Answer:
2.66666666667
Step-by-step explanation:
Answer:
8/3 = 2.666666667 = 2 2/3
Step-by-step explanation:
do 2/9 × 4/9 first= 8/27 ÷ 1/9
= 8/27 × 9/1
8/27 × 9 = 72/27 = 8/3 = 2 2/3
how many ways are there to seat four of a group of ten people around a circular table where two seatings are considered the same when everyone has the same immediate left and immediate right neighbor?
The number of ways which are there to seat four of a group of ten people around a circular table is 1260.
To choose 4 people from a group of ten we need to count such people, which can be found using 10! / 4! × (10-4)! , after solving this we need to multiply 3! by this to get the desired answer. This is done because for that 4 people to sit in a circle, the possibilities for n people to sit around a circle is (n-1)! , and since n here is 4 the possibilities will also be (4-1)! which is 3! here.
Hence the final answer: 3! × 10! / 4! × (10-4)! = 1260
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Determine whether the eigenvalues of each matrix are distinct real, repeated real, or complex. -5 -2 - 3] Complex 8 41 18] Distinct Real 90 40 3 3 Distinct Real -4 3 4 E .] Distinct Real -2 -9
- Matrix A has distinct real eigenvalues.
- Matrix B has repeated real eigenvalues.
- Matrix C has distinct real eigenvalues.
- Matrix D has a distinct real eigenvalue.
To determine the nature of the eigenvalues of each matrix, we need to find the eigenvalues by solving the characteristic equation and then examine their properties.
Let's consider each matrix:
1. Matrix A:
[-5 -2 -3]
[ 8 41 18]
[90 40 3]
To find the eigenvalues, we solve the characteristic equation det(A - λI) = 0, where λ is the eigenvalue and I is the identity matrix.
det(A - λI) = 0
| -5-λ -2 -3 |
| 8 41-λ 18 |
| 90 40 3-λ| = 0
Expanding the determinant and solving, we find the eigenvalues:
λ₁ ≈ 40.256
λ₂ ≈ 6.664
λ₃ ≈ -1.919
The eigenvalues are distinct real numbers.
2. Matrix B:
[ 3 3]
[-4 3]
[ 4 -2]
Again, solving the characteristic equation, we find the eigenvalues:
λ₁ = 3
λ₂ = 3
λ₃ = -2
The eigenvalues are repeated real numbers.
3. Matrix C:
[-9 -2]
[-4 3]
Solving the characteristic equation, we find the eigenvalues:
λ₁ ≈ -5.928
λ₂ ≈ -5.072
The eigenvalues are distinct real numbers.
4. Matrix D:
[-2 -9]
The only entry of this matrix corresponds to a single eigenvalue:
λ = -2
The eigenvalue is a distinct real number.
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In QRS, the measure of angle S=90°, the measure of angle Q=6°, and RS = 20 feet. Find the
length of SQ to the nearest tenth of a foot.
R
20
6°
s
Q
X
The length of SQ in triangle QRS is approximately 19.8 feet to the nearest tenth of a foot.
To find the length of SQ in triangle QRS, where angle S = 90°, angle Q = 6°, and RS = 20 feet, we can use the sine function. Here's a step-by-step explanation:
1. Identify the given information: In triangle QRS, we have angle S = 90°, angle Q = 6°, and side RS = 20 feet.
2. Since the sum of angles in a triangle is always 180°, we can find angle R: angle R = 180° - angle S - angle Q = 180° - 90° - 6° = 84°.
3. Now we can use the sine function to find the length of side SQ. Since we know angle R and side RS, we can use the sine of angle R to relate side SQ to side RS:
\(sin(angle R) = \frac{opposite side (SQ)}{ hypotenuse side (RS)}\)
\(sin(84°) =\frac{SQ}{20 feet}\)
4. Solve for SQ: \(SQ = (20 feet) sin(84°) = 19.8 feet.\).
So, the length of SQ in triangle QRS is approximately 19.8 feet to the nearest tenth of a foot.
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A ________ is calculated by adding up all the values in a dataset and dividing by the total number of values in the dataset.
a. median
b. mean
c. percentage
d. mode
The mean, also known as the average, is calculated by adding up all the values in a dataset and dividing by the total number of values in the dataset. The correct answer is b. mean.
The mean, also known as the average, is calculated by adding up all the values in a dataset and dividing by the total number of values in the dataset. It is the sum of all the values divided by the count of values in the dataset. The mean is a measure of central tendency and is commonly used to represent the "typical" or "average" value in a dataset.
