Let p, (t) 6+t, P2(t) =t-3t, p3 (t) = 1 +t-2t. Complete parts (a) and (b) below. Use coordinate vectors to show that these polynomials form a basis for P2. What are the coordinate vectors corresponding to p, p2, and pa? P- Place these coordinate vectors into the columns fa matrix A. What can be said about the matrix A? O A. The matrix A forms a basis for R3 by the Invertible Matrix Theorem because all square matrices are row equivalent to I3. O B. The matrix A is invertible because it is row equivalent to I and therefore the row reduced columns of A forma basis for R3 by the Invertible Matrix Theorem. O C. The matrix A is invertible because it is row equivalent to I3 and therefore the null space of A, denoted Nul A, forms a basis for R3 by the Invertible Matrix Theorem. O D. The matrix A is invertible because it is row equivalent to l3 and therefore the original columns of A form a basis for R3 by the Invertible Matrix Theorem.
Answers
the matrix A is row equivalent to the identity matrix I3, it is invertible. Therefore, the original columns of A form a basis for R3 by the Invertible Matrix Theorem. So, the correct answer is option D.
To show that p, p2, and p3 form a basis for P2, we need to show that they are linearly independent and span P2. To show linear independence, we assume that a linear combination of the polynomials equals the zero polynomial: a1p + a2p2 + a3p3 = 0 This means that a1(6+t) + a2(t-3t) + a3(1+t-2t) = 0 Simplifying, we get a1 + a2t + a3t = 0 a1 - 3a2 + a3 = 0 a3 = 0 Solving the system of equations, we get a1 = a2 = 0, which means that p, p2, and p3 are linearly independent. To show that they span P2, we need to show that any polynomial in P2 can be expressed as a linear combination of p, p2, and p3. Let's take a polynomial f(t) = at^2 + bt + c as an example. We want to find constants a1, a2, and a3 such that a1p + a2p2 + a3p3 = at^2 + bt + c Substituting the given polynomials, we get a1(6+t) + a2(t-3t) + a3(1+t-2t) = at^2 + bt + c Simplifying, we get a1 + a2t + a3t = a -a2 + a3 = b 6a + a3 = c Solving the system of equations, we get a1 = 2a - b - c a2 = -b a3 = c - 6a Therefore, any polynomial in P2 can be expressed as a linear combination of p, p2, and p3, which means that they span P2. To find the coordinate vectors corresponding to p, p2, and p3, we need to express them as linear combinations of the standard basis polynomials in P2: p = 0(1) + 0(t) + 6 p2 = -3(1) + 1(t) + 0(t^2) p3 = 1(1) + 1(t) - 2(t^2) Therefore, the coordinate vectors corresponding to p, p2, and p3 are (0, 0, 6), (-3, 1, 0), and (1, 1, -2), respectively. We can place these coordinate vectors into the columns of a matrix A: A = [0 -3 1; 0 1 1; 6 0 -2] To determine what can be said about the matrix A, we need to use the Invertible Matrix Theorem. According to the theorem, a square matrix A is invertible if and only if its row reduced echelon form is the identity matrix. We can row reduce A: [0 -3 1 | 0] [0 1 1 | 0] [6 0 -2 | 0] R1 <- R1 + 3R2 [0 1 1 | 0] [0 1 1 | 0] [6 0 -2 | 0] R3 <- R3 - 6R2 [0 1 1 | 0] [0 1 1 | 0] [6 0 -8 | 0] R3 <- R3/(-8) [0 1 1 | 0] [0 1 1 | 0] [-3 0 1 | 0] R1 <- R1 - R2 [0 0 0 | 0] [0 1 1 | 0] [-3 0 1 | 0] Therefore, the row reduced echelon form of A is [1 0 0] [0 1 1] [0 0 0] Since it is not the identity matrix, A is not invertible. However, the columns of A still form a basis for R3, since they are linearly independent Invertiblespan R3.
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Related Questions
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. I estimate that the probability of my getting married in the next 3 years is 0.7. math
Answers
The statement "I estimate that the probability of my getting married in the next 3 years is 0.7" does make sense.
As individuals, we can make personal estimates or predictions about events that are relevant to our lives, such as the probability of getting married in a certain timeframe. These estimates are based on our own subjective beliefs, experiences, and expectations. While they may not be based on precise mathematical calculations or rigorous statistical analysis, they can still reflect our personal opinions or perceptions.
In this case, the person is providing an estimate that they believe there is a 0.7 (or 70%) probability of getting married within the next 3 years. This estimate is a subjective assessment of their own chances based on various factors such as their current relationship status, personal goals, or cultural norms.
It is important to note that personal estimates like this are not necessarily based on concrete evidence or universally applicable probabilities. They can vary greatly from person to person and are subjective in nature. However, they can still hold personal meaning and influence one's decision-making or expectations regarding future events.
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Write an equation for the line perpendicular to the line y =
5
3 + 7 which passes through the point (-5,6).
4
5
o
A
4* + 5
4
y= - 5* +7
4
с
y = - 5* + 2
D
y =
-
5
4
-2 + 7
E
-
4
5
5y = 2+2
Answers
Answer:
Whenever I'm alone with you
You make me feel like I am home again
Whenever I'm alone with you
You make me feel like I am whole again
Whenever I'm alone with you
You make me feel like I am young again
Whenever I'm alone with you
You make me feel like I am fun again
However far away
I will always love you
However long I stay
I will always love you
Related
Whatever words I say
I will always love you
I will always love you
Whenever I'm alone with you
You make me feel like I am free again
Whenever I'm alone with you
You make me feel like I am clean again
However far away
I will always love you
However long I stay
I will always love you
Whatever words I say
I will always love you
I will always love you
However far away
I will always love you
However long I stay
I will always love you
whatever words I say
I will always love you
I'll always love you
I'll always love you
I love you
-Adele
tep-by-step explanation:
2 × 10 + 10 – 8 = ? show work
Answers
10 - 8 = 2
20 + 2 = 22
2 x 10=20
20+10=30
30-8=22
An event is successful 1 out of every 5 attempts. what is the probability of the complement of that event?0.15cannot be determined0.800.20
Answers
The probability of the complement of the event is 0.8 or 80%.
Suppose we have an event that is successful in 1 out of every 5 attempts. This means that the probability of the event occurring is 1/5 or 0.2. We can represent this probability as P(A) = 0.2, where A is the event of being successful.
Now, the complement of an event is the probability of the event not occurring. In this case, the complement of A is the probability of not being successful. We can represent this probability as P(A').
To find the probability of the complement of an event, we use the formula:
P(A') = 1 - P(A)
where P(A') is the probability of the complement of A, and P(A) is the probability of A.
Using the values given, we have:
P(A) = 0.2
P(A') = 1 - 0.2
P(A') = 0.8 or 80%
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This recipe makes 5 portions of fajitas. Carly has 700 g of chicken, 800 g of peppers, 200 g of onion, 50 g of spice mix and 16 tortillas. How much more of each ingredient will she need to make 15 portions by following this recipe?
Recipe:
Serves 5
400 g
chicken
600 g peppers
70 g onion
20 g spice mix
10 tortillas
?g chicken
? g peppers
? g onion
? g spice mix tortillas
Answers
Answer:
Chicken = 500 g
Peppers = 1 kg
Onions = 10 g
Spice mix = 10 g
Tortillas = 14
Step-by-step explanation:
5 × 3 = 15
What the recipe indicates she needs
400 × 3 = 1200
600 × 3 = 1800
70 × 3 = 210
20 × 3 = 60
10 × 3 = 30
Subtract what she needs from what she has
1200 - 700 = 500 g
1800 - 800 = 1000 g
210 - 200 = 10 g
60 - 50 = 10 g
30 - 16 = 14 tortillas
Answer:
qhdlqywylvly
Step-by-step explanation:hqiufqwbuif
find the horizontal and vertical asymptotes of the curve. y = 3ex ex − 5
Answers
The graph of y = 3ex ex − 5 has a horizontal asymptote of y = 3 and a vertical asymptote of x = -3/5.
The equation y = 3ex ex − 5 can be rewritten as y = 3x2ex − 5. In order to find the horizontal and vertical asymptotes of this function, we must first find its degree of the numerator and denominator. The numerator is a second degree polynomial while the denominator is a first degree polynomial.
The horizontal asymptote will be the line y = b/a, where b and a are the coefficients of the highest degree terms in the numerator and denominator, respectively. In this case, b = 3 and a = 1, so the horizontal asymptote is y = 3.
The vertical asymptote of a function is the line x = a/b, where a and b are the coefficients of the highest degree terms in the numerator and denominator, respectively. In this case, a = 3 and b = -5, so the vertical asymptote is x = -3/5.
Therefore, the graph of y = 3ex ex − 5 has a horizontal asymptote of y = 3 and a vertical asymptote of x = -3/5.
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Help please?????????????????
Answers
Answer:
3²
Step-by-step explanation:
3⁸ × 3⁴ = 3⁸ ⁺ ⁴ = 3¹²
3² × 3⁸ = 3² ⁺ ⁸ = 3¹⁰
3¹² ÷ 3¹⁰ = 3¹² ⁻ ¹⁰ = 3²
Select all the correct answers.
Which expressions are equal to 105?
0 (104)
103.102
105
(103)
10-10-10-10-10
Answers
Answer:
105
Step-by-step explanation:
0 (104) is equal to 0, so let's cross that out. 103 times 102 is definitely not equal to 105. The third one is 105. The fourth one is not 105. The last one is not 105 either.
Find the measures of the numbered angles of rhombus DEFG
Answers
Answer: m<1= 90
m<2= 42
m<3= 42
m<4= 48
m<5= 48
Step-by-step explanation: Reasoning= 8th grade nerd
Just kidding, the diagonals bisect the angles(vertices) and opposite angles are congruent thanks to nasty proofs, which means <4=<5. The same goes with angle 2 and 3. The sum of interior angles of a rhombus is 360 degrees. So, 48 times 4, is 192, and 360-192 is 168. 168 divided by 4 is 42. There's your messy explanation. You(the person asking) probably turned this in already but to those who are searching for this answer days, weeks, months, even years ahead, good luck. Geometry is kinda rough but you'll (might) get the hang of it if you pay enough attention.
The angles are as follows:
∠1 = 90°
∠2 = 42°
∠3 = 42°
∠4 = 48°
∠5 = 48°
The figure is a rhombus
The diagonals of a rhombus are perpendicular bisector of each other.
Adjacent angle are supplementary too.
Therefore,
∠1 = 90°
The diagonal cut the angles into 2 equal half. Therefore,
∠4 = 48°
opposite angles are equal . Therefore,
∠5 = 48°
Sum of angles in a quadrilateral = 360°. Therefore,
48(2) + 48(2) + 2(∠2 + ∠3) = 360
2(∠2 + ∠3) = 360 - 192
(∠2 + ∠3) = 168 / 2
∠2 + ∠3 = 84°
∠2 = 1 /2 × 84
∠2 = 42°
∠3 = 42°
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Margaret drove to an appointment at 50 miles per hour. Her speed on her return was 40 miles per hour. The trip back took one quarter of an hour longer. How far did Margaret drive to her appointment in miles
Answers
Given that, Margaret drove to an appointment at 50 miles per hour. Her speed on her return was 40 miles per hour. The trip back took one quarter of an hour longer.
The question is asking to determine the distance Margaret drove to her appointment in miles. The formula used to solve the problem is as follows;
distance = speed × time Given that the distance to and from the appointment are the same. Distance to the appointment (going) = Distance from the appointment (returning)Distance = Distance Going = Distance Returning Let's determine the time it took Margaret to drive to her appointment using the formula above. Distance = speed × time Distance Going = 50 mph × t (where t represents time)Distance Going = 50tThe time it took her to drive back is (t + 0.25) since the return took one quarter of an hour longer. Distance = speed × timeDistance Returning = 40 mph × (t + 0.25)Distance Returning = 40t + 10Using the formula Distance = Distance Going = Distance Returning50t = 40t + 10Subtract 40t from both sides.50t - 40t = 10t = 10Thus, t = 1The distance going to the appointment is;Distance Going = 50tDistance Going = 50 × 1Distance Going = 50 , Margaret drove 50 miles to her appointment.Answer: Margaret drove 50 miles to her appointment.
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Suppose if you have a lot of training data from an arbitrary distribution, would you expect the lda classifier to give similar boundaries to the bayes classifier?
Answers
No, the LDA classifier and the Bayes classifier would not necessarily give similar boundaries when trained on a large amount of training data from an arbitrary distribution.
The LDA (Linear Discriminant Analysis) classifier assumes that the input features are normally distributed and that the class covariances are equal. It finds linear boundaries that maximize the separation between classes based on these assumptions. On the other hand, the Bayes classifier makes decisions based on the class conditional probabilities and prior probabilities of the classes. It can handle arbitrary distributions and does not make assumptions about the class covariances. Therefore, even with a large amount of training data, if the distribution of the data does not conform to the assumptions of LDA (e.g., non-normal distributions or unequal class covariances), the LDA classifier may not give similar boundaries to the Bayes classifier.
The LDA and Bayes classifiers may not give similar boundaries when trained on data from an arbitrary distribution, as the LDA classifier relies on specific assumptions about the data distribution that may not hold true in practice.
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The boys football team is selling game tickets for a football game. Adult admission is $8 and student admission is $6 there are usually twice as many students than adults at the game. If the goal is to make $3000. Write 2 equations. Solve the system of equations, how many student and adult tickets must be sold? Let a = the number of adults and b = the number of students
Answers
To make $3000 selling game tickets, the boys football team needs to sell a combination of adult and student tickets. Solving the system of equations gives the number of adult and student tickets that must be sold 150 adult tickets and 300 student tickets.
The first equation relates the number of adults and students: since there are twice as many students as adults, we can write
b = 2a
where b is the number of students and a is the number of adults.
The second equation relates the revenue from ticket sales to the number of adults and students
8a + 6b = 3000
where 8a is the revenue from adult tickets and 6b is the revenue from student tickets.
Now we can substitute the first equation into the second equation to get
8a + 6(2a) = 3000
Simplifying, we get
20a = 3000
Dividing by 20, we get
a = 150
This means we need to sell 150 adult tickets. Using the first equation, we can find the number of student tickets
b = 2a = 2(150) = 300
So we need to sell 300 student tickets.
Therefore, the boys football team must sell 150 adult tickets and 300 student tickets to reach their goal of making $3000.
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problem 7. let a = 4 1 2 0 −3 3 0 0 2 . (a) (5 pts) describe the set of all solutions to the homogeneous system ax = 0. (b) (12 pts) find a−1, if it exists.
Answers
(a) To describe the set of all solutions to the homogeneous system ax = 0, we need to find the null space (also known as the kernel) of the matrix A.
Given matrix A:
a = [4 1 2
0 -3 3
0 0 2]
To find the null space, we need to solve the equation Ax = 0, where x is a column vector.
Setting up the augmented matrix [A | 0]:
[4 1 2 | 0
0 -3 3 | 0
0 0 2 | 0]
Row-reducing the augmented matrix:
[R2 = R2 + (3/2)R1]
[R3 = (1/2)R3]
[4 1 2 | 0
0 -2 6 | 0
0 0 1 | 0]
[R2 = (-1/2)R2]
[4 1 2 | 0
0 1 -3 | 0
0 0 1 | 0]
[R1 = R1 - 2R3]
[R2 = R2 + 3R3]
[4 1 0 | 0
0 1 0 | 0
0 0 1 | 0]
[R1 = R1 - (1/4)R2]
[4 0 0 | 0
0 1 0 | 0
0 0 1 | 0]
The row-reduced echelon form of the augmented matrix is:
[1 0 0 | 0
0 1 0 | 0
0 0 1 | 0]
From the row-reduced echelon form, we can see that the only solution to the homogeneous system ax = 0 is x = [0, 0, 0] (the zero vector).
Therefore, the set of all solutions to the homogeneous system ax = 0 is the singleton set {0}.
(b) To find the inverse of matrix A, we need to check if it is invertible. If A is invertible, then its inverse A^(-1) exists.
Determine if A is invertible by calculating its determinant. If the determinant is non-zero, then A is invertible.
Given matrix A:
a = [4 1 2
0 -3 3
0 0 2]
Calculating the determinant of A:
det(A) = 4 * (-3) * 2 = -24
Since the determinant of A is non-zero (-24 ≠ 0), matrix A is invertible.
To find the inverse of A, use the formula:
A^(-1) = (1 / det(A)) * adj(A)
Calculating the adjoint of A:
adj(A) = [(-3)(2) (2)(2) (-3)(1)
0 (-3)(2) (0)(1)
0 0 (4)(1)]
adj(A) = [-6 4 -3
0 -6 0
0 0 4]
Calculating the inverse of A:
A^(-1) = (1 / det(A)) * adj(A)
= (1 / -24) * [-6 4 -3
0 -6 0
0 0 4]
A^(-1) = [1/4 -1/
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assume that blood pressure readings are normally distributed with and a blood pressure reading of 145 or more may require medical attention. what percent of people have a blood pressure reading greater than 145?
Answers
0.08891% percent of people have a blood pressure reading greater than 145.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
145) = (145-120)/8 = 25/8.P(x > 145) = P(z > 27/8) = 0.0008891.. = 0.08891%Hence, 0.08891% percent of people have a blood pressure reading greater than 145.
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What is the volume of the composite solid? 6 m 4 m 3 m 4 m 4 m
Answers
Answer:
Please read explanation
Step-by-step explanation:
A picture would be helpful, but I think the answer might be (6x4x3)+(3x4x4). If your shape is made up of many parts, you should find the volume of each shape then add them up to find the total volume. (To find volume, multiply base x height x width) If you could give a picture, it would be very helpful because I don't really know which numbers I should multiply to find volume. I hope this explanation helps, and please comment if you need to ask me anything.
Answer:
Answer is 136 cubic meters
Step-by-step explanation:
Which pairs of events are independent? (Select all thatapply.)
P(A) = .40,P(B) = .60, (A ∩ B) =.14.
P(A) = .60,P(B) = .40, (A ∩ B) =.24.
P(A) = .70,P(B) = .40, (A ∩ B) =.28.
Answers
The only pair of events that are independent among the three given pairs is the one where the probability of A is 0.6, the probability of B is 0.4, and the probability of the intersection of A and B is 0.24.
Pairs of events that are independent have probabilities that are not affected by the occurrence or non-occurrence of the other event. In other words, if A and B are independent events, then the probability of A occurring does not change based on whether or not B occurs, and vice versa.
To determine which pairs of events are independent, we need to calculate the probability of each event occurring and the probability of their intersection. If the probabilities satisfy the formula P(A ∩ B) = P(A)P(B), then the events are independent.
For the given pairs of events, we have:
P(A) = .40, P(B) = .60, P(A ∩ B) = .14. These events are not independent because P(A ∩ B) ≠ P(A)P(B) (.14 ≠ .24).
P(A) = .60, P(B) = .40, P(A ∩ B) = .24. These events are independent because P(A ∩ B) = P(A)P(B) (.24 = .24).
P(A) = .70, P(B) = .40, P(A ∩ B) = .28. These events are not independent because P(A ∩ B) ≠ P(A)P(B) (.28 ≠ .28).
Therefore, the pair of events that are independent is P(A) = .60, P(B) = .40, and (A ∩ B) = .24.
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PLEASEEEEE HELPPPPPPP!!!! WILL GIVE BRAINLIEST Which of Euclid's postulates seems most unlike the others?
-A straight line segment can be drawn between any two points.
-Any straight line segment can be extended indefinitely.
-A circle can be drawn with any center and radius.
-All right angles are equal to one another.
-If two straight lines in a plane are met by another line, and if the sum of the interior angles on one side is less than two right angles, then the straight lines, if extended sufficiently, will meet on the side upon which the sum of the angles is less than two right angles.
Answers
Answer:If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles
Tamar's house is greater than 472 and less than 500 which number can be on Tamar's house?
Answers
490
472 <490<500
it fits the criteria
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answers
Answer:
4x-2
Step-by-step explanation:
4x(3x+5)-2(3x+5)
(4x-2)(3x+5)
you can see that 4x-2 is a factor
The graph shows the cube root parent function
Which statement best describes the function?
(image attached)
Answers
Answer:
Step-by-step explanation:
As you move from left to right along the graph, each y-value gets larger and larger. Therefore the y value is always increasing. The correct answer is D.
Please helpppppp
Given m
11
n, find the value of x and y.
(9x+1)
m
jo
(7x+13)
n
Answers
2x+1=13
2x=12
x=6
7(6)+13
42+13
55
180-55
125
y= 125°
Answer:
x = 6
y° = 125°
Step-by-step explanation:
9x + 1 and 7x + 13 are alternate angles and has same measurement
9x + 1 = 7x + 13
9x - 7x = 13 - 1
2x = 12
x = 6
y° and 7x + 13 are supplementary angles so their sum is 180°
7x + 13 ➡ 7×6 + 13 = 55°
55 + y° = 180 subtract 55 from both sides
y° = 125°
Question 1 (Multiple Choice Worth 2 points)
(Multiplying Linear Expressions MC)
Simplify ---
O
45
m²
8.
45
8
45
2
m²-m
35
2
-m² + m
35
8
45
2
·m² + m
35
Answers
Answer:
\( - \frac{2}{5} m( - \frac{4}{9} m - \frac{1}{7} ) = \)
\( \frac{8}{45} {m}^{2} + \frac{2}{35} \)
Steve has 84 basketball cards,which is 7 times as many as claire.Claire buys 63 more cards,if b is the number of cards that claire has now then what is the value of b
Answers
Answer: Value of B= 75 Basketball cards
Step-by-step explanation:
STEP 1
let number of cards Steve has be =a
let number of cards Claire has be =b
STEP 2
Steve has a= 84 basketball cards
Claire has 7 times less than Steve = 84 /7 = 12=b
STEP 3
if Claire buys 63 more cards
The present value of card Clare now has = 12 +63 = 75 basket ball cards=b
what would (9, 10) be after a rotation 270 degrees counterclockwise around the origin?
Answers
The new coordinates of the point (9, 10) after a rotation of 270 degrees counter-clockwise around the origin are (10, -9).
The coordinates of the point are (9, 10). We perform a transformation on the point. The type of transformation performed is rotation. The rotation is done at an angle of 270 degrees in a counter-clockwise direction around the origin. First of all, we need to convert the angle of rotation from degrees to radians. The angle θ is 270*(π/180) = 3π/2. Let the original coordinates be denoted by (a, b) and the coordinates after rotation be (x, y). We can write the following equations using the theory of rotation.
x = a×cos(θ) - b×sin(θ) = 9×cos(3π/2) - 10×sin(3π/2) = 0 - 10(-1) = 10
y = b×cos(θ) + a×sin(θ) = 10×cos(3π/2) + 9×sin(3π/2) = 0 + 9(-1) = -9
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Order 7 of the following sentences so that they form a direct proof of the statement: If nu is even, then n? + 3n +5 is odd. Direct proof of the statement (in order): Choose from this list of sentences 2k2 + 3x + 2 is an integer It follows that n2 + 3 + 5 = (2k)? + 3(2k) +5 4k? + 6k+5 = 2(2k2 + 3k + 2) +1 Since k is an integer and integers are closed under multiplication and addition By the definition of even, there exists an integer k such that n = 22 Thus, by the definition of odd, PR,282 + 3k + 2) +1 is oda Hence, na +3n +5 is odd Let T be even Let n be odd By the definition of odd, there exists an integer k such that n 2k +1 2 + 3k + 2 is even
Answers
Since 2k2 + 5k + 4 is an integer, it follows that n2 + 3n + 5 is odd.
Direct proof of the statement (in order):
Let T be even. By the definition of even, there exists an integer k such that T = 2k.
Let n be odd. By the definition of odd, there exists an integer k such that n = 2k + 1.
It follows thatn
2 + 3n + 5 = (2k + 1)2 + 3(2k + 1) + 5
= 4k2 + 10k + 9
= 2(2k2 + 5k + 4) + 1.
Since 2k2 + 5k + 4 is an integer, it follows that n2 + 3n + 5 is odd.
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[Romeo:] But, soft! What light through yonder window breaks?
It is the east, and Juliet is the sun!
Arise, fair sun, and kill the envious moon,
Who is already sick and pale with grief,
That thou her maid art far more fair than she
—Romeo and Juliet,
William Shakespeare
What do these lines of the soliloquy show?
Which words best describe the mood of these lines?
[Romeo:] But, soft! What light through yonder window breaks?
It is the east, and Juliet is the sun!
Arise, fair sun, and kill the envious moon,
Who is already sick and pale with grief,
That thou her maid art far more fair than she
—Romeo and Juliet,
William Shakespeare
What do these lines of the soliloquy show?
Which words best describe the mood of these lines?
[Romeo:] But, soft! What light through yonder window breaks?
It is the east, and Juliet is the sun!
Arise, fair sun, and kill the envious moon,
Who is already sick and pale with grief,
That thou her maid art far more fair than she
—Romeo and Juliet,
William Shakespeare
What do these lines of the soliloquy show?
Which words best describe the mood of these lines?
[Romeo:] But, soft! What light through yonder window breaks?
It is the east, and Juliet is the sun!
Arise, fair sun, and kill the envious moon,
Who is already sick and pale with grief,
That thou her maid art far more fair than she
—Romeo and Juliet,
William Shakespeare
What do these lines of the soliloquy show?
Which words best describe the mood of these lines?
[Romeo:] But, soft! What light through yonder window breaks?
It is the east, and Juliet is the sun!
Arise, fair sun, and kill the envious moon,
Who is already sick and pale with grief,
That thou her maid art far more fair than she
—Romeo and Juliet,
William Shakespeare
What do these lines of the soliloquy show?
Which words best describe the mood of these lines?
Answers
words: romantic, passionate and heartfelt
If Cody does a job in 87 hours and with the help of Patricia they can do it together in 58 hours, how long would it take Patricia to do it alone? hours
Answers
We can establish a "work rate" or velocity for Cody. It will represent the fraction of the job he does in an hour, or the "job per hour". If he does 1 job in 87 hours, it means that he does 1/87 of the job in an hour.
Similarly, when both Cody and Patricia work at the same time, they can do 1/58 of the job in an hour.
The combined job velocity (when they work together) is the sum of their individual velocities. Let's call P the velocity for Patricia:
\(\frac{1}{87}+P=\frac{1}{58}\)Now we can solve for P, which will give us the fraction of work Patricia is able to do in 1 hour:
\(P=\frac{1}{58}-\frac{1}{87}=\frac{87-58}{5046}=\frac{29}{5046}\)We can simplify the fraction, but for now, let's say Patricia does 29/5046 of the work in an hour. The time she would take to do the hob will be the inverse of that: 5046/29, which simplified gives us:
\(\text{Time Patricia takes}=\frac{5046}{29}=\frac{174}{1}\)Then, Patricia will take 174 hours to do the job alone.
a fair coin is tossed repeatedly. find the probability that a coin comes up heads for the first time after an odd number of coin flips.
Answers
The probability that a fair coin comes up heads for the first time after an odd number of coin flips is 1/2. This means that there is an equal chance of getting heads or tails on any given flip, and the outcome of each flip is independent of previous flips.
When a fair coin is tossed, the probability of getting either heads or tails is 1/2. Let's consider the possible scenarios for getting heads for the first time after an odd number of flips. The first flip can either be heads (with probability 1/2) or tails (also with probability 1/2). If the first flip is tails, we are back to the starting point and have to repeat the process. In each subsequent round, the probability of getting heads for the first time after an odd number of flips remains the same, 1/2.
Therefore, the probability of getting heads for the first time after an odd number of flips is the sum of an infinite geometric series with a first term of 1/2 and a common ratio of 1/2. Using the formula for the sum of an infinite geometric series, which is a/(1-r), where a is the first term and r is the common ratio, we can calculate the probability as 1/2 divided by (1 - 1/2), which simplifies to 1/2. Hence, the probability is 1/2.
Learn more about probability here: brainly.com/question/32117953
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Work out the size of angle x.
Answers
Answer:
x = 46°
Step-by-step explanation:
Angles on a straight line sum to 180°.
Therefore, the interior angle of the triangle that forms a linear pair with the exterior angle marked 130° is:
⇒ 180° - 130° = 50°
The interior angle of the triangle that forms a linear pair with the exterior angle marked 96° is:
⇒ 180° - 96° = 84°
The interior angles of a triangle sum to 180°. Therefore:
⇒ 50° + 84° + x = 180°
⇒ 134° + x = 180°
⇒ 134° + x - 134° = 180° - 134°
⇒ x = 46°
Therefore, the size of angle x is 46°.
(3 x 5) x 2 = 3 x ( blank x 2 )
Answers
Answer:
the answer is 5 for blank
Step-by-step explanation:
30=6×blank
blank = 30÷6
blank= 5