Decide whether or not the matrices are inverses of each other.
10 1
-1 0
and
0 1
-1 10
AB ≠ I and BA ≠ I, the two matrices are not inverses of each other.
To check if two matrices are inverses of each other, we can multiply them and see if we get the identity matrix.
Let A be the first matrix and B be the second matrix. Then, the product of A and B is:
AB = 10(0) + 1(-1) 10(1) + 1(10)
(-1)(0) + 0(1) (-1)(1) + 0(10)
= -1 11
0 -1
Similarly, the product of B and A is:
BA = 0(10) + 1(-1) 0(1) + 1(10)
(-1)(0) + 10(1) (-1)(1) + 10(0)
= -1 -1
0 10
Since AB ≠ I and BA ≠ I, the two matrices are not inverses of each other.
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attached is a histogram of the ages of actors and actresses who won the oscar for best actor and actress from 1928 through 2007. describe the shape of this distribution.
From the information provided in this question, it is not possible to accurately determine the proportion of winning actresses who were between 30 and 40 years old when they won the Oscar or the shape of the distribution.
The histogram only provides the frequencies (proportions) of actresses at different age ranges (e.g. 0.39, 0.40, 0.41, 0.45), but it does not provide information about the actual ages or the number of actresses.
In order to determine the proportion of winning actresses within a specific age range, additional information such as the number of actresses in each age group or a plot of the actual ages would be necessary. Similarly, the shape of the distribution cannot be determined accurately based on the information provided, as the histogram only provides the frequencies.
Therefore, the information provided is not sufficient to answer the questions asked.
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A pie has a diameter of 9 inches. What is the circumference of the pie
Answer:
pretty sure it is 56.55
Step-by-step explanation:
a play starts at 7:30pm, first act last 46 minutes, interval lasts 20 minutes. second act lasts 53 minutes, what time does the second act end?
Answer:
9:thirty one
Step-by-step explanation:
Add 46 twenty and 5three then add the answer in 7:thirty
HELP !!!! HELP ASAPPPP
Determine if the relation is a function and explain your reasoning.
Day of the week Whether I went for a walk
Monday
No walk
Tuesday
Walked
Wednesday
No walk
Thursday
Walked
Friday
No walk
Saturday
Walked
Sunday
Walked
O The relation is a function because all of the input values have different output values.
O The relation is not a function because the output value Walking has different input values, and the same with No walk.
O The relation is not a function because some of the input values have different output values.
O The relation is not a function because there are 7 different input values.
Is the relation a function and explain your reasoning: B. The relation is not a function because the output value Walking has different input values, and the same with No walk.
How to determine whether or not the relation represent a function?In Mathematics, a function is generally used for uniquely mapping an independent value (domain or input variable) to a dependent value (range or output variable).
This ultimately implies that, an input value (domain) represents the value on the x-coordinate of a cartesian coordinate while a dependent value (range) represents the output value on the y-coordinate of a cartesian coordinate.
Based on the table, we can logically deduce that the relation does not represent a function because each of its input value (domain) has more than one dependent value (range) i.e Walked and No Walk.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
A spherical balloon is inflated so that its volume is increasing at the rate of 3.9 ft^3/min. How rapidly is the diameter of the balloon increasing when the diameter is 1.7 feet?
The diameter of the balloon is increasing at a rate of approximately 0.47 ft/min when its diameter is 1.7 feet.
To find the rate at which the diameter is increasing, we can use the relationship between the volume and the radius of a sphere. The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius (half of the diameter).
We are given that the volume is increasing at a rate of 3.9 ft^3/min. Taking the derivative of the volume equation with respect to time, we have dV/dt = 4πr^2(dr/dt), where dV/dt is the rate of change of volume with respect to time and dr/dt is the rate of change of the radius with respect to time.
Since we are interested in finding the rate of change of the diameter, which is twice the rate of change of the radius, we can rewrite the equation as dV/dt = (4/3)π(2r)(2dr/dt) = (8/3)πr(dr/dt).
Plugging in the given values, we have 3.9 = (8/3)π(0.85)(dr/dt), where the diameter is 1.7 feet and the radius is half of that (0.85 feet). Solving for dr/dt, we find that dr/dt ≈ 0.47 ft/min. Therefore, the diameter of the balloon is increasing at a rate of approximately 0.47 ft/min when the diameter is 1.7 feet.
