A time complexity cheat sheet is a reference guide that provides an overview of the time complexity of common algorithms and operations in computer science.
Time complexity is a measure of the amount of time an algorithm takes to solve a problem, expressed in terms of the input size of the problem. It is typically denoted using Big O notation, which provides an upper bound on the amount of time an algorithm takes.
A time complexity cheat sheet can be useful for quickly determining the time complexity of an algorithm or operation, as well as for comparing the time complexity of different algorithms. Some common time complexities that may be included in a time complexity cheat sheet are:
O(1): Constant time complexity. An algorithm with O(1) time complexity takes a fixed amount of time, regardless of the input size.
O(log n): Logarithmic time complexity. An algorithm with O(log n) time complexity takes time proportional to the logarithm of the input size.
O(n): Linear time complexity. An algorithm with O(n) time complexity takes time proportional to the input size.
O(n log n): Log-linear time complexity. An algorithm with O(n log n) time complexity takes time proportional to the input size multiplied by the logarithm of the input size.
O(n^2): Quadratic time complexity. An algorithm with O(n^2) time complexity takes time proportional to the square of the input size.
O(2^n): Exponential time complexity. An algorithm with O(2^n) time complexity takes time proportional to two raised to the power of the input size.
Other time complexities may also be included, depending on the complexity of the algorithm or operation. A time complexity cheat sheet can be a helpful tool for understanding and analyzing algorithms, but it is important to remember that time complexity is not the only factor to consider when evaluating the performance of an algorithm.
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Why was algebre made?
Answer: to solve a problem and make a solution easier to find.
Algebra was made to solve mathematical problems that involve unknown quantities.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Algebra was developed to solve mathematical problems that involve unknown quantities.
It provides a way to represent and manipulate mathematical equations using symbols and rules, making it easier to solve complex problems and answer questions about relationships between variables.
The earliest known algebraic text is the "Al-jabr wa'l muqabalah" by the Persian mathematician Al-Khwarizmi, which was written in the 9th century.
Hence, Algebra was made to solve mathematical problems that involve unknown quantities.
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A study showed 64% of those surveyed prefer coke to pepesi. If 275 people were surveyed how many said they prefer coke
Out of the 275 people surveyed, 176 prefer Coke to Pepsi. It took 64% of the total participants.
According to the information provided in the question, 64% of those surveyed prefer Coke to Pepsi. To find out how many people prefer Coke out of the 275 people surveyed, we need to multiply the percentage by the total number of people surveyed.
We can do this by following these steps:
Step 1: Convert the percentage to a decimal by dividing it by 100. In this case, 64% becomes 0.64.
Step 2: Multiply the decimal by the total number of people surveyed. In this case, 0.64 x 275 = 176.
Step 3: The result is the number of people who prefer Coke. In this case, 176 people prefer Coke.
Therefore, out of the 275 people surveyed, 176 of them prefer Coke to Pepsi.
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Convert 130mm to inches
The value of 130 mm is 5.118 inches and both are unit of measurement of length.
To convert 130mm to inches, simply divide 130 by 25.4 which is the conversion factor , which is the number of mm in an inch.
This will give you 5.118 inches. Alternatively, you can use an online converter or look up a conversion chart to find the exact conversion. 130mm is a common size for wheel bolt patterns, and the conversion to inches is 4 x 5.118, or 4 x 4 7/8.
This is important to know when purchasing wheels, as they must have the correct fitment for the vehicle they are being installed on.
Additionally, many measurements in the automotive industry are given in metric measurements, so it is important to be familiar with the conversion between metric and imperial units.
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Determine which of the explicit rules represent the table of values. Select all that apply.
