The range of probability is:
c. zero to one
THE RANGE OF PROBABILITYProbability is a measure of the likelihood of an event occurring. It is a value that ranges between 0 and 1, where 0 represents an impossible event, and 1 represents a particular event. In other words, a probability of 0 means that an event will not happen, and a probability of 1 means that an event will happen. Any probability value between 0 and 1 can be written as a decimal or a percentage. For example, a probability of 0.5 can also be written as 50%.
It is important to note that probability values cannot be negative or greater than 1. In probability theory, events that are impossible to happen have a probability of 0, and events that are certain to happen have a probability of 1. For example, a probability value of 0.5 means a 50% chance of an event and a 50% chance of it not happening. Therefore, the range of probability is between 0 and 1, as any value outside of this range would not be a valid probability.
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Select the correct answer from each drop-down menu.
The first drop down box is - 20$, 30$, 40$, 50$
the second drop down box is - 15$, 30$, 45$, 60$
Since Ten students compared the amount (in dollars) they spent on books each week with the box plot showing the results, the median amount they spent each week is $50. The difference of the first and third quartiles of the data set is $45.
What is a box-and-whisker plot?In Mathematics, a box plot is also referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the box-and-whisker plot (box plot) shown above, the five-number summary for the given data set include the following:
Minimum = 5.First quartile = 20.Median = 50.Third quartile = 65.Maximum = 90.For the difference, we have:
Difference = Third quartile - First quartile
Difference = 65 - 20
Difference = 45.
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Solve the following system of equations by substitution.
x+2y=-5
-x-2y=5
Answer: The solution to the system of equations is x = -5 and y = 0.
Step-by-step explanation:
To solve this system of equations by substitution, you can start by solving one of the equations for one of the variables. For example, you can solve the first equation for x:
x + 2y = -5
x = -5 - 2y
Then, you can substitute this expression for x into the second equation to solve for y:
-(-5 - 2y) - 2y = 5
5 + 2y - 2y = 5
5 = 5
Now that you have solved for y, you can substitute this value back into one of the original equations to solve for x. If you substitute y = 0 back into the first equation, you get:
x + 2(0) = -5
x = -5
So, the solution to the system of equations is x = -5 and y = 0.
Solve for X.
log4 1/64 = x
Answer:
Step-by-step explanation:
0.00940718736
If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate (in cm/min) at which the diameter decreases when the diameter is 8 cm. (Round your answer to three decimal places.)
The surface area of a snowball decreases at a rate of 6 cm²/min. Its diameter decreases at rate of 0.119 cm/minute
The surface area of a ball is given by:
A = 4πr²
= πd²
Where:
A = surface area
r = radius of the ball
d = diameter of the ball
When the surface area decreases, so does the diameter.
To find the rate of change, take the derivative with respect to time (t)
A = πd²
dA/dt = 2πd dd/dt
Substitute dA/dt = 6 cm²/min, d = 8 cm:
6 = 2π x 8 dd/dt
dd/dt = 0.119 cm/minute
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For questions 19-27, use the ellipse defined by the following equation: 2(x+4)^2+3(y-1)^2=24.
19. write the equation of the ellipse in standard form.
20. What are the coordinates of the center?
21. What is the length of the major axis?
22. What is the length of the minor axis?
23. What is the sum of the focal radii?
24.What are the coordinates of the foci?
25. What are the coordinates of the vertices?
26. Find the eccentricity of the ellipse.
27. Draw a sketch of the ellipse.
PLEASE SHOW WORK!!
