To solve the problem, we need to find all the classes of the relation Ron the set A in roster notation. And also, we need to pick one element of A to represent each distinct equivalence class. The relation Ron A is defined as:
aRb ⇔ a+b=3k, k ∈ ZLet A = {2, 3, 5, 11, 12, 13} be a set.
The distinct equivalence classes of A in roster notation are distinct equivalence[2] = {2, 5, 11},[3] = {3, 12},[13] = {13},[a], [5] = {5, 2, 11}Each equivalence class consists of elements in A that are related to each other by the given relation, i.e., by R. Therefore, aRb means that a and b are related in some way, and the equivalence class [a] is the set of all elements in A that are related to a by R.
Therefore, the distinct equivalence classes in roster notation are given as above, and we can pick any one element of A to represent each class. Thus, we have the following:A = {2, 3, 5, 11, 12, 13}[2] = {2, 5, 11} and can be represented by 2.[3] = {3, 12} and can be represented by 3.[13] = {13} and can be represented by 13.[5] = {5, 2, 11} and can be represented by 5.
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Use the coordinate plane to answer the question. Information A coordinate plane is shown. No points are plotted. Question What is the perimeter of a quadrilateral with vertices at the point negative 5 comma negative 2, the point negative 4 comma negative 2, the point negative 5 comma 1, and the point negative 4 comma 1? Enter the answer in the box. Response area with 1 text input box units
The perimeter of the quadrilateral is 8 units. Therefore, the answer to the question is 8 units.
What is perimeter?The perimeter of a quadrilateral is the sum of the lengths of its sides. To calculate the perimeter, we need to calculate the distances between the points of the quadrilateral.
To draw a quadrilateral with the given points on the coordinate plane, we can draw four lines connecting the given points. The first line will connect the points (–5, –2) and (–4, –2), which is a horizontal line with a length of 1 unit. The second line will connect the points (–4, –2) and (–4, 1), which is a vertical line with a length of 3 units. The third line will connect the points (–4, 1) and (–5, 1), which is a horizontal line with a length of 1 unit. The fourth line will connect the points (–5, 1) and (–5, –2), which is a vertical line with a length of 3 units.
The total length of the sides of the quadrilateral is calculated by adding the lengths of the four lines. Thus, the perimeter of the quadrilateral is 8 units.
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Solve for y.
115°
108°
90°
130°
Answer:y=115
Step-by-step explanation:
find the sum of the angles:
=(n-2)180
=(5-2)180
=540
find the value of y:
y=540-(135+112+88+90)
y=115
Answer:
115°
Step-by-step explanation:
the sum of the interior angles of a pentagon is 540°
135+90+112+88+y=540
y= 540-135-90-112-88
y= 155°
what type of data is a questionnaire
Answer:
A questionnaire can collect quantitative, qualitive or both types of data.
Step-by-step explanation:
Answer:
Categorical data
Step-by-step explanation:
Data that relates to certain categories e.g males, females or any types of car
An object moves in the xy-plane so that its position at any time tis given by the parametric equations X(0 = ? _ 3/2+2andy (t) = Vt? + 16.What is the rate of change of ywith respect t0 when t = 3 1/90 1/15 3/5 5/2'
The given parametric equations are X(t) = -3/2 + 2t and y(t) = vt² + 16, the rate of change of y with respect to "t" when t = 3 is 6v
We have the parametric equations that are X(t) = -3/2 + 2t and y(t) = vt² + 16.
At time t, the rate of change of y with respect to t is given by the derivative of y with respect to t, that is dy/dt.
So, y(t) = vt² + 16
Differentiating with respect to t, we get
⇒ dy/dt = 2vt.
Now, t = 3 gives us,
y(3) = v(3)² + 16 ⇒ 9v + 16.
Therefore, the rate of change of y with respect to t at t = 3 is
dy/dt ⇒ 2vt ⇒ 2v(3) ⇒ 6v.
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7. Complete a dilation with scale factor of ½ around the origin and then
reflect over the y-axis. What are the new ordered pair of A'?
The new ordered pairs of points A', B', and C' after the reflection over the y-axis are (1,-2.5), (0,1.5), and (-3,-1.5), respectively.
