Answer:
8
Step-by-step explanation:
I just put it in the calculator thint
By inspection, determine if each of the sets is linearly dependent.
(a) S = {(1, 3), (3, 2), (-2, 6)}
O linearly independent
O linearly dependent
(b) S = {(1, -5, 4), (4, -20, 16)}
O linearly independent
O linearly dependent
(c) S = {(0, 0), (1, 0)}
O linearly independent
O linearly dependent
(a) S = {(1, 3), (3, 2), (-2, 6)} O linearly independent set, (b) S = {(1, -5, 4), (4, -20, 16)} O linearly dependent and (c) S = {(0, 0), (1, 0)} O linearly dependent.
(a) S = {(1, 3), (3, 2), (-2, 6)}
O linearly independent set
S is linearly independent because no vector in S can be expressed as a linear combination of the others, without considering the coefficients all equal to zero.
(b) S = {(1, -5, 4), (4, -20, 16)}
O linearly dependent
We can see that 4 × (1, −5, 4) = (4, −20, 16).
Thus, S is linearly dependent because there are non-zero scalars a,b that satisfies a(1, −5, 4) + b(4, −20, 16) = 0.
(c) S = {(0, 0), (1, 0)}
O linearly dependent
vector (0, 0) is a linear combination of (1, 0) because 0(1, 0) = (0, 0).
Thus, S is linearly dependent because there are non-zero scalars a,b that satisfies a(0, 0) + b(1, 0) = 0.
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in a certain lottery, you must correctly select 5 numbers (in any order) out of 29 to win. you purchase one lottery ticket. what is the probability that you will win?
To calculate the probability of winning a certain lottery where you must select 5 numbers out of 29 in any order, we can use the concept of combinations. The probability of winning can be determined by dividing the number of successful outcomes (winning combinations) by the total number of possible outcomes.
In this lottery, you need to select 5 numbers out of 29, and the order of selection doesn't matter. The total number of possible outcomes is given by the combination formula, which is denoted as C(29, 5) and calculated as
29! / (5! * (29-5)!).
To win, you have only one successful outcome, which is the combination of the 5 winning numbers. Therefore, the probability of winning can be calculated as 1 / C(29, 5). Evaluating this expression will give you the probability of winning the lottery with a single-ticket purchase.
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The information for this question was obtained from the study linked here.) When a person consumes a drug, the drug is absorbed into the bloodstream over a period of time. In this question, we investigate the peak concentration of a drug in the blood stream. Caffeine is a drug that is absorbed and eliminated according to first-order kinetics. Suppose that a person's rate of caffeine absorption is 8 and that the person's rate of elimination is 7. Then after a dose D of caffeine, the concentration c of caffeine in the person's blood as of time t is given by
c(t)=(D/(1-(7/8))((e^-7t)-(e^-8))
Find the exact time at which the maximum concentration occurs.
t= ___
The exact time at which the maximum concentration occurs is given by: [tex]t = (ln(7/8) + 8) / 7[/tex]
To find the exact time at which the maximum concentration occurs, we need to determine the value of t that maximizes the concentration function c(t).
Given the concentration function:
[tex]c(t) = (D / (1 - (7/8))) * ((e^{-7t}) - (e^{-8}))[/tex]
To find the maximum concentration, we can differentiate c(t) with respect to t and set the derivative equal to zero, then solve for t.