Answer:
A. f(x) = 0.8 (5)ˣ
Step-by-step explanation:
This is the only one that fits the x and f(x) values
x 0.8 (5)ˣ
------------------------------------------------------
1 0.8 x 5¹ = 0.8 x 5 = 4
2 0.8 x 5² = 0.8 x 25 = 20
3 0.8 x 5³ = 0.8 x 125 = 100
4 0.8 x 5⁴= 0.8 x 625 = 500
The others will not eve yield proper results for x = 1, you can try them out
d) The cheetah traveled 1.75 times faster for the first 8 minutes than it did for the second 8 minutes. Was the distance traveled during the first 8 minutes 1.75 times greater than the distance traveled during the second 8 minutes
The distance traveled in the first 8 minutes is 1.75 d2
What is speed?Speed is the rate of change of distance with time. it is a scalar quantity and it is measured in meter per second.
speed = distance /time
time = distance /speed
total time = 16
represent u by the first 8minutes and v by the second 8 minutes
u = 1.75v
8 = d1/1.75v
8 = d2/v
d1/1.75v = d2/v
d1 ×v = 1.75v × d2
d1 = 1.75d2
therefore ;
d1 = 1.75d2
where d1 and d2 are the distances for the first 8 minutes and second 8minutes respectively.
therefore the distance in the first 8minutes is 1.75 times greater than the second 8 minutes
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
The focus of a parabola is (0,-2). The directrix is the line y = 0. What is the equation of the parabola in vertex form?
in the equation y= 1/4p(x-k)² +h, the value of p is______.
The vertex of the parabola is the point (___,___)
The equation of this parabola in vertex form is y =_____2²-1
The equation of this parabola in vertex form is y = 1/4x^2 - 1.
Describe Parabola?A parabola is a type of curve that occurs in nature, science, and mathematics. It is a symmetrical, U-shaped curve that is created by the intersection of a plane and a right circular cone. The shape of the curve is defined by its equation, which can be expressed in standard form as y = ax^2 + bx + c. In this equation, the coefficient a determines the shape of the parabola, with a positive value creating an upward-opening parabola and a negative value creating a downward-opening parabola.
The focus of a parabola is (0,-2). The directrix is the line y = 0. What is the equation of the parabola in vertex form?The vertex of a parabola is equidistant from the focus and the directrix. Since the directrix is the line y = 0, which is the x-axis, the vertex is halfway between the focus and the x-axis, at (0, -1).
The distance from the vertex to the focus is p, which is also the distance from the vertex to the directrix. Since the directrix is the line y = 0, the distance from the vertex to the directrix is simply the y-coordinate of the vertex, which is 1.
Therefore, p = 1, and the equation of the parabola in vertex form is:
y = 1/4p(x - h)^2 + k = 1/4(1)(x - 0)^2 - 1 = 1/4x^2 - 1
in the equation y= 1/4p(x-k)² +h, the value of p is 1.
The vertex of the parabola is the point (0, -1).
The equation of this parabola in vertex form is y = 1/4x^2 - 1.
To solve 2²-1:
2² - 1 = 4 - 1 = 3.
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Answer:
The guy above is somewhat right.
Hope this helps!
Step-by-step explanation:
In the figure, QR≅ST. What is the length of QR ?
There are 2 chords inside the circle parallel to each other on opposite sides of the circle. Chord QR=7x+3 and Chord ST=5x+25
How do you find the derivative of the function using the definition of derivative f(x)=10?
The derivative of of f(x) = 10 is 0
The derivative of a function is the measure of the rate of change of the function. They are fundamental to the solution of problems in calculus and differential equations.
Here the function is not changing as 10 is a constant. So, if f(x) = c where c is a constant then f'(x) = 0 as the derivative of a constant is always zero.
Mathematically:
d(f(x))/dx = [tex]\lim_{h \to 0}[/tex] (f(x+h) - f(x))/h
There is no x to substitute for x + h so no difference is noticed:
[tex]\lim_{h \to 0}[/tex] (f(x+h) - f(x))/h = [tex]\lim_{h \to 0}[/tex] (10 - 10)/h = 0
Hence, the derivative of f(x) = 10 is 0
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(Systems of Linear Equations MC)
Which point is a solution to the system of linear equations?
y = -x + 6
x - 3y = 18?
O (9, -3)
(6, 1)
O (1,3)
O(-1,6)
The solution to the system of linear equations is: A. (9, -3)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that the system of equation as;
y = -x + 6
x - 3y = 18
Substitute y = -x + 6 into eqn. 2.
x - 3(-x + 6) = 18
x + 3x - 18 = 18
4x = 36
x = 9
Substitute x = 9 into Eqn. 1 to find y
y = -x + 6
y = -9 + 6
y = -3
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A significance test about a proportion is conducted using a significance level of 0.05. The sample statistic is 0.12. The p-value is 0.03.
a) If H0 were true, for what probability of a Type I error was the test designed?
b) What conclusion (reject or fail to reject) would you make for this test?
c) If this test resulted in a decision error, what type of error was it?