WHAT IS AXIS ?
An axis is a straight line around which an object rotates or is symmetrical. In geometry, it is a reference line that is used to measure distances, angles, and other geometric properties of objects. In a two-dimensional plane, there are two axes: the x-axis and the y-axis. The x-axis is the horizontal line that runs from left to right, while the y-axis is the vertical line that runs from bottom to top. Together, the x-axis and y-axis form a coordinate system that is used to plot points and graph functions. In three-dimensional space, there is also a z-axis that runs perpendicular to the x-axis and y-axis
To perform a dilation with a scale factor of 1/2 around the origin, we need to multiply the coordinates of each point by 1/2. This gives us:
A' = (1/2)A = (1/2)(-2,-5) = (-1,-2.5)
B' = (1/2)B = (1/2)(0,3) = (0,1.5)
C' = (1/2)C = (1/2)(6,-3) = (3,-1.5)
The new coordinates of points A, B, and C after the dilation are (-1,-2.5), (0,1.5), and (3,-1.5), respectively.
To reflect each point over the y-axis, we need to change the sign of its x-coordinate, while leaving the y-coordinate unchanged. This gives us:
A" = (-x,y) = (-(-1),-2.5) = (1,-2.5)
B" = (-x,y) = (-0,1.5) = (0,1.5)
C" = (-x,y) = (-3,-1.5) = (-3,-1.5)
The new ordered pairs of points A', B', and C' after the reflection over the y-axis are (1,-2.5), (0,1.5), and (-3,-1.5), respectively.
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Solve the system of equations:
y = 2x + 1
y=x²+2x-8
OA. (-3,-5) and (3,7)
B. (-4, 0) and (2,0)
C. (0, 1) and (2, 5)
OD. (-3, 5) and (3, 2)
The solutions of the system of equations are option (A) (3, 7) and (-3, -5)
Solving system of equations:
To solve the system of equations, use the concept of substitution, which involves solving one equation for one variable and then substituting that expression into the other equation to eliminate one variable and solve for the other variable.
In this case, solve equation (1) for y in terms of x and substitute that expression into equation (2), which allowed us to solve for x. Then we used the values of x to find the corresponding values of y.
Here we have
y = 2x + 1 --- (1)
y = x²+ 2x -8 --- (2)
From (1) and (2)
=> x²+ 2x - 8 = 2x + 1
Subtract 2x + 1 from both sides
=> x²+ 2x - 8 - 2x - 1 = 2x + 1 - 2x - 1
=> x² - 9 = 0
Now add 9 on both sides
=> x² - 9 = 0 + 9
=> x² = 9
=> x = √9
=> x = ± 3
From (1)
At x = 3
=> y = 2(3) + 1 = 7
At x = - 3
=> y = 2(-3) + 1 = - 5
Therefore,
The solutions of the system of equations are option (A) (3, 7) and (-3, -5)
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find an equation of the line throught the point (3,5) that cuts iff the least area from the first quadrant
The equation of the line y = (5/3)x + (10/3) represents the line passing through the point (3, 5) that cuts off the smallest area from the first quadrant.
To find the equation of the line that passes through the point (3, 5) and cuts off the least area from the first quadrant, we need to consider the slope of the line.
Any line passing through the point (3, 5) can be written in a point-slope form as:
y - 5 = m(x - 3)
where m is the slope of the line. We want to find the slope that minimizes the area cut off by the line.
Consider a line passing through the origin with slope m. The area cut off by this line in the first quadrant is given by:
A(m) = (1/2)(3)(m*3) = (9/2)m
Note- that the area cut off by the line passing through (3, 5) with slope m is equal to the area cut off by the line passing through the origin with slope m plus the area of the triangle formed by the point (3, 5), the origin, and the point where the line intersects the y-axis. The y-intercept of the line passing through (3, 5) with slope m is given by:
y - 5 = m(x - 3)
y = mx - 3m + 5
Setting x = 0, we get:
y = -3m + 5
The coordinates of the point where the line intersects the y-axis are (0, -3m + 5), and the area of the triangle is:
(1/2)(3)(|-3m + 5 - 0|) ⇒ (3/2)|-3m + 5|
Therefore, the total area cut off by the line passing through (3, 5) with slope m is:
A(m) = (9/2)m + (3/2)|-3m + 5|
To find the slope that minimizes this expression, we need to consider two cases:
Case 1: -3m + 5 ≥ 0, i.e., m ≤ 5/3
In this case, the expression simplifies to:
A(m) = (9/2)m + (9/2)m - (3/2)(5)
= (9m - (15/2)
This expression is minimized when m = 5/3, which is within the range of possible slopes.