Differentiating c(t) with respect to t:
[tex]c'(t) = (D / (1 - (7/8))) * ((-7e^{-7t}) - (-8e^{-8}))\\ = (D / (1 - (7/8))) * (-7e^{-7t} + 8e^{-8})[/tex]
Setting c'(t) equal to zero:
[tex](D / (1 - (7/8))) * (-7e^{-7t} + 8e^{-8}) = 0[/tex]
Since D is a positive constant, we can ignore it in the equation. So we have:
[tex]-7e^{-7t} + 8e^{-8} = 0[/tex]
[tex]-7 + 8e^{-8+7t} = 0\\8e^{-8+7t} = 7\\e^{-8+7t} = 7/8\\-8 + 7t = ln(7/8)\\7t = ln(7/8) + 8\\t = (ln(7/8) + 8) / 7[/tex]
Therefore, the exact time at which the maximum concentration occurs is given by: t = (ln(7/8) + 8) / 7
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Given that CAT = DOG select all statements that are true,
Answer:
The answer to this problem Is A I think
Step-by-step explanation:
A triangle with a perimeter of 139 units is dilated by a scale factor of 1/4. Find the perimeter of the triangle after dilation. Round your answer to the nearest tenth, if necessary.
Answer:
173.8 units
Step-by-step explanation:
If it's asking for a
139 * 1/4= x
34.75= x
34.75 + 139= 173.75
round to get 173.8
EH is a diameter is D. The measure of EF is (10x + 8) and the measure of GH is (11x). What's the value of X
Answer:
x = 5°
EF = 58°
GH = 55°
Step-by-step explanation:
From The diagram :
Recall ; Angle on a straight line = 180°
This means :
EF + FG + GH = 180
EF = (10x + 8)°
GH = (11x)°
FG = 67°
HENCE;
10x + 8 + 11x + 67 = 180
21x + 75° = 180°
21x = 180 - 75
21x = 105
x = 105 / 21
x = 5
EF = 10x + 8 = 50 + 8 = 58°
GH = 11x = 11 * 5 = 55°
How to find volume of a cylinder by using the same dimensions of a cone but only knowing the volume of the cone
Answer:
Multiply the volume of the cone by 3
Step-by-step explanation:
Required
Volume of a cylinder from a cone of the same dimension
The volume of a cone is:
[tex]V_1 = \frac{1}{3}\pi r^2h[/tex]
The volume of a cylinder is:
[tex]V_2 = \pi r^2h[/tex]
Recall that:
[tex]V_1 = \frac{1}{3}\pi r^2h[/tex]
Split:
[tex]V_1 = \frac{1}{3}*[\pi r^2h][/tex]
Substitute: [tex]V_2 = \pi r^2h[/tex]
[tex]V_1 = \frac{1}{3}*V_2[/tex]
Make V2 the subject
[tex]V_2 =3V_1[/tex]
This implies that, we simply multiply the volume of the cone by 3
find the volume of the solid enclosed by the surface z = 1 −x2 −y2 and the xy-plane.
The integral becomes:
V = ∫₀¹ ∫₀²π (1 − r²) r dθ dr
To find the volume of the solid enclosed by the surface z = 1 − x² − y² and the xy-plane, we need to integrate the function f(x, y) = 1 − x² − y² over the region in the xy-plane where z is positive.
Since the surface z = 1 − x² − y² represents a downward-opening paraboloid, we can set up the integral as follows:
V = ∬R (1 − x² − y²) dA
Here, R represents the region in the xy-plane bounded by the curve x² + y² = 1. To evaluate this integral, we can switch to polar coordinates. In polar coordinates, the region R corresponds to the interval 0 ≤ θ ≤ 2π and 0 ≤ r ≤ 1. The differential area element dA in polar coordinates is r dr dθ.
Evaluating this double integral will give us the volume of the solid enclosed by the surface and the xy-plane.
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Hilary walked 18 yards from her house to the library. Then she walked 288 feet to the post office. What is the total distance in yards Hilary walked? Use the conversion chart below to solve.
Answer:
37 yards
Step-by-step explanation:
Given data
Distance from house to the library= 18 yards
Distance from the library to the post office= 288 feet
Total distance in yards, first let us have all units to yards
288ft to yard= 96 yards
Hence the total distance in yards is
=18+19
=37 yards
(a) Find the determinant of the given matrix M. Show all your work. 2 2 -1 9 M= 4 2 8 8 1 17 24 0 10-13 1 determinant of the matrix -2B³A-CTB-¹AT.