With a significance test about a proportion is conducted using a significance level of 0.05, sample statistic is 0.12, p-value is 0.03.
a) If H0 were true, the test was designed for a probability of a Type I error of 0.05.
b) Based on the p-value of 0.03, you would reject the null hypothesis.
c) If this test resulted in a decision error, it would be a Type II error.
a) If H0 were true, the test was designed for a probability of a Type I error of 0.05. When conducting a hypothesis test, we set a significance level, often denoted by alpha (α), to control the probability of making a Type I error.
A common value for alpha is 0.05, which means that we are willing to accept a 5% chance of making a Type I error.
b) Based on the p-value of 0.03, which is less than the significance level of 0.05, you would reject the null hypothesis. This means that the sample statistic provides enough evidence to suggest that the population proportion is different from the hypothesized value.
c) If this test resulted in a decision error, it would be a Type II error. A Type II error occurs when you fail to reject a false null hypothesis. In this case, the p-value of 0.03 suggests that the population proportion is different from the hypothesized value, so if the null hypothesis were actually false and you still failed to reject it, it would be a Type II error.
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what function is equivalent to y = 3x(x+2)^2+7?
The function equivalent to y = [tex]3x(x+2)^2+7[/tex] is [tex]y = 3x^3[/tex]+[tex]12x^2[/tex] + 12x + 7.
Which function is equivalent functionally?Functionally equivalent refers to when a design, material, practice, method, technique, procedure, or component serves the same purpose and offers the same or better utility as is needed by the rule.
When we add the parenthesis to the expression, we get:
[tex]y = 3x(x^2 + 4x + 4) + 7[/tex]
If we simplify, we get:
[tex]y = 3x^3 + 12x^2 + 12x + 7[/tex]
As a result, y = 3x(x+2)2+7 is identical to y = 3x3 + 12x2 + 12x + 7.
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what is the difference between instance variables and static variables?
Answer:
Step-by-step explanation:
Instance variables are created when an object is created with the use of the keyword 'new' and destroyed when the object is destroyed. Static variables are created when the program starts and destroyed when the program stops
ANSWER TODAY!!!!!!!!!!!!!!!!! PLEASE
The reason we can see this star pattern in the summer, but not in the winter is the earth has moved to a different side of the sun in the winter. The Option A is correct.
Why do Stars pattern change with the seasons?We must remember that the earth rotates on its axis every day while revolving around the sun once a year, and that you can only see the constellations at night, when your part of the earth is facing away from the sun.
As the Earth orbits the Sun, constellations slowly move to the west over the course of a year, and we see different parts of the sky at night because we are looking in a different direction in space as the seasons change. The stars appear to rise in the east, cross the sky, and set in the west from our location on Earth.
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the sides of an isosceles triangle are 29,29 and 20m long . what is the area of the triangle? do not round any intermediate computations and round your answer to the nearest tenth.
if the sides of an isosceles triangle are 29,29 and 20m long then the area of the triangle is, 613.52 m²
What is an isosceles triangle ?Any triangle with any two sides that have the same length is known as an isosceles triangle. An isosceles triangle has two angles that are equal in size and opposed to its equal sides.
Given that,
The sides of an isosceles triangle are 29,29 and 20m long
The area of the triangle = ?
To find the area of the isosceles triangle, we can use the formula:
A = (b x h)/2
b = 20m
h = ?
h² = (b/2)² + c²
h = √[(b/2)² + c²]
= √[ (10)² + 29²]
= 30.676
A = (20 x 30.676)/2
= 613.52 m²
Therefore, the area of the isosceles triangle is approximately 613.52 m².
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Is the AP Calculus BC exam multiple choice?
Yes, the AP Calculus BC exam includes multiple choice questions.
The exam is divided into two sections, with Section I consisting of 45 multiple choice questions and Section II consisting of 6 free-response questions.
