To define a SCHEME procedure named (heap-insert f x H) that adds element x to heap H using the first-order relation f to determine which element belongs at the root of each (sub)tree, we can follow these steps:
1. First, we need to check if the heap H is empty. If it is, then we can simply create a new node with x as the value and return it as the new heap.
2. If H is not empty, we need to compare x with the value at the root of H using the first-order relation f.
3. If x is smaller than the root value, we can create a new node with x as the value and make it the new root, with the previous root as its left child.
4. If x is larger than the root value, we need to recursively insert x into the right subtree of H using the same procedure, heap-insert f x (right-subtree H).
5. After inserting x into the heap, we need to maintain the heap property, which means that the value at the root of each subtree should be smaller (or larger, depending on the first-order relation f) than the values of its children. We can do this by swapping the values of the new node and its parent as necessary until the heap property is satisfied.
Here's the SCHEME code for the heap-insert procedure:
(define (heap-insert f x H)
(cond
((null? H) (list x () ()))
((f x (car H))
(list x (caddr H) (heap-insert f (car H) (cadr H))))
(else
(list (car H) (cadr H) (heap-insert f x (caddr H))))))
Let's test this procedure using the examples you provided.
To create a min-heap, we use the "less than" function as our first-order relation:
(heap-insert < 100 (heap-insert < 10 (list)))
=> (10 () (100 () ()))
To create a max-heap, we use the "greater than" function as our first-order relation:
(heap-insert > 100 (heap-insert > 10 (list)))
=> (100 () (10 () ()))
Learn more about scheme procedure:
https://brainly.com/question/31385877
#SPJ11
Martin traveled at an average rate of 40 miles per hour for the first half of his trip. For the second half of his trip, he traveled at a rate of 60 miles per hour. How far did he travel in the 4-hour trip?
Answer:
Total distance traveled = 200 miles
Step-by-step explanation:
Total time taken for the trip = 4 hours
∴ The trip can be divided into two halves of 2 hours each.
1st half:
speed = 40 miles per hour
distance = speed × time
when time = 2 hours
distance = 40 × 2 = 80 miles
2nd half:
distance = speed × time
speed = 60 miles per hour
time = 2 hours
∴ distance = 60 × 2 = 120 miles
Combined distance traveled = 80 + 120 = 200 miles
Why can you not combine the 8a2 and 8a?
Answer:
you can't add or subtract numbers that don't have the same variable or the same exponent
Answer:
You cannot combine the terms \(8a^2\) and \(8a\) because they are not like terms, which are terms that consist of both the same power, and the same variable. Seen with the two terms given, they both share the same variable (\(a\)), but not the same power (\(2\)).
4. When two functions are combined (by addition, subtraction, multiplication, division, composition), does the domain of the new function get smaller or larger? Justify your answer.
When working with combined functions, we must exercise caution and pay attention to any values that could produce an undefined result.
When two functions are combined (by addition, subtraction, multiplication, division, composition), the domain of the new function can get smaller or remain the same, but it can never get larger.
What is a function?
A function is a mathematical concept used to link every member of a set with another.
A set of input values, known as the domain, is linked to a set of output values, known as the range, in a one-to-one manner.
In order for a combined function to exist, both the component functions must have overlapping domains.
Because the domain of the composite function is the set of all values that can be inputted into both the inner and outer functions, the domains of the two component functions must be combined to form the domain of the composite function.
This suggests that the domain of the new function will either stay the same or decrease.
To add to this, it is worth mentioning that the domain of the new function will be defined by any value(s) that cause the original functions to become undefined or illegal.
As a result, when working with combined functions, we must exercise caution and pay attention to any values that could produce an undefined result.
To know more about functions visit:
https://brainly.com/question/31062578
#SPJ11
use traces to sketch and identify the surface 4x^2-16y^2 z^2=16
The surface given by the equation \(4x^2 - 16y^2 + z^2 = 16\) is a hyperboloid of two sheets. It consists of two distinct surfaces that intersect along the z-axis and open upwards and downwards.
To identify the surface defined by the equation \(4x^2 - 16y^2 + z^2 = 16,\) we can analyze the equation and determine its geometric properties.
First, let's rewrite the equation in a standard form:
\(4x^2 - 16y^2 + z^2 = 16\)
By rearranging terms, we have:
\((x^2/4) - (y^2/1) + (z^2/16) = 1\)
Comparing this equation to the standard form of a hyperboloid, we can see that the x and z terms have positive coefficients, while the y term has a negative coefficient. This indicates that the surface is a hyperboloid of two sheets.