(b) Let A, B, C be 3 x 3 matrices with det A= -2
In part (a) of the problem, the task is to find the determinant of the given matrix M by showing all the steps of the calculation. In part (b), we are given three matrices A, B, and C with det A = -2.
(a) To find the determinant of matrix M, we can use various methods such as cofactor expansion or row operations. Let's use cofactor expansion along the first row:
det M = 2 * (-1)^(1+1) * det [[2 8 0] [17 24 0] [10 -13 1]]
- 2 * (-1)^(1+2) * det [[4 8 0] [1 24 0] [10 -13 1]]
Simplifying and evaluating the determinants of the 2x2 matrices, we get:
det M = 2 * (2 * 24 - 17 * (-13))
- 2 * (4 * 24 - 1 * (-13))
After performing the calculations, we find the determinant of matrix M.
(b) The given information states that det A = -2. However, no specific task or question is mentioned regarding matrices A, B, and C. Further instructions or requirements are needed to provide a specific answer or analysis based on the given information.
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Help please I’m trying to go to sleep
Answer: y > -4 (red)
Step-by-step explanation:
State a decomposition theorem for finite generated modules over the PID a Z(p) = {{ = : a : a,b € Z and płb}.
Decomposition theorem for finite generated modules over the PID $\mathbb{Z}(p) = \{a = (a, b) \in \mathbb{Z} \times \mathbb{Z} | p | ab\}.$
The decomposition theorem states that any finite generated module over a principal ideal domain can be written as a direct sum of finitely many cyclic submodules. Additionally, these cyclic submodules are uniquely determined up to isomorphism, which means that the module has a unique decomposition up to isomorphism. In the case of $\mathbb{Z}(p)$, we can write it as a direct sum of cyclic submodules generated by elements of the form $p^k$ for $k \in \mathbb{Z}$. This decomposition is unique up to isomorphism. The primary decomposition theorem enables us to represent a vector space as a direct sum of invariant subspaces by using the smallest polynomial of a matrix. It is essential to comprehending and interpreting the data the minimal polynomial provides.
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Which expression is equivalent to 2x + 2
A (2 + x) + 2
B 2(x + 2)
C 2(x + 1)
D 4x
Find the volume of this cylinder.
Round to the nearest tenth.
8ft
-5ft
[?] ft3
Answer:
628 ft
Step-by-step explanation:
The volume of cylinder is, V= 628 ft³.
What is Volume?The amount of space occupied by a three-dimensional figure as measured in cubic units.
Given:
radius,r= 5 ft, height, h = 8 ft
Volume= πr²h
V= 3.14 * 5 *5 * 8
V= 628 ft³
Hence, the volume of cylinder is 628 ft³.
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Using the greatest common factor (GCF), what is the factored form of: 24v-36
Answer:
12(2v - 3)
Step-by-step explanation:
GCF of 24 and 36 is 12
24v - 36
12(2v - 3)
Tell whether the angle measures can be those of a triangle.
20°, 160°, 20°
Yes, can be those of a triangle.
No, cannot be those of a triangle.
No.
The 3 angles of a triangle need to equal 180 degrees.
The sum of the 3 given angles is greater than 180 ( 160 + 20 + 20 = 200) so it cannot form a triangle.
I NEED HELP!! with this homework please. For B,C,and D, if you know the answer please tell me I’m kinda confused.
I’ll make you a brainlist for the reward:)
Answer:
Step-by-step explanation:
Location Reflect over x Reflect over y
B -0.75 ,1 -0.75 ,-1 +0.75 ,1
C 1.75 ,-1 1.75,1 -1.75,+1
D -2,-2 -2,+2 +2 ,-2
write an expression describing all the angles that are coterminal with 358°. (please use the variable in your answer. give your answer in degrees, but do not include a degree symbol in your answer.)
Answer: 358 + 360n where n is an integer
Reason:
Coterminal angles point in the same direction.