Case 2: -3m + 5 < 0, i.e., m > 5/3
In this case, the expression simplifies to:
A(m) = (9/2)m - (9/2)m + (3/2)(5)
= (15/2)
This expression is minimized when m = 5/3, which is again within the range of possible slopes.
Therefore, the line passing through (3, 5) with slope m = 5/3 cuts off the least area from the first quadrant. The equation of the line is:
y - 5 = (5/3)(x - 3)
Simplifying, we get:
y = (5/3)x + (10/3)
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A jar contains 24 coins: 10 quarters, 6 dimes, 2 nickels, and 6 pennies.
What is the probability of randomly drawing _____ ?
1. a penny
2. a quarter
3. a coin that is not a penny
The probability of randomly drawing a penny is 6/24 or 1/4, since there are 6 pennies out of a total of 24 coins.
How to solve and What is Probability?
The probability of randomly drawing a quarter is 10/24 or 5/12, since there are 10 quarters out of a total of 24 coins. The probability of randomly drawing a coin that is not a penny is 18/24 or 3/4, since there are 18 coins that are not pennies out of a total of 24 coins.
Probability is the branch of mathematics that deals with measuring the likelihood or chance of an event or outcome occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
Probability theory is used to make predictions and informed decisions based on available data in various fields, including statistics, finance, engineering, and science.
It involves understanding and analyzing random events, and determining the likelihood of specific outcomes. Probability is an essential tool for decision-making in various applications, such as risk analysis, game theory, and quality control.
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An investigation into the fair valuation of jewelry of two Pawn Shops used a random sample of 32 pieces of expensive jewelry selected from a very large jewelry collection of a wealthy woman. Each of the 32 pieces of jewelry was taken, one at a time, by different people into to two different pawn shops for assessment. The goal was to estimate the mean difference in assessed value.
The results showed that the mean difference in assessed value between the two pawn shops was $20.
What is value in mathematics?Value is the worth or importance that something has to an individual or group. It is often determined by ideas such as usefulness, importance, or desirability. Value can also be determined by material or monetary worth, such as the amount of money someone is willing to pay for an item or service.
The research team conducted a hypothesis test to determine if the difference in the assessed values was statistically significant. The null hypothesis was that there was no difference in the assessed values between the two pawn shops. The alternative hypothesis was that there was a statistically significant difference in the assessed values between the two pawn shops. The researchers used a two-tailed t-test to determine if the difference in the assessed values was statistically significant.
The t-test results showed that the difference in assessed values between the two pawn shops was statistically significant, with a p-value of 0.0001. This indicated that the difference in assessed values between the two pawn shops was not due to chance. The research team concluded that the two pawn shops were not assessing jewelry of the same value.
The findings of this research are important for the jewelry industry. This research showed that two pawn shops were assessing jewelry differently, indicating that there is a need for a standardized approach to assess jewelry value. The findings of this study can help improve the accuracy of jewelry valuations and help ensure that consumers are paying a fair price for their jewelry. It can also help jewelers, pawn shops, and other jewelry buyers and sellers determine a fair value for their jewelry purchases.
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5cm 8cm 11cm 10cm Find the volume of the prism above
Therefore, the volume of the prism is 200 cubic centimeters.
What is volume?Volume is a measurement of the amount of space occupied by a three-dimensional object. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet. The volume of an object can be calculated using a variety of formulas, depending on its shape. The concept of volume is used in various fields, including physics, engineering, architecture, and manufacturing.
Here,
Identify the base of the prism. In this case, the base is a right triangle with legs of 5 cm and 8 cm, and a hypotenuse of 11 cm.
