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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 =
Answers
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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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
Answers
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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In the original plan for area codes in 1945, the first digit could be any number from 2 through 9, the second digit was either 0 or 1, and the third digit could be any number except 0. With this plan, how many different area codes are possible
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Using multiple principle, The different area codes that are possible are 144
What is meant by the multiplication principle?The multiplication principle is a counting principle that states the total number of possible outcomes of a series of independent events is equal to the product of the number of outcomes for each event. It is used in probability theory and other areas of mathematics and science.
According to the question
Under the original plan for area codes in 1945, the first digit could be any number from 2 through 9, the second digit was either 0 or 1, and the third digit could be any number except 0.
Therefore, the number of possible area codes can be calculated as follows:
For the first digit, there are 8 possibilities (2, 3, 4, 5, 6, 7, 8, or 9). Here 9 is inclusive.
For the second digit, there are 2 possibilities (0 or 1).
For the third digit, there are 9 possibilities (any digit except 0).
Using the multiplication principle, the total number of possible area codes can be determined by multiplying the number of choices for each digit:
8 × 2 × 9 = 144
So there are 144 different area codes possible according to this plan.
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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)
Answers
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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1) y = |x+2| how do i make a table and graph this solution! someone help!!
Answers
Answer:
(-1,1)
(0,2
(1,3)
(2,4)
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?
Answers
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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The data in the table below shows the number of passengers and number of suitcases on various airplanes.
Estimate to the nearest whole number the number of suitcases on a flight carrying 250 people.
[____________]
Answers
In linear equation, The number of suitcases are 503.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
Equation
y = 1.98x + 7.97
Where,
x = Number of passengers
y = Number of suitcases
Finding the number of suitcases:
y = 1.98x + 7.97
y = 1.98(250) + 7.97
y = 495 + 7.97
y = 502.97 ≈ 503
Hence,
The number of suitcases are 503.
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The data in Exercise 1 were taken from the following functions. Compute the actual errors in Exercise 1, and find error bounds using the error formulas.
a. f ( x ) = sin x b. f (x) = ex − 2x2 + 3x – 1
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The actual errors for Exercise 1 can be computed by subtracting the calculated values from the true values of the functions. For example, the actual error for sin(1.1) can be found by subtracting sin(1.1) = 0.8912 from the calculated value of 0.8890. The actual error in this case is 0.0022.
Error bounds for these functions can be found using the error formulas. For the function f(x) = sin x, the error bound can be found using the formula |E| <= M|x-a|, where M is the maximum value of the first derivative of the function, and a is the value of x at which the error is computed. In this case, M = 1 and a = 1.1, so the error bound is |E| <= 1 * |1.1 - 1.1| = 0.
For the function f(x) = ex - 2x2 + 3x - 1, the error bound can be found using the formula |E| <= M|x-a|2, where M is the maximum value of the second derivative of the function, and a is the value of x at which the error is computed. In this case, M = e and a = 1.1, so the error bound is |E| <= e * |1.1 - 1.1|2 = 0.
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Find the derivative of the function f(x), below. It may be to your advantage to simplify first. f(x)=x⋅5x
f′(x)=
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The derivative of f(x) = x⋅5x is f'(x) = 10x, which means that the rate of change of the function at any point x is 10 times the value of x at that point.
Using the product rule of differentiation, we can find the derivative of the function f(x) = x⋅5x as follows:
f'(x) = (x)'(5x) + x(5x)'
where (x)' and (5x)' are the derivatives of x and 5x with respect to x, respectively.
(x)' = 1 (the derivative of x with respect to x is 1)
(5x)' = 5 (the derivative of 5x with respect to x is 5)
Substituting these values, we get:
f'(x) = 1⋅5x + x⋅5
Simplifying further, we get:
f'(x) = 5x + 5x
Therefore, f'(x) = 10x.
In conclusion, the derivative of f(x) = x⋅5x is f'(x) = 10x, which means that the rate of change of the function at any point x is 10 times the value of x at that point.
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1. find the indefinite integral and check the result by differentiation. (use c for the constant of integration.) S (16׳ – 15x² + 6) dx 2. Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.)S (7 cos(x) +5 sin(x)) dx
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For the first question, the indefinite integral of [tex]16x³ - 15x² + 6[/tex] is [tex]4x⁴ - 5x³ + 6x + C[/tex], where C is the constant of integration.
For the second question, the indefinite integral of 7cos(x) + 5sin(x) is [tex]7sin(x) + 5cos(x) + C,[/tex]where C is the constant of integration.
1)To check the result, differentiate the indefinite integral using the power rule and product rule: [tex](16x³ - 15x² + 6)' = 64x² - 30x + 6.[/tex]
2)To check the result, differentiate the indefinite integral using the sum rule and product rule: [tex](7sin(x) + 5cos(x))' = 7cos(x) - 5sin(x).[/tex]
In summary, to find the indefinite integral of a function, use the power rule and product rule to integrate the individual terms. To check the result, differentiate the indefinite integral.
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uppose m professors randomly choose from n time slots to hold their final exams. If two professors pick the same time slot, we say that they are in conflict. (If three professors all pick the same time slot, that gives three pairs of professors in conflict.) What is the expected number of pairs of professors in conflict? Your answer should depend on m and n.
Answers
The expected number of pairs of professors in conflict is given by (m choose 2) * 1/n.
It can be calculated using the principle of linearity of expectation. We can first calculate the probability that any two professors pick the same time slot, which is 1/n. Then, we can count the number of pairs of professors, which is given by the binomial coefficient (m choose 2) = m(m-1)/2. Therefore, the expected number of pairs of professors in conflict is:
Expected number of pairs in conflict = (m choose 2) * 1/n
This formula holds when the selection of time slots by each professor is independent of the choices made by all other professors. Note that this formula assumes that each professor selects only one time slot, and does not consider the possibility of a professor selecting multiple time slots. If professors are allowed to select multiple time slots, then the formula would need to be modified accordingly.