Therefore, the mean is calculated by adding up all the values in a dataset and dividing by the total number of values in the dataset.
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Which function has an inverse that is also a function? • g(x)=2x-3 •k(x) = -9x² • f(x) = |x + 2| •w(x) = -20
The function has an inverse that is also a function is g(x)=2x-3
What is Inverse function?A function that can turn into another function is known as an inverse function or anti function. In other terms, the inverse of a function "f" will take y to x if any function "f" takes x to y. The inverse function is designated by f⁻¹ or F⁻¹ if the function is written by f or F. Here, (-1) should not be confused with an exponent or an inverse.
A function takes in values, applies specific procedures to them, and produces an output. The inverse function works, agrees with the outcome, and returns to the initial function.
The solution in which x and y have been reversed is known as an inverse function.
The vertical line test determines whether a function succeeds or fails when you solve for y once more.
1. Here g(x) = 2x - 3 has inverse x = 2y - 3 which simplifies to;
\(y=\frac{x-3}{2}\)
This is a line and is a function;
\(y=\frac{x}{2} +\frac{1}{2}\)
2. k(x) = -9x² has the inverse x = -9y² which simplifies to;
\(y=\sqrt{x/(-9)}\)
This is a function but only for certain values of x.
3. f(x) = |x+2| is an absolute value function.
Not all absolute value functions have function-based inverses.
4. A function's inverse does not exist for the equation w(x) = -20.
The function therefore has a negative that is also a function, which is
g(x)= 2x – 3.
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When Nellie Newton hangs at rest in the middle of a clothesline, tensions will be the same in each side of the rope when:
a. the lengths of each rope are the same
b. the angles for both sides of the rope are equal
c. she is in equilibrium
The tensions in each side of the rope will be the same when Nellie Newton hangs at rest in the middle of a clothesline and the lengths of each rope are the same.
When Nellie Newton is in equilibrium, meaning she is at rest and not experiencing any acceleration or movement, the forces acting on her must be balanced. In the case of a clothesline, the tension in each side of the rope contributes to the balancing of forces.
For the tensions to be the same in each side of the rope, the lengths of the ropes must also be the same. This ensures that the forces applied to each side are equal and balanced, resulting in Nellie Newton remaining in a stable position without any net force acting on her.
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plz help fast!!!!!!!!!!!!!!!!!!!!!
Answer:
D) 156/100 = n/70
Step-by-step explanation:
n = 156% of 70
% indicates a fraction over 100.
"of" indicates multiplication.
n = 156/100 • 70
Let's divide both sides by 70 to have one fraction one each side.
n/70 = 156/100
This is equal to D) \((\frac{156}{100}) = (\frac{n}{70})\)
The following questions apply to the matrices below: 1 -13 0 6 9 2-30 and B= 6 --5 10 1 (a) Find AB (b) Is it possible to find BA? Why or why not? (e) Find det [A], That is, find the determinant of matrix A. 4. (8 points) For the matrices below, find 3A +2B. 0 - 1 A=0 6 2 0 3 9 and BE - 2 -3 0 -5 --7 5 -1
(a) To find AB, perform matrix multiplication of matrices A and B.
(b) It is not possible to find BA because the number of columns in matrix A does not match the number of rows in matrix B.
(e) To find the determinant of matrix A, evaluate the determinant using the provided matrix.
4. To find 3A + 2B, perform scalar multiplication and matrix addition using matrices A and B.
(a)Matrix A:
A = |1 -13|
|0 6|
|9 2|
Matrix B:
B = |6 -5|
|10 1|
Performing matrix multiplication:
AB = |(1 * 6) + (-13 * 10) (1 * -5) + (-13 * 1)|
|(0 * 6) + (6 * 10) (0 * -5) + (6 * 1)|
|(9 * 6) + (2 * 10) (9 * -5) + (2 * -7)|
Simplifying the multiplication:
AB = |-124 -18|
| 60 -5|
| 76 -53|
Therefore, AB = |-124 -18|
| 60 -5|
| 76 -53|
(b)Matrix A has 2 columns and matrix B has 3 rows. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. Since the dimensions do not match (2 columns vs. 3 rows), we cannot find the product BA.