Use the formula for the area of a triangle to find the area of the base. The formula for the area of a right triangle is A = (1/2)bh, where b and h are the lengths of the base and height, respectively. In this case, we can use the legs of the triangle as the base and height, since they are perpendicular. So, the area of the base is:
A = (1/2)(5 cm)(8 cm) = 20 cm²
Multiply the area of the base by the height of the prism to find the volume. The height of the prism is given as 10 cm, so:
Volume = (Area of base) x (Height)
= (20 cm²) x (10 cm)
= 200 cm³
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3x+4y=34. In the equation, what is the y-value when x=10? x= 10 , y= ?
When x=10, the value of y in the equation 3x+4y=34 is y=1.
To find the value of y when x=10 in the equation 3x+4y=34, we can substitute x=10 into the equation and solve for y:
3x+4y=34
3(10) + 4y = 34
30 + 4y = 34
4y = 34 - 30
4y = 4
y = 1
An equation is a mathematical statement that shows the relationship between two or more variables using symbols and numbers. It is a statement that asserts the equality of two expressions. An equation typically consists of two sides, separated by an equals sign (=). Each side of the equation may contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
Solving an equation involves manipulating the expressions on both sides of the equation to isolate the variable and find its value. Equations are used in various branches of mathematics, physics, engineering, economics, and other sciences to model and solve problems. For example, the equation "2x + 5 = 11" has two sides, left-hand side (2x + 5) and right-hand side (11), separated by an equals sign.
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1. Create a cubic function that is not the parent function.
2. Explain how to graph your cubic function using transformations from the parent function. Be specific in your response and use correct mathematical language.
Number your responses 1 and 2 so your instructor can tell which question you're responding to.
This is the graph of the parent function. For example is I wanted to shift it down the function becomes: f(x)=x^3-7 (vertical transformation; shifted 7 down).
y=x²
When a function is shifted, stretched (or compressed), or flipped in any way from its "parent function, it is said to be transformed, and is a
transformation of a function
The given cubic function [tex]$f(x) = (x+2)^3 - 5$[/tex] is obtained by translating the parent cubic function [tex]$f(x) = (x+2)^3 - 5$[/tex] 2 units to the left and 5 units down.
What are cubic function?A cubic function is a function of the form that is, a polynomial function of degree three. In many texts, the coefficients a, b, c, and d are supposed to be real numbers, and the function is considered as a real function that maps real numbers to real numbers or as a complex function that maps complex numbers to complex numbers.
Cubic function:
[tex]$f(x) = (x+2)^3 - 5$[/tex]
Graphing the cubic function using transformations:
To graph the given cubic function [tex]$f(x) = (x+2)^3 - 5$[/tex] using transformations from the parent function [tex]$f(x) = (x+2)^3 - 5$[/tex] we can follow the following steps:
a) Start with the parent function [tex]$y=x^3$[/tex] and mark the points on the graph.
b) Translate the graph horizontally by 2 units to the left to obtain [tex]$y=(x+2)^3$[/tex].
c) Shift the graph vertically down by 5 units to get the final graph [tex]$y=(x+2)^3-5$[/tex]
d) Check the intercepts and end behavior of the function to ensure the graph is correct.
Therefore, the given cubic function [tex]$f(x) = (x+2)^3 - 5$[/tex] is obtained by translating the parent cubic function [tex]$f(x) = (x+2)^3 - 5$[/tex] 2 units to the left and 5 units down.
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If a distribution is normal, then it is not possible to randomly select a value that is more than 4 standard deviations from the mean.True or false
The Given statement "If a distribution is normal, then it is not possible to randomly select a value that is more than 4 standard deviations from the mean" is a true statement.
A normal distribution is a bell-shaped curve that represents how data is spread out around an average value. About 99.99% of the data in a normal distribution falls within 4 standard deviations from the average.
This means that it is very rare to find a data point that is more than 4 standard deviations away from the average. Therefore, if a distribution is normal, it is not possible to randomly select a value that is more than 4 standard deviation from the mean.
The answer is true.
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 HELP PLEASE!!!
calculate the distance between the points B= (0,6) and M= (8, -2) on the coordinate plane . round to the nearest 100th.