We add on multiples of 360 to rotate a full circle, and we get back to the same direction that 358 degrees points in (almost directly to the east). The variable n is an integer {..., -3, -2, -1, 0, 1, 2, 3, ...}
If n is negative, then we subtract off multiples of 360.
Find a harmonic conjugate v(x, y) of u(x, y) = 2x(1 - y)
The harmonic conjugate of u(x, y) = 2x(1 - y) is v(x, y) = 2y - y² - x² + C, where C is an arbitrary constant.
How to find the harmoic conjugate?Here we want to find the harmonic conjugate of:
u(x, y) = 2x*(1 - y)
To do so, we need to use the Cauchy-Riemann equations state that for a function f(z) = u(x, y) + iv(x, y) to be analytic (holomorphic), the partial derivatives of u and v must satisfy the following conditions:
∂u/∂x = ∂v/∂y
∂u/∂y = -∂v/∂x
Let's find the harmonic conjugate by solving these equations:
Given u(x, y) = 2x(1 - y)
∂u/∂x = 2(1 - y)
∂u/∂y = -2x
Setting these derivatives equal to the respective partial derivatives of v:
∂v/∂y = 2(1 - y)
∂v/∂x = -2x
Now, integrate the first equation with respect to y, treating x as a constant:
v(x, y) = 2y - y² + f(x)
Differentiate the obtained equation with respect to x:
∂v/∂x = f'(x)
Comparing this derivative with the second equation, we have:
f'(x) = -2x
Integrating f'(x) with respect to x:
f(x) = -x² + C
where C is a constant of integration.
Now, substitute f(x) into the equation for v(x, y):
v(x, y) = 2y - y² - x² + C
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bro please i need the correct answer i will give u a brainliest to please i really need help
Answer:
A
Step-by-step explanation:
Because I am smart and u best mark me brainlist
Rating the contingency table to the right to (a) calculate the nal frequencies, and (b) find the expected frequency for call in the contingency table. Assume that the variables ndependent Size of restaurant Seats 100 or fewer Seats over 100 Excent 182 185 200 316 + alculate the marginal frequencies and samples stre of restaurant Seats 100 or fewer Seats over 100 Total Excellent 182 186 368 Rating Fair 200 316 516 Poor 161 155 356 Total 513 557 1200 And the expected frequency for each of in the contingency table Rating Excellent Poor e of restaurant Beats 100 or fewer Beats over 100 Round to two decimal places as needed Ip me solve this View an example Get more help Clear all Check on & MacBook Air.
(a) To calculate the final frequencies in the contingency table, we need to sum up the frequencies for each combination of variables. The final frequencies are as follows:
Size of restaurant: Seats 100 or fewer
- Excellent: 182
- Fair: 200
- Poor: 161
Size of restaurant: Seats over 100
- Excellent: 186
- Fair: 316
- Poor: 155
(b) To find the expected frequency for each cell in the contingency table, we can use the formula:
Expected Frequency = (row total * column total) / grand total
The expected frequencies for each cell in the contingency table are as follows:
Size of restaurant: Seats 100 or fewer
- Excellent: (513 * 368) / 1200 ≈ 157.60
- Fair: (513 * 516) / 1200 ≈ 220.95
- Poor: (513 * 356) / 1200 ≈ 151.77
Size of restaurant: Seats over 100
- Excellent: (557 * 368) / 1200 ≈ 171.53
- Fair: (557 * 516) / 1200 ≈ 237.85
- Poor: (557 * 356) / 1200 ≈ 164.62
(a) The final frequencies in the contingency table are obtained by summing up the frequencies for each combination of the variables "Size of restaurant" and "Rating." This gives us the observed frequencies for each category.
(b) The expected frequency for each cell is calculated using the formula mentioned above. It considers the row total, column total, and grand total of the contingency table.