The trace of the surface can be obtained by setting one variable constant and examining the resulting equation. Let's consider the traces in the xz-plane (setting y = 0) and the xy-plane (setting z = 0).
When y = 0, the equation becomes:
\(4x^2 + z^2 = 16\)
This represents an ellipse in the xz-plane centered at the origin, with the major axis along the x-axis and the minor axis along the z-axis.
When z = 0, the equation becomes:
\(4x^2 - 16y^2 = 16\)
This represents a hyperbola in the xy-plane centered at the origin, with the branches opening along the x-axis and the y-axis.
Learn more about hyperbola here:
https://brainly.com/question/27799190
#SPJ11
identify the surface from the following equation \(4x^2-16y^2 z^2=16\)
a)
In a certain game of gambling a player tosses a fair coin; if it falls head he wins GH¢100.00 and if it falls tail he loses GH¢100.00. A player with GH¢800.00 tosses the coin six times. What is the probability that he will be left with GH¢600.00?
b)
Suppose the ages of children in a particular school have a normal distribution. It is found that 15% of the children are less than 12 years of age and 40% are more than 16.2 years of age. Determine the values of the mean and standard deviation of the distribution of the population
b) To determine the mean and standard deviation of the distribution of the population, we can use the z-score formula.
Given:
P(X < 12) = 0.15 (15% of the children are less than 12 years of age)
P(X > 16.2) = 0.40 (40% of the children are more than 16.2 years of age)
Using the standard normal distribution table, we can find the corresponding z-scores for these probabilities.
For P(X < 12):
Using the table, the z-score for a cumulative probability of 0.15 is approximately -1.04.
For P(X > 16.2):
Using the table, the z-score for a cumulative probability of 0.40 is approximately 0.25.
The z-score formula is given by:
z = (X - μ) / σ
where:
X is the value of the random variable,
μ is the mean of the distribution,
σ is the standard deviation of the distribution.
From the z-scores, we can set up the following equations:
-1.04 = (12 - μ) / σ (equation 1)
0.25 = (16.2 - μ) / σ (equation 2)
To solve for μ and σ, we can solve this system of equations.
First, let's solve equation 1 for σ:
σ = (12 - μ) / -1.04
Substitute this into equation 2:
0.25 = (16.2 - μ) / ((12 - μ) / -1.04)
Simplify and solve for μ:
0.25 = -1.04 * (16.2 - μ) / (12 - μ)
0.25 * (12 - μ) = -1.04 * (16.2 - μ)
3 - 0.25μ = -16.848 + 1.04μ
1.29μ = 19.848
μ ≈ 15.38
Now substitute the value of μ back into equation 1 to solve for σ:
-1.04 = (12 - 15.38) / σ
-1.04σ = -3.38
σ ≈ 3.25
Therefore, the mean (μ) of the distribution is approximately 15.38 years and the standard deviation (σ) is approximately 3.25 years.
Learn more about z-score formula here:
https://brainly.com/question/30557336
#SPJ11
John spent 80% of his money and saved the rest. Peter spent 75% of his money and saved the rest. If they saved the same amount of money, what is the ratio of John’s money to Peter’s money? Express your answer in its simplest form.
The ratio of John's money to Peter's money is 5/4. This means if John has a total amount of 5 then Peter will have a total of 4 as his amount.
Let's assume John has 'x' amount of money, Peter has 'y' amount of money, The money John saved is 'p' and the money Peter saved is 'q'
So,
p = x - 80x/100 (equation 1)
q = y - 75y/100 (equation 2)
According to the given question, the amount John saved is equal to the amount Peter saved. Hence, we can equate equations 1 and 2.
p = q
x- 80x/100 = y - 75y/100
x - 0.8x = y - 0.75y
0.2x = 0.25y
x = 0.25y/0.2
x/y = 0.25/0.2
x/y = 25/20
x/y = 5/4
Hence, the ratio of John's money to Peter's money is 5/4.
To learn more about Ratio:
https://brainly.com/question/13419413
let f be a function with derivative given by f'(x)=x^3-8x^2 3/
The derivative of the function f is f'(x) = x^3 - 8x^2, and the original function f can be obtained by integrating the derivative.
The given derivative, f'(x) = x^3 - 8x^2, represents the rate of change of the function f with respect to x. To find the original function f, we need to integrate the derivative.
Integrating the derivative f'(x), we obtain:
f(x) = ∫(x^3 - 8x^2) dx
To integrate x^3, we add 1 to the exponent and divide by the new exponent:
∫x^3 dx = (1/4)x^4 + C1, where C1 is the constant of integration.
To integrate -8x^2, we use the same process:
∫-8x^2 dx = (-8/3)x^3 + C2, where C2 is another constant of integration.
Combining the two results, we have:
f(x) = (1/4)x^4 - (8/3)x^3 + C, where C = C1 + C2 is the overall constant of integration.
Thus, the original function f, corresponding to the given derivative, is f(x) = (1/4)x^4 - (8/3)x^3 + C.
Learn more about Derivative click here :brainly.com/question/18722002
#SPJ11
How many unique 4 digits integers ( excluding leading zeros) are there that the sum of the 4 digits is 6?
There are 84 unique 4-digit integers (excluding leading zeros) whose sum of the digits is 6.
To find the number of unique 4-digit integers (excluding leading zeros) where the sum of the digits is 6, we can use a combinatorial approach.
Let's consider the four digits as four distinct positions: A, B, C, and D. The sum of the four digits is 6, so we need to distribute these six units among these four positions.
We can solve this problem using stars and bars. Imagine we have six stars (representing the six units) and three bars (representing the three dividers between the positions). The bars help us separate the units into four distinct positions.
For example, if we have the configuration "* | * * | * * | *," it represents the digits 1, 2, 2, and 1. The sum of these digits is 6.
The number of ways to arrange the six stars and three bars is given by the binomial coefficient (6 + 3 choose 3). Using the formula for combinations, we have:
(6 + 3) C 3 = (9 C 3) = 9! / (3! * (9 - 3)!) = 84.
So, there are 84 unique 4-digit integers (excluding leading zeros) whose sum of the digits is 6.
Learn more about formula for combinations here:
https://brainly.com/question/13090387
#SPJ11
Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6), and all the outcomes are equally likely. Find P(Odd number). Express your answer in exact form. P(odd number) Х 3 alle Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6), and all the outcomes are equally likely. Find P(less than 5). Write your answer as a fraction or whole number. illa P(less than 5) . Assume that a student is chosen at random from a class. Determine whether the events A and B are independent, mutually exclusive, or neither. A: The student is a man. B: The student belongs to a fraternity. The events A and B are independent. The events A and B are mutually exclusive. The events A and B are neither independent nor mutually exclusive.
When a fair die is rolled, the probability of getting an odd number is 1/2. The probability of rolling a number less than 5 is 4/6 or 2/3. In the context of randomly choosing a student from a class, the events A (student is a man) and B (student belongs to a fraternity) are neither independent nor mutually exclusive.
In the case of rolling a fair die, the sample space consists of six equally likely outcomes: {1, 2, 3, 4, 5, 6}. The favorable outcomes for getting an odd number are {1, 3, 5}, which means there are three odd numbers. Since the die is fair, each outcome has an equal chance of occurring, so the probability of getting an odd number is P(Odd number) = 3/6 = 1/2.
For finding the probability of rolling a number less than 5, we consider the favorable outcomes as {1, 2, 3, 4}. There are four favorable outcomes out of six possibilities, leading to a probability of P(less than 5) = 4/6 = 2/3.
Moving on to the events A and B, where A represents the event "the student is a man" and B represents the event "the student belongs to a fraternity." In this case, the events A and B are not independent, as the gender of the student may have an influence on their likelihood of being in a fraternity. At the same time, A and B are not mutually exclusive either since it is possible for a male student to belong to a fraternity. Therefore, the events A and B are neither independent nor mutually exclusive.
Learn more about odd number here: https://brainly.com/question/16898529
#SPJ11
Multiply. Express your answer in simplest form.
1
5
х
8
6
Answer:
1290
Step-by-step explanation:
15 x 86 = 1290
what is the location of earths center relative to a great circle defined by a pair of widely spaced flagpoles on earths surface
The location of earths center relative to a great circle defined by a pair of widely spaced flagpoles on earths surface is:
directly beneath the great circle defined by the two flagpoles.
The great circle defined by two flagpoles on the Earth's surface is a line that bisects the sphere of the Earth into two equal parts. This line passes directly through the center of the Earth, so the center of the Earth is located directly beneath the great circle.
The Earth is a three-dimensional object, so if two points on its surface are connected with a line, that line must pass directly through the center of the Earth.
This line is called a great circle because it is the largest possible circle that can be drawn on the surface of the Earth. The great circle formed by two widely spaced flagpoles on the Earth's surface serves as a reference point for determining the exact location of the Earth's center relative to the surface.
Learn more about earths surface:
brainly.com/question/9382932
#SPJ4
a shipment of 13 televisions sets contains 6 defective sets. a hotel purchases 6 of these televisions sets. what is the probability that the hotel receives at least one of the defective sets?
The probability that the hotel receives at least one of the defective sets is 99.59%
To find the probability that the hotel receives at least one defective set, we can use the concept of complementary probability.
The probability of the hotel receiving at least one defective set is equal to 1 minus the probability of the hotel receiving no defective sets.
The probability of the hotel receiving no defective sets can be calculated as the ratio of the number of ways to choose 6 non-defective sets out of the total number of ways to choose any 6 sets.
The total number of ways to choose 6 sets from the shipment of 13 sets is given by the binomial coefficient C(13, 6).
The number of ways to choose 6 non-defective sets from the remaining 13 - 6 = 7 non-defective sets is given by the binomial coefficient C(7, 6).
Therefore, the probability of the hotel receiving no defective sets is:
P(no defective sets) = C(7, 6) / C(13, 6)
To find the probability of receiving at least one defective set, we subtract this probability from 1:
P(at least one defective set) = 1 - P(no defective sets)
Calculating the values:
C(7, 6) = 7
C(13, 6) = 1716
P(no defective sets) = 7 / 1716
P(at least one defective set) = 1 - 7 / 1716
Therefore, the probability that the hotel receives at least one defective set is approximately:
P(at least one defective set) ≈ 1 - 0.0041 ≈ 0.9959 or 99.59%
To learn more about Probability from the link
brainly.com/question/13604758
#SPJ11
An inch is exactly 2.54 centimeters. Write an equation to convert the number of inches x to the corresponding length in centimeters.
Answer:
What's 2.54 cm in inches?
To convert cm to inches, divide your cm figure by 2.54 or multiply it by 0.3937. As an example, let's say you have a piece of wood measuring 50cm and you want to convert it into inches. To get your answer, divide your cm figure by 2.54. So, 50 ÷ 2.54 = 19.685 inches.
Step-by-step explanation:
Answer: 2.54x12 is 30.48
We can write:
2.54x
Where 'x' is the number of inches.
Plug in 12 for 'x':
2.54(12)
30.48
So 12 inches is approximately 30.48 centimeters.
properties of equality
Plssss hellllppppp meeeeeeee
The areas of section 1, 2 and 3 are 8 inches square, 80 inches square and 8 inches square respectively.
The area of the trapezium is 96 inches square.
What is the area of the trapezium?Section 1 and 2 are right triangles.
Area of a right triangle = 1/2 x base x height
Height = 8cm
Base = (14 - 10) / 2 = 2cm
Area of a right triangle = 1/2 x 2 x 8 = 8cm²
Section 3 is a rectangle.
Area of a rectangle = length x width
8 x 10 = 80 cm²
A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs
Area of a trapezoid = 1/2 x (sum of the lengths of the parallel sides) x height
= 1/2 x (10 + 14) x 8
1/2 x 24 x 8 = 96cm²
To learn more about trapeziums, please check: https://brainly.com/question/25044638
#SPJ1
Any help would be great thanks
Answer:
5x
Step-by-step explanation:
U should use a website called math.way, its much faster than brainly :P
Answer: 5x
Step-by-step explanation: Hope this helps. You just divide 20 by 4, x^2 by x, and y by y.
Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y=64(0.13)
For exponential decay, the percentage rate of decrease is given by 100 * (1 - b). So, in this case, the percentage rate of decrease is 100 * (1 - 0.13) = 100 * 0.87 = 87%.
The given function is an exponential function of the form y = ab^x, where a is the initial value and b is the growth factor. The growth factor in this case is 0.13, which is less than 1, so it represents decay, not growth.
To determine the percentage rate of decrease, we can find what percentage of the initial value remains after one time period. In this case, the value of y after one time period (x = 1) is:
y = 64(0.13)^1 = 64 * 0.13 = 8.32
So, the initial value of 64 has decreased to 8.32, or by 87.5%. This means the percentage rate of decrease is 87.5%.
For more such questions on Exponential function
https://brainly.com/question/2456547
#SPJ4
Find an equation of the plane. the plane through the points (0, 9, 9), (9, 0, 9), and (9, 9, 0)
The equation of the plane, the plane through the points (0, 9, 9), (9, 0, 9), and (9, 9, 0) is mathematically given as
X+Y+Z=18
What is the equation of the plane? the plane through the points (0, 9, 9), (9, 0, 9), and (9, 9, 0)?Solve' (0,9,9),(9,0,9),(9,9,0)
Parameters
\(\quad A=(0,9,9), \\ \quad B=(9,0,9)\\&c=(9,9,0)\\\)
Generally, the equation for AB is mathematically given as
\(&A B=\langle 9,-9,0\rangle\\&\overrightarrow{B C}=\langle 0,9,-9\rangle\\&\text { equation of Plane }\\&(\bar{r}-\overline{O A}) \cdot(\overline{A B} \times \overline{B C})=0\\\\&\overline{A B} \times \overline{B C}=\left|\begin{array}{ccc}i & j & i \\9 & -9 & 0 \\0 & 9 & -9\end{array}\right|\\\)
\(&=\{(B)-0)-\hat{j}(-81-0)+k(81-0)\\\\&\overline{A B} \times \overline{B C}=81 \hat{\imath}+81 \hat{\jmath}+81 k)\)
In conclusion, the equation of the plane
81(x-0)+81(y-9)+81(z-9)=0
X+Y+Z=18
Read more about the plane
https://brainly.com/question/1962726
#SPJ4
Let f(x) = x3. Estimate the values of f '(0), f '(1/2), f '(2), f '(3), and f '(4) by using a graphing device to zoom in on the graph of f.
The estimated values of f '(0), f '(1/2), f '(2), f '(3), and f '(4) are approximately 0, positive, greater, greater, and greater, respectively, based on the graph of f(x) = \(x^{3}\)
By analyzing the graph of f(x) = x^3, we can estimate the values of the derivatives f '(0), f '(1/2), f '(2), f '(3), and f '(4) by zooming in on the graph using a graphing device.
When x is close to 0, the slope of the graph of f(x) is also close to 0. Therefore, we can estimate that f '(0) is approximately 0.
Similarly, when x is close to 1/2, the slope of the graph of f(x) is positive and relatively steep. Hence, we can estimate that f '(1/2) is a positive value.
As x increases, the slope of the graph of f(x) becomes steeper. Therefore, we can estimate that f '(2) is greater than f '(1/2) and f '(3) is greater than f '(2).
Finally, as x gets larger, the slope of the graph of f(x) continues to increase but at a decreasing rate. Hence, we can estimate that f '(4) is greater than f '(3) but less than f '(2).
By zooming in on the graph of f(x) using a graphing device, we can obtain more accurate estimations for the values of f '(0), f '(1/2), f '(2), f '(3), and f '(4).
Learn more about derivatives here:
https://brainly.com/question/25324584
#SPJ11
Find the length of the third side. If necessary, round to the nearest tenth.
Ex. 900. x(t)= C0 + C1*sin(w*t+theta1) + C2*sin(2*w*t+theta2)
x(t)= A0 + A1*cos(w*t) + B1*sin(w*t) + A2*cos(2*w*t) + B2*sin(2*w*t)
A0= 2, A1=-8, B1=-7, A2=-2, B2=-7, w=600 rad/sec.
Express all angles between plus and minus 180 degrees.
Determine C0, C1, theta1 (deg), C2, theta2 (deg)
The final values of the angles are:
C0 = A0 = 2
C1 = B1 = -7
theta1 = 0 degrees
C2 = B2 = -7
theta2 = 0 degrees
Here, we have,
To determine the values of C0, C1, theta1 (in degrees), C2, and theta2 (in degrees), we need to match the given expressions for x(t) with the given values for A0, A1, B1, A2, B2, and w.
Comparing the expressions:
x(t) = C0 + C1sin(wt+theta1) + C2sin(2wt+theta2)
x(t) = A0 + A1cos(wt) + B1sin(wt) + A2cos(2wt) + B2sin(2w*t)
We can match the constant terms:
C0 = A0 = 2
For the terms involving sin(wt):
C1sin(wt+theta1) = B1sin(w*t)
We can equate the coefficients:
C1 = B1 = -7
For the terms involving sin(2wt):
C2sin(2wt+theta2) = B2sin(2wt)
Again, equating the coefficients:
C2 = B2 = -7
Now let's determine the angles theta1 and theta2 in degrees.