Answer:
Step-by-step explanation:
Using the distance formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d=\sqrt{(8-0)^2+(-2-6)^2}[/tex]
[tex]=\sqrt{64+64} \\[/tex]
[tex]=\sqrt{128}[/tex]
[tex]=11.3[/tex]
Radioactive decay tends to follow an exponential distribution; the half-life of an isotope is the time by which there is a 50% probability that decay has occurred. Cobalt-60 has a half-life of 5.27 years. (a) What is the mean time to decay? (b) What is the standard deviation of the decay time? (c) What is the 99th percentile? (d) You are conducting an experiment which first involves obtaining a single cobalt-60 atom, then observing it over time until it decays. You then obtain a second cobalt-60 atom, and observe it until it decays; and then repeat this a third time. What is the mean and standard deviation of the total time the experiment will last?
The exponential distribution is a probability distribution that models the time between events in a Poisson process, where events occur randomly and independently at a constant average rate.
It is commonly used in reliability theory, queuing theory, and other fields to model the failure or waiting times of systems.
(a) The mean time to decay for Cobalt-60 is 5.27 years.
(b) The standard deviation of the decay time is 2.6355 years.
(c) The 99th percentile is 13.6825 years.
(d) The mean time of the experiment is 15.8175 years and the standard deviation is 4.86788 years.
Note: The answers are calculated based on the exponential distribution of radioactive decay with a half-life of 5.27 years for Cobalt-60.
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Let a sample space be partitioned into three mutually exclusive and exhaustive events, B1, B2, and, B3. Complete the following probability table. (Round your answers to 2 decimal places.)
Prior
Probabilities Conditional
Probabilities Joint
Probabilities Posterior
Probabilities
P(B1) = 0.11 P(A | B1) = 0.45 P(A ∩ B1) = P(B1 | A) = P(B2) = P(A | B2) = 0.62 P(A ∩ B2) = P(B2 | A) = P(B3) = 0.38 P(A | B3) = 0.85 P(A ∩ B3) = P(B3 | A) = Total = P(A) = Total =
Let a sample space be partitioned into three mutually exclusive and exhaustive events, B1, B2, and, B3.We have to complete the following probability table, prior probabilities, conditional probabilities, joint probabilities, and posterior probabilities, and also we have to round our answers to 2 decimal places.
Given information:Probability of B1, P(B1) = 0.11 Probability of A given B1, P(A | B1) = 0.45 Probability of A intersection B1, P(A ∩ B1) = ?
Probability of B1 given A, P(B1 | A) = ? Probability of B2, P(B2) = ? Probability of A given B2, P(A | B2) = 0.62, Probability of A intersection B2, P(A ∩ B2) = ? Probability of B2 given A, P(B2 | A) = ?
Probability of B3, P(B3) = 0.38. Probability of A given B3, P(A | B3) = 0.85. Probability of A intersection B3,
P(A ∩ B3) = ?
Probability of B3 given A, P(B3 | A) = ?
Total probability of A, P(A) = ?
Total probability of sample space = 1. Let's complete the probability table:Prior probabilities, Conditional probabilities, Joint probabilities, Posterior probabilities P(B1) = 0.11P(A | B1) = 0.45P(A ∩ B1) = P(A | B1) * P(B1) / P(A)P(B1 | A) = P(A | B1) * P(B1) / P(A)P(B2) = 1 - (P(B1) + P(B3)) = 1 - (0.11 + 0.38) = 0.51P(A | B2) = 0.62P(A ∩ B2) = P(A | B2) * P(B2) / P(A)P(B2 | A) = P(A | B2) * P(B2) / P(A)P(B3) = 0.38P(A | B3) = 0.85P(A ∩ B3) = P(A | B3) * P(B3) / P(A)P(B3 | A) = P(A | B3) * P(B3) / P(A)Total = 1P(A) = P(A ∩ B1) + P(A ∩ B2) + P(A ∩ B3) = 0.11 * 0.45 + 0.51 * 0.62 + 0.38 * 0.85 = 0.6579. So, the probability table is as follows:Prior probabilities,Conditional probabilities,Joint probabilities,Posterior probabilities
P(B1) = 0.11P(A | B1) = 0.45P(A ∩ B1) = 0.0495P(B1 | A) = 0.3419P(B2) = 0.51P(A | B2) = 0.62P(A ∩ B2) = 0.3162P(B2 | A) = 0.4857P(B3) = 0.38P(A | B3) = 0.85P(A ∩ B3) = 0.3217P(B3 | A) = 0.1724Total = 1P(A) = 0.6579
Hence, the completed probability table is as shown above.