Answer:
[tex]\textsf{19.} \quad \dfrac{(x+4)^2}{12}+\dfrac{(y-1)^2}{8}=1[/tex]
[tex]\textsf{20.} \quad \textsf{Center}: \;\;(-4, 1)[/tex]
[tex]\textsf{21.} \quad \textsf{Major axis}:\;\;4\sqrt{3}[/tex]
[tex]\textsf{22.} \quad \textsf{Minor axis}:\;\;4\sqrt{2}[/tex]
[tex]\textsf{23.} \quad \textsf{Sum of the focal radii}:\;\;4 \sqrt{3}[/tex]
[tex]\textsf{24.} \quad \textsf{Foci}:\;\;(-6, 1)\;\; \textsf{and}\;\;(-2,1)[/tex]
[tex]\begin{aligned}\textsf{25.} \quad &\textsf{Vertices}:\;\;(-4-2\sqrt{3}, 1) \;\; \textsf{and}\;\; (-4+2\sqrt{3}, 1)\\ &\textsf{Co-vertices}:\;\;(-4, 1-2\sqrt{2}) \;\; \textsf{and}\;\; (-4, 1+2\sqrt{2})\end{aligned}[/tex]
[tex]\textsf{26.} \quad \textsf{Eccentricity}\;\;\dfrac{\sqrt{3}}{3}[/tex]
27. See attachment.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{General equation of an ellipse}\\\\$\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$\\\end{minipage}}[/tex]
Given equation:
[tex]2(x+4)^2+3(y-1)^2=24[/tex]
To write the equation of the ellipse in standard form, divide both sides by 24 so that the right side of the equation is equal to one:
[tex]\implies \dfrac{2(x+4)^2}{24}+\dfrac{3(y-1)^2}{24}=\dfrac{24}{24}[/tex]
[tex]\implies \dfrac{(x+4)^2}{12}+\dfrac{(y-1)^2}{8}=1[/tex]
Therefore:
[tex]h = -4[/tex][tex]k = 1[/tex][tex]a^2 = 12 \implies a=2\sqrt{3}[/tex][tex]b^2 = 8 \implies b=2 \sqrt{2}[/tex]The center of the ellipse is (h, k).
Therefore, the coordinates of the center are (-4, 1).
As a > b, the ellipse is horizontal, so 2a is the major axis and 2b is the minor axis. Therefore:
Major axis = 2 × 2√3 = 4√3Minor axis = 2 × 2√2 = 4√2The focal radius is the distance from a point on the ellipse to a focus.
The sum of the focal radii is equal to the length of the major axis.
Therefore, the sum of the focal radii is 4√3.
As a > b, the coordinates of the foci are (h±c, k).
As c² = a² - b², first find the value of c:
[tex]\implies c^2=12-8[/tex]
[tex]\implies c=\sqrt{4}=2[/tex]
Therefore, the coordinates of the foci are:
(-4+2, 1) = (-2, 1)(-4-2, 1) = (-6, 1)As a > b, the coordinates of the vertices are (h±a, k):
(-4-2√3, 1) and (-4+2√3, 1)and the coordinates of the co-vertices are (h, k±b):
(-4, 1-2√2) and (-4, 1+2√2)The eccentricity of the ellipse is:
[tex]\implies e=\dfrac{c}{a}=\dfrac{2}{2\sqrt{3}}=\dfrac{\sqrt{3}}{3}[/tex]
________ are measures that marketers can use to watch the performance of their marketing efforts.
Answer:
Step-by-step explanation:
-10[tex]-10\sqrt{x} 11-11\sqrt{x} 11\\[/tex]
The radical would to become -10 -21√x11.
What are like radicals?We define the term like radicals as the kind of radicals that have the same kind of values inside the radical sign. This implies that they have similar values in the square root sign. When this is the case, we can be able to handle the radical as an algebraic expression and then simplify it accordingly.
In this case, we would have that;
-10 -10√x11 - 11√x11
-10 -21√x11
This is now the simplified form of the expression that has been shown here.
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The trend line passes through the points (0,428) and (10,332). Write the equation of a trend line for the data shown in the graph. After how many minutes is the balloon at an altitude of 370.4 feet above sea level?
The time when the altitude of the balloon is 370.4 feet is 6 minutes.