(e)Matrix A:
A = |0 -1|
|6 2|
|5 -1|
Using the formula for a 2x2 matrix determinant:
det(A) = (0 * 2) - (-1 * 6)
= 0 + 6
= 6
Therefore, the determinant of matrix A, det(A), is 6.
4.Matrix A:
A = |0 -1|
|6 2|
|5 -1|
Matrix B:
B = |0 -3|
|0 -7|
|5 -1|
Performing scalar multiplication and matrix addition:
3A = |3 * 0 3 * -1| = |0 -3|
|3 * 6 3 * 2| |18 6|
|3 * 5 3 * -1| |15 -3|
2B = |2 * 0 2 * -3| = |0 -6|
|2 * 0 2 * -7| |0 -14|
|2 * 5 2 * -1| |10 -2|
Adding 3A and 2B:
3A + 2B = |0 -3| + |0 -6| = |0 -9|
|18 6| |0 -14| |18 -8|
|15 -3| |10 -2| |25 -5|
Therefore, 3A + 2B = |0 -9|
|18 -8|
|25 -5|
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State which metric unit you would probably use to measure item.
Mass of a beach ball
The basic unit of mass of the ball in the metric system is the gram.
What is mass?The base units of length (distance), capacity (volume), and weight (mass) in the metric system are the meter, liter, and gram, respectively. We utilize units that are derived from metric units to measure smaller or greater quantities.
Mass is a physical body's total amount of matter. Inertia, or the body's resistance to acceleration when a net force is applied, is also measured by this term. The strength of an object's gravitational pull to other bodies is also influenced by its mass.
Therefore, the basic unit of mass of the ball in the metric system is the gram.
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2x-3y+z=0
3x+2y=35
4y-2z=14
Which of the following is a solution to the given system?
A. (2, 3, 5)
B. (3, 2, 0)
C. (1, 16, 0)
D. (7, 7, 7)
Based on the evaluations, only Option D: (7, 7, 7) satisfies all three equations and is a solution to the given system.
To determine which of the given options is a solution to the system of equations, we can substitute the values into the equations and check if they satisfy all three equations simultaneously. Let's evaluate the options one by one:
Option A: (2, 3, 5)
Checking the equations:
2(2) - 3(3) + 5 = 4 - 9 + 5 = 0 (satisfies the first equation)
3(2) + 2(3) = 6 + 6 = 12 (does not satisfy the second equation)
4(3) - 2(5) = 12 - 10 = 2 (does not satisfy the third equation)
Option B: (3, 2, 0)
Checking the equations:
2(3) - 3(2) + 0 = 6 - 6 + 0 = 0 (satisfies the first equation)
3(3) + 2(2) = 9 + 4 = 13 (does not satisfy the second equation)
4(2) - 2(0) = 8 - 0 = 8 (does not satisfy the third equation)
Option C: (1, 16, 0)
Checking the equations:
2(1) - 3(16) + 0 = 2 - 48 + 0 = -46 (does not satisfy the first equation)
3(1) + 2(16) = 3 + 32 = 35 (satisfies the second equation)
4(16) - 2(0) = 64 - 0 = 64 (does not satisfy the third equation)
Option D: (7, 7, 7)
Checking the equations:
2(7) - 3(7) + 7 = 14 - 21 + 7 = 0 (satisfies the first equation)
3(7) + 2(7) = 21 + 14 = 35 (satisfies the second equation)
4(7) - 2(7) = 28 - 14 = 14 (satisfies the third equation)
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equation of a circle with center at the origin and radius 10
The equation of a circle with the center at the origin and radius 10 can be determined by using the standard form of the equation of a circle, which is given by the equation x² + y² = r², where (x, y) are the coordinates of any point on the circle, and r is the radius of the circle. If the center of the circle is at the origin,
then the coordinates of the center are (0, 0), and the equation can be written as x² + y² = 10². This equation represents a circle with center at the origin and radius 10. This equation can be used to graph the circle by plotting the points that satisfy the equation.
The circle will be a perfect circle with a radius of 10 units and centered at the origin. It will pass through the points (-10, 0), (0, -10), (10, 0), and (0, 10). These points can be found by solving the equation for x and y. When x = -10, 0, and 10, y will be equal to 0, and when y = -10, 0, and 10, x will be equal to 0. This is how the circle can be graphed using the equation.