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The Jones family has two dogs whose ages add up to 15 and multiply to 44. How old is each dog?
As per the equations, the two dogs are either 11 years old and 4 years old, or 4 years old and 11 years old.
What is factoring?Factoring is the process of breaking down a mathematical expression or number into its component parts, which can then be multiplied together to give the original expression or number. In algebra, factoring is often used to simplify or solve equations.
What is an equation?An equation is a statement that shows the equality of two expressions, typically separated by an equals sign (=). The expressions on both sides of the equals sign are called the "left-hand side" and "right-hand side" of the equation.
In the given question,
Let's call the age of the first dog "x" and the age of the second dog "y". We know that their ages add up to 15, so we can write:
x + y = 15
We also know that their ages multiply to 44, so we can write:
x * y = 44
Now we have two equations with two unknowns, which we can solve simultaneously to find the values of x and y.
One way to do this is to use substitution. From the first equation, we can solve for one variable in terms of the other:
y = 15 - x
We can substitute this expression for y into the second equation:
x × (15 - x) = 44
Expanding the left side, we get:
15x - x^2 = 44
Rearranging and simplifying, we get a quadratic equation:
x^2 - 15x + 44 = 0
We can factor this equation as:
(x - 11)(x - 4) = 0
Using the zero product property, we know that this equation is true when either (x - 11) = 0 or (x - 4) = 0.
Therefore, the possible values of x are x = 11 and x = 4.If x = 11, then y = 15 - x = 4, which means that the ages of the two dogs are 11 and 4.
If x = 4, then y = 15 - x = 11, which means that the ages of the two dogs are 4 and 11.
Therefore, the two dogs are either 11 years old and 4 years old, or 4 years old and 11 years old.
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A train leaves the station traveling north at 85 km/h. Another train leaves at the same time and travels south at 95 km/h. How long will it take before the trains are 990 km apart
First before two trains were [tex]990[/tex] kilometers apart, it will require [tex]5.5[/tex] hours.
What is the mathematical formula for train?Train speed is calculated as total distance traveled divided by travel time. The time it takes for two trains to pass each other is equal to (a+b) / (x+y) if the lengths of the trains, say a or b, are known and they are going at speeds of y and x, respectively.
What fuels trains use?Typically, a locomotive fueled by electricity or diesel powers trains. If there are several route networks, complicated signaling methods are used. One of the quickest forms of land transportation is rail.
[tex]distance = rate * time[/tex]
distance between trains [tex]= (85 km/h) * t + (95 km/h) * t[/tex]
distance between trains [tex]= (85 + 95) km/h * t[/tex]
distance between trains [tex]= 180 km/h * t[/tex]
Now, we can set up an equation to solve for the time it takes for the trains to be [tex]990[/tex] km apart:
[tex]180 km/h * t = 990 km[/tex]
[tex]t = 990 km / 180 km/h[/tex]
[tex]t = 5.5[/tex] hours
Therefore, it will take [tex]5.5[/tex] hours before the two trains are [tex]990[/tex] km apart.
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The performance of a cyclist in a race is affected by whether it rains or not that day.
The probability the cyclist crashes is
4/5 when it's raining and
1/10 when it's dry.
On any given day, the probability of rain is
1/4
What is the probability it was raining given the cyclist crashes?
In light of the cyclist crashes, the likelihood of it being raining is 16/33, or roughly 0.485.
What are examples and probability?It is predicated on the likelihood that something will occur. The fundamental underpinning of theoretical probability is the justification for probability. For instance, the theoretical chance of receiving a head while tossing a coin is ½. If it rains, let R stand for that, and if the cyclist crashes, let C stand for that. We're looking for P(R|C), or the likelihood that it will rain given the crashes involving cyclists. The Bayes theorem can be used to resolve this issue:
P(R|C) = P(C|R) × P(R) / P(C)
Where P(R) is the likelihood of rain, P(C) is the likelihood that the cyclist will crash regardless of the weather, and P(C|R) is the likelihood that the cyclist will crash given that it is raining.