For the term C1sin(wt+theta1), we know that C1 = -7. Comparing this with the given expression, we have:
C1sin(wt+theta1) = -7sin(wt)
Since the coefficients match, we can equate the arguments inside the sin functions:
wt + theta1 = wt
This implies that theta1 = 0.
Similarly, for the term C2sin(2wt+theta2), we have C2 = -7. Comparing this with the given expression, we have:
C2sin(2wt+theta2) = -7sin(2w*t)
Again, equating the arguments inside the sin functions:
2wt + theta2 = 2wt
This implies that theta2 = 0.
Therefore, the final values are:
C0 = A0 = 2
C1 = B1 = -7
theta1 = 0 degrees
C2 = B2 = -7
theta2 = 0 degrees
To learn more on angle click:
brainly.com/question/28451077
#SPJ4
What is the slope of the line that passes through the points (8, -6) and (5,−1)? Write your answer in simplest form.
Answer:
-5/3
Step-by-step explanation:
To find the slope of the two points, use the formula: Y2-Y1/X2-X1
-1 is Y2, -6 is Y1, so that will be our numerator in this equation
5 is X2, 8 is X1, so that will be our denominator in this equation
So our equation becomes, -1+6/5-8 (Two negative signs create a positive so instead of -6 it becomes +6)
When we solve this, we get 5/-3
So our slope is -5/3
Hope this helps!
The slope of the line that passes through the points (8, -6) and (5,−1) is -5/3.
We have given that,
The slope of the line that passes through the points (8, -6) and (5,−1).
To determine the slope of the given points.
To find the slope of the two points,
What is the formula for the slope?use the formula: Y2-Y1/X2-X1
(8, -6)
Therefore, -1 is Y2, -6 is Y1,
So that will be our numerator in this equation
(5,−1)
5 is X2, 8 is X1, so that will be our denominator in this equation
So our equation becomes, -1+6/5-8 (Two negative signs create a positive so instead of -6 it becomes +6)
When we solve this, we get 5/-3
So our slope is -5/3.
Therefore the slope of the given point is -5/3.
To learn more about the slope visit:
https://brainly.com/question/1884491
#SPJ2
Barry can do a piece of work in 20 days Malaysia is 25% more efficient and then her barry. the number of days taken by Malaysia to do the same piece of work is?
Answer:
15days
Step-by-step explanation:
number of days Barry work = 20
If Malaysia is 25% efficient
Number of days less than Barry = 25% of 20
Number of days less than Barry = 0.25 * 20
Number of days less than Barry = 5
Number of days worked by Malaysia = 20 - 5
Number of days worked by Malaysia = 15days
Given: rt || sp, rq ≅ qp, rp bisects st at q prove: δrqt ≅ δpqs triangles r q t and p q s are connected at point q. lines r t and s p are parallel. the lengths of lines r q and q p are congruent. tamir is working to prove the triangles congruent using sas. after stating the given information, he states that tq ≅ qs by the definition of segment bisector. now he wants to state that ∠rqt ≅ ∠pqs. which reason should he use? alternate interior angles theorem corresponding angles theorem linear pair postulate vertical angles theorem
Answer:
(d) vertical angles theorem
Step-by-step explanation:
Vertical angles have a common vertex and are formed from opposite rays.
__
Angles RQT and PQS share vertex Q, Rays QR and QP are opposite, creating line RP. Rays QT and QS are opposite, creating line ST. Hence angles RQT and PQS are vertical angles. The vertical angles theorem says those angles are congruent.
if we have a sample with a mean of 4, what is the z-score of an observation of 4? group of answer choices -0.25 .55 0 not enough information to answer the question.
TheThe z-score of an observation of 4, with a sample mean of 4, is 0, indicating that the observation is at the same value as the mean.
The z-score measures how many standard deviations an observation is away from the mean. In this case, the sample mean is 4, and the observation value is also 4. To calculate the z-score, we use the formula: z = (x - μ) / σ, where x is the observation value, μ is the mean, and σ is the standard deviation.
Since the observation value (4) is equal to the mean (4), the numerator of the formula becomes 0. Dividing 0 by any number does not change its value. Therefore, the z-score of the observation value of 4, given a sample mean of 4, is 0.
