if a and b are matrix functions such that the matrices a(0) and b(0) are the same, then a and b are the same matrix function
Answers
If a and b are matrix functions such that the matrices a(0) and b(0) are the same, then a and b are the same matrix function is "false" statement.
What is matrix function?A matrix function can be defined in a variety of ways (or matrix-valued function). One manner is in which the function takes the shape of a matrix, rather than numbers, the matrix contains functions. A(t), for example, is a 2 x 2 matrix function.
Some key features regarding the matrix function are-
The function is designated only for t values that specify all 4 of the elements in the this example matrix.A matrix function can also be defined as a function which calculates a (generally square) matrix A; in other words, it is a process of mapping one matrix to another. Some researchers defined matrix functions just on complex plane ℂ. Higham (2008), for example, emphasizes the definition as involving a scalar function f and a matrix A ∈ ℂ∧(n x n).To know more about complex plane, here
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The complete question is-
If a and b are matrix functions such that the matrices a(0) and b(0) are the same, then a and b are the same matrix function. (True/False)
Related Questions
Jacob bought a deluxe computer system for his home business. The system cost
$2,395. The value of the computer system will depreciate at a rate of 12% a year.
What will be the cash value of the computer system in 3 years? Round your answer to
the nearest dollar.
O $287
O $2108
O $1632
O $2682
Answers
The cash value of the computer system in 3 years will be $1632. The correct option is the third option $1632
DepreciationFrom the question, we are to determine the cash value of the computer system in 3 years
From the given information,
The computer system cost $2,395 and it will depreciate at a rate of 12% a year
After the first year, the worth of the computer system will be
$2,395 - (12% of $2,395)
$2,395 - (0.12 × $2,395)
= $2,395 - $287.4
= $2107.6
After the second year, the worth of the computer system will be
$2107.6 - (12% of $2107.6)
$2107.6 - (0.12 × $2107.6)
= $2107.6 - $252.912
= $1854.688
After the third year, the worth of the computer system will be
$1854.688 - (12% of $1854.688)
$1854.688 - (0.12 × $1854.688)
= $1854.688 - $222.56256
= $1632.12544
≅ $1632
Hence, the cash value of the computer system in 3 years will be $1632. The correct option is the third option $1632
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Find the area of the irregular shape !!!
Answers
Step-by-step explanation:
Area of triangle = base × height ×½
triangle = 9×8×½=36cm²
rectangle = length×width
rectangle = 15×26=390cm²
area of irregular fig= 390+36 =426cm²
Explain why two variables must both be quantitative in order to find the correlation between them
Answers
If the variables are not quantitative we cannot do the arithmetic required in the formulas for r.
What is a variable?A variable in mathematics is a symbol and placeholder for a changing quantity or any mathematical object.A variable can specifically represent a number, a vector, a matrix, a function, a function's argument, a set, or an element of a set.Quantitative order:
Quantitative methods emphasize objective measurements and statistical, mathematical, or numerical analysis of data gathered through polls, questionnaires, and surveys, as well as by manipulating pre-existing statistical data using computational techniques. Ordinal-level measurement data can be quantitative or qualitative. They can be arranged in ranked order, but differences between entries are meaningless. Measurement data at the interval level are quantitative. They can be arranged in any order, and meaningful differences between data entries can be calculated. We can't do the arithmetic required in the r formulas if the variables aren't quantitative.Therefore, if the variables are not quantitative we cannot do the arithmetic required in the formulas for r.
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Help ASAP with c....
Answers
Answer:
(7,0)
Step-by-step explanation:
using the results of part (a) find an orthonormal should be parallel to v0 and {w0,w1} should span the same subspace as {v0,v1}.
Answers
Given that v0 = (2, 1, -2), v1 = (-2, 1, 1), and v2 = (1, 2, 2), we can find the orthonormal basis that should be parallel to v0, and w0 and w1 should span the same subspace as v0 and v1.To find the orthonormal basis that should be parallel to v0.
we need to follow these steps:
Let v0 be a vector in Rn with nonzero norm ||v0||, and let V be the subspace of Rn that is perpendicular to v0 (so if y is in V, then y·v0 = 0).
Then, we can construct an orthonormal basis {v1, . . . , vp} for V, and {v0/v0, v1, . . . , vp} will be an orthonormal basis for Rn.