What is slope?The slope is the rate of change of the y-axis with respect to the x-axis.
The equation of a line in slope-intercept form is y = mx + b, where
slope = m and y-intercept = b.
We know the greater the absolute value of a slope the steeper is its graph or the rate of change is large.
We know The slope of the line is (y₂ - y₁)/(x₂ - x₁).
Therefore, The slope of the line passing through the points
(0,428) and (10,332) is,
Slope(m) = (332 - 428)/(10 - 0).
Slope(m) = - 9.6, So the balloon is descending at a rate of - 9.6 feet per minute.
Now, To obtain the y-intercept.
428 = - 9.6(0) + b.
b = 428.
Therefore, The equation of the required line is,
y = - 9.6x + 428, where y is the altitude and x is the number of minutes.
So, The time in minutes when the altitude of the balloon is 370.4 feet is,
370.4 = - 9.6x + 428.
- 9.6x = - 57.6.
x = 57.6/9.6.
x = 6 minutes.
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Classify the following Graphs as "(1) Function" or "(2) Not a Function"
HELPPP!!!!
1.
Function
2.
Not a function
The relations in this problem are classified as functions or not as follows:
1. Not a function.
2. Function.
3. Not a function.
4. Function.
5. Function.
When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output.
Hence, a graph will represent a function if, and only if, it contains no vertically aligned points, that is, if there isn't a vertical line that will cross the graph of the relation in more than one point.
Then the graphs that are not functions in this problem are given as follows:
Graph 1, as there are points inside the pentagon, such as x = 2, for which the vertical line would cross the pentagon twice.Graph 3, as there are two dots for x = 1, which are y = -2 and y = 3.More can be learned about relations and functions at https://brainly.com/question/29701528
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The ratio of the sides of two similar regular octagons is 3:11. If the measure of each side of the larger octagon is 33 cm, then the measure of each side of the smaller octagon is Ci. , Enter a number answer only
The measure of each side of the smaller octagon is 9cm. Therefore, Enter 9
How find the measure of each side of the smaller octagon?
Given that:
The ratio of the sides of two similar regular octagons is 3:11.
The measure of each side of the larger octagon is 33
The measure of each side of the smaller octagon is Ci
we can write that:
smaller octagon : larger octagon = 3 : 11
smaller octagon / larger octagon = 3 / 11
smaller octagon / 33 = 3 / 11
smaller octagon = (3 × 33)/11 = 99/11 = 9 cm
Thus, Ci = 9 cm
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Given: ∆FGH~∆JKH. List all congruent angles and write a proportion that relates the corresponding sides.
The congruent angles are - ∠GHF ~ ∠KHJ, ∠GFH ~ ∠KJH and ∠FGH ~ ∠JKH.
The proportion that relates corresponding sides are -
HG/HK = GF/JK = HF/HJ
What is congruency?
Congruent in geometry refers to being the same size and shape. Congruence can be used with figures, angles, and line segments. If any two line segments are equal in length, they are said to be congruent.
It is given that ΔFGH is congruent to ΔJKH.
If two triangles are similar.
Then it is known that -
HG/HK = GF/JK = HF/HJ
And all the corresponding angles are equal.
Angles that are congruent to each other is -
Angle GHF ~ KHJ as they are vertically opposite angles.
Angle GFH ~ KJH as they are corresponding angles.
Angle FGH ~ JKH as they are corresponding angles.
The sides which are corresponding and equal are -
HG/HK = GF/JK = HF/HJ
So, GF = JK
GH = HK
FH = HJ
Therefore, all the corresponding angles and sides are listed.
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What’s the surface area of a sphere if the radius is is 15cm?
Answer :
2827.43 cm²
Step-by-step explanation:
1/5/2023
7:20PM
Answer:
2827.4 cm²
Step-by-step explanation:
A = 4πr²
A = 4π(15)² = 2827.4 cm²
Which is the largest fraction?