The multiple choice section of the exam is further divided into two parts, with Part A including 30 questions that do not allow the use of a calculator and Part B including 15 questions that do allow the use of a calculator.
Each section of the exam is weighted equally and contributes to 50% of the overall score.
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Jen and Cade paint rectangular pictures. Jens picture is 36 centimeteters long and 24 centimeters wide. Cades picture has the same area as Jens picture. Cades picture is 48 inches long. what is the perimeter, in inches, of cades picture?
The width of Cade's picture is 7.09cm. The perimeter of Cade's picture is 101.58 inchs.
What is a rectangular object?
A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can also be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal (360°/4 = 90°). A square is a rectangle with four equally long sides.
Given that Jens's picture is 36 centimeters long and 24 centimeters wide.
The area of a rectangular object is the product of length and width.
The area of Jens's picture is 36 × 24 cm² = 864 cm².
1 inches = 2.54 cm
The length of Cade's picture is 48 inches = 48× 24 cm = 121.92 cm
Assume that the width of Cade's picture is x.
The area of Cade's picture is 121.92x cm².
Given that the area of Cade's picture is the same as that of Jens's picture.
According to the question,
121.92x = 864
Divide both sides by 121.92:
x = 7.086
x = 7.09
The perimeter of a rectangular object is 2(l + w)
The perimeter of Cade's picture is 2(121.92 + 7.09) = 258.02 cm
Now convert it cm to inches:
= 258.02/2.54 inch
= 101.58 inchs
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W 41° 16 100° V I don't get it at all
The angle U is 39 degrees, when W is 41 degrees and V is 100 degrees.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given that a triangle UVW in which the angle W is 41 degrees.
V is 100 degrees.
We have to find the angle U.
By angle sum property we have the sum of three angles is 180 degrees.
∠U+∠V+∠W=180
∠U+100+41=180
∠U+141=180
Substitute 141 from both sides
∠U=180-141
∠U=39 degrees.
Hence, the angle U is 39 degrees, when W is 41 degrees and V is 100 degrees.
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Complete question
In a triangle UVW, the angles W is 41 degrees, V is 100 degrees then what is angle U.
In a region where there is a uniform electric field, the potential, v1, is 1. 3 v at position y1=26 cm. At position y2=28 cm , the potential, v2, is 3. 9 v. What is the change in electric potential energy of an alpha particle (charge = +2e) if it is moved from y1 to y3?.
The change in electric potential energy of an alpha particle is:
1.3V/cm
"Information available from the question"
In a region where there is a uniform electric field, the potential, v1, is 1. 3 v at position y1=26 cm.
At position y2=28 cm , the potential, v2, is 3. 9 v.
Now, According to the question:
Calculation of magnitude:
Since V1 is 1.3 V at position y1=26 cm. At position y2=28 cm, the potential, V2, is 3.9 V
So, We know that
[tex]E =\frac{V_2-V_1}{Y_2-Y_1}[/tex]
[tex]E=\frac{3.9-1.3}{28-26}[/tex]
[tex]E=\frac{2.6}{2}[/tex]
E = 1.3V/cm
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9. Liam ran 12 miles total over the weekend. He
ran 5.5 miles on Saturday. Which equation can
be used to find m, the number of miles he ran
on Sunday?
A. 12 + 5.5 = m
B. 5.5m= 12
C. m-5.5 = 12
D. 5.5+ m = 12
Answer:
x=6.5
Step-by-step explanation:
I'm not sure if it's correct
The function is used to model the height of an object being tossed from a tall building, where h(t) is the height in meters and t is the time in seconds. What are the domain and range? round to the nearest hundredth. Domain: [0, 12. 76] range: [1. 80, 590. 90] domain: range: [1. 80, 590. 90] domain: range: [0, 590. 90] domain: [0, 12. 76] range: [0, 590. 90].
For the function f(t) the domain and range is [0, 12.76] and [1.80, 590.90] respectively.
A function is a mathematical tool used to associate one value with another.
In this case, the function models the height of an object being tossed from a tall building. The height of the object is given by the function h(t), where h represents the height in meters and t represents the time in seconds.