To find {v1, . . . , vp}, we apply Gram-Schmidt to the basis {v0, v1, . . . , vp}.
Specifically, we compute vi' = vi - projv0vi for i = 1, . . . , p.
This ensures that {v1, . . . , vp} are all in V and that {v0/v0, v1, . . . , vp} is an orthonormal basis for Rn that is parallel to v0.
So, in this case, we can take v0 = (2, 1, -2), which has norm ||v0|| = sqrt(2^2 + 1^2 + (-2)^2) = sqrt(9) = 3.
Now, we need to find w0 and w1 that span the same subspace as v0 and v1. Since {v0, v1} is a basis for this subspace, any two linearly independent vectors in this subspace will span the same subspace. So, we can just pick any two such vectors. Let w0 = (2, 1, -2) and w1 = (-2, 5, 1).
We claim that {w0, w1} is linearly independent and spans the same subspace as {v0, v1}.To show that {w0, w1} is linearly independent, suppose that aw0 + bw1 = 0 for some scalars a and b. Then, we have(2a - 2b, a + 5b, -2a + b) = (0, 0, 0).This gives us two equations:2a - 2b = 0a + 5b = 0
Solving for a and b, we geta = 5/7 and b = -2/7.
Since a and b are not both zero, this shows that {w0, w1} is linearly independent.
To show that {w0, w1} spans the same subspace as {v0, v1}, we need to show that every vector in this subspace can be written as a linear combination of w0 and w1. Let (x, y, z) be any vector in this subspace.
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1. find the general solution of the system of differential equations hint: the characteristic polynomial of the coefficient matrix is λ 2 − 14λ 65.
Answers
The general solution of the system of differential equations is given by:
[x1(t); x2(t)] = c1 [2t; t] e^(5t) + c2 [t; t] e^(9t)
where c1 and c2 are constants.
Let's first find the eigenvalues of the coefficient matrix. The characteristic polynomial is given as:
λ^2 - 14λ + 65 = 0
We can factor this as:
(λ - 5)(λ - 9) = 0
So, the eigenvalues are λ = 5 and λ = 9.
Now, let's find the eigenvectors corresponding to each eigenvalue:
For λ = 5:
(A - 5I)x = 0
where A is the coefficient matrix and I is the identity matrix.
Substituting the values, we get:
[3-5 1; 1 -5] [x1; x2] = [0; 0]
Simplifying, we get:
-2x1 + x2 = 0
x1 - 4x2 = 0
Taking x2 = t, we get:
x1 = 2t
So, the eigenvector corresponding to λ = 5 is:
[2t; t]
For λ = 9:
(A - 9I)x = 0
Substituting the values, we get:
[-1 1; 1 -3] [x1; x2] = [0; 0]
Simplifying, we get:
-x1 + x2 = 0
x1 - 3x2 = 0
Taking x2 = t, we get:
x1 = t
So, the eigenvector corresponding to λ = 9 is:
[t; t]
Therefore, the general solution of the system of differential equations is given by:
[x1(t); x2(t)] = c1 [2t; t] e^(5t) + c2 [t; t] e^(9t)
where c1 and c2 are constants.
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PLS HELP I WILL MARK YOU BRAINLIEST!!! ANSWER QUICKLY!!!! :,(
compare. use <, =, or > 11 ____-7
a. >
b. =
c. <
THANK YOU!!! <3
Answers
Answer:a. >
Step-by-step explanation:
What is the HCF of 40 and 60 ?
[1 marks]
50
40
15
20
Answers
Answer:
20
Step-by-step explanation:
Write the equation g(x) in vertex form of a
quadratic function for the transformations given
the function f(x) = x2.
Let g(x) be the function whose graph is a
translation 4 units left and 1 unit up of the
graph of f(x).