Learn more about Standard deviation here: brainly.com/question/13498201
#SPJ11
What is the positive root of the equation x^2− 5x = 14?
The positive root of the quadratic equation x² - 5x = 14 is 7.
What is the positive root of the given equation?A quadratic equation in its standard form is expressed as;
ax² + bx + c = 0
Where x is the unknown
To solve for x, we use the quadratic formula
x = (-b±√(b² - 4ac)) / (2a)
Given the equation in the question.
x² - 5x = 14
Rearrange in standard form
x² - 5x - 14 = 0
Plug the values of a, b and c into the quadratic formula and solve for x.
x = (-b±√(b² - 4ac)) / (2a)
x = ( -(-5) ±√( (-5)² - ( 4 × 1 × -14) )) / (2 × 1)
x = ( 5 ±√( 25 - ( -56 ) )) / 2
x = ( 5 ±√( 25 + 56 )) / 2
x = ( 5 ±√( 81 )) / 2
x = ( 5 ± 9 )/2
x = ( 5 - 9 )/2, x = ( 5 + 9 )/2
x = (-4)/2, x = (14)/2
x = -2, x = 7
Therefore, the solutions are x = -2 and x = 7.
Learn more about quadratic equations here: brainly.com/question/1863222
#SPJ1
Help me please! Will mark brainlist!
Answer:
B...................
When a number is divided b 7, the quotient is 247 and the rimainder is 3,what is the number
The number, which on divided by 7 gives a quotient of 247 and a remainder of 3 is 1732. Computed using linear equations.
In the question, we are informed that a number when divided by 7, gives a quotient of 247 and a remainder of 3.
Assuming the number to be x.
We can say that x is our dividend, 7 is the divisor, 247 is the quotient, and 3 is the remainder.
The division algorithm equation is:
Dividend = Divisor*Quotient + Remainder,
Substituting values in this equation, we get a linear equation:
x = 7*247 + 3.
To solve for the unknown number x, we solve the equation as follows:
x = 7*247 + 3,
or, x = 1729 + 3,
or, x = 1732.
Thus, the number, which on divided by 7 gives a quotient of 247 and a remainder of 3 is 1732. Computed using linear equations.
Learn more about linear equations at
https://brainly.com/question/9507543
#SPJ4
whats 255x67777675456745675676745
Answer: 1.728330724e+25 thats what it said when I calcuated it.
which of the differential equations listed matches the slope field shown in the image.
We can conclude that the differential equation that matches the given slope field is dy/dx = y² - x², which is option 2.
The given slope field is comprised of lines that are almost vertical. This indicates that the slope of the tangent lines of the corresponding differential equation is very large. The only option that has a slope with such characteristics is option 2: dy/dx = y² - x².
To verify this, we can compute the slope of the tangent line for different values of x and y using the differential equation in option 2. For instance, when x=0 and y=1, we have dy/dx = 1² - 0² = 1. This means that the tangent line at (0,1) has a slope of 1, which is consistent with the slope field in the image.
On the other hand, the differential equations in options 1, 3, and 4 do not match the slope field. Option 1 has a negative slope in the region where the slope field is positive. Option 3 has a slope that oscillates between positive and negative values, which is not consistent with the almost vertical lines in the slope field. Finally, option 4 has a slope that is always positive, which is not consistent with the negative slopes in the slope field.
To learn more about differential equation click here
brainly.com/question/31583235
#SPJ11
Complete Question
Which of the following differential equations matches the slope field shown below?
dy/dx = y2-3
dy /dx = y² - x²
dy /dx = x cos(y)
dy /dx = y sin(x)
The differential equation that matches the slope field shown is
dy/dx = y² - 3.
This is because the slope of each line segment in the slope field depends only on the y-value of the corresponding point, and is given by y² - 3.
We can see this by noting that the slope of a tangent line to a solution curve passing through a point (x,y) is given by the value of dy/dx at that point.
So, if we draw many short tangent lines to solution curves at different points on the slope field, the slopes of those tangent lines should match the slopes of the line segments in the slope field.
In this case, we can see that the slope of each line segment in the slope field is steeper when y is larger, which matches the y² term in
dy/dx = y² - 3.
Additionally, the slope is negative when y is less than the square root of 3 and positive when y is greater than the square root of 3, which matches the -3 term in the differential equation.
Learn more about tangent line here : brainly.com/question/23416900
#SPJ11