We can use the Pythagorean theorem to find the length of the short cut up the flight of stairs. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let's call the length of the short cut "x". Then, we can set up the following equation:
x^2 = 60^2 + 80^2
Expanding the squares:
x^2 = 3600 + 6400
x^2 = 10000
Taking the square root of both sides:
x = sqrt(10000)
x = 100
So, the length of the short cut up the flight of stairs is 100 meters.
SIMPLIFY THE MONOMIAL. YOUR ANSWER SHOULD CONTAIN POSITIVE EXPONENTS ONLY.
Based on the information, the equation can be simplified as follows: 7xy - 2x² - y
How do you simplify an equation?To simplify an equation we must carefully observe all the values that make up the equation. Once we identify the values with the same symbols, (x or y) we can group them. According to this procedure we can group the values of x as shown below:
7xy - 2x² - andIn this case the 2x was added with the 5x to form the 7x. In the case of 2x², it cannot be added with the other values of x because it has an exponent of ².
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Ravi buys candy that costs $5 per pound. He will spend at least $45 on candy. What are the possible numbers of pounds he will buy?
Use p for the number of pounds Ravi will buy.
Write your answer as an inequality solved for p.
Answer:
90p or 9p
Step-by-step explanation:
if he will spend 5p per pound then do 5x9P=45P
a cone is sliced such that the cross section is perpendicular to its base and the cross section intersects its vertex. what is the shape of the cross section?
The cross section is shaped like a circle.
A cone is a three-dimensional geometric object with a flat base and a smooth transition to the apex or vertex.
If a cone is sliced such that the cross section is perpendicular to its base and intersects its vertex, the cross section will be a circular shape. This is because the cross section cuts through the entire cone at a right angle, producing a circle that is defined by the curved surface of the cone and the slicing plane. The diameter of the circle is equal to the base diameter of the cone, and its center is located at the midpoint of the base.
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Leah measured a line to be 2.1 inches long. If the actual length of the line is 2.2 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answer:
Step-by-step explanation:
divide the required value by the total value and multiply by 100.
a/bx100= y
2.2 - 2.1 =0.1 inches
percentage of error=
0.1 / 2.2 x100
4.54 %
The amount, in dollars, of Marisa’s savings account can be represented by the expression 5x + 40. Marisa saved the same amount x each month for a period of 5 months. Her mother contributed an additional amount each month to Marisa’s savings account. How much did her mother contribute each month? The amount, in dollars, of Marisa’s savings account can be represented by the expression 5x + 40. Marisa saved the same amount x each month for a period of 5 months. Her mother contributed an additional amount each month to Marisa’s savings account. How much did her mother contribute each month?
The amount of money that the mother contributes each month will be $5.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The expression that represents the amount of savings is given as,
Amount of saving = 5x + 40
Where 'x' is the number of months.
The slope is 5 which represents the amount of savings in each month and the y-intercept is 40 which represents the amount already saved.
The amount of money that the mother contributes each month will be $5.
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cambia 89° a radianes
Answer:
acute angle
Step-by-step explanation:
1. Typically, the lowest number your credit score can be is:
What is cluster sampling?
Cluster sampling is a sampling technique used in statistics and research methodology where a population is divided into groups, or clusters, and a sample is randomly selected from each cluster to be included in the study.
This method is often used when it is difficult or impractical to obtain a simple random sample of individuals from a large and diverse population. For example, in a study of public schools in a state, it may be easier to randomly select a sample of schools and then include all students in those schools in the study, rather than attempting to randomly select individual students from the entire state.
The advantages of cluster sampling include lower costs and greater efficiency than other sampling techniques, particularly when working with large populations. However, it can also increase the risk of sampling bias and decrease the precision of estimates if the clusters are not representative of the larger population. Therefore, it is important to carefully choose clusters that are as heterogeneous as possible within and as similar as possible between clusters.
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How much is 1 HEROES in USD?
As of 22/02/2023, the value of 1 HERO (cryptocurrency) is $0.01 USD. This means that if you have 1 HERO, it can be exchanged for $0.01 USD.