Answers
The equation g(x) in vertex form of a quadratic function for the transformations whose graph is a translation 4 units left and 1 unit up of the graph of f(x) is (x-4)² + 1
Given a quadratic function for the transformations given the function f(x) = x²
If the function g(x) of the graph is translated 4 units to the left, the equation becomes (x-4)² (note that we subtracted 4 from the x value
Translating the graph 1 unit up will give the final function g(x) as (x-4)² + 1 (We added 1 since it is an upward translation.)Hence the equation g(x) in vertex form of a quadratic function for the transformations whose graph is a translation 4 units left and 1 unit up of the graph of f(x) is (x-4)² + 1
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Write the following numbers in scientific notation: a. 20405000 b. 0.0202020 c. 0.3450 d. .000011111 e. 101010 f. 0.090650 2. Write the answers to the correct significant figures: a. 10.0592+5.601+4.210 b. (19.341−7.23)×6.9111/4.321= c. 2.34965×8.231= d. 51.41/5.42= e. (7.59+9.20)/(6.23×1.110) 3. Convert 425 K to
∘
F 4. Convert 30
∘
C to
∘
F 5. Conver 97
∘
F to K 6. 10 grams of Al occupy 4ml. What is the density 7. 30 grams of one item in 1.1 quarts. What is the density in g/ml 8. Convert 10Km to miles by using all the steps
Answers
a. 2.0405 x 10^7
b. 2.0202 x 10^-2
c. 3.450 x 10^-1
d. 1.1111 x 10^-5
e. 1.0101 x 10^2
f. 9.0650 x 10^-2
a. To convert 20405000 to scientific notation, we move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. This gives us 2.0405, and since we moved the decimal point 7 places to the left, we multiply by 10^7. Therefore, 20405000 can be expressed as 2.0405 x 10^7.
b. To convert 0.0202020 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 2.0202, and since we moved the decimal point 2 places to the right, we multiply by 10^-2. Therefore, 0.0202020 can be expressed as 2.0202 x 10^-2.
c. To convert 0.3450 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 3.450, and since we moved the decimal point 1 place to the right, we multiply by 10^-1. Therefore, 0.3450 can be expressed as 3.450 x 10^-1.
d. To convert 0.000011111 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 1.1111, and since we moved the decimal point 5 places to the right, we multiply by 10^-5. Therefore, 0.000011111 can be expressed as 1.1111 x 10^-5.
e. To convert 101010 to scientific notation, we move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. This gives us 1.01010, and since we moved the decimal point 2 places to the left, we multiply by 10^2. Therefore, 101010 can be expressed as 1.0101 x 10^2.
f. To convert 0.090650 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 9.0650, and since we moved the decimal point 1 place to the right, we multiply by 10^-1. Therefore, 0.090650 can be expressed as 9.0650 x 10^-2.
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a bank in alice springs (australia), also known as alice, wants to send a lot of financial data to the bank of baltimore, also known as bob. they want to use aes, but they do not share a common key. all of their communications will be on public airwaves. describe how alice and bob can accomplish this using rsa.
Answers
To securely send data using AES, Alice and Bob can utilize RSA for key exchange. RSA is a public-key cryptosystem, which means that each party has a public and private key.
To initiate the key exchange, Bob generates a public and private key and sends his public key to Alice. Alice then encrypts the AES key with Bob's public key and sends it back to Bob. Since only Bob has the private key, only he can decrypt the message and obtain the AES key.
Alice and Bob can now use the AES key to encrypt and decrypt their financial data. This ensures that even if someone intercepts their communication on public airwaves, the data remains secure since the AES key is only known to Alice and Bob.It is important to note that RSA is used only for the key exchange, not for encrypting the data itself.The data is encrypted using AES, which is much faster and more efficient than RSA for large amounts of data.
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someone please explain how to make a fraction into a decimal im confused will give brainliest to best answer also worth 25 points
Answers
Answer:
divide the numerator by the denominator and it should give you a decimal
Answer:if u don't get it tell me.
Step-by-step explanation:
is it possible to obtain a negative value of ss (sum of squares), variance, and standard deviation? why?
Answers
No, it is not possible to obtain a negative value for the ss, variance, or standard deviation. They represent the amount of spread in data, and the values are always positive or zero.
Sum of squares (SS) measures the deviation of each data point from the mean of the set, squared. The formula for SS is:
SS = Σ (X - μ)^2
Variance is the average of the sum of squares, and it is calculated by dividing the SS by the degrees of freedom (n-1), where n is the number of data points in the set:
Variance = SS / (n - 1)
Standard deviation is the square root of variance and it is a measure of how far each data point is from the mean of the set:
Standard deviation = √Variance
Since both variance and standard deviation are based on the sum of squares, which is always non-negative, variance and standard deviation are also always non-negative.
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If f(x)=7x+3 ,what is f^-1(x)?