The domain and range of a function describe the set of all possible input values (domain) and the set of all possible output values (range) of a function. The domain and range of the function h(t) are as follows:
The domain of the function h(t) is the set of all possible values of t for which the function h(t) is defined. In this case, the domain of the function h(t) is [0, 12.76], which means that the function h(t) is only defined for time values between 0 and 12.76 seconds.
The range of the function h(t) is the set of all possible values of h(t) that the function can produce. In this case, the range of the function h(t) is [1.80, 590.90], which means that the height of the object can only be between 1.80 meters and 590.90 meters.
Therefore, the correct option is (a).
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True/False based on the t-test assuming equal variances on the t-testequal worksheet, it is reasonable to assume that the variances are equal?
Based on the t-test assuming equal variances a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal."
It is vital to establish whether or not the variances of the two groups being compared are indeed identical before performing a t-test under the assumption of equal variances. This is significant since the t-calculation statistic depends on the assumption that variances are equal.
One can look at the ratio of the variances between the two groups to evaluate the assumption of equal variances. Typically, it is acceptable to infer that the variances are not equal if the ratio of the variances is more than two or lower than half. One can presume that the variances are equal in the absence of such proof. Since the variances are not equal, it is not logical to infer that they are.
Complete and correct Question:
Based on the t-test assuming equal variances on the T-Test Equal worksheet, is it reasonable to assume that the variances are equal?
a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal.
b. Whether the variances are equal or not is not relevant for this situation.
c. Examining the ratio of the variances, it is reasonable to conclude that the variances are equal.
d. It is impossible to determine if the variances are equal given the data we have.
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What is the orientation of the vertices in transformation?
What is the orientation of the figure in transformation?
Are they the same?
The orientation of the figure may be unchanged, while in other cases it may be altered. For example, in a rotation transformation, the orientation of the vertices will change but the orientation of the figure as a whole will remain unchanged.
What is the orientation of the vertices in transformation?The orientation of the vertices in transformation refers to the position and arrangement of the vertices of a figure after a transformation has been applied. A transformation is a change in position or size of a figure, such as a translation, rotation, reflection.
While the orientation of the figure in transformation refers to the overall shape and arrangement of the figure after a transformation has been applied. This can be thought of as the orientation of the entire figure, including the position of its vertices, edges, and any other features.
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if line 1= y=-1/2x-4 and line 2= x+2y=-8 how many soloutions are there and what is the coordinate.
Answer:
No solutions
Step-by-step explanation:
I graphed the equations and the lines overlap, so no solution.
Please give brainliest if this helps :)
Please help please now help ASAP
Answer:
2
Step-by-step explanation:
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answer:
A. 2 + x = 5
B x + 1 = 4
E -5 + x = -2
Step-by-step explanation:
2 + 3 = 5
3 + 1 + 4
-5 + 3 + -2
if this correct mark me as brainliest please
Rina spins the spinner below 30 times. A success occurs when the spinner lands on a number that is greater than 6.
A spinner is divided into 8 equals sections and the sections are labeled 1 through 8.
What is the probability of a success and a failure for this experiment?
P (success) = one-fourth; P (failure) = Seven-eighths
P (success) = one-fourth; P (failure) = Three-fourths
P (success) = three-fourths; P (failure) = one-fourth
P (success) = seven-eighths; P (failure) = One-eighth
The probability of an event can not be more than the number 1.
The probability of success is 1/4.The probability of failure is 3/4.What is probability?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
As the probability of an event can not be more than the number 1.
Thus the probability of failure of a event is equal to the difference of the 1 to the success of the event. As,
[tex]Probability[/tex] [tex]of[/tex] [tex]faliure=1-[/tex] [tex]Probability[/tex] [tex]of[/tex] [tex]success[/tex]
Given information-Rina spins the spinner less than the 30 times.
A success occurs when the spinner lands on a number that is greater than 6.
A spinner is divided into 8 equals sections and the sections are labeled 1 through 8.
As the probability of success occurs when the spinner lands on a number that is greater than 6, thus the number should grater than six.
This number should be less than 30 as the spinner spins less than the 30 times.
