180
240
Answer:
Representation B does not show the amount of time Kaleigh spent watching TV at this rate. Representation B only shows the total time she would have spent based on the number of episodes watched, assuming each episode is 30 minutes long. It does not take into account the actual time it took for Kaleigh to watch the episodes, which may have varied depending on how quickly she watched them.
Step-by-step explanation:
we can descirbe 3x-2 as an expression
Answer: In each of the terms 3x 2 and 7x, x is a variable, and in both terms, we are multiplying a number by the variable. In the first term, 3x 2, 3 is being multiplied by the variable, so 3 is a coefficient. In the second term, 7x, 7 is being multiplied by the variable, so 7 is a coefficient.
Step-by-step explanation:
Tanner is spray painting an arrow on the side of a building to point to the entrance of his store. The can of gold spray paint he wants to use covers up to 12 square feet. Does Tanner have enough spray paint for his arrow?
Yes, Tanner has enough spray paint for his arrow.
What is an Area?
The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area. A planar figure's area is the area that its perimeter encloses. The quantity of unit squares that completely encircle the surface of a closed figure is its area. Square measurements for area include cm2 and m2.
Given : paint available in can = 12 ft²
We know that the arrow is comprised of a triangle and a rectangle.
So, the area of given arrow = area of rectangle + area of triangle
Now, area of triangle = 1/2 ×base × height
= 1/2 × 3 × (6 - 5 1/3)
= 3/2 × ( 6 - 16/3)
= 3/2 × ( 18-16)/3
= 3/2 × 2/3
= 1 ft²
Similarly, area of rectangle = length × breadth
= 5 1/3 × 2
= 16/3 × 2
= 32/3 ft²
Hence, area of arrow = area of triangle +area of rectangle
= 1 + 32/3
= 35/3 ft²
= 11.67 ft²
So, he has sufficient paint to cover the arrow.
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What was Mika's estimate and what is the actual sum of the numbers? (Look at the picture below)
Mika's estimate was 216 and the actual sum of the numbers is 216.27. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
All real numbers are supposed to be explicable by the four fundamental operations, often known as "arithmetic operations". Quotient, product, sum, and difference are the four operations in mathematics that follow division, multiplication, addition, and subtraction.
We are given numbers as 189.27, 15.8 and 11.2.
Mika's estimate is as follows:
189 + 16 + 11 = 216
Actual sum of numbers is as follows:
189.27 + 15.8 + 11.2 = 216.27
Hence, Mika's estimate was 216 and the actual sum of the numbers is 216.27.
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Show that the associationA \mapsto g_{A}is an isomorphism between the space of m x n matrices with coefficients in K and the space of bilinear forms in Km x Kn
The associationA \mapsto g_{A} is an isomorphism between the space of m x n matrices with coefficients in K and the space of bilinear forms in Km x Kn.
The associationA \mapsto g_{A} is an isomorphism between the space of m x n matrices with coefficients in K and the space of bilinear forms in Km x Kn if it satisfies the following conditions:
1. It is a one-to-one correspondence, meaning that for every matrix A there is a unique bilinear form g_{A} and vice versa.
2. It preserves the structure of the spaces, meaning that the operations of addition and scalar multiplication are preserved.
To show that the associationA \mapsto g_{A} is a one-to-one correspondence, we can start by assuming that g_{A} = g_{B} for two matrices A and B. Then, for any vectors u \in Km and v \in Kn, we have:
g_{A}(u,v) = g_{B}(u,v)
A \cdot (u \otimes v) = B \cdot (u \otimes v)
(A - B) \cdot (u \otimes v) = 0
Since this is true for all u and v, we can conclude that A - B = 0, or A = B. This means that the associationA \mapsto g_{A} is a one-to-one correspondence.
To show that the associationA \mapsto g_{A} preserves the structure of the spaces, we can start by considering the addition of two matrices A and B and the scalar multiplication of a matrix A by a scalar c. Then, for any vectors u \in Km and v \in Kn, we have:
g_{A + B}(u,v) = (A + B) \cdot (u \otimes v) = A \cdot (u \otimes v) + B \cdot (u \otimes v) = g_{A}(u,v) + g_{B}(u,v)
g_{cA}(u,v) = (cA) \cdot (u \otimes v) = c(A \cdot (u \otimes v)) = c g_{A}(u,v)
This means that the associationA \mapsto g_{A} preserves the operations of addition and scalar multiplication.
Therefore, the associationA \mapsto g_{A} is an isomorphism between the space of m x n matrices with coefficients in K and the space of bilinear forms in Km x Kn.