Answers
Answer:
\(\displaystyle{f^{-1}(x)=\dfrac{x}{7}-\dfrac{3}{7}}\)
Step-by-step explanation:
Swap f(x) and x position of the function, thus:
\(\displaystyle{x=7f(x)+3}\)
Then solve for f(x), subtract 3 both sides and then divide both by 7:
\(\displaystyle{x-3=7f(x)}\\\\\displaystyle{\dfrac{x}{7}-\dfrac{3}{7}=f(x)}\)
Since the function has been inverted, therefore:
\(\displaystyle{f^{-1}(x)=\dfrac{x}{7}-\dfrac{3}{7}}\)
And we can prove the answer by substituting x = 1 in f(x) which results in:
\(\displaystyle{f(1)=7(1)+3 = 10}\)
The output is 10, now invert the process by substituting x = 10 in \(f^{-1}(x)\):
\(\displaystyle{f^{-1}(10)=\dfrac{10}{7}-\dfrac{3}{7}}\\\\\displaystyle{f^{-1}(10)=\dfrac{7}{7}=1}\)
The input is 1. Hence, the solution is true.
The volume of a prism is the product of its height and area of its base, V = Bh. A rectangular prism has a volume of 16y4 + 16y3 + 48y2 cubic units. Which could be the base area and height of the prism?
a base area of 4y square units and height of 4y2 + 4y + 12 units
a base area of 8y2 square units and height of y2 + 2y + 4 units
a base area of 12y square units and height of 4y2 + 4y + 36 units
a base area of 16y2 square units and height of y2 + y + 3 units
Answers
Answer:
We have a prism with a volume of 16y⁴ + 16y³ + 48y² cubic units.
Its volume is equal to the area of its base times its height.
Of course, for those to be the base area and height of this prism, they would have to multiply to 16y⁴ + 16y³ + 48y² cubic units.
Let's test each of these answers to see which gives us the correct volume.
--------------------------------------------------------------------------------------------------
a base area of 4y square units and height of 4y² + 4y + 12 units
We find the volume by multiplying the base area by the height...
4y(4y² + 4y + 12)
Distribute the 4y to each term inside the parentheses.
16y³ + 16y² + 48y
This is not the right volume, so these can not be dimensions of our prism.
--------------------------------------------------------------------------------------------------
a base area of 8y² square units and height of y² + 2y + 4 units
We find the volume by multiplying the base area by the height...
8y²(y² + 2y + 4)
Distribute the 8y² to each term inside the parentheses.
8y⁴ + 16y³ + 32y²
This is not the right volume, so these can not be dimensions of our prism.
--------------------------------------------------------------------------------------------------
a base area of 12y square units and height of 4y² + 4y + 36 units
We find the volume by multiplying the base area by the height...
12y(4y² + 4y + 36)
Distribute the 12y to each term inside the parentheses.
48y³ + 48y² + 432y
This is not the right volume, so these can not be dimensions of our prism.
--------------------------------------------------------------------------------------------------
a base area of 16y² square units and height of y² + y + 3 units
We find the volume by multiplying the base area by the height...
16y²(y² + y + 3)
Distribute the 16y² to each term inside the parentheses.
16y⁴ + 16y³ + 48y²
The volume fits, so these could be the base area and height of our prism.
--------------------------------------------------------------------------------------------------
D. a base area of 16y² square units and height of y² + y + 3 units
--------------------------------------------------------------------------------------------------
Step-by-step explanation:
What is the equation of the line that is parallel to the
given line and passes through the point (-3, 2)?
3x - 4y = -17
3x - 4y = -20
4x + 3y = -2
4x + 3y =-6
Answers
Step-by-step explanation:
Let, the given point of the equation of the line are (3,-1) and (0,3) i.e
(x1,y1)=(3,-1) and (x2,y2) = (0,3)
Now,
The slope of the line (m1) = y2-y1 ÷ x2-x1
= 3-(-1) ÷ 0-3
= 3+1 ÷ -3
= 4/-3
since, the lines are parallel i.e.
m1 = m2
or, m2 = -4/3
Again,
The required equation of the line passing through the point (-3,2)=(x1,y2) is
y-y1 = m2(x-x1)
or, y-2 = -4/3 ( x +3)
or, 3(y-2) = -4(x+3)
or, 3y-6 = -4x - 12
or, 4x+3y = -12+6
Therefore, 4x+3y = -6 is the right answer.