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please answer im on number 10 easy question
One paperclip has the mass of 1 gram. 1,000 paperclips have a mass of 1 kilogram. How many kilograms are 5,600 paperclips?
560 kilograms
56 kilograms
5.6 kilograms
0.56 kilograms
Answers
Answer:
Since 1 000 paperclips = 1 kilogram
5,600 paperclips x 0.001 kilograms per paperclip = 5.6 kilograms
Answer: 5.6 kilograms
Step-by-step explanation:
5,600 grams = 5.6 kilograms
a chef at a restaurant uses 12 pound of butler each day
Answers
Answer:
Every day, the chef consumes 5443.20 grams of butter, which is calculated using the conversion coefficients 16 oz/1 pound and 28.35 grams/1oz.
A restaurant chef uses 12 pounds of butter every day, as specified in the question.
We need to figure out how much butter the chef uses each day in grams.
Applying the conversion parameters provided, 16 oz/1 lb and 28.35 grams/1oz
According to the data provided, the needed solution is as follows: 12 lb 16 oz/1 lb 28.35 g/1 ounce 5443.20 grams
As a result, the chef consumes 5443.20 grams of butter every day.
Step-by-step explanation:
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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.
Answers
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
a square whose side measures 2 centimeters is dilated by a scale factor of 3 . what is the difference between the area of the dilated square and the original square?
Answers
After figuring out the given issue, we discovered that the original square's area and the dilated square's area differ by 32 square centimeters.
What is the area of square formula?Square Area = Side x Side. Hence, Side2 square units are equivalent to the area of the square. and four side units make up a square's perimeter.
The formula for calculating the area of a initial square with sides that are 2 centimeters long is:
A = s²
A = 2²
A = 4 square centimeters
The revised side length of this square after dilation by a scale factor of 3 is:
s' = 3s
s' = 3(2)
s' = 6 centimeters
Calculations for the dilated square's area are as follows:
A' = s'²
A' = 6²
A' = 36 square centimeters
The area of a dilated square differs from the size of the original square by:
A' - A = 36 - 4
A' - A = 32 square centimeters
As a result, the original square's area and the dilated square's area differ by 32 square centimeters.
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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
Answers
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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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.
Answers
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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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
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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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In the following code, add another array declaration thatcreates an array of 5 doubles called prices and another array of 5Strings called names and corresponding System.out.printlncommands.public class Test1{public static void main(String[] args){// Array exampleint[] highScores = new int[10];// Add an array of 5 doubles called prices.// Add an array of 5 Strings called names.System.out.println("Array highScores declared with size " +highScores.length);// Print out the length of the new arrays}
Answers
In the following code, you can add another array declaration that creates an array of 5 doubles called prices and another array of 5 Strings called names and corresponding System.out.println commands.
public class Test1 {
public static void main(String[] args) {
// Array example
int[] highScores = new int[10];
// Add an array of 5 doubles called prices.
double[] prices = new double[5];
// Add an array of 5 Strings called names.
String[] names = new String[5];
System.out.println("Array highScores declared with size " + highScores.length);
// Print out the length of the new arrays.
System.out.println("Array prices declared with size " + prices.length);
System.out.println("Array names declared with size " + names.length);
}
}
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What is the circumference of the circle with a radius of 5.5 meters? Approximate using π = 3.14.
6.45 meters
34.54 meters
38.47 meters
199.66 meters
Answers
2•3.14• 5.5 = 34.54
Option B
-4
-2
Intro
ty
8
4
-4
-8
N
X
Find the indicated function values.
f(-4)=
f(0) =
f(1) =
O
(>
De
Answers
Answer: 1
Step-by-step explanation:
because it not zero and not 4
What is the ratio of the radius of circle A to the radius of circle B?
Answers
The ratios of the radius of the two circles from their circumferences is 19.09 to 25.11
How to determine the ratios of the circlesWe have the following readings from the question:
Circumference A = 19.09
Circumference B = 25.11
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference and r is the radius of the circle.
We are given the circumferences of circle A and circle B. Let's use the formula to write two equations:
Circumference A = 2πrA = 19.09
Circumference B = 2πrB = 25.11
We can divide these two equations to eliminate π and get the ratio of the radii:
(2πrA) / (2πrB) = 19.09 / 25.11
Simplifying, we get:
rA / rB = 19.09 / 25.11
So, the ratio is 19.09 to 25.11
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For the function f(x)=x^2+4x-12 solve the following. F(x) ≤0
Answers
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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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'
Answers
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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Are the following statements equivalent? a>b and there is the number c ,so that a=b+c
Answers
No, the statements are not equivalent as the statement "a > b" simply means that "a" is greater than "b" and there exists a number "c" such that when added to "b", it equals "a". This does not necessarily mean that "a" is greater than "b".
The statements "a>b" and "there is the number c, so that a=b+c" are not equivalent. The statement "a>b" simply means that "a" is greater than "b," while the statement "there is the number c, so that a=b+c" means that "a" can be expressed as the sum of "b" and another number "c."
These statements are not equivalent because even if "a" is greater than "b," it may not be possible to express "a" as the sum of "b" and another number "c."
Additionally, even if "a" can be expressed as the sum of "b" and another number "c," it may not necessarily be true that "a" is greater than "b."
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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
Answers
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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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'?
Answers
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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find an equation of the line throught the point (3,5) that cuts iff the least area from the first quadrant
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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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what type of data is a questionnaire
Answers
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 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.
Answers
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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