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Suppose 45% of all students at aiden's school brought a can of food to contribute to a canned food drive. aiden picks a representative sample of 25 students and determines the samples percentage he expects the percentage for this sample will be 45% do you agree? explain your reasoning
A z-score of 0 means that the sample proportion is equal to the population proportion. Therefore, after using sampling distribution we can conclude that we agree with Aiden's expectation that the percentage for this sample will be 45%.
Based on the given information, we can assume that the population proportion of students who brought a can of food to contribute to the canned food drive is 0.45. Aiden picks a representative sample of 25 students, and he expects the percentage for this sample will be 45%.
We can use the sampling distribution formula to calculate the expected sample proportion:
SE = sqrt[p(1-p) / n]
where p is the population proportion, n is the sample size, and SE is the standard error.
Plugging in the values, we get:
SE = sqrt[0.45(1-0.45) / 25] = 0.0984
Next, we can use the normal distribution to find the z-score corresponding to a sample proportion of 0.45:
z = (0.45 - 0.45) / 0.0984 = 0
A z-score of 0 means that the sample proportion is equal to the population proportion. Therefore, we can conclude that we agree with Aiden's expectation that the percentage for this sample will be 45%.
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Simplify the expression.
-10-6+)
12
12
12
Need help ASAP
i dont understand this test question
Answer:
Step-by-step explanation:
An example of a hypothesis is: a person is innocent until proven guilty.
a. True
b. False
The example of a hypothesis is: a person is innocent until proven guilty. The statement is true
Here the given situation is
A person is innocent until proven guilty.
The hypothesis test is defined as the test in statistics whereby an analyst tests an assumption regarding a population parameter. In hypothesis test using the data from the different types of t sample and the determine the other parameters of the population
The null hypothesis is defined as the a statement of what the statistician expects NOT to find.
Here the given situation is a person is innocent until proven guilty. Therefore, it is a null hypothesis.
In hypothesis test we assume that null hypothesis until it is proven
Therefore, the given statement true
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let x be a random variable with a uniform distribution on the interval (1, a) where a>1. if e(x) = 6*var(x), then what is the value of a?
For x being a random variable with a uniform distribution on the interval (1, a) where a>1 the value of a is 11.
In statistics, variance is a measure of how spread out a set of data is. It is calculated by taking the average of the squared differences of each value from the mean of the data set.
The expected value (e(x)) of a random variable x is defined as the mean of the values of x.
The variance (var(x)) of a random variable x is defined as the average of the squared differences from the expected value. Therefore, we can find the value of a by setting up the following equation:
6*var(x) = e(x) = (1+a)/2
Therefore, a = 11.
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What is 3gh 2 x 4g 3h 3
Answer:
(3•22g4h5)
Step-by-step explanation:
Step 1: ((3gh2 • 4) • g3) • h3
Step 2: ((3•22gh2) • g3) • h3
Step 3: 3.1 h2 multiplied by h3 = h(2 + 3) = h5
Final answer: (3•22g4h5)
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Answer:
Cost of 9 shirts is wrong
Step-by-step explanation:
shirt to cost = 1 to $15
9 x 15 is not 120, it is 135
Answer:
No, the cost of the 9 shirts is incorrect.
Step-by-step explanation:
each side of the rhombus is 5cm and the height is 3cm. which is the area of the rhombus
Answer:
15
Step-by-step explanation:
using the formula a= based x height the answer would be 15
Answer:
15 cm
Step-by-step explanation:
you multiply 3*5
the height of a house is 52 ft. a tree beside the house is 7 ft more than twice as tall. what is the height of the tree? enter your answer in the box. ft
Answer: 111 ft tall. Thats a big tree!
Step-by-step explanation: if its seven more than two times the height of the house, do 52 X 52 + 7 which equals 111 ft.
Can someone pls help me
Solve for x
Please show ur work
Answer:
9=x
Step-by-step explanation:
80º=(8x+8)º
80=8x+8
Subtract 8 from both sides of the equation.
72=8x
Divide 8 from both sides of the equation.
9=x
Hope this helps :)
Makayla leans a 26-foot ladder against a wall so that it forms an angle of 69 with the ground. What’s the horizontal distance between the base of the ladder and the wall?
The horizontal distance between the base of the ladder and the wall is approximately 8.892 feet.
Here, we have,
To find the horizontal distance between the base of the ladder and the wall, we can use trigonometric functions.
In this case, the ladder forms an angle of 69 degrees with the ground. We can label this angle as θ.
We know the length of the ladder is 26 feet. We can label the horizontal distance as x.