NEED HELP ASAP PLEASE WILL GIVE BRAINLIEST
Review the diagram.
On a coordinate plane, a rectangle sits on the x-axis. A horizontal vector is 30 degrees from a vector labeled 40 pounds, and is 45 degrees from a vector labeled 35 pounds.
Two students are pulling an object with ropes. One student pulls with a force of 40 pounds at an angle of 30° above the ground, and the other student pulls with a force of 35 pounds at an angle 45° above the ground. What is the direction of the resultant force?
approximately 37.33° above the ground
approximately 42.27° above the ground
approximately 47.73° above the ground
approximately 53.13° above the ground
Answers
Answer: A. approximately 37.33° above the ground
Step-by-step explanation:
edge2020
The correct solution to the problem is that the direction of the resultant force will be approximately 37.33° from the horizontal above the ground.
What is Vector and how do we do component of a Vector ?In a coordinate plane there are two axis one is x axis and the second one is y axis.If a vector is lying in the coordinate plane then no matter what is its direction, we can always divide it in two components which are x component and y component for easier calculations.If the magnitude of the vector is R, then the magnitude of the X component along x axis will be R cos θ and the magnitude of the Y component along y axis will be R sin θ.We can find the final resultant magnitude and direction of the vector from the components by adding the the components.How to solve this question ?For 30° Vector of 40 pounds :-
If we divide it in components it will become
40 cos 30° Î + 40 sin 30° Ĵ
40 × ( √3 / 2 ) Î + 40 × ( 1 / 2 ) Ĵ
34.64 Î + 20 Ĵ ( approximately )
For 45° Vector of 35 pounds :-
If we divide it in components it will become
35 cos 45° Î + 35 sin 45° Ĵ
35 × ( 1 / √2 ) Î + 35 × ( 1 / √2 ) Ĵ
24.75 Î + 24.75 Ĵ ( approximately )
Now adding both vectors
( 24.75 + 34.64 ) Î + ( 24.75 + 20 ) Ĵ ( approximately )
59.39 Î + 44.74 Ĵ ( approximately )
Now Using formula of Tan θ to find the value of θ
( Tan θ = Perpendicular / Base )
Tan θ = 44.74 / 59.39
Tan θ = 0.75 ( approximately )
θ = Tan⁻¹ (0.75) ( approximately )
θ = 36.87° ( approximately )
We are calculated the value of θ as 36.87° which is approximate value as we used a lot of approximations while calculating and, the closest option given is 37.33° which is again an approximate value.
So we can say that the correct answer to this problem is The direction of the resultant force will be approximately 37.33° from the horizontal above the ground.
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What is the following sum?
Answers
Answer:
i think its c
Step-by-step explanation:
Which system is represented in the graph?
y < x2 – 2x + 4
y < x2 + 4
y ≥ x2 – 2x + 4
y < –x2 + 4
y ≥ x2 – 2x + 4
y ≤ –x2 + 4
y > x2 – 2x + 4
y ≤ x2 + 4
Answers
The system that is represented by the graph is inequality 3
What is system of inequalities?
A group of two or more inequalities in one or more variables is referred to as a system of inequalities. When a problem requires a variety of solutions and those solutions must satisfy multiple constraints, systems of inequalities are used.
We are given the graph of inequalities and given 4 choices out which 1 is the correction representation of the inequalities given in the graph
Now As you can see one the parabolas open downwards that means the term x^2 is negative in that case where as the other parabola opens upwards hence the term x^2 is positive.
So second and third options are the options which satisfies this criteria
if we put x = 0 in the second equation of both the inequalities we get y= 4
This criteria is satisfied by only inequality 3 hence the correct system of inequality is inequality 3
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Answer:y ≥ x2 – 2x + 4
y < –x2 + 4
Step-by-step explanation:
What is the meaning of a relative frequency of 0. 56
Answers
A relative frequency of 0.56 means that out of the total number of observations in a given sample or population, 56% of those observations belong to a particular category or have a certain characteristic.
In other words, it is the proportion or fraction of the observations that fall into that particular category or have that characteristic, relative to the total number of observations. For example, if we had a sample of 100 people and 56 of them had brown hair, then the relative frequency of brown hair would be 0.56 or 56%.