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100 points! Answer 40 and 42.
Answer:
1) 3 sides
2) 5 sides
3) 10 sides
4) 15 sides
Step-by-step explanation:
360 / 120 = 3
360 / 72 = 5
360 / 36 = 10
360 / 24 = 15
Answer:
Answer:
1) 3 sides
2) 5 sides
3) 10 sides
4) 15 sides
Step-by-step explanation:
360 / 120 = 3
360 / 72 = 5
360 / 36 = 10
360 / 24 = 15
Step-by-step explanation:
If the density of blood is 1.060 g/ml, what is the mass of 6.56 pints of blood? [1 l = 2.113 pints]
The mass of 6.56 pints of blood is 3.92 grams.
Given
The density of blood = 1.060 g/mL and mass of 6.56 pints
We have 1L = 2.113 pints
The density of a substance can be defined as the ratio of the mass of the substance to the volume of the substance. In chemistry, density is used to measure the concentration of the substance in the solution.
The expression for density = mass/volume
ρ = m/V
m = ρV
Mass = 1.060(1000ml/1L) × 6.56(1L/ 2.113)
= 3290.8 /1000
= 3.29g
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for the function y=-1+6 cos(2 pi/7(x-5)) what is the maximum value
the maximum value of the function is y = -1 + 6cos(2π/7(26.75-5)) = 5.
The function y = -1 + 6cos(2π/7(x-5)) is a periodic function with a period of 7. The maximum value of the function occurs when the cosine function reaches its maximum value of 1.
So, we need to find the value of x that makes the argument of the cosine function equal to an odd multiple of π/2, which is when the cosine function is equal to 1.
2π/7(x-5) = (2n + 1)π/2, where n is an integer
Simplifying this equation, we get:
x - 5 = (7/4)(2n + 1)
x = 5 + (7/4)(2n + 1)
Since the function has a period of 7, we can restrict our attention to the interval [5, 12].
For n = 0, we get x = 5 + 7/4 = 23/4
For n = 1, we get x = 5 + (7/4)(3) = 26.75
For n = 2, we get x = 5 + (7/4)(5) = 33.25
For n = -1, we get x = 5 + (7/4)(-1) = 1.75
For n = -2, we get x = 5 + (7/4)(-3) = -4.75
Out of these values of x, the only one that lies in the interval [5, 12] is x = 26.75.
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h(x) = -x - 1, find h(-2)
Answer:
I think the answer is 1
Step-by-step explanation:
-(-2)-1
=1
Solve for n in the scientific formula PV = nRT.n =
We have to solve for n the following equation (Ideal Gas Law):
\(\begin{gathered} PV=nRT \\ \frac{PV}{RT}=\frac{nRT}{RT} \\ \frac{PV}{RT}=n \end{gathered}\)Answer: n = PV / RT
Select all the true statements.if vertical angles are congruent, then two lines cut by a transversal are parallel. if two parallel lines are cut by a transversal, then corresponding angles are congruent. if two parallel lines are cut by a transversal, then alternate interior angles are congruent. points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints. points on a perpendicular bisector of a line segment are never equidistant from the segment’s endpoints.
By the property of alternate interior angles, Option (1) is the correct statement.
∠XWY ≅ ∠ZYW
Property of the alternate angles states, if two parallel lines are cut by a transversal, then the alternate angles are congruent.
By this property,
Lines XW and YZ are the parallel lines intersected by a transversal WY.
Here, ∠XWY and ∠ZYW represent the interior angles between the parallel lines and the transversal.
Therefore, interior alternate angles ∠XWY and ∠ZYW will be congruent.
Hence, Option (1) will be the correct option.
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A security car is parked 25 ft from a movie theater. Find at what speed the reflection of the security strobe lights is moving along the wall of the movie theater when the reflection is 30 ft from the car. The strobe lights are rotating with the speed 2 revolutions per second.
Answer:
v=20π ft/s
Step-by-step explanation:
Given:
Distance from the security car to the movie theater, D=25 ft
Distance of the reflection from the car, d=30 ft
Speed of rotation of the strobe lights, 2 rev/s
To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.
We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.