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QUICK
HELP ME PLS
I NEED ERGENT HELP
Answer:
Step-by-step explanation:
For any cube the total edge length is equal to 12n, with n being the length of an edge side. Knowing this:
Cube A - Total edge length = 12(3) or 36
Cube B - 12(5) or 60
Cube C - 12(9.5) or 114
If any cube has edge length s, the total edge length is 12s
Hope this helps!
New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $205 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $54. A. What is the probability that a hotel room costs $227 or more per night (to 4 decimals)?
The probability that a hotel room costs $227 or more per night in New York City is 0.3406.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Lets standardize the value of $227 per night using the formula:
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean of the distribution, and σ is the standard deviation of the distribution. Substituting the given values, we get:
z = (227 - 205) / 54
z = 0.4074
We need to find the probability that a hotel room costs $227 or more per night, which is equivalent to finding the probability that a standardized value is greater than or equal to 0.4074.
Using a standard normal table, we find:
P(Z ≥ 0.4074) = 1 - P(Z < 0.4074)
P(Z ≥ 0.4074) = 1 - 0.6594
P(Z ≥ 0.4074) = 0.3406
Therefore, the probability that a hotel room costs $227 or more per night in New York City is approximately 0.3406.
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The probability that a hotel room costs $227 or more per night is 0.3446
What is probability distribution?Probability distribution yields the possible outcomes for any random event. It is also defined based on the underlying sample space as a set of possible outcomes of any random experiment. These settings could be a set of real numbers or a set of vectors or a set of any entities. It is a part of probability and statistics.
Random experiments are defined as the result of an experiment, whose outcome cannot be predicted. Suppose, if we toss a coin, we cannot predict, what outcome it will appear either it will come as Head or as Tail. The possible result of a random experiment is called an outcome. And the set of outcomes is called a sample point. With the help of these experiments or events, we can always create a probability pattern table in terms of variables and probabilities.
GIven,
The mean hotel room rate ( [tex]\mu[/tex]) is $205 per night and standard deviation ([tex]\sigma[/tex]) of $54. A.
p( x > 225 )
we can't this to standard normal using [tex]z =\frac{X- \mu}{\sigma}[/tex]
[tex]z=\frac{227-205}{54} \approx0.4074[/tex]
p (z > 0.4074 ) = area to the right at 0.4074
p( x > 225 ) = p (z > 0.4074 ) = 1 - p (z < 0.4074)
= 1 - 0.6554 (from z table)
= 0.3446
Hence, probability that a hotel room costs $227 or more per night (to 4 decimals) 0.3446
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Find f ∘ g, g ∘ f, and g ∘ g.
f(x) = x4, g(x) = 1/x
(a)
f ∘ g
(b)
g ∘ f
(c)
g ∘ g
Hello there! To find f ∘ g, g ∘ f, and g ∘ g, let's first recall the definition of function composition: given two functions f and g, their composition f ∘ g is defined as the function that results from applying g to the result of applying f to its argument. Specifically, for a given input x, we can express the composition f ∘ g as follows: (f ∘ g)(x) = f(g(x)).
Given f(x) = x4 and g(x) = 1/x, we can find each composition as follows:
(a) f ∘ g = f(g(x)) = f(1/x) = (1/x)4
(b) g ∘ f = g(f(x)) = g(x4) = 1/(x4)
(c) g ∘ g = g(g(x)) = g(1/x) = 1/(1/x) = x
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Helppppp What is the volume of this figure
The volume of the figure is 144 cubic inches.
What is the volume of an object?The volume of an object is the three dimensional space that it fills up. Since there are different shapes, thus their volume can be expressed with different equations.
In the given shape, divide it into two cuboid so that;
volume of a cuboid = length*width*height
volume of cuboid 1 = 12 * 2* 4
= 96
volume of cuboid 1 is 96 cubic inches.
volume of cuboid 2 = 12*4*1
= 48
Volume of the figure = 96 + 48
= 144 cubic inches
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in the whitch of blackbird pond chapters 13-15 what causes several townsmen to gather at the wood household until late at night
Answer:
In the novel "The Witch of Blackbird Pond" by Elizabeth George Speare, in chapters 13-15, several townsmen gather at the Wood household until late at night because they suspect that Kit's grandfather, Matthew Wood, is hiding royalist sympathies. The men search through Matthew's belongings and find books and pamphlets that are considered to be treasonous, including a pamphlet by William Penn. They also find a prayer book that Matthew had brought with him from England. The men take the items and leave, warning the Woods to be careful about their political leanings. This event foreshadows the tension and conflict that will arise later in the novel between the royalists and the patriots.