The value of HERO, like most cryptocurrencies, can fluctuate rapidly due to market demand and supply. As a result, the value of HERO can change significantly over short periods of time. It's important to keep this in mind when buying or investing in cryptocurrencies, as the value can both rise and fall quickly. Investors in cryptocurrencies should do their research and consider the risks associated with investing in a volatile and relatively new asset class.
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Y^2 + 6y+8 when y is -3
What is the solution for : y=-2/3x+7
4x+6y=42
The equation y =-2/3x+7 , 4x+6y=42 has many solution.
How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method. Let's solve the system of equation using substitution method.
y = -2/3 x + 7
4x + 6y = 42
Let's substitute the value of y in equation 2
Therefore,
4x + 6(- 2/3 x + 7) = 42
4x - 12 / 3 x + 42 = 42
4x - 4x + 42 = 42
4x - 4x = 42 - 42
0 = 0
Therefore, it numerous solution
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Mrs. Flips sold 300 cookies for her bake
sale. She sold two types of cookies: large
chocolate chip and small peanut butter
cookies. She charged $1 for the chocolate
chip and 50-cents for the peanut butter
cookies and collected $270 total. How
many of each type did she sell?
Mrs. Flips sold 240 large chocolate chips.
Mrs. Flips sold 60 small peanut butter cookies.
How to write the required expressions?In order to write the required expressions that models the situation, we would assign variables to the number of large chocolate chips and the number of small peanut butter cookies, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of large chocolate chips.Let the variable y represent the total number of small peanut butter cookies.Since Mrs. Flips charged $1 for the chocolate chip and 50-cents for the peanut butter cookies and collected $270 total, an expression that models the situation is given by:
x + 0.5y = 270
Additionally, she sold a total of 300 cookies:
x + y = 300
270 - 0.5y + y = 300
0.5y = 30
y = 60 small peanut butter cookies.
x = 270 - 0.5(60)
x = 240 large chocolate chips.
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the length of a rectangle is 3 times its width. Given that its area is 27 cm, find the length and the width of the rectangle
Answer:
The width is 3 cm and the length is 9 cm.
Step-by-step explanation:
L --> Length
W --> Width
L = 3W
LW = 27
3W(W) = 27
3W^2 = 27
W^2 = 9
W = 3
L = 3(3) = 9
Assuming a Poisson distribution, on the average, 6 cars arrive at the drive-up window of a bank every hour.Compute the probability that no more than 5 cars will arrive in the next half-hour.
Assuming a Poisson distribution, on the average, 6 cars arrive at the drive-up window of a bank every hour, the probability that no more than 5 cars will arrive in the next half-hour is 0.75.
The Poisson distribution can be used to model the number of events that occur in a fixed interval of time. In this case, the average number of cars arriving at the drive-up window of a bank is 6 cars per hour, so we can use the Poisson distribution to calculate the probability of a certain number of cars arriving in a half-hour interval.
To calculate the probability that no more than 5 cars will arrive in the next half-hour, we can use the cumulative Poisson distribution function, which gives the probability that the number of events is less than or equal to a given value.
The cumulative Poisson distribution function can be calculated using the following formula:
P(X <= x) = Σ P(X = i) for i = 0, 1, 2, ..., x
Where X is the number of cars arriving in a half-hour interval, and x is the given value (in this case, x = 5).
The mean number of cars arriving in a half-hour interval is 3 (6 cars per hour / 2), so the cumulative Poisson distribution function can be calculated as follows:
P(X <= 5) = Σ P(X = i) for i = 0, 1, 2, 3, 4, 5
= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
= (e^-3) * (3^0) / 0! + (e^-3) * (3^1) / 1! + (e^-3) * (3^2) / 2! + (e^-3) * (3^3) / 3! + (e^-3) * (3^4) / 4! + (e^-3) * (3^5) / 5!
= 0.0498 + 0.1494 + 0.224 + 0.224 + 0.1494 + 0.0498
= 0.75
Therefore, the probability that no more than 5 cars will arrive in the next half-hour is approximately 0.75, or 75%.
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What is expression mean in math?
Answer: a type of equation
Step-by-step explanation:
Lebo buys seven icecreams for R37,65 how much will five icecreams cost?
Answer:
R2689 IS THE CORRECT ANSWER
What is a unit normal table?
To calculate the z-score, the formula is: z-score = (x - μ)/σ, where x is the value, μ is the mean, and σ is the standard deviation. Once the z-score is calculated, it can be used to look up the area, or probability, in the table.
A unit normal table is a type of probability table that is used to determine the area, or probability, under the normal curve. It is based on the standard normal probability distribution, which is a normal distribution with a mean of 0 and a standard deviation of 1. To use the unit normal table, one first needs to calculate the z-score, which is the number of standard deviations away from the mean a given value is. To calculate the z-score, the formula is: z-score = (x - μ)/σ, where x is the value, μ is the mean, and σ is the standard deviation. Once the z-score is calculated, it can be used to look up the area, or probability, in the table.
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I NEED HELP ASAP!!!
Answer:
A. B is correct
B. A is correct
C. B is correct
Step-by-step explanation:
Area of triangle: A = 1/2bh
A. Area of each triangle: A = 1/2 x 11.5 x 12 = 69
Total surface areas = 4(area of triangle) + area of square = 4(69) + 12^2 = 420
So A is incorrect and B is correct
B. Area of triangle: A = 1/2 x 13.9 x 16 = 111.2
Surface area = 4(area of triangle) = 4(111.2) = 444.8
So A is correct and B is incorrect
C. Area of triangle with base of 10: A = 1/2 x 10 x 7 = 35
Area of triangle with base of 8.1: A = 1/2 x 8.1 x 16 = 64.8
Total surface areas = 2(area of triangle base of 10) + 2(area of triangle base of 8.1) + area of rectangle = 2(35) + 2(64.8) + (10x8.1) = 280.6
So A is incorrect and B is correct.
Jake worked on his garden for 3 hours. Adrian worked on his garden 3 times as long as Jake. Precious worked on her garden 2% times as long as Jake. Select all that are true: Adrian worked longer than Jake in his garden. O Precious worked less time in her garden. Precious worked more time than Adrian. □ Adrian worked the least amount of time.
Answer:
The answer is to get it wrong on khan academy the go-to progress report(click on the percent to get to it and find the problem and go to hints and it should show the answer.
Step-by-step explanation:
Answer:
Adrian worked the least amount of time. (False, Precious worked the least amount of time with 0.06 hours)
Step-by-step explanation:
The following statements are true:
Adrian worked longer than Jake in his garden. (Adrian worked 3 times as long as Jake, so Adrian worked 3 hours * 3 = 9 hours)
Precious worked less time in her garden. (Precious worked 2% of the time that Jake worked, which is 2% of 3 hours = 0.06 hours, which is less than both Jake and Adrian)
The following statement is false:
Precious worked more time than Adrian. (As calculated above, Precious worked 0.06 hours, which is less than Adrian's 9 hours)
And finally:
Adrian worked the least amount of time. (False, Precious worked the least amount of time with 0.06 hours)
Write the expression in quadratic form. If possible. Otherwise, write NOT POSSIBLE.
16x^10 + 2x^5 + 6
Answer:
5X^4 + 2X^2 – 8
Step-by-step explanation
Its quadratic form is 5(x²)² +2x² -8
Let be X²=p, so the final expression is 5p²+2p-8
hope this help's
Which statement correctly compares the values of the 7s in 7.825 and 3.7?
Answer:
Step-by-step explanation:
The statement that correctly compares the values of the 7s in 7.825 and 3.7 is:
The 7s in 7.825 are greater than the 7s in 3.7.
The 7s refer to the units place (the "ones" place) in decimal numbers. In 7.825, the 7s are 7 and in 3.7, the 7s are 7. When comparing the two numbers, we can see that the number 7.825 is greater than 3.7, which means the 7s in 7.825 are greater than the 7s in 3.7.
If 0° ≤ Θ≤ 360°, then find angle(s) Θ.
cosΘ= -1/2
Answer:
There are two possible solutions for angle Θ, as cosine is negative in the second and third quadrants.
Using the inverse cosine function on a calculator, we can find the two possible solutions for Θ:
Θ = 120° (in the second quadrant)
Θ = 240° (in the third quadrant)
Therefore, the possible angles for Θ are 120° and 240°.
what is the inverted matrix calculator symbol?