7/8
8/10
12/15
3/4​
In the figure below find the exact value of z (do not approximate your answer)
z = √35 is the ratio of the long leg to the hypotenuse and the exact value of z are shown in the diagram below.
what is triangle ?Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners. The points where the three sides meet are known as the triangle's corners.
given
The ratios of the long leg to hypotenuse are the same for all right triangles since they are similar:
z/7 = 5/z
When z2 equals 35, multiply by 7z.
z = √35
z = √35 is the ratio of the long leg to the hypotenuse and the exact value of z are shown in the diagram below.
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Arleen has a gift card for a local lawn and garden store. She uses the gift card to rent a tiller for 4 days. It cost $35 per day to rent the tiller. She also buys a rake for $9.A. Find the change to the value on the gift card. (Question #1)
B. The original amount on the gift card was $200. Does Arleen have enough to buy a Wheelbarrow for $50?
Answer:
A. The total change in the value on the gift card will be -149$
B. Yes, Arleen has enough to buy a Wheelbarrow for 50$
Step-by-step explanation:
A.
To calculate the total change in value of the gift card we need to sum all expenses.
4 days of rental + cost of the rake = total change in value
(4 * -35$) - 9$ = -149$
B.
If the value of the gift card was 200$, then we have to subtract the expenses from the gift card value and check whether we have enough to buy a Wheelbarrow.
200$ - 149$ = 51$ > 50$
What is the height in feet geometry
The height of the zip line is 203 feet.
What are trigonometric functions?Trigonometric functions are required when the value of an unknown side or internal angle of a right triangle are to be determined. Some of the basic functions are: sine, cosine, tangent etc.
Tangent of an angle is the ration of the opposite side to the angle and the adjacent side.
Tan θ = opposite/ adjacent
To determine the height of the zip line required in the question, we have;
let the height be represented by h,
Tan θ = opposite/ adjacent
Tan 10 = h/ 1150
h = Tan 10 * 1150
= 0.1763*1150
= 202.745
h = 202.8 feet
The height of the zip line is 203 feet.
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A four-part spinner is spun once. spinner with four parts labeled q, r, s, and t list the sample space for the experiment. s = {q, r, r, t} s = {q, r, s, t} s = {r, a, t} s = {s, q, q}
The sample space for the experiment of spinning a four-part spinner is the set of all possible outcomes of the experiment.
In this case, the sample space would be: s = {q, r, s, t}
This means that the possible outcomes of the experiment are q, r, s, and t. Each of these outcomes is equally likely to occur when the spinner is spun.
Option s = {q, r, r, t} is incorrect because it includes two occurrences of the outcome r, which is not possible in this experiment.
Option s = {r, a, t} is incorrect because it includes the outcome a, which is not part of the sample space.
Option s = {s, q, q} is incorrect because it includes two occurrences of the outcome q, which is not possible in this experiment.
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what is the slope of (-4,-9) and (4,-9)
Answer: m (slope) = 0
Step-by-step explanation:
The slope can be found through the equation (y2-y1)/(x2-x1)
(-4, -9) and (4, -9) can be: (x1, y1) and (x2, y2)
We can plug the variables into the formula above:
(-9-(-9))/(4-(-4) = 0/8
The slope is 0.
Answer: slope=0
Step-by-step explanation:
usually slopes are found by taking
change in y
-----------------
change in x
but in all horizontal lines (matching y values, -9 in this case) the line has no slope as it doesn't go up or down.