The expected frequencies represent the frequencies we would expect to see in each cell if the variables were independent of each other. These values are used to assess the association between the two variables.
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6v=-9 v= what does v =
Answer:
v = -3/2
Step-by-step explanation:
6v = -9
v = -9/6
v = -3/2
Consider the subtraction problem, 2013 - 40, for which Allie gets the answer 1073. What is most likely Allie's misunderstanding, and, if uncorrected, what would Allie's answer be for 304 - 9?
The correct answer is 295.
If Allie's misunderstanding is not corrected, she might incorrectly subtract 9 from 304 and get an incorrect answer.
We have,
Based on the given information, Allie's misunderstanding is likely related to the concept of regrouping or borrowing when performing subtraction.
Allie may not have correctly subtracted the tens digit from the hundreds digit, resulting in an incorrect answer.
If Allie's misunderstanding is not corrected, her answer for 304 - 9 would also be incorrect.
Let's calculate it correctly:
When subtracting 9 from 304, we start with the one digit: 4 - 9.
However, since 4 is smaller than 9, we need to borrow from the tens digit. Therefore, we regroup 1 ten as 10 ones, making the tens digit 3 - 1 = 2, and the one's digit becomes 14 - 9 = 5.
Thus,
The correct answer is 295.
If Allie's misunderstanding is not corrected, she might incorrectly subtract 9 from 304 and get an incorrect answer.
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(PLEASE PLEASE HELP)
Find the area of the triangle.
Answer:
40.2 in²
Step-by-step explanation:
h*b/2
h= 6.7
b= 12
HELPPPPPP!!!!!!!!!!!!!!!!
Answer: [tex]w\geq 20[/tex]
Step-by-step explanation:
Solve this like it's an equation
6w+30>150 (i know it is larger than or equal to)
6w>120
w>120/6
w>20
Answer:
The answer is 20
Step-by-step explanation:
6w+30≥150
6w≥150-30
6w≥120
divide both sides by 6
6w/6≥120/6
w≥20
we can say
w=20 since w is greater than or equal to
pls help 42−6×4(12)3=
Answer:
-822
Step-by-step explanation:
i just typed it in the calculator
but if you're doing it by hand, 1st multiply 4*12*3*6 and then subtract 42 from it
word form? 132 = 132
Answer:
one hundred thirty-two
Step-by-step explanation:
should be it if it is can i get brainliest?
3. The ratio of the side lengths of a pentagon is 1:3:4:6:9, and the perimeter is 115 yds. What is the measure of the 3rd longest side?
Answer:
20 yards
Step-by-step explanation:
By the given ratio, the side measurements are 1x, 3x, 4x, 6x, and 9x
We are given the perimeter of this shape is 115. Therefore, 1x+3x+4x+6x+9x=115.
We can solve that for x, so we can find each side measurements' numerical value.
(1+3+4+6+9)x=115
(23)x=115
x=115/23
x=5
So the side measurements are:
1x=1(5)=5
3x=3(5)=15
4x=4(5)=20
6x=6(5)=30
9x=9(5)=45
The third longest sife is 20 yards.
Please help and explain!
Find the total surface area shown down below
Ignore the colors!
If f(x) = 2x³ + Ax² +8x-3 and f(2)= 1, what is the value of A?
the value of A in the function f(x) = 2x³ + Ax² + 8x - 3 is -7.
To find the value of A in the function f(x) = 2x³ + Ax² + 8x - 3, we are given that f(2) = 1. Substituting x = 2 into the function, we have:
f(2) = 2(2)³ + A(2)² + 8(2) - 3
Simplifying further:
1 = 2(8) + 4A + 16 - 3
1 = 16 + 4A + 13
Combining like terms:
1 = 29 + 4A
To isolate A, we subtract 29 from both sides:
-28 = 4A
Finally, we divide both sides by 4 to solve for A:
A = -7
Therefore, the value of A in the function f(x) = 2x³ + Ax² + 8x - 3 is -7.
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