Let P be the vector space of polynomials of degree at most.
(a) is a subspace of P.
(b) is not a subspace of P.
(c) is a subspace of P.
(d) is a subspace of P.
(a) {p(x) = P₂|p(2)=0}
This subset consists of polynomials in P₂ that evaluate to 0 at x = 2. To check if it is a subspace, we need to verify the three conditions:
The zero polynomial is in this subset since it evaluates to 0 at x = 2.
Let p₁(x) and p₂(x) be two polynomials in this subset. If p₁(2) = 0 and p₂(2) = 0, then (p₁ + p₂)(2) = p₁(2) + p₂(2) = 0 + 0 = 0. Hence, the subset is closed under vector addition.
Let p(x) be a polynomial in this subset, and c be a scalar. If p(2) = 0, then (cp)(2) = c(p(2)) = c(0) = 0. Hence, the subset is closed under scalar multiplication.
Therefore, (a) is a subspace of P.
(b) {p(z) € P₂ | x-p'(x) + p(x) = 0}
This subset consists of polynomials in P₂ that satisfy the equation x - p'(x) + p(x) = 0. To check if it is a subspace, we need to verify the three conditions:
The zero polynomial is not in this subset since it does not satisfy the equation x - p'(x) + p(x) = 0.
If p₁(x) and p₂(x) are two polynomials in this subset, (p₁ + p₂)(x) = p₁(x) + p₂(x) satisfies the equation x - (p₁ + p₂)'(x) + (p₁ + p₂)(x) = 0. However, we need to check if it satisfies the equation x - (p₁ + p₂)'(x) + (p₁ + p₂)(x) = 0 for all x, not just at certain points. This condition may not hold, so the subset is not closed under vector addition.
Let p(x) be a polynomial in this subset, and c be a scalar. If we consider cp(x), the equation x - (cp)'(x) + cp(x) = 0 may not hold for all x, depending on the value of c. Therefore, the subset is not closed under scalar multiplication.
Therefore, (b) is not a subspace of P.
(c) {p(z) E P₂|p(0) = p(1)}
This subset consists of polynomials in P₂ that satisfy the equation p(0) = p(1). To check if it is a subspace, we need to verify the three conditions:
The zero polynomial is in this subset since it satisfies the equation p(0) = p(1) (both sides are 0).
If p₁(x) and p₂(x) are two polynomials in this subset, (p₁ + p₂)(x) = p₁(x) + p₂(x) satisfies the equation (p₁ + p₂)(0) = p₁(0) + p₂(0) and (p₁ + p₂)(1) = p₁(1) + p₂(1). Since p₁(0) = p₁(1) and p₂(0) = p₂(1), it follows that (p₁ + p₂)(0) = (p₁ + p₂)(1). Hence, the subset is closed under vector addition.
Let p(x) be a polynomial in this subset, and c be a scalar. If we consider cp(x), the equation (cp)(0) = (cp)(1) holds since p(0) = p(1). Hence, the subset is closed under scalar multiplication.
Therefore, (c) is a subspace of P.
(d) {ar² + (a + 1)x + b | a, b ∈ R}
This subset consists of all polynomials of the form ar² + (a + 1)x + b, where a and b are real numbers. To check if it is a subspace, we need to verify the three conditions:
The zero polynomial is in this subset since it can be written as 0r² + (0 + 1)x + 0 = x.
If p₁(x) and p₂(x) are two polynomials in this subset, their sum p₁(x) + p₂(x) is of the form ar² + (a + 1)x + b, where a and b are real numbers. Hence, the subset is closed under vector addition.
Let p(x) be a polynomial in this subset, and c be a scalar. Then cp(x) is of the form car² + (ca + c)x + cb, where a, b, and c are real numbers. Hence, the subset is closed under scalar multiplication.
Therefore, (d) is a subspace of P.
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I need help on this plz
My restaurant budget should not go over $100. If I bought main dish for $50 and $12 for each pizza, how many pizza's can I buy?
inequality :
50 + 12x ≤ 100
How many pizza's can I buy?
Answer:
x = 25
Step-by-step explanation:
50 + 12x <_ 100
12x <_ 100 - 50
12x <_ 50
x <_ 50 / 12
x <_ 25
You can buy about 4 pizzas.
I didn't use the way that I probably should have but you can subtract 50 from 100 and then divide the 50 by 12 and you will get 4.1666667.
Find the area of this parallelogram.
A)
20 cm2
B)
24 cm²
40 cm²
Answer:
It's 40cm²
Step-by-step explanation:
Base times height.
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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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.
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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Help please I’m trying to go to sleep
Answer: y > -4 (red)
Step-by-step explanation:
The probability distribution of a game is shown in the table. Find the expected number of points won per play. Round to the nearest tenth if needed.
a) 5.7 b) 4.5 c) 4.7 d) 5
Answer:
4.5
Step-by-step explanation:
I just did this lesson and i just guessed, but i got it wrong and it said the answer was 4.5. basically, you multiply the fractions and the number value first,(like 1/6 X 0) and you do that to all of them. and then you add up all your answers, simplify them and put it in decimal form. and you get 4.5. hopefully that made enough sense.
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.