According to the problem statement, we know that:
P(C|R) = 4/5 (the probability of crashing given that it's raining)
P(C|not R) = 1/10 (the probability of crashing given that it's not raining)
P(R) = 1/4 (the probability of rain)
We may use the rule of total probability to determine P(C):
P(C) = P(C|R) × P(R) + P(C|not R) × P(not R)
where P(not R) = 1 - P(R) = 3/4.
When we change the values, we obtain:
P(C) = (4/5) × (1/4) + (1/10) × (3/4) = 11/40
We can now enter each value into Bayes' theorem as follows:
P(R|C) = (4/5) × (1/4) / (11/40) = 16/33
As a result, there is a 16/33, or roughly 0.485, chance that it had been raining when the cyclists crashed.
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Consider the following statements about a system of linear equations with augmented matrix A. In each case either prove the statement or give an example for which it is false.a. If the system is homogeneous, every solution is trivial.b. If there exists a trivial solution, the system is homogeneousNow assume that the system is homogeneous.c. If there exists a nontrivial solution, there is no trivial solution.
In conclusion for a. If the system is homogeneous , every solution is trivial true. b. If there exists a trivial solution, the system is homogeneous false. c. If there exists a nontrivial solution, there is no trivial solution false.
How to solve?
a. If the system is homogeneous, every solution is trivial.
This statement is true. A homogeneous system of linear equations has the form Ax = 0, where A is the coefficient matrix and x is the vector of variables. The trivial solution is always x = 0, which satisfies the equation. Any other solution would require a nonzero x vector, but then Ax would be nonzero, contradicting the fact that it equals zero in a homogeneous system.
b. If there exists a trivial solution, the system is homogeneous.
This statement is false. A system of linear equations can have a trivial solution (i.e., all variables are equal to zero) without being homogeneous. For example, the system
x + y = 0
2x + 2y = 0
has a trivial solution (x = 0, y = 0) but is not homogeneous.
c. If there exists a nontrivial solution, there is no trivial solution.
This statement is false. A homogeneous system of linear equations can have both trivial and nontrivial solutions. For example, the system
x + y = 0
2x + 2y = 0
has both a trivial solution (x = 0, y = 0) and a nontrivial solution (x = 1, y = -1).
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The mean age of n men in a club is 50 years. Two men aged 55 and 63 left the club and mean age reduced by one year. Find the value of n.
Answer:
n=20
Sum of age of men = 50n
when 2 left,
(50n-55-63)/n-2=50-1
50n-55-63=49n-98
50n-55=49n-35
50n-49n=-35+55
n=20
The charity drive was held over two days. On the first day, the 20 artists worked for 6 hours. On the second day, 25 artists turned up and worked for 12 hours. Find the total number of art installations completed over the two days.
Answer:
The charity drive was held over two days. On the first day, the 20 artists worked for 6 hours. On the second day, 25 artists turned up and worked for 12 hours. Find the total number of art installations completed over the two days.
Step-by-step explanation:
Let's start by finding the total number of art installations completed on the first day by the 20 artists who worked for 6 hours. If each artist creates one art installation, then the total number of installations created by the 20 artists is:
20 artists x 6 hours/artist = 120 art installations
On the second day, 25 artists worked for 12 hours. Using the same assumption that each artist creates one art installation, the total number of installations created by the 25 artists is:
25 artists x 12 hours/artist = 300 art installations
Therefore, the total number of art installations completed over the two days is:
120 + 300 = 420
So, the charity drive produced 420 art installations over the two days.
For the function f(x)=x^2+4x-12 solve the following. F(x) ≤0
The solution to the inequality f(x) ≤ 0 is the interval [-6, 2]. In other words, the values of x that satisfy the inequality are those that lie between -6 and 2, inclusive.
To solve the inequality f(x) ≤ 0, we need to find the values of x for which the function f(x) is less than or equal to zero.