To calculate relative frequency, you divide the frequency of a specific event or category by the total number of observations. In this case, the specific event or category occurs 56% as often as the total events or categories observed.
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3. The length of one leg of a 45-45-90 triangle is 7 m. What is the length of the other leg and the length of the hypotenuse?
The other leg is 7 m, and the hypotenuse is 7 m.
O The other leg is 7 m, and the hypotenuse is 14 m.
O The other leg is 7√2 m, and the hypotenuse is 7 m.
The other leg is 7 m, and the hypotenuse is 7√2 m.
Answers
the length of the other leg is 7m and the length of the hypotenuse is 7√2 m.
Pythagoras Theorem StatementIn the right-angled triangle, the square of the hypotenuse side is equals to the sum of the squares of the other two sides, according to Pythagoras's Theorem. This triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Because to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
The definition yields the following as the Pythagoras Theorem formula:
Hypotenuse² = Perpendicular² + Base²
c² = a² + b²
Length of one leg=7m
Angles of triangle are 45°,45° and 90°
According to Pythagoras theorem,
x²=7²+7²
x=7√2
the length of the other leg is 7m and the length of the hypotenuse is 7√2 m.
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michelle, a basketball player, has made 14 of her 20 free throws this season. if she never misses again, how many free throws would she need to shoot to have a shooting percentage of 90 percent?
Answers
Michelle would need to shoot an additional 40 free throws to have a shooting percentage of 90%.
Let's denote the number of additional free throws that Michelle needs to make as "x." Since she has made 14 out of her 20 free throws this season, her current shooting percentage is:
Current shooting percentage = (Number of made free throws / Total number of attempted free throws) * 100
= (14 / 20) * 100
= 70%
To find the number of additional free throws she needs to shoot to achieve a shooting percentage of 90%, we set up the following equation:
(14 + x) / (20 + x) = 90/100
We can now solve this equation to find the value of x:
(14 + x) / (20 + x) = 0.9
Cross-multiplying gives:
0.9 * (20 + x) = 14 + x
18 + 0.9x = 14 + x
0.9x - x = 14 - 18
-0.1x = -4
Dividing both sides by -0.1 gives:
x = 40
Therefore, Michelle would need to shoot an additional 40 free throws to have a shooting percentage of 90%.
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30 + 10 ⋅ 5 – 45 ÷ 5
Answers
Answer:
71
Step-by-step explanation:
30+10×5-45÷5= 30+50-9=71
centers of adjacent faces of a unit cube are connected to form a regular octahedron. what is the volume of this octahedron?
Answers
The volume of octahedron when centers of adjacent faces of a unit cube are connected to form a regular octahedron is 1/16 unit ³.
Let the side length of a cube is 1unit.
Therefore length of all edges of the regular octahedron =2√2 unit .
Now the base of the pyramids is a square are will be (2√2)² =12 unit.
Now clearly the height of the pyramid is half the height of the cube, i.e.,1/2.
So volume of the Pyramid will be ⇒ 1/3× (Base area) × (height) = 1/3×1/2×1/2 = 1/12.
Therefore, the volume of the octahedron= 2 × volume of Pyramid= 2 ×1/12=1/6 unit³.
Hence, the volume of octahedron when centers of adjacent faces of a unit cube are connected to form a regular octahedron is 1/16 unit ³.
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2. The speed limit on a city street is 35 kilometers per hour. Write and graph an inequality to
describe a car’s possible speed.
Answers
Answer:
\(x\leq 35\) where \(x\) denotes speed of the car
Step-by-step explanation:
Given: The speed limit on a city street is 35 kilometers per hour.
To write and graph: an inequality to describe a car’s possible speed.
Solution:
Let the speed of a car be \(x\) kilometers per hour.
As the speed limit on a city street is 35 kilometers per hour,
\(x\leq 35\)
First draw the graph of \(x=35\) (see figure a.)
Plot the points \((35,0),(35,5),(35,10),(34,15)\)
Take a point on the left side of line x = 35 say \((x,y)=(0,0)\) and put it in \(x\leq 35\)
\(0\leq 35\) which is true.