Using trigonometric functions, specifically cosine, we have:
cos(θ) = adjacent/hypotenuse
cos(69) = x/26
To find x, we can rearrange the equation:
x = 26 * cos(69)
Using a calculator, we can calculate:
x ≈ 26 * 0.3420
x ≈ 8.892
Therefore, the horizontal distance between the base of the ladder and the wall is approximately 8.892 feet.
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given the line y=-2x - 1 and the point (4,4) find the equation of the line perpendicular to the given line
Answer:
y= (1/2)x + 2
Step-by-step explanation:
yeah-ya.......... right?
Driving on the highway, you can safely drive 70 miles per hour. “How far can you drive in ‘h’ hours?” What is the domain of the function which defines this situation?
Answer:
70 +60muinte= 13
Step-by-step explanation:
so that the ans
In h hours you will go 70h far from the original position and domain of the function is the amount of hours you drive option (C) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The complete question is:
Driving on the highway, you can safely drive 70 miles per hour. “How far can you drive in ‘h’ hours?” What is the domain of the function which defines this situation?
A.)The amount of gas you use.
B.) 70.
C.) The amount of hours you drive.
D.)The distance you drive
We have:
Driving on the highway, you can safely drive 70 miles per hour.
The speed of the vehicle = 70 miles per hour
As we know,
Distance = speed×time
1 hour → 70 miles
h hour → D miles
D(t) = 70h
The above expression represents the situation.
Thus, in h hours you will go 70h far from the original position and domain of the function is the amount of hours you drive option (C) is correct.
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A recipe uses 3 eggs for every 8 cups of flour. What is the ratio of eggs to flour in the recipe
Answer:
3:8
Step-by-step explanation: :)
Answer:
3 eggs : 8 cups of flour
=3:8
Which of the following statements concerning happiness is false? A. One's happiness depends on one's current circumstances or expectations. B. Individuals are often accurate in predicting what would make them happy. C. Research indicates that happiness is related to one's age. D. Happiness has been found to be related to one's level of optimism.
Individuals are often accurate in predicting what would make them happy.
The correct option is B.
What is happiness?Happiness is a feeling of contentment, that life is just as it should be. Perfect happiness, enlightenment, comes when you have all of your needs satisfied. While the perfect happiness of enlightenment may be hard to achieve, and even harder to maintain, happiness is not an either /or case.
The statements that are considered truly related to happiness are as follows;
The happiness of one person should be based on the present situation.Happiness should be related to the age of the person.Also, it is the optimal level.Hence, Individuals are often accurate in predicting what would make them happy.
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Answer:
B. Individuals are often accurate in predicting what would make them happy.
Explanation:
Edge 2022
Yusef drove 130 miles in 2.5 hours. Which equation can be used to calculate r, the average speed at which Yusef drove?
A.
r=130−2.5
B.
130=r2.5
C.
r=1302.5
D.
130=r+2.5
PLEASE HELP! ITS FOR A TEST!!
Answer:
B
Step-by-step explanation:
It's B my guy
Answer:
B.)
Step-by-step explanation:
r= 130/2.5
130=r2.5
it would be 52 because you have to divide.... so you would divide 130 by 2.5 and then you would get 52. hope this helps.
DRIVERS ED(TRUE OR FALSE) When passing another vehicle you must be able to complete the pass by returning to the right side before coming within a distance of at least 100 feet of any oncoming vehicles.
True
False
Answer:
It
Step-by-step explanation:
Is true because if you didn’t, who know what would happen
A grocer noticed that customers buy both pet and baby supplies with a probability of 0.12. Considered separately, the probability that
customer buys pet supplies is P(A) = 0.64, and the probability that a customer buys baby supplies is P(B) = 0.25.
Move expressions and numbers into the blanks to create an equation that represents the probability that a customer buys either pet
supplies or baby supplies.
Answer:
0.77
Step-by-step explanation:
Given that:
P(A) = 0.64
P(B) = 0.25
P(AnB) = 0.12
Probability that customer buys either pet or baby supplies ; P(AuB)
P(AuB) = P(A) + p(B) - p(Ann)
P(AuB) = 0.64 + 0.25 - 0.12
P(AuB) = 0.77
Write a while loop that prints a. All squares less than n. For example, if n is 100, print 0 1 4 9 16 25 36 49 64 81.
Answer:
n = input()
a = 0
while pow(a, 2) < n:
print(pow(a, 2))
a += 1
Step-by-step explanation: