1. Given the plane P with equation 2x + y - z = 3, and line M with symmetric equation x = 1 - y = z, determine if they intersect. If not, find the distance between them.
2. Let R1 be the plane containing the points (1, 1, 0), (1, 0, 1) and (0,1,1), and R2 be the plane with equation x + y + z = 1. Let L be the line of intersection of R1 and R2. (
2.1) Find an equation for R1
(2.2) Find parametric equations for L
(2.3) Find the distance between the origin and the line L
Answers
To find the distance between the origin and the line L, we can use the formula
:|a × b|/|b|,
where a is the vector from the origin to any point on the line L, b is the direction vector of L, and | · | denotes the magnitude of a vector. Choosing the point (1, 1, 0) on L, we get a = (-1, 0, 1). Substituting into the formula gives
:|a × b|/|b| = |(2, 1, 2)|/|i - 2j - k| = 3/√6.
Therefore, the distance between the origin and the line L is 3/√6 units.
Given the plane P with equation
2x + y - z
= 3,
and line M with symmetric equation
x
= 1 - y
= z,
we are to determine if they intersect or not, if not, we find the distance between them. Two lines intersect if and only if they have at least one point in common. Therefore, we must verify whether there is a point that satisfies the equation of the plane and the equation of the line. Substituting x, y, and z in the plane equation with the x, y, and z equations of the symmetric equation, we get
;2x + y - z
= 3⟹2(1 - y) + y - (1 - y)
= 3⟹2 - 2y + y - 1 + y
= 3⟹y = 2
This means the value of y is 2.Substituting y
= 2 in the symmetric equation of the line, we get
;x = 1 - y
= z ⟹x
= -1
We see that the value of x is -1.Therefore, the point of intersection of the line and plane is (-1, 2, 3).2. Given R1 as the plane containing the points (1, 1, 0), (1, 0, 1) and (0,1,1), and R2 as the plane with equation
x + y + z
= 1,
L is the line of intersection of R1 and R2.2.1) To find an equation for R1, we take two points from the plane, and we can take (1,1,0) and (1,0,1). We get the normal vector by taking the cross product of the vectors formed from the two points which is i - j + k.
Hence, the equation of
R1 is: i - j + k · (x - 1, y - 1, z)
= 0,
which simplifies to
i - j + k · (x + y - 1)
= 0.2.2)
To find the parametric equations of L, we first find the direction vector of L. This is given by the cross product of the normal vectors of R1 and R2, which is i - 2j - k. To find the coordinates of L, we set z
= t, and
x
= 1 - y
= 1 - 2t.
Thus, the parametric equation of
L is x
= 1 - 2t, y
= 1 + t, and z
= t.2.3)
To find the distance between the origin and the line L, we can use the formula:|a × b|/|b|, where a is the vector from the origin to any point on the line L, b is the direction vector of L, and | · | denotes the magnitude of a vector. Choosing the point (1, 1, 0) on L, we get
a = (-1, 0, 1).
Substituting into the formula gives
:|a × b|/|b|
= |(2, 1, 2)|/|i - 2j - k|
= 3/√6.
Therefore, the distance between the origin and the line L is 3/√6 units.
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Related Questions
Lins father is paying for a 20 dollar meal. He has a 15% - off coupon for the meal. After the discount, a 7% sales tax is applied
Answers
20x0.85=17
17x(1.07)=18.19
standard error of an estimator is not affected by the multiple choice question. population standard deviation. sample size. population size
Answers
The term that is not affected the standard error of an estimator is population size, from the provide data in options. So, option (c) is right one.
The standard error is a statistical term that used to measured the accuracy that a sample distribution represents a population by using standard deviation. The standard error(SE) is very similar to standard deviation of a distribution. Both are used to measure the spread of distribution. Higher the value SE, the more spread out your data is. In statistical way, standard error is also called standard error of mean, SEM, it represents the deviation of sample mean deviates from the actual mean of a population.
It is calculated simply by dividing the standard deviation by the square root of the sample size. That is \(SE = \frac{σ }{\sqrt{n}}\)
where , n --> sample size
σ --> population standard deviations
Now, from the above formula it is clearly seen that standard error term or an estimator affected by sample size (n) and population standard deviations ( σ). So, right choice for answer is population size.
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Complete question:
standard error of an estimator is not affected by the multiple choice question.
a) population standard deviation
b) sample size
c) population size
Answer Today Please! No Links or empty Answers... or it'll break my brainly... if not then it will just be deleted... im serous, virus links have broken my brainly to the point that it wont allow new answers.
the lucky person to answer gets an extra point UuU
Screenshot will show answer choices, the angle shape, & a better version of the question im asking
if Line CE interacts Line DF at Middle Point X, which angle must be congruent to Angle CXD?
Answers
Step-by-step explanation:
option D angle FXE as they are pair of vertically opposite angles.
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Answers
Answer:
Yes, Alternate Exterior Angles
Step-by-step explanation:
A testicle cuff is a ring-shaped device around the scrotum between the body and the testicles which when closed does not allow the testicles to slide through it. A common type has two connected cuffs, one around the scrotum and the other around the base of the penis. They are just one of many devices to restrain the male genitalia. A standard padlock, which cannot be removed without its key, may also be locked around the scrotum.
If the diameter of a circle is 20 , what is the area ?
Answers
the diameter of a circle is 20
The radius of circle is the half of the diameter of the circle :
Radius = Diamter/2
In the given question , we have Diameter = 20
So,
Radius = 20/2
Radius = 10
The expression for the radius 'r' of the circle is express as :
\(\text{ Area of Circle =}\Pi(radius)^2\)Substitute the value of Radius r = 10 in the expression of the area of circle:
\(\begin{gathered} \text{ Area of Circle =}\Pi(radius)^2 \\ \text{ Area of Circle =}\Pi(10)^2 \\ \text{ Area of Circle =}3.14\times10\times10 \\ \text{ Area of Circle =}3.14\times100 \\ \text{ Area of Circle =}314 \end{gathered}\)Area of the circle is 314
Answer : 314 unit square.
URGENT!!! ABCD is parallelogram. If m
Answers
Answer:
angle BAD= angle BCD = 100
then,
angle BCD + angle ECD = 180
100+ angle ECD = 180
angle ECD= 180-100 = 80
angle ECD =80
What is the equation of the line?
y = 3/4 x + 1
y = 4/3 x − 1
y = 4/3 x + 1
y=3/4x−1
Answers
Answer: 15
Step-by-step explanation:
what is the perimeter of a square if one of the sizes is 3mi
Answers
Given the side length of the square = 3 mi
The perimeter of the square = 4 times the length of one side
So, the perimeter = 4 x 3 = 12 mi
So, the answer will be perimeter = 12 mi
one of the five quadratics below has a repeated root. (the other four have distinct roots.) what is the repeated root? \begin{align*}
Answers
Form the given five quadratics , the one representing the repeated roots is equal to option d. 25x² - 30x + 9 and repeated roots are 3/5 or 3/5.
Quadratics representing repeated roots has discriminant equals to zero.
Standard quadratic equation is:
ax² + bx + c = 0
Discriminant 'D' = b² - 4ac
option a. -x²+ 18x + 81
Discriminant
'D' = 18² - 4(-1)(81)
= 324 + 324
= 648
D>0 has distinct roots.
option b. 3x²- 3x - 168
Discriminant
'D' = (-3)² - 4(-3)(-168)
= 9 - 2016
= -2007
D< 0 has distinct roots.
option c. x²- 4x - 4
Discriminant
'D' = (-4)² - 4(1)(-4)
= 16 + 16
= 32
D>0 has distinct roots.
option d. 25x²- 30x + 9
Discriminant
'D' = (-30)² - 4(25)(9)
= 900 - 900
= 0
D = 0 has repeated roots.
Repeated roots are:
x = ( -b ±√D ) / 2a
= [-(-30)±√0 ]/ 2(25)
= 30/ 50
= 3/5.
option e. x² - 14x + 24
Discriminant
'D' = (-14)² - 4(1)(24)
= 196 - 96
= 100
D>0 has distinct roots.
Therefore, the quadratics which represents the repeated roots are given by option d. 25x² - 30x + 9 and its repeated roots are 3/5 or 3/5.
The above question is incomplete, the complete question is:
One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?
a. -x²+ 18x + 81
b. 3x² - 3x - 168
c. x² - 4x - 4
d. 25x² - 30x + 9
e. x² - 14x + 24
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The scatter plot shows a hiker's elevation above sea level during a hike from the base to the top of a mountain. The equation of a trend line for the hiker's elevation is y=9.27x+622, where x represents the number of minutes and y represents the hiker's elevation in feet. Use the equation of the trend line to estimate the hiker's elevation after 140 minutes.
Answers
By using the equation of the trend line, it can be estimated that the hiker's elevation after 140 minutes will be, 1919.8 feet
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
The equation of a trend line for the hiker's elevation is,
y = 9.27x + 622
x represents the number of minutes
y represents the hiker's elevation in feet
Elevation after 140 minutes = ?
Now, putting value of x as 140 in the given equation,
y = (9.27 x 140) + 622
= 1297.8 + 622
= 1919.8
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1. BD bisects
2. < RQT is a straight angle. What are m
3.
Answers
Answer:
16.:
x = 5
m ∠ABC = 60°
17.:
m ∠RQS is 102°.
m ∠TQS is 78°
18.:
m ∠EFG = 75°
m ∠GFH = 105°
Step-by-step explanation:
16.:
An angle bisector splits one angle into two equal angles. Thus, ∠ABD + ∠CBD = ∠ABC and ∠ABD = ∠CBD.Solving for x:
We can now find x by setting angles ABD and CBD equal to each other:
ABD = CBD
(7x - 5 = 5x + 5) + 5
(7x = 5x + 10) - 5x
(2x + 10) / 2
x = 5
Thus, x = 5.
Finding the measure of ∠ABC:
Now we can find the measure of ∠ABC by plugging in 5 for x in either 7x - 5 or 5x + 5 and multiplying by 2. Let's do 7x - 5:
m∠ABC = 2 * (7(5) - 5)
m ∠ABC = 2 * (35 - 5)
m ∠ABC = 2 * (30)
m ∠ABC = 60
Thus, the measure of ∠ABC is 60°.
17.:
A straight angle is 180°.Thus, the measure of ∠RQT is 180.Solving for x:
Since RQS + TQS = 180°, we can first find x by setting the sum of the two angles equal to 180:
14x + 4 + 11x + 1 = 180
(14x + 11x) + (4 + 1) = 180
(25x + 5 = 180) - 5
(25x = 175) / 25
x = 7
Thus, x = 7
Finding m∠RQS:
Now we plug in 7 for x in 14x + 4 to find m ∠RQS:
m ∠RQS = 14(7) + 4
m ∠RQS = 98 + 4
m ∠RQS = 102
Thus, m ∠RQS is 102°.
Finding m ∠TQS:
Since m ∠RQS + m ∠TQS = 180°, we can find m ∠TQS by subtracting 102 from 180:
m ∠RQS + m ∠TQS = 180
m ∠TQS = 180 - m ∠RQS
m ∠TQS = 180 - 102
m ∠TQS = 78
Thus, m ∠TQS is 78°
18.:
A linear pair is defined as two adjacent angles that form a straight angle.This means that the sum of a linear pair is 180°.Finding n:
We can first find n by setting the sum of m ∠EFG and m ∠GFH equal to 180°:
m ∠EFG + m ∠GFH = 180°
3n + 24 + 4n + 37 = 180
(3n + 4n) + (24 + 37) = 180
(7n + 61 = 180) - 61
(7n = 119) / 7
n = 17
Thus, n = 17.
Finding m ∠EFG:
Now we can find m ∠EFG by plugging in 17 for n in 3n + 24:
m ∠EFG = 3(17) + 24
m ∠EFG = 51 + 24
m ∠EFG = 75
Thus, m ∠EFG = 75°.
Finding m ∠GFH:
Now we can find m ∠GFH by plugging in 17 for n in 4n + 37:
Now we can find m ∠GFH by plugging in 17 for n in 4n + 37:
m ∠GFH = 4(17) + 37
m ∠GFH = 68 + 37
m ∠GFH = 105
Thus ,m ∠GFH = 105°.
The question is:Find the total surface area of the rectangular prism.A. 546 in^2B. 480 in^2C. 238 in ^2D. 250 in^2
Answers
The formula for determining the total surface area of a rectangular prism is exprssed as
Total surface area = 2lw + 2lh + 2wh
Where
l = length = 11 inches
w = width = 5 inches
h = height = 4 inches
Therefore,
Total surface area = 2(11 * 5) + 2(11 * 4) + 2(5 * 4)
Total surface area = 110 + 88 + 40
Total surface area = 238 in^2
The correct option is C
Joshua watched 1 3 of a movie in the morning, and he watched some more at night. By the end of the day, he still had 1 5 of the movie left to watch. How much of the movie did Joshua watch at night
Answers
We can start solving the problem by using algebra. Let x be the total length of the movie in minutes. Then we know that:
1/3 of the movie is x/3 minutes.
1/5 of the movie is x/5 minutes.
We are told that Joshua watched 1/3 of the movie in the morning and had 1/5 of the movie left to watch at night. Therefore, we can set up the equation:
x/3 + y = x/5, where y is the length of the movie that Joshua watched at night.
We can then solve for y by isolating it on one side:
y = x/5 - x/3
We know that 1/3 + 1/5 = 8/15.
We can simplify by multiplying both sides of the equation by 15:
y = (8/15)*x = 8x/15
We can conclude that Joshua watched 8/15 or approximately 53.33% of the movie at night.
HOW MANY TRIANGLES ARE THERE?????
Answers
Answer:
I count 10 triangles.....
Answer:
3
Step-by-step explanation:
t think it's the because everything else is 4 sided
someone help me thank you
Answers
Step by step :
90-53= 37
X = 37
Solve for x. -3 < x - 10
Answers
Answer:
7 < x
Step-by-step explanation:
-3 < x - 10
+10 +10
------------------
7 < x
Answer:
x > 7
Step-by-step explanation:
-3 < x -10
=> x - 10 > -3
=> x > 10 - 3
=> x > 7
HELP MEEEEEEEEEEE, Ed's living room is 4 yards wide and 7 yards long. He wants to install yellow carpet that costs $5.00 per square yard. How much will it cost to buy enough carpet for the living room?
Answers
It will cost 140 dollars to buy enough carpet for the living room.
What is a rectangle?A rectangle is a four-sided figure in which opposite sides are equal and the diagonals are also of the same length.
Given Ed's living room is 4 yards wide and 7 yards long.
We know that the area of a triangle is the product of its length and width.
∴ The area of Ed's living room is (4×7) sq yards = 28 sq yards.
Also given to install yellow carpet that costs $5.00 per square yard,
∴ For 28 sq yards, the cost of installing a yellow carpet will be,
= (28×5) dollars.
= 140 dollars.
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Someone help please hurry !!! ASAP
Answers
Answer:
it's -4
Step-by-step explanation:
hope it helped!!!!!!
Answer:
-4
Step-by-step explanation:
The answer will be the same as a positive square root, just add a negative.
Find the exact length of the arc intercepted by the given central angle in the figure to the right. r= 12 sudut 3phi/4 The length of the intercepted arc is (Type an exact answer in terms of Use integers or fractions for any numbers in the expression.)
Answers
So the exact length of the intercepted arc is 9π.
When a circle is divided into 360 equal parts, each part is called a degree. A central angle is an angle whose vertex is at the center of the circle, and whose sides intersect the circle at two points, thereby cutting off an arc on the circle. The length of the intercepted arc is proportional to the measure of the central angle in radians.
The length of an arc intercepted by a central angle is given by the formula:
length of arc = radius × central angle in radians
Here, the radius is given as r = 12, and the central angle is given as 3π/4. Therefore, the length of the intercepted arc is:
length of arc = 12 × (3π/4) = 9π
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. If Ya/n and Y2/n are the respective independent relative frequencies of success associated with the two binomial distributions b(n, P1) and b(n, P2), compute n such that the approximate probability that the random
interval (Y1/n - Y2/n) ‡ 0.05 covers pi - p2 is at least 0.80. HINT: Take p* = P° = 1/2 to provide an upper bound
for n.
Answers
we would need a sample size of at least 502 for the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 to be at least 0.80.
To compute n, we can use the formula:
n = ((zα/2)^2 * 2p*(1-p*)) / (ε^2)
Where zα/2 is the z-score associated with a confidence level of 1-α, p* is the probability of success for a binomial distribution, and ε is the margin of error.
Since we are given that the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 is at least 0.80, we can set α = 0.20 to find the corresponding z-score of 1.28.
Using p* = 1/2 as an upper bound for both P1 and P2, we can calculate the margin of error as:
ε = zα/2 * sqrt((p*(1-p*)) / n)
Plugging in the values, we get:
0.05 = 1.28 * sqrt((0.25) / n)
Solving for n, we get:
n = 501.76
Therefore, we would need a sample size of at least 502 for the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 to be at least 0.80.
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21. A triangle has vertices A(-2,4), B(6,2), and C(1,-1). Prove using the Distance Formula and
Slope Formula that ABC is an isosceles right triangle.
Answers
To prove that triangle ABC is an isosceles right triangle, we need to show that two sides of the triangle are equal in length and one angle is a right angle.
Distance Formula:
The distance between two points (x₁, y₁) and (x₂, y₂) is given by the distance formula:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Using the distance formula, we can calculate the lengths of the three sides of the triangle:
Side AB: d₁ = √[(6 - (-2))² + (2 - 4)²] = √[8² + (-2)²] = √(64 + 4) = √68
Side BC: d₂ = √[(1 - 6)² + (-1 - 2)²] = √[(-5)² + (-3)²] = √(25 + 9) = √34
Side AC: d₃ = √[(-2 - 1)² + (4 - (-1))²] = √[(-3)² + 5²] = √(9 + 25) = √34
Slope Formula:
The slope between two points (x₁, y₁) and (x₂, y₂) is given by the slope formula: m = (y₂ - y₁) / (x₂ - x₁)
Using the slope formula, we can calculate the slopes of the three sides of the triangle:
Slope AB:
m₁ = (2 - 4) / (6 - (-2)) = (-2) / 8 = -1/4
Slope BC:
m₂ = (-1 - 2) / (1 - 6) = (-3) / (-5) = 3/5
Slope AC:
m₃ = (4 - (-1)) / (-2 - 1) = 5 / (-3) = -5/3
From the distances calculated and the slopes of the sides, we can see that side AB is equal in length to side BC (both √34), indicating that two sides are equal. Additionally, the slope of side AC (m₃ = -5/3) is the negative reciprocal of the slope of side AB (m₁ = -1/4), indicating that the two sides are perpendicular, and hence, one angle is a right angle.
Therefore, triangle ABC is an isosceles right triangle.
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slope of (-2,2) and (3,4)
Answers
Answer:
2/5
Step-by-step explanation:
Good luck!
Assume that 22 kids have their names (all different) put into a hat. the teacher is drawing 5 names to see who will speak first, second, etc,. for the day. how many permutations of names can the teacher draw?
225
522
22/17
22!
Answers
The number of names that the teacher can draw is 22! / 17!. The Option D.
The teacher can draw 5 names from the hat in approximately 5,048,800 different permutations.
The number of permutations of drawing 5 names out of 22 without replacement can be calculated using the formula for permutations:
P(n, r) = n! / (n - r)!
Where:
n is the total number of items (names)
r is the number of items selected (in this case, 5)
Using the given values, we have:
P(22, 5) = 22! / (22 - 5)!
= 22! / 17!
Calculating this expression, we find:
P(22, 5) ≈ 22 × 21 × 20 × 19 × 18
≈ 5,048,800
Therefore, the teacher can draw 5 names from the hat in approximately 5,048,800 different permutations or 22! / 17!. The Option D.
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1 example of factoring sum of two cubes
Answers
7^3+8^3=(7+8)(7^2−(7*8)+8^2)
(15)(49-56+64)
(15)(57)
7^3+8^3=855
Let X and Y denote the tarsus lengths of male and female grackles, respectively. Assume that X is N(,) and Yis N(4,²). Given that the sample number of X and Y are n=m=25, and X = 33.8, S=3.9,Y=32.5, S=5.1. Use these observations to give a level a=0.05 test for H₁:μx = μy VS Hoxy. Give the p-value of this test. (10 pts)
Answers
To test the hypothesis H₁: μx = μy versus Hoxy, where μx and μy represent the means of X and Y respectively, we can perform a two-sample t-test. The test compares the means of two independent samples to determine if they are significantly different from each other.
The given information provides the sample means (X = 33.8, Y = 32.5) and the sample standard deviations (Sx = 3.9, Sy = 5.1). The sample sizes for both X and Y are n = m = 25.