Step-by-step explanation:
cuz graaa thag boys a lier da boys a lier
The graph below shows the variation in the average temperature of Earths surface from 1950-2000, according to one source
The years 1960–1965 saw the greatest change in temperature variation per unit of time.
What is Slope?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
The graph for average temperature variation v/s time is given.
To find during which year maximum temperature variation with time:
We have to find the year with maximum magnitude of slope |m|.
Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}\\[/tex]
Consider m for year 1950-1955:
m = 0 [line parallel to x-axis]
Consider m for year 1955-1960:
[tex]\frac{-0.05-0}{1955-1960}\\\\= 0.01[/tex]
Consider m for year 1960-1965:
[tex]\frac{-0.15-0}{1965-1960}\\\\= -0.03[/tex]
Consider m for year 1965-1970:
m = 0.01 {same as of 1955-1960}
Consider m for year 1970-1975:
m = 0 [line parallel to x-axis]
Consider m for year 1975-2000:
[tex]\frac{0.4-(-0.1)}{2000-1975}\\\\= 0.02\\[/tex]
|m| is maximum for year 1960-1965
Hence, the temperature variation changed the most per unit time in the year 1960-65.
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The volume of a sphere is 1230pi what is the radius
i need help with this answer
Calculate the perimeter of the trapezoid in millimeters
Answer:
135 mm
Step-by-step explanation:
The perimeter is found by adding all sides together. Since the answer is to be in millimeters, two side lengths must be converted.
1 centimeter = 10 millimeters
1.5 x 10 = 15 mm
6 x 10 = 60 mm
Now, add all sides together:
60 + 15 + 20 + 40 = 75 + 60 = 135 mm
12. The amount of money in a savings account earning yearly interest is represented by the
expression 750(1+0.012), where t is in years since the account was opened. What does
(1+0.012) represent?
A
B
C
D
The account earns $0.012 in yearly interest.
The account earns $1.20 in yearly interest.
The account earns 1.2% in yearly interest.
The account earns 12% in yearly interest.
Answer:
C. The account earns 1.2% in yearly interest.
Step-by-step explanation:
The expression 750(1+0.012) represents the amount of money in a savings account earning yearly interest after t years, where t is the number of years since the account was opened.
The expression (1+0.012) represents the interest rate as a decimal. The value 0.012 represents 1.2% in decimal form, which is the yearly interest rate earned by the account.
Therefore, (1+0.012) represents the account's yearly interest rate as a decimal, which is 1.2%.
The mean earnings of a university undergraduate student is enrolled in a Business program is $28,000 per year. Assume that the average salaries follow a normal distribution with a standard deviation of $2,500.
Required
a. Find the probabilities that a student makes more than $30,000?
b. What is the probability that a student would make between $27,000 and $32,000?
c. What is the probability that a student would make less than $23,150?
a. The probability that a student makes more than $30,000 is 0.0668.
b. The probability that a student makes between $27,000 and $32,000 is 0.9545.
c. The probability that a student makes less than $23,150 is 0.0062.
Probability is the likelihood that something will occur. When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various events. Statistics is the study of occurrences that follow a chance distribution.
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If matrix A = [-4,k; -7,2]
for what value of k does the matrix have one eigenvalue of
multiplicity 2?
To find the value of k for which the matrix A has one eigenvalue of multiplicity 2, we can use the characteristic equation of the matrix. The characteristic equation is det(A-λI)=0. For a given matrix, this equation will yield a polynomial equation of degree equal to the dimension of the matrix.
In this case, the equation is (λ+4)(λ-2) = 0. Solving this equation gives us two distinct eigenvalues of λ= -4 and λ=2. This means that for any value of k, the matrix A will have two distinct eigenvalues, and thus cannot have one eigenvalue of multiplicity 2. Therefore, the matrix A cannot have one eigenvalue of multiplicity 2 no matter what value of k is used.
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In a group of 100 students, 60 liked mathematics and 50 liked science.If 10 did not like any of the subjects , by using Venn-diagram, find the numbers of students who like both the subjects
Answer:
Below
Step-by-step explanation:
See Venn diagram below :
Does anyone know the answer?
Answer:
33.7°
Step-by-step explanation:
the direction angle is calculated as
tanΘ = [tex]\frac{y}{x}[/tex] ( Θ is the direction angle ) , then
tanΘ = [tex]\frac{-4}{-6}[/tex] = [tex]\frac{2}{3}[/tex]
Θ = [tex]tan^{-1}[/tex] ( [tex]\frac{2}{3}[/tex] ) ≈ 33.7° ( to the nearest tenth )
Order the numbers from least to greatest
Step-by-step explanation:
-10, -8, 0, 7 is the answer
The answer should be:
-10, -8, 0, 7