What is the volume of each right triangular prism
The volume of the right triangular prisms are 1000cm³ and 14, 400mm³ respectively
How to determine the volume of the prismsThe formula for determining the volume of a right triangular prism is expressed as;
V = 1/2 bhl
Where;
V is the volume of the prismb is the base of the prismh is the height of the prisml is the length of the prismNow, substitute the values, we have;
Volume, V = 1/2 × 25 × 20 × 4
Multiply the values
Volume, V = 2000/2
Divide through
Volume = 1000cm³
For the second prism;
Volume = 1/2 × 16 × 50 ×36
Volume = 14, 400mm³
Hence, the values are 1000cm³ and 14, 400mm³
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5. A shoe store employee sets up a display by placing shoeboxes in 10 stacks. The numbers of boxes in each stack are 5, 7, 9, 11, 13, 10, 9, 8, 7, and 5. a. What is the mean of the number of boxes in a stack? T b. Find the median of the number of boxes in a stack. c. If one box is removed from each stack, how will the mean and median be affected?
Answer:
a) 8.4
b) 8.5
c) The mean and median will be one less (7.4 and 7.5).
Step-by-step explanation:
Given number of boxes in each stack:
5, 7, 9, 11, 13, 10, 9, 8, 7, 5Part (a)To find the mean of the number of boxes in a stack, divide the total number of boxes by the number of stacks:
[tex]\implies \sf Mean=\dfrac{5+7+9+ 11+13+ 10+9+ 8+ 7+5}{10}=\dfrac{84}{10}=8.4[/tex]
Part (b)The median is the middle value when all data values are placed in order of size.
To find the median of the number of boxes in a stack, first place the numbers in order of size:
5, 5, 7, 7, 8, 9, 9, 10, 11, 13As there is an even number of boxes (10), the median is the mean of the two middle values:
[tex]\implies \sf Median=\dfrac{8+9}{2}=\dfrac{17}{2}=8.5[/tex]
Part (c)If one box is removed from each stack, the total number of boxes is 10 less than before. Therefore:
[tex]\implies \sf Mean=\dfrac{84-10}{10}=\dfrac{74}{10}=7.4[/tex]
The number of boxes in each stack will be (in order of size):
4, 4, 6, 6, 7, 8, 8, 9, 10, 12Therefore, the median is 7.5.
So, if one box is removed from each stack:
The mean decreases by 1.The median decreases by 1.PLEASE HELP!!!
Corine wants to take guitar lessons. She called two different music schools to compare their prices.
The cost of music lessons at Sweet Sounds Music School can be represented by the equation y=20x, where x is the number of hours of lessons taken, and y is the total cost.
She displayed the prices of the first five hours of guitar lessons at Mozart's Music House, which charges a registration fee, in the following graph.
Select all statements that are true about the situation represented by the functions.
A. The registration fee at Sweet Sounds Music School is $20.
B. There is no registration fee at Sweet Sounds Music School.
C. The registration fee at Mozart's Music House is $25.
D. The registration fee at Sweet Sounds Music School is greater than the registration fee at Mozart's Music House.
E. There is no registration fee at Mozart's Music House.
Triangle Inequalities
The inequality that represents the third side of the given triangle is 3 < x <19.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given, The side length of the triangle are 8, 11, and x.
From the General property of the triangle
The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is more than the length of the 1/3 side. In the same way, the difference between the various 2 sides of a triangle is a great deal much less than the length of the 3rd side.
Since the sum of two sides should be greater than the third
x < 8 + 11
=> x < 19
Since the difference between the two sides of a triangle is less than the length of the third side.
=> x > 11 - 8
=> x > 3
therefore, The inequality that represents the third side of the given triangle is 3 < x <19.
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Consider this quotient (x^3-8x+6) / (x^2-2x+1)
The expression in the form of q(x) + r(x) / b(x) is
(x + 2) + (-13x + 4) / (x² + 2x + 1).
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
(x³ - 8x + 6) ÷ (x² + 2x + 1)
Using the long division.
x² + 2x + 1 ) x³ - 8x + 6 ( x + 2
x³ + 2x² + x
(-) (-) (-)
2x² - 9x + 6
2x² + 4x + 2
(-) (-) (-)
-13x + 4
Quotient = x + 2
Remainder = -13x + 4
Thus,
Quotient + Remainder / Divisor
= (x + 2) + (-13x + 4) / (x² + 2x + 1).