So, shade the graph on the left side of line x = 35
See the graph b.
the pink part represents the inequality \(x\leq 35\)
For flights from a particular airport in January, there is a 30 percent chance of a flight being delayed because of ley weather. If a flight is delayed because of icy weather, there is a 10 percent change the flight will also be delayed because of a mechanical problem. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem. If one flight is selected at random from the airport in January, what is the probability that the flight selected will have at least one of the two types of delays? a. 0. 65.
b. 0. 335.
c. 0. 350.
d. 0. 450
Answers
The probability that a randomly selected flight from the airport in January will have at least one type of delay is 0.335.
To calculate the probability of a flight having at least one type of delay, we need to consider the probabilities of delays due to icy weather and mechanical problems separately and then combine them. The probability of a delay due to icy weather is 0.3.
If there is a delay due to icy weather, the probability of an additional delay due to a mechanical problem is 0.1. On the other hand, if there is no delay due to icy weather, the probability of a delay due to a mechanical problem is 0.05. To calculate the combined probability, we subtract the probability of no delays from 1.
The probability of no delays is given by (1 - 0.3) * (1 - 0.05) = 0.7 * 0.95 = 0.665. Therefore, the probability of at least one type of delay is 1 - 0.665 = 0.335. Thus, option b, 0.335, is the correct answer.
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what is the answer to 16(5-4v)=-5-v
Answers
Write the slope-intercept form of the equation
of the line through the given point with the
given slope.
17) through: (-5, -3), slope
5
A) y = x - 2
B) y=1/5x - 2
C) y = -x - 2
D) y=-3x - 2
Answers
Answer:
y=5x+22
Step-by-step explanation:
y-y1=m(x-x1)
y-(-3)=5(x-(-5))
y+3=5(x+5)
y=5x+25-3
y=5x+22
PLSSSS HELP IF YOU TRULY KNOW THISSS
Answers
Hello :))))
When converting 0.550 into a simplified fraction, you will get 11/20
Explanation:
0.550 times 1000/ 1 times 1000 = 550/1000
550/1000 = 11/20
Hope this helps! :)
Answer: 11/20
Answer:
\(\Huge \boxed{\boxed{\frac{11}{20}}}\)
Step-by-step explanation:
To turn 0.550 into a fraction, we need to write it in the form of \(\frac{p}{q}\) where \(p\) and \(q\) are both positive integers. Here are the steps to do that:
Step 1: Take your decimal number and set it as the numerator of a fraction with denominator of 1.
So, we have:
\(\large \boxed {\frac{0.550}{1}}\)
Step 2: Multiply both the numerator and denominator by 1000 to get rid of the decimal point.
This gives us:
\(\large \boxed {\frac{550}{1000}}\)
Step 3: Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF).
In this case, the GCF of 550 and 1000 is 50. So, we can simplify the fraction by dividing both the numerator and denominator by 50. This gives us:
\(\large \boxed {\frac{11}{20}}\)
Therefore, 0.550 as a fraction is \(\bold {\frac{11}{20}}\).
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Find the exact value of the area between the graphs of y = cos x and y = e x for 0 ≤ x ≤ 1.
Both graphs start at y = 1 when x = 0, and then the exponential graph goes above the
cosine graph. Therefore, the area we are looking for is defined by the integral of (upper
function) - (lower function):
Answers
The exact value of the area between the graphs y = cos x and y = eˣ is 0.877.
What is Integration?Integration is the process reverse to differentiation. It is a method of adding the parts to get the whole.
The exponential graph goes above the cosine graph. Therefore, the area we are looking for is the difference of the area formed by the exponential graph and the area formed by the cosine graph.
Let A be the required area.
Let A₁ be the area of the graph formed by the cosine function. Then this area is the integral of the cosine function from the limit 0 to 1.
A₁ = \(\int\limits^1_0 {cos x} \, dx\)
= [sin x]¹₀
Giving the values of the limits, we get
A₁ = sin 1 - sin 0
Now, the value of sin 0 equals 0.
A₁ = sin 1
Let A₂ be the area formed by the graph of exponential function.
A₂ = \(\int\limits^1_0 {e^x} \, dx\)
= [eˣ]¹₀
= e¹ - e⁰
= e - 1 ( Since any value raise to 0 equals 1, e⁰ = 1.
Now, A = A₂ - A₁
= e - 1 - sin 1
Value of e equals 2.718 and value of sin 1 equals 0.841
A = 2.718 - 1 - 0.841 = 0.877
Hence the exact value of the area between the graphs y = cos x and y = eˣ is 0.877.
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