Thus the total number of outcome of this event is,
[tex]=30-6[/tex]
[tex]=24[/tex]
Thus the probability of success is,
[tex]P=\frac{6}{24}[/tex]
[tex]P=\frac{1}{4}[/tex]
Hence the probability of success is 1/4.
As the probability of failure of a event is equal to the difference of the 1 to the success of the event.
Thus the probability of failure is,
[tex]P^-=1-P[/tex]
[tex]P^-=1-\frac{1}{4}[/tex]
[tex]P^-=\frac{4-1}{4}[/tex]
[tex]P^-=\frac{3}{4}[/tex]
The probability of failure is 3/4.
Hence,
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An August 2022 report from The College Board states that, among all test takers who graduated high school in 2022 , the average SAT score was 1050 points, with a standard deviation of 216 points. The SAT score distribution can be assumed to follow a normal distribution. Question 3 Subquestions 3.a 1 point(s) Let a test taker who scores more than 1320 points be considered a top performer. What proportion of test takers are considered top perfors?
0.8400
0.1600
0.1056
0.8944
0.6800
3.b 1 nnint(s) What is approximately the minimum SAT score needed for a test taker to be in the top
20%
of the distribution? If a test taker has scored in the top
20%
of the distribution, what is the likelihood that the test taker is a top performer? Recall that a test taker who scores more than 1320 points is considered a top performer.
0.124
0.352
0.727
0.627
0.704
0.528
The proportion of test takers that are considered top performers is given as follows:
0.1056.
The minimum SAT score needed for a test taker to be in the top 20% is given as follows:
1231.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation of SAT scores are given as follows:
[tex]\mu = 1050, \sigma = 216[/tex]
The proportion of scores above 1320 points is one subtracted by the p-value of Z when X = 1320, hence:
Z = (1320 - 1050)/216
Z = 1.25
Z = 1.25 has a p-value of 0.8944
1 - 0.8944 = 0.1056.
The minimum SAT score needed for a test taker to be in the top 20% is the 80th percentile, which is X when Z = 0.84, hence:
0.84 = (X - 1050)/216
X - 1050 = 216 x 0.84
X = 1231.
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Is he right explain if no explain as well and this is my last question I need to answer for my test Thank you.
Scott's statement that (13g + 1) + (-2 - 5g) and 8/3(3g + 9/8) are equivalent is wrong
How to determine if he is right or notFrom the question, we have the following parameters that can be used in our computation:
(13g + 1) + (-2 - 5g)
Remove the brackets
So, we have
13g + 1 - 2 - 5g
Evaluate the like terms
8g - 1
When factorized, we have
8/3(3g - 3/8)
This is not the same as Scott's expression
Hence, Scott is incorrect
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Alice makes porridge from milk and oats.
The ratio of milk to oats is 1:2
What proportion of Alice's porridge is milk?
The proportion of Alice's porridge is milk is 1/3.
What is a proportion?A proportion is an equation that sets two ratios at the same value.
A ratio is a numerical relationship showing how often one value includes or is included inside another. It is used to compare two numbers.
Given:
Alice makes porridge from milk and oats.
The ratio of milk to oats is 1:2.
Let x and 2x be the amount of milk and the number of oats in the porridge respectively.
The proportion of Alice's porridge is milk,
= x/3x
= 1/3
Hence, 1/3rd of the amount of milk is in the porridge.
And 2/3rd of the number of oats is in the porridge.
Therefore, the required proportion is 1/3.
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What is the LCM and GCF of 12 and 18?
Answer:
Step-by-step explanation:
The least common multiple (LCM) of two numbers is the smallest number that is divisible by both of the numbers. The greatest common factor (GCF) of two numbers is the largest number that divides both of the numbers evenly.
For the numbers 12 and 18, we can find the LCM and GCF as follows:
Prime factorize the numbers:
12 = 2^2 * 3
18 = 2 * 3^2
Find the LCM by taking the highest exponent for each prime factor:
LCM(12, 18) = 2^2 * 3^2 = 36
Find the GCF by taking the lowest exponent for each prime factor:
GCF(12, 18) = 2 * 3 = 6
So, the LCM of 12 and 18 is 36 and the GCF is 6.