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The acceleration of an object moving through the air at a high
speed v near the earth's surface is in a particular case 32-(v^2)/8
ft. per .sec. per sec. If such an object falls to the ground in one minute from
rest, find the height from which it fall
The object falls from 115200 ft above the ground.
What is the quadratic equation?
A quadratic equation is any algebraic equation of the highest degree. The standard form of the quadratic equation in a variable is ax² + bx + c = 0, where a and b are coefficients, are constant, and is a non-zero numbers.
The acceleration of the object is given by the equation a = 32 - (v^2)/8 ft/s^2. Since the object is initially at rest, we can assume that v = 0 at the start of its fall.
To find the height from which the object fell, we need to use the equations of motion for uniformly accelerated motion. The equation for the distance traveled by an object under constant acceleration is:
d = 1/2 at^2 + vt + d0
where d is the distance traveled, a is the acceleration, t is the time, and d0 is the initial distance (which is zero in this case, since the object is initially at rest).
We know that the object is falling for one minute, and we can convert that to seconds by multiplying by 60. The acceleration is given by a = 32 - (v^2)/8, we know that v = 0, so a = 32 - (0^2)/8 = 32 ft/s^2.
Plugging in the values, we get:
d = 1/2 (32 ft/s^2) (60 s)^2
d = 32 x (3600)
d = 115,200 ft
This is the distance that the object fell. To find the height from which it fell, we simply have to take the distance and negate it.
So the height from which the object fell is:
-115,200 ft
Hence, the object falls from 115200 ft above the ground.
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b Given that C = n = n( / / T (1 + $²3) k 25 i make S the subject of the formula ii find the value of S when C = 6, n = 8, T = 1 and k = 18.
The value of the variable, S when C = 6, n = 8, T = 1 and k = 18 is 1. 036
How to determine the valueTo make a variable the subject of formula, we have to make it stand alone on one end of the equality sign.
From the information given, we have the equation as;
C = n/Tk(1 + S²)
Now, let's cross multiply to make 'S' the subject of formula, we get;
C× Tk(1 + S²) = n
Divide both sides by the coefficient of S
1 + S² = n/CTk
collect '1' to the other side;
S² = n/CTk + 1
Take the square root of both sides
S = [tex]\sqrt{\frac{n}{CTk} + 1 }[/tex]
Now, substitute the values
S = [tex]\sqrt{\frac{8}{6* 1 * 18} + 1 }[/tex]
Multiply the values
S = [tex]\sqrt{1. 074}[/tex]
S = 1. 036
Thus, the value is 1. 036
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y+2x-3+4x squared+3x-5y
The required solution to the given expression is 4x² + 5x - 4y - 3.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The expression is given in the question, as follows:
y + 2x - 3 + 4x² + 3x - 5y
We have to determine the solution to the given expression.
As per the question, we have
y + 2x - 3 + 4x² + 3x - 5y
Rearrange the variables in the above expression,
4x² + 2x + 3x + y - 5y - 3
Combine likewise terms in the expression,
4x² + 5x - 4y - 3
Thus, the required solution is 4x² + 5x - 4y - 3.
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The question seems to be incomplete the correct question would be:
Find the solution to the below expression.
y + 2x - 3 + 4x² + 3x - 5y
I’m a 10th grade geometry student and I can’t figure these out and these are due by noon tomorrow, please help me out I need help
Answer:
See the explanation below.