ω=2πf
=> ω=2π(2)
=> ω=4π rad/s
The distance between the security car and the reflection on the wall of the theater is...
r=30-25= 5 ft
The speed of reflection is given as (this is the linear velocity)...
v=ωr
Plug our know values into the equation.
v=ωr
=> v=(4π)(5)
∴ v=20π ft/s
Thus, the problem is solved.
The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.
To solve this problem, we can use the concept of related rates. Let's consider the following variables:
x: Distance between the security car and the movie theater wall
y: Distance between the reflection of the security strobe lights and the security car
θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights
We are given:
x = 25 ft (constant)
y = 30 ft (changing)
θ = 2 revolutions per second (constant)
We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.
Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:
x^2 + y^2 = z^2
Differentiating both sides of the equation with respect to time (t), we get:
2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)
Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.
Plugging in the known values, we have:
2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)
Simplifying the equation, we find:
60(dy/dt) = 120π
Dividing both sides by 60, we get:
dy/dt = 2π ft/s
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the composite method for determining the location of the center of gravity of a composite body requires . a) integration b) differentiation c) simple arithmetic d) all of the above
The composite method for determining the location of the center of gravity of a composite body requires integration.
So, the answer is A.
What is the center of gravity?The center of gravity is the point at which the entire weight of a body appears to act when the body is in equilibrium.
The concept of a center of gravity is used to calculate the behavior of a body when subjected to external forces. The composite method for determining the location of the center of gravity of a composite body involves integration.
The center of gravity is found by dividing the sum of the products of individual masses with their corresponding distance from an arbitrary reference line by the total mass of the system. When there is more than one weight distribution involved, the composite method is employed.
Hence, the answer of the question is A.
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Two figures have a similarity ratio of 5:8. If the volume of the smaller figure is 875 mm, what is the
volume of the larger figure in cubic millimeters? Solve and explain the process you used to solve the
problem
Answer:
Step-by-step explanation:
I don’t get this please show your work to see how I do it
Answer:
i havent learned this in a while it has been some years from i was in 6 grade so i might get it wrong.
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Okay, so basically its trying to say you need to do 1.94k x 340 and you get = 673.18
Step-by-step explanation:
hellppp meeeeee......
Angle 4 and 7= Interior angles
Angle 12 and 16= Corresponding angles
Angle 1 and 14= Alternate exterior angles
Angle 5 and 10=Alternate angles
angle 6 and 7 are alternate angles I think.
What is the equation of the graphed line written in standard form? 1. 2x + 3y = -6 2. 2x + 3y = 6 3. y= -2/3 x -24. y= 2/3 x -2
Step 1
Write the point form slope equation of a line
\(y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)Wherefrom the graph
\(\begin{gathered} y_2=0 \\ x_2=-3 \\ x_1=0 \\ y_1=-2 \end{gathered}\)Step 2
Substitute and get the equation
\(\begin{gathered} y\text{ -(-2)=}\frac{0-(-2)}{-3-0}(x-0) \\ y+2=\frac{2}{-3}x \\ y\text{ = -}\frac{2}{3}x-2 \end{gathered}\)Hence the right answer is option C
1 point) solve the system using elimination. ⎧⎩⎨⎪⎪−6x3x−4x−5y−6y−3y−3z−6z 2z===39314 {−6x−5y−3z=393x−6y−6z=3−4x−3y 2z=14 x=x= y=y= z=z=
Equation 6: x = (11y + 3z - 303) / 16
Equation 9: 811y + 387z = 2,745
What is Elimination?
The method of elimination is where you actually eliminate one of the variables by adding two equations. In this way, you remove one variable in order to solve for the other variable. In a system of two equations, since you have two variables, eliminating one greatly simplifies the process of solving for the other.
To solve the system of equations using elimination, we'll eliminate one variable at a time until we find the values of x, y, and z.
Multiply the second equation by 2 and the third equation by -3 to make the coefficients of z the same in both equations:
Equation 2: 2x - 12y - 12z = 6
Equation 3: 12x - 9y - 6z = -42
Add the first equation to the modified second equation and the modified third equation:
Equation 1 + Equation 2: -6x - 5y - 3z + 2x - 12y - 12z = 393 + 6
=> -4x - 17y - 15z = 399 (Call this Equation 4)
Equation 1 + Equation 3: -6x - 5y - 3z + 12x - 9y - 6z = 393 - 42
=> 6x - 14y - 9z = 351 (Call this Equation 5)
Multiply Equation 5 by 2 and subtract Equation 4 from it:
2 * Equation 5 - Equation 4: 12x - 28y - 18z - (-4x - 17y - 15z) = 702 - 399
=> 16x - 11y - 3z = 303 (Call this Equation 6)
Multiply Equation 4 by 16 and add it to Equation 6:
16 * Equation 4 + Equation 6: -64x - 272y - 240z + 16x - 11y - 3z = 16 * 399 + 303
=> -48x - 283y - 243z = 6,399 (Call this Equation 7)
Divide Equation 7 by -1 to simplify the coefficients:
Equation 7: 48x + 283y + 243z = -6,399
Now we have the following system of equations:
Equation 6: 16x - 11y - 3z = 303
Equation 7: 48x + 283y + 243z = -6,399
We can solve this system using further elimination or substitution. Let's solve it using substitution.
From Equation 6, solve for x:
16x = 11y + 3z - 303
x = (11y + 3z - 303) / 16
Substitute this value of x into Equation 7:
48[(11y + 3z - 303) / 16] + 283y + 243z = -6,399
Simplify the equation:
528y + 144z - 9,144 + 283y + 243z = -6,399
Combine like terms:
811y + 387z = 2,745 (Call this Equation 8)
Now we have the following system of equations:
Equation 6: x = (11y + 3z - 303) / 16
Equation 8: 811y + 387z = 2,745
We can solve this system by further substitution or using a numerical method. Let's solve it using substitution.
From Equation 6, solve for x:
x = (11y + 3z - 303) / 16
Substitute this value of x into Equation 8:
811y + 387z = 2,745
Simplify the equation:
811y + 387z = 2,745 (Call this Equation 9)
Now we have the following system of equations:
Equation 6: x = (11y + 3z - 303) / 16
Equation 9: 811y + 387z = 2,745
We can solve this system by further substitution or using a numerical method. Let's solve it using a numerical method such as Gaussian elimination or matrix inversion.
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I really need help 5th grade math please I beg !!!!!!!!!!!
Answer:
Mean is 87.5.
Mode is 90.
Step-by-step explanation:
Part A:
Mean means the average.
So let's start adding up
70+70+80+80+80+80+90+90+90+90+90+90+100+100+100+100=1400
There are 16 test scores.
So divide 1400 by 16 to get the average.
1400/16 = 87.5
The mean is 87.5.
Part B:
Mode means the number that repeats the most. That's 90. 90 is the mode.
If k is a positive integer, find the radius of convergence of the series: Sum from n=0 to infinity of [(n!)^(k)/(kn)!]*[x^(n)].
The radius of convergence of the series is k. This can be found using the ratio test and applying Stirling's approximation to estimate the factorials.
To find the radius of convergence of the series, we can use the ratio test.
The ratio test states that if the limit of the absolute value of the ratio of consecutive terms in a series is a finite number L, then the series converges if L < 1 and diverges if L > 1. If L = 1, the test is inconclusive and we need to try another test.
Let's apply the ratio test to the given series:
|[(n+1)!^k / (k(n+1))!] * x^(n+1)| / |[n!^k / (kn)!] * x^n)|
= [(n+1)!^k / (kn+k)!] * |x|
= (n+1)(n+1-k)(n+2)(n+2-k)...(n+k)/(k(k+1)...(n+k+1)) * |x|
As n approaches infinity, this expression approaches |x|/k. Therefore, the series converges if |x|/k < 1, or |x| < k, and diverges if |x|/k > 1, or |x| > k.
Thus, the radius of convergence is k.
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Which expressions are equivalent to the on below select all that apply 9x
Answer:
B and D
Step-by-step explanation:
Multiplying exponents just adds them.