DELL 5+5
what's a girl Raymond
Solve: 3x - 18 = 6
Please answer and give the correct answer. Thank You! :)
Answer:
x = 8
Step-by-step explanation:
Hope this helps have a great day
Fitting a straight line to a set of data yields the following prediction line.
Y_i = 14 - 0.2X_i I
nterpret the meaning of the Y-intercept, b_0.
The Y-intercept (b_0 = 14) represents the predicted value of Y when X is zero.
In the given prediction line equation, Y_i = 14 - 0.2X_i, the Y-intercept is represented by the term '14', which is the coefficient of the constant term.
The Y-intercept, denoted as b_0, represents the predicted value of the dependent variable (Y) when the independent variable (X) is equal to zero. In this case, when X is zero, the equation becomes:
Y_i = 14 - 0.2(0) = 14
Therefore, the Y-intercept (b_0 = 14) represents the predicted value of Y when X is zero. It is the point where the prediction line intersects the Y-axis. In practical terms, it means that when the independent variable has no effect or has a value of zero, the predicted value of the dependent variable is 14.
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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
If you add Natalie's age and Fred's age, the result is 42. If you add Fred's age to 3 times
Natalie's age, the result is 70. Write and solve a system of equations to find how old Fred and
Natalie are.
Answer:
N+F=42 & F+3N=70 System Solved: Natalie is 14 and Fred is 28
Step-by-step explanation:
Using variables N=natalies age and F=Freds age
N+F=42 ----> N=42-F (take this and plug it into the other equation)
F+3N=70 so F+3(42-F)=70 [simplify] F+126-3F=70 [further simplify]
-2F=-56 [divide -56 by -2] F=28 [then plug this number into the orig. equation]
So N+28=42 or N=14.
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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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
Mrs. Hall records the height of 50 students in a spreadsheet the mean height is 60 inches after looking at the date again she realize that the two other observations were allies it must’ve been typos 82 and 86 inches she deleted these two observations what is the new mean rounded to the nearest hundredth
Answer:
67. 33 inches
Step-by-step explanation:
[50(68) - 82 - 86] / 48 = 67.33rounded to the thousands place :) thank you!!
5e^3x – 4 = 31
Step-by-step explanation:
Add 4 to both sides: 5e^3x = 35, or
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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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 store is having a buy one get one 30% off sale. During the sale Christopher buys two pairs of shoes that each have a regular price of 48$. How much does Christopher pay for the two pairs of shoes?
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)
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°
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.
Here are some possible examples of two families of orthogonal functions. Identify each of them as being definitely incorrect or potentially correct and explain why. I'm not asking you to solve three complete orthogonal trajectory problems! a. y = cx5 and 5x2 + y2 = k b. x2 + y2 = 2cy and x2 + y2 = 2kx c. x2 = y2 + c and y = ke
(a) y = cx⁵ and 5x² + y² = k are do not satisfy the conditions for orthogonality.
(b) x² + y² = 2cy and x² + y² = 2kx potentially represent families of orthogonal functions .
(c) x² = y² + c and y = kx potentially represent families of orthogonal functions .
a. y = cx⁵ and 5x² + y² = k: Definitely incorrect. The equation 5x² + y² = k represents an ellipse, whereas the equation y = cx⁵ represents a polynomial function. These two functions do not satisfy the conditions for orthogonality.
b. x² + y² = 2cy and x² + y² = 2kx: Potentially correct. Both equations represent circles in the xy-plane. However, for them to be orthogonal functions, the centers of the circles need to coincide at the origin (0, 0). If the centers are at the origin, then these equations can be potentially correct as orthogonal functions.
c. x² = y² + c and y = kx: Potentially correct. The equation x² = y² + c represents a hyperbola, and the equation y = kx represents a straight line passing through the origin. If the hyperbola is centered at the origin and the line passes through the origin, then these equations can be potentially correct as orthogonal functions.
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Find the inverse of the one-to-one function. State the domain and the range of the inverse function. {(2, 11), (3, -4), (4, -1), (5, -14), (6, 1)} The inverse function is The domain of the inverse function is The range of the inverse function is
The inverse function is given by the set of points {(11, 2), (-4, 3), (-1, 4), (-14, 5), (1, 6)}, the domain of the inverse function is {11, -4, -1, -14, 1}, and the range of the inverse function is {2, 3, 4, 5, 6}.
To find the inverse of the one-to-one function defined by the given set of points {(2, 11), (3, -4), (4, -1), (5, -14), (6, 1)}, we need to swap the x-values with the y-values to obtain the reversed pairs of points.
The inverse function is {(11, 2), (-4, 3), (-1, 4), (-14, 5), (1, 6)}.
The domain of the inverse function is the set of all x-values from the original function, which in this case is {11, -4, -1, -14, 1}.
The range of the inverse function is the set of all y-values from the original function, which in this case is {2, 3, 4, 5, 6}.
Therefore, the inverse function is given by the set of points {(11, 2), (-4, 3), (-1, 4), (-14, 5), (1, 6)}, the domain of the inverse function is {11, -4, -1, -14, 1}, and the range of the inverse function is {2, 3, 4, 5, 6}.
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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
Someone help me please need ASAP
Answer:
x = 1/2
Step-by-step explanation:
all of its sides are equal;
4x - 6 = 2x - 5
2x = 1 , x = 1/2
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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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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