The given equation is exact. An equation is said to be exact if it can be written in the form
M(x,y)dx + N(x,y)dy = 0
where M and N are functions of x and y, and their partial derivatives with respect to y and x, respectively, are equal.
In this case, we have:
M(x,y) = 2y^3
N(x,y) = 3y^2x + 2xy^2
Taking the partial derivative of M with respect to y gives:
∂M/∂y = 6y^2
Taking the partial derivative of N with respect to x gives:
∂N/∂x = 3y^2
Since ∂M/∂y = ∂N/∂x, the equation is exact.
To solve the equation, we need to find a function F(x,y) such that ∂F/∂x = M and ∂F/∂y = N.
Integrating M with respect to x gives:
F(x,y) = y^2x^2 + g(y)
where g(y) is an arbitrary function of y.
Taking the partial derivative of F with respect to y and comparing it with N, we get:
∂F/∂y = 2xy + g'(y) = N
Comparing the coefficients of y and the constant terms, we get:
2x = 3y^2, g'(y) = 2y^2
Solving these equations gives:
x = (3/2)y^2 and g(y) = (2/3)y^3 + C
where C is an arbitrary constant.
Substituting these values in F(x,y), we get:
F(x,y) = (2/3)y^3 + y^2x^2 + C
Therefore, the general solution of the given equation is:
(2/3)y^3 + y^2x^2 = C
where C is an arbitrary constant.
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Listed below are brain volumes (cm3) of unrelated subjects used in a study. Use the sample data to construct a 99% confidence interval estimate of the mean of the brain volume of the population. 963 1027 1272 1079 1070 1173 1067 1347 1100 1204
The 99% confidence interval estimate of the mean of the brain volume of the population is given as follows:
(1009.5, 1250.9).
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 10 - 1 = 9 df, is t = 3.2498.
Using a calculator, the parameters are given as follows:
[tex]\overline{x} = 1130.2, s = 117.45, n = 10[/tex]
The lower bound of the interval is of:
1130.2 - 3.2498 x 117.45/sqrt(10) = 1009.5.
The upper bound of the interval is of:
1130.2 + 3.2498 x 117.45/sqrt(10) = 1250.9.
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add the quotient of 0.4 and 0.7 to the quotient of 1.4 and 0.4
The solution to the statement "add the quotient of 0.4 and 0.7 to the quotient of 1.4 and 0.4" is 4.07
How to determine the solutionFrom the question, we have the following parameters that can be used in our computation:
add the quotient of 0.4 and 0.7 to the quotient of 1.4 and 0.4
Using the above as a guide, we have the following:
0.4/0.7 + 1.4/0.4
Simplify the fractions
4/7 + 7/2
Evaluate the sum
4.07 (approximated)
Hence, the solution is 4.07
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in a recent research poll, 27 of 90 randomly selected men in the u.s. were able to identify india on a map. when 100 randomly selected women in the u.s. were asked, 38 were able to identify india on a map. construct and interpret a 95% confidence interval for the true difference in the proportion of u.s. men and the proportion of u.s. women who can identify india on a map.STATE:99% CI for _____ where______ = The _______of all U.S. men who can identify India on the map and ______= the______ of all US women who can identify India on the map,
State: 99% CI for the true difference in proportions where p1 = the proportion of all U.S. men who can identify India on the map and p2 = the proportion of all US women who can identify India on the map. The main answer is (-0.216, 0.056).
The 95% confidence interval for the true difference in the proportion of U.S. men and women who can identify India on a map is (-0.206, 0.066). This means that we are 95% confident that the true difference in proportions lies between -0.206 and 0.066.
To construct this confidence interval, we use the formula:
CI = (p1 - p2) ± z*SE
where p1 and p2 are the sample proportions for men and women respectively, z is the critical value for a 95% confidence level (1.96), and SE is the standard error of the difference in proportions.
The sample proportion for men is 27/90 = 0.3, and for women it is 38/100 = 0.38. Therefore, p1 - p2 = -0.08. The standard error is:
SE = sqrt(p1*(1-p1)/n1 + p2*(1-p2)/n2) = sqrt(0.30.7/90 + 0.380.62/100) = 0.084
Substituting these values into the formula, we get:
CI = (-0.08) ± 1.96*0.084 = (-0.206, 0.066)
Thus, we can say with 95% confidence that the true difference in proportions of U.S. men and women who can identify India on a map lies between -0.206 and 0.066. This means that there may not be a significant difference between the two proportions.