The formula D = inv (A) returns the inverse of a symbolic matrix A. The symbol will be [tex]A^{-1}[/tex].
If A is a non-singular square matrix, then [tex]A^{-1}[/tex], often known as the inverse matrix of A, must exist if it is to satisfy the following property:
A[tex]A^{-1}[/tex] =[tex]A^{-1}[/tex]A = I, where I is the identity matrix.
Finding the minors and cofactors of the given matrix's components is one of the most crucial steps in determining its inverse. To comprehend this approach clearly, follow the steps listed below.
The following formula may also be used to find the inverse matrix:
[tex]A^{-1}[/tex]= adj(A)/det (A).
The calculation for the inverted matrix is done.
Hence they are the symbol and methods to find the inverted matrix.
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6 - Which statement best explains whether the following table represents a linear or nonlinear function?
x −2 −1 0 1 2
y −4 −2 0 2 −2
The table represents a nonlinear function because there is not a constant rate of change in the output values.
The table represents a nonlinear function because there is not a constant rate of change in the input and output values.
The table represents a linear function because there is a constant rate of change in the input and output values.
The table represents a linear function because there is not a constant rate of change in the input and output values.
Answer:
The table represents a linear function because the rate of change is constant or all the points lie on a straight line.
Step-by-step explanation:
From the given table it is noticed that the line passing through the points (2,5), (4,10), (6,15) and (8,20).
The slope of the line is
The slope of line is . It means the value of y increased by 5 if the value of x increased by 2.
From the given points we can noticed that the value of y increased by 5 if the value of x increased by 2. So, the function has same slope for any two points.
Since the rate of change (slope) is same for all points, therefore the table represents a linear function.
If we plot these points on a coordinate plane and connect then we get a straight line. I means it is a linear function.
(11 × 4) ÷ 2 × 1 = [?]
Answer:
22
Step-by-step explanation:
(11 x 4) / 2 x 1
= 44/2 x 1
= 22 x 1
= 22
Jose's parabola opens downward
A parabola is a mirror-symmetrical, roughly U-shaped planar curve in mathematics. Many seemingly unrelated mathematical descriptions that all correlate to the same curves can be used to define it.
What is a parabola?In mathematics, a parabola is a roughly U-shaped, mirror-symmetrical planar curve.
The same curves can be defined by a number of seemingly unrelated mathematical definitions, which all correspond to it.
A line and a point (the focus) are two components of one definition of a parabola (the directrix).
The directrix is not the main focus.
The locus of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.
A right circular conical surface and a plane parallel to another plane that is tangential to the conical surface intersect to form a parabola, which is also known as a conic section.
Therefore, a parabola is a mirror-symmetrical, roughly U-shaped planar curve in mathematics. Many seemingly unrelated mathematical descriptions that all correlate to the same curves can be used to define it.
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Complete question:
What is a parabola?
What is the Systematic Approach algorithm?
The Systematic Approach algorithm is a problem-solving methodology that is widely used in many different fields, such as engineering, business, and science.
It is a structured and systematic process that involves identifying a problem, analyzing it, generating possible solutions, evaluating these solutions, and selecting the best one. The algorithm is also known as the "systems engineering process" or "systems analysis and design."
The algorithm is typically divided into several phases, including:
Problem identification: This involves defining the problem, its boundaries, and its scope. This step also involves identifying the objectives and constraints of the problem. Analysis: This step involves gathering data and information related to the problem, and identifying the root cause of the problem. This may involve conducting surveys, interviews, or experiments. Design: In this step, potential solutions are generated, and a conceptual design is created. The design should be flexible enough to allow for the incorporation of new information and changes. Evaluation: The potential solutions are evaluated based on predetermined criteria, and the best solution is selected. Implementation: The selected solution is implemented and monitored to ensure it is working effectively. Any necessary modifications or adjustments are made during this phase.
The Systematic Approach algorithm is a powerful tool for problem-solving as it provides a structured, step-by-step approach to analyzing and solving complex problems. It also allows for a thorough understanding of the problem and its potential solutions, as well as the ability to evaluate and select the best solution based on predefined criteria.