Step-by-step explanation:
17) 40=x+45
x = -5
18) 70 = -2 + 8x
72 = 8x
x = 9
19) 19x - 3 = 17x + 11
2x = 14
x = 7
20) -2 + 14x = 12x + 14
2x = 16
x = 8
21) 11x - 3 + 18x + 9 = 180
29x + 6 = 180
29x = 174
x = 6
22) 6x - 4 + 14x + 4 = 180
20x = 180
x = 9
23) 68 + x + x + 128 = 180
196 + 2x = 180
2x = -16
x = -8
24) x + 87 + x + 107 = 180
2x + 194 = 180
2x = -14
x = -7
25) 70 + 12x - 10 = 180
60 + 12x = 180
12x = 120
x = 10
How many comparisons are required to order an array of 5 elements using the selection sort?
Total comparisons required to order an array of 5 elements using the selection sort =29
Selection sort finds the smallest element and swaps it into the first position. The, from the remaining N-1 elements after the first one (which we know is the smallest), it finds the next smallest and swaps it into the 2nd position. And so on.
To find the smallest element from a group of N elements takes N-1 comparisons. Basically, compare item 1 to 2, remember the smallest. Compare item 3 to smallest and remember which ever is smaller, and so on. You end up doing 1 comparison for every element from 2 through N.
We have to find the smallest element N-1 times*, but each time we have a smaller list to look through.
So let’s turn to an array of 5 elements. To find the smallest element will take4 comparisons. Next time through we do 3 comparisons and so on:
Total comparisons = 4+3+2+1 = 10
For N elements it takes 1+2+3+…+N-1 = (N-1)N/2 comparisons.
You don’t have to run through an Nth time because after sorting N-1 items, the Nth item must be in the correct position already. Or, if you like, the Nth loop does N-N=0 comparisons so we can ignore it.
only counting comparisons of elements in the array. A loop is going to have to do a comparison of the loop variable to the length of the array every time it repeats. Usually those comparisons are disregarded because, unless the elements of the array are integers, the item comparisons take considerably more time than the index comparisons, and any way, it won’t increase the asymptotic complexity, only the constant of proportionality. If you want to count the index comparisons, you have one for every item comparison (because the inner loop does one item comparison per loop iteration) + 1 for each end of the inner loop (a loop that runs X times does X+1 comparisons) and then another N-1 for the outer loop + 1 for the loop end. For N = 5 there will be 10 + 4 + 4 + 1 = 19 index comparisons and 10 + 19 = 29 total comparisons.
total comparisons required to order an array of 5 elements using the selection sort =29
of course, if you write this in a language like java that does array bounds checking, you’ll add two more comparisons for each array access. And the compare function is probably a function call, so you’re increasing stack depth which potentially adds comparisons to make sure that doesn’t overflow… you know what? I think I’ll just stop there.
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Wright the equation of the line through the point (7,8) and (-12, -11)
A) y= x +15
B) y= -x -1
C) y =x +1
D) y = -x -23
The equation of the line through the point (7,8) and (-12, -11) is y = x + 1. Thus, option c is correct.
What is linear equation?Linear equations are characterised by variables with a power of one. Where ax+b = 0 is one example with one variable, where a and b are real numbers and x is the variable.
Linear algebra covers a wide range of topics. Applications, abstract, and numerical methods are all part of its range. Numerous other disciplines, including fractal geometry, differential equations, difference equations, relativity, archaeology, and demography, depend on linear algebra.
Using the slope formula, we can find the equation of the line [passing through the point (7,8) and (-12, -11) i.e.
y₂ - y₁ = m(x₂ - x₁)
Putting the values
-11 - 8 = m(-12 - 7)
-19 = m(-19)
m = -19/-19
m = 1
Now, we have slope so find the line
y - 8 = 1(x - 7)
y = x - 7 + 8
y = x + 1
y - (-11)= 1(x - (-12))
y + 11= x 12
y = x + 1
Thus, The equation of the line through the point (7,8) and (-12, -11) is y = x + 1.
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6 balls for $4.00 or 4 balls for $2.50. What's the better deal?
Answer:
4 balls for $2.50
Step-by-step explanation:
If 4 balls=$2.50
Then,$2.50+2.50= $6.25
$6.25 for 8 balls