Using this information, we can calculate the test statistic, which is given by:
t = (X - Y) / sqrt((Sx^2 / n) + (Sy^2 / m))
Plugging in the values, we get:
t = (33.8 - 32.5) / sqrt((3.9^2 / 25) + (5.1^2 / 25))
Next, we need to determine the degrees of freedom for the t-distribution. Since the sample sizes are equal (n = m = 25), the degrees of freedom for the test is given by (n + m - 2).
Using the t-distribution table or software, we can find the critical value corresponding to a significance level of α = 0.05 and the degrees of freedom.
Finally, we compare the calculated test statistic with the critical value. If the test statistic falls within the rejection region (i.e., the absolute value of the test statistic is greater than the critical value), we reject the null hypothesis. The p-value can also be calculated, which represents the probability of observing a test statistic as extreme or more extreme than the calculated value, assuming the null hypothesis is true.
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On which interval is the function increasing? (–[infinity], –4) (–[infinity], 4) (–4, [infinity]) (4, [infinity]).
Answers
Answer:on which interval is the function increasing
Answer:(4, infinity
Step-by-step explanation:
M measures 12°
(a) Find the supplement of M.
(b) Find the complement of M.
Answers
168° is the supplementary angle of 12°.
The complement of the initial angle, which is 12 degrees, is 90 – 12 degrees, or 78 degrees.
What is an example of a supplementary angle?
Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°.
Two angles are said to be supplementary angles if they add up to 180 degrees. For example, if ∠A + ∠B = 180°, then ∠A and ∠B are called supplementary angles. Supplementary angles always form a straight angle (180 degrees) when they are put together.
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If the original angle is 12 degrees, then 90-12 = 78 degrees is the complement of that angle. Therefore, the angles of 12 degrees and 78 degrees are complimentary.
What is supplemetary and complementary angles?Two angles are said to be supplementary angles because they combine to generate a linear angle when their sum is 180 degrees. When two angles add up to 90 degrees, however, they are said to be complimentary angles and together they make a right angle.
complementary angles have a sum of 180 degrees. Supplementary and complementary angles can share a vertex or side but are not need to be near to one another.
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pls help i need a good grade in english !!
Answers
Answer:
Recursive formula → \(a_n=-9n+19\)
Step-by-step explanation:
Recursive formula given for the sequence is,
\(a_1=10\) and \(a_n=a_{n-1}-9\)
Therefore, sequence will be,
10, 1, -8, -17........
Explicit formula for an arithmetic sequence is,
\(a_n=a_1+(n-1)d\)
Here, n = number of term
d = common difference
Therefore, recursive formula will be,
\(a_n=10+(n-1)(-9)\)
= 10 - 9n + 9
= 19 - 9n
\(a_n=-9n+19\)
c. show the result of using the buildheap general algorithm described in the class to build a binary heap using the same input as in a.
Answers
Using the build heap general algorithm described in class, the result of building a binary heap using the same input as in part a would be a complete binary tree where each node is greater than or equal to its children (if any).
The algorithm first starts by building a binary tree by inserting each element of the input list into the tree in level order. It then iteratively performs heapify operations on each non-leaf node starting from the last node and moving up to the root. The heapify operation swaps the node with its largest child (if it exists) until the node is greater than or equal to its children. This process ensures that the resulting binary tree is a heap.
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Choose one answer and explain your choice: Suppose A and B are
disjoint events. Are A and B independent
events? i) Yes
ii) No
iii) It depends.
Answers
If A and B are disjoint events, then the probability of A or B is the sum of their individual probabilities. However, this does not necessarily mean that A and B are independent events.
If A and B are independent events, then the probability of both A and B occurring is the product of their individual probabilities. However, if A and B are disjoint, then the probability of both A and B occurring is zero. Therefore, A and B cannot be independent if they are disjoint events.Hence, the correct answer is (ii) No. A and B are disjoint events, which means that they do not have any outcomes in common. If A and B are independent events, then the occurrence of one event will not affect the occurrence of the other event. If A and B are not independent events, then the occurrence of one event will affect the occurrence of the other event.
Since A and B are disjoint events, they cannot be independent events. If A and B are independent events, then they cannot be disjoint events. Hence, the correct answer is (ii) No
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