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F(x) has zeros equal in x=1 with multiplicity =2 x= 0 with the multiplicity =1 find the degree of polynomial?
The degree of polynomial is 3
How to find the degree of polynomial?From the question, we have the following parameters that can be used in our computation:
zeros equal in x=1 with multiplicity =2 x= 0 with the multiplicity =1
The degree of a polynomial is the sum of the multiplicities
Using the above as a guide, we have the following:
Degree = 2 + 1
Evaluate
Degree = 3
Hence, the degree is 3
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5). When
Error analysis: Ali factored the above problem, c, and got 2x(10y) she checked it using the distributive property, she got the original problem! Since her check worked, she thinks she has the correct answer. How can that be? Explain her mistake.
+
3. Error analysis: Jamie incorrectly factored 15x20xy. She got 5x(3-4xy).
Factor the expression correctly.
What error did she likely make?
a. She did not have the correct operation inside parentheses.
b. She did not factor the variable from the first term.
c. She did not factor the variable from the second term.
d. She did not simplify the terms inside the parentheses.
30
The error she made is option c. Jamie did not factor the variable from the second term.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given expression is 15x - 20xy.
We have to factor the expression.
Common factor of both the terms 15x and 20xy is 5x.
Taking the term 5x outside and using the distributive property,
15x - 20xy = 5x (3 - 4y)
But Jamie got it as 5x (3 - 4xy)
So the variable in the second term has not been factored correctly.
Hence the error in the process is that She did not factor the variable from the second term.
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Draw a triangle with vertices A(0, 4), B(2, -2), and C(-2, -2). Apply a dilation centered at the origin with scale factor to this triangle and draw the resulting triangle,A'B'C'. In complete sentences, describe the following:
a,The relationship between corresponding sides in terms of their lengths.
b.The relationship between corresponding sides in terms of their orientations.
c.The relationship between corresponding angles in terms of their measures.
a) Relationship between corresponding sides: the corresponding sides are parallel and have a ratio of k in length.
b) Relationship between corresponding sides' orientations: The corresponding sides will still be parallel to the original sides.
c) Relationship between corresponding angles:the corresponding angles are congruent.
What do you mean by congruent angles?
Congruent angles are angles that have the same measure or size. In other words, if two angles have the same number of degrees or radians, they are said to be congruent. When we say that two angles are congruent, it means that they are exactly the same shape and size, and they can be superimposed on each other without any rotation or scaling. Congruent angles play an important role in geometry, as they allow us to prove that two figures are similar or congruent.
To apply a dilation with scale factor k centered at the origin, we multiply the coordinates of each vertex by k. So, to find the coordinates of A', B', and C', we will multiply the coordinates of A, B, and C by the scale factor.
a) The relationship between corresponding sides in terms of their lengths:
Let's denote the scale factor by k. The distance between two points (x1, y1) and (x2, y2) is given by the distance formula, which is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
When we multiply each coordinate by k, the distance between the two points is multiplied by k as well. So, if AB has length dAB and A'B' has length dA'B', we have:
dA'B' = k * dAB
Similarly, we can find the relationship between the lengths of BC and B'C', as well as between the lengths of AC and A'C'.
b) The relationship between corresponding sides in terms of their orientations:
The orientation of a line is given by its slope. If two lines have the same slope, they are parallel or collinear. If they have slopes that are negative reciprocals of each other, they are perpendicular. When we multiply the coordinates of a point by k, the slope of any line passing through that point is multiplied by k as well. So, if the slope of AB is mAB and the slope of A'B' is mA'B', we have:
mA'B' = k * mAB
We can use this to find the relationship between the slopes of BC and B'C', as well as between the slopes of AC and A'C'.
c) The relationship between corresponding angles in terms of their measures:
The measure of an angle is determined by the slope of the line that contains the angle. When we multiply the coordinates of a point by k, the slope of any line passing through that point is multiplied by k as well. This means that the measure of any angle that includes the origin is unchanged by the dilation. However, the measure of any angle that does not include the origin is multiplied by a factor of k. So, if angle ABC has measure x and angle A'B'C' has measure y, we have:
y = k * x
We can use this to find the relationship between the measures of angles BAC and B'A'C', as well as between the measures of angles CBA and C'B'A'.
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