Answer:
B + D
Step-by-step explanation:
Find the general solution of the given system. dx/dt = 4x+ 5y dy/dt = 10x + 9y
(x(t), y(t)) =
x(t) = \(c_1e^1^4^t+c_2e^-^t\) , y(t) = \(2c_1e^1^4^t-c_2e^-^t\) is the general solution of the sytem of differention eqution dx/dt = 4x+ 5y , dy/dt = 10x + 9y .
given dx/dt = 4x+ 5y and dy/dt = 10x + 9y
X'(t) = \(\left[\begin{array}{ccc}4&5\\10&9\end{array}\right]\) X
where X = \(\left[\begin{array}{ccc}x\\y\\\end{array}\right]\)
so A = \(\left[\begin{array}{ccc}4&5\\10&9\end{array}\right]\)
now we need to find eigen value of the matrix and the corresponding eigen vector.
| A- λI | = 0
so after equation the value to zero
λ = 14 and λ = -1
now for the λ = 14 corresponding eigen vector = \(\left[\begin{array}{ccc}1\\2\\\end{array}\right]\)
for λ = -1 corresponding eigen vector = \(\left[\begin{array}{ccc}1\\-1\\\end{array}\right]\)
So general equation is given by:
X(t) = \(c_1e^1^4^t\) \(\left[\begin{array}{ccc}1\\2\\\end{array}\right]\) + \(c_2e^-^t\) \(\left[\begin{array}{ccc}1\\-1\\\end{array}\right]\)
after solving this
x(t) = \(c_1e^1^4^t+c_2e^-^t\)
y(t) = \(2c_1e^1^4^t-c_2e^-^t\)
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The length is 2 units,the width is 5 units,and the height is 7 units
how do you find the value of √a⁴ ??
(ill give brainliest)
Answer:
\(a^{2}\)
Step-by-step explanation:
√a^4 is the same as:
√a × √a × √a × √a
group them as 2 pairs of
(√a × √a) × (√a × √a)
which makes
a × a
which is the same as \(a^{2}\)
Select the values of x that make the inequality true: choose three
Answer:
C,D,B
Step-by-step explanation:
You can earn money by shoveling your neighbors' driveways in the winter and get paid $10 per hour. What is a function that would define this situation?
Answer:
Total income= $100
Step-by-step explanation:
Giving the following information:
Hourly rate=$10
To calculate the total income, we need to use the following formula:
Total income= hourly income*number of hours
For example, for 10 hours shoveling in a week:
Total income= 10*10
Total income= $100
which expression is equal to 5/2? Write a situation that could represent the fraction above.
Answer:
3/2 + 2/2. A teacher has to give 2 pencils to one student. 1 student gives him 3 pencils, another student give him 2 pencils. How much pencils does the teacher have?
Step-by-step explanation:
All you do is you find a problem that would give you 5/2 then create a word problem.
Using the information below, compute the cycle efficiency:
Days' sales in accounts receivable 23 days
Days' sales in inventory 80 days
Days' payable outstanding43 days
The cycle efficiency, also known as the operating cycle or cash conversion cycle, is a measure of how efficiently a company manages its working capital.
In this case, with 23 days' sales in accounts receivable, 80 days' sales in inventory, and 43 days' payable outstanding, the cycle efficiency can be calculated.
The cycle efficiency measures the time it takes for a company to convert its resources into cash flow. It is calculated by adding the days' sales in inventory (DSI) and the days' sales in accounts receivable (DSAR), and then subtracting the days' payable outstanding (DPO).
In this case, the DSI is 80 days, which indicates that it takes 80 days for the company to sell its inventory. The DSAR is 23 days, which means it takes 23 days for the company to collect payment from its customers after a sale. The DPO is 43 days, indicating that the company takes 43 days to pay its suppliers.
To calculate the cycle efficiency, we add the DSI and DSAR and then subtract the DPO:
Cycle Efficiency = DSI + DSAR - DPO
= 80 + 23 - 43
= 60 days
Therefore, the cycle efficiency for the company is 60 days. This means that it takes the company 60 days, on average, to convert its resources (inventory and accounts receivable) into cash flow while managing its payable outstanding. A lower cycle efficiency indicates a more efficient management of working capital, as it implies a shorter cash conversion cycle.
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If the ratio of m to n is equal to 5 then which of the following is true?
If ratio of m to n is equal to 5 then, m = 5n
What are ratios?Ratios :- The quantitative relation between two amounts showing the number of times one value contains or is contained within the other are known as ratios.
m/n = 5
m = 5
Therefore, option b is correct i.e. m = 5.
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