We start by factoring the quadratic expression f(x) = x^2 + 4x - 12:
f(x) = (x + 6)(x - 2)
Setting this expression to zero, we get:
(x + 6)(x - 2) = 0
This gives us two solutions: x = -6 and x = 2.
Now, we need to determine the sign of f(x) in the intervals between these two solutions. We can use a sign chart to do this:
x f(x)
-∞ +
-6 0
2 0
+∞ +
From the sign chart, we see that f(x) is positive for x < -6 and for x > 2, and it is negative for -6 < x < 2.
To summarize, the solution to the inequality f(x) ≤ 0 for the function f(x) = x^2 + 4x - 12 is the interval [-6, 2].
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1) y = |x+2| how do i make a table and graph this solution! someone help!!
Answer:
(-1,1)
(0,2
(1,3)
(2,4)
Jeremiah bought 9 apples and 6 apricots for $8.50 yesterday.
He bought 3 apples and 2 apricots for $7.40 today.
Enter a system of linear equations to find the cost of an apple and the cost of an apricot.
Cost of an Apple
Cost of an Apricot
The system of linear equations to find the cost of an apple and the cost of an apricot is as follows:
9x + 6y = 8.50
3x + 2y = 7.40
How to solve system of equation?Jeremiah bought 9 apples and 6 apricots for $8.50 yesterday. He bought 3 apples and 2 apricots for $7.40 today.
The system of linear equation to find the cost of an apple and the cost of an apricot can be represented as follows:
Therefore, system of equation can be solved using different method such as elimination method, substitution method and graphical method.
The linear equation is as follows:
9x + 6y = 8.50
3x + 2y = 7.40
where
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-4
-2
Intro
ty
8
4
-4
-8
N
X
Find the indicated function values.
f(-4)=
f(0) =
f(1) =
O
(>
De
Answer: 1
Step-by-step explanation:
because it not zero and not 4
Write the reciprical of 2/3
Answer:
the answer is 3/2
Step-by-step explanation:
Answer:
the answer si 3/2
The original price of a television is reduced by 25%.
This new price is then increased by 25%.
Calculate the price of the television now as a percentage of the original price.
The new price of the television is 15/16 of the original price
What is percentage?Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number.
Represent the original price by x
x × 25/100 = x/4%
The new price will be
x - x/4
= (4x- x)/4
= 3x/4
The new price is now increased by 25%
25/100 × 3x/4
= 1/4 × 3x/4
= 3x/16
the new price
3x/16 + 3x/4
= (12x + 3x)/16
= 15x/16
Therefore the new price is 15/16 of the original price.
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9(-14)(−2)=
A -15
B 128
C 252
D -252
Answer:
the answer is c
Step-by-step explanation:
add 14 9 times and then whatever that number is double it and remove the negative sign
You have 25 coupons for the hotel A, and 20 coupons for the hotel B. What is the maximum number of coupons for the hotel C that you can use if you are not allowed to spend two consecutive nights at the same hotel? How would I set up an equation to solve this problem?
The maximum number of coupons that we use for hotel C is 21. In order to make an equation for this problem, we follow the process given below.
To maximize the number of coupons for hotel C, we should use as many coupons as possible for hotel A and hotel B. Let y be the number of nights we spend at hotel A, and z be the number of nights we spend at the hotel B.Then we have the following equations:
y + z + x = 45 (the total number of nights we stay in hotels A, B, and C)
y <= 25 (we use a maximum of 25 coupons for hotel A)
z <= 20 (we use a maximum of 20 coupons for hotel B)
x <= minimum of (y, z) (we can spend at most one night at hotel C before switching to another hotel)
To maximize x, we need to minimize y and z. Since we cannot spend two consecutive nights at the same hotel, we should alternate between hotels A, B, and C. Thus, we can either start with hotel A or hotel B and then alternate between the two.
Let's assume we start with hotel A. Then we can spend one night at hotel A, one night at hotel C, one night at hotel B, and repeat. This means that y = z = 12 (we spend 12 nights at each of hotel A and hotel B) and x = 21 (we spend 21 nights at hotel C).
Therefore, the maximum number of coupons for hotel C that can be used is 21.
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