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The following data show the ages of recent award-winning male actors at the time when they won their award. Make a frequency table for the data, using bins of 20-29, 30-39, and so on.
Click the icon to view the ages of male actors.
Complete the table below.
Age
20-29
30-39
40-49
50-59
60-69
70-79
No. of actors
Here is the frequency table for the data, using bins of 20-29, 30-39, and so on:
Age
20-29: 14 actors30-39: 14 actors40-49: 14 actors50-59: 7 actors60-69: 4 actors70-79: 1 actorWhat is a Frequency Table?A table that is created to display the distribution of a characteristic's frequency of occurrence in accordance with a specific set of class intervals.
With the ages and data sets given, we are able to compute the frequency of occurrence in the data set using the specific class interval given.
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the velocity of a vehicle is given in fig. \( 1.8 \). a. determine the equation of \( v(t) \) for i. \( 0 \leq t \leq 3 \) s ii. \( 3
The linear equation for the vehicle on each given time is:
0s ≤ x ≤ 3s: y = -4x + 283s ≤ x ≤ 6s: y = 126s ≤ x ≤ 9s: y = -4x + 36t ≥ 9s: y = 0Please refer to the attached picture for the complete question and the graph.
From the case, we know take several points based on the given time:
(0, 24)(3, 12)(6, 12)(9, 0)We can find the linear equation for each given time by finding the slope of the line and the constant of c. Remember that the linear equation formula is:
y = mx + c
where:
m = slope of line
c = constanta
We take the first 2 points:
(0, 24)
(3, 12)
slope (m) = y₂ - y₁
x₂ - x₁
m = (12 - 24) / (3 - 0)
m = (-12)/3 = - 4
We take the value of m into the linear equation and test it on one of the point we have:
(0, 24)
y = mx + c
24 = (-4)(0) + c
24 = - 4 + c
c = 28
Linear equation: y = -4x + 28
Next, we will take another pair of points:
(3, 12)
(6, 12)
slope (m) = (12 - 12) / (6 - 3)
m = 0
This shows that the linear equation for this part of graph is:
y = 12 --> because no matter changes on x, the value of y remains.
We take another pair of points:
(6, 12)
(9, 0)
slope (m) = (0 - 12) / (9 - 6)
m = (-12)/3 = -4
We take the value of m into the linear equation and test it on one of the point we have:
(9, 0)
y = -4x + c
0 = -4 (9) + c
c = 36
The linear equation for this part of graph is y = -4x + 36
The other part of graph's linear equation is y = 0 because the car has come into stop.
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Q. 2 Transmission Trials In a wireless automatic meter reading system, a base station sends out a wake up signal to nearby electric meters. Upon receiving the wake up signal, a meter transmits a message indicating the electric usage. This message is repeated 4 times. A single transmission of the message is error-free with probability
p=0.9
, independent of the other transmissions. 1. Let
N
be a random variable that denotes the number of error-free transmissions for a single meter upon receiving the wake-up call. Find the PMF of
N
2. In practice, the system does not know which messages are error-free. It uses an error correction scheme which is able to decode the correct message if at least 3 out of 4 transmissions are error-free. What is the probability that the system is able to decode the correct message?
The probability that the system can decode the correct message is approximately 0.9477.
The random variable N denotes the number of error-free transmissions for a single meter upon receiving the wake-up call.
Since each transmission is error-free with probability p=0.9 and the transmissions are independent, the number of error-free transmissions follows a binomial distribution with parameters n=4 (number of trials) and p=0.9 (probability of success in each trial).
The probability mass function (PMF) of N is given by:
P(N=k) = (4 choose k) × [tex]0.9^k[/tex] × [tex]0.1^{(4-k)}[/tex], for k = 0, 1, 2, 3, 4
where (4 choose k) is the binomial coefficient, which represents the number of ways to choose k successes out of 4 trials.
The error correction scheme can decode the correct message if at least 3 out of 4 transmissions are error-free. Let X be the number of error-free transmissions for a single meter.
Then the probability that the system can decode the correct message is:
P(X >= 3) = P(X = 3) + P(X = 4)
To find these probabilities, we use the PMF of N from part 1:
P(X = 3) = P(N = 3) + P(N = 4) = (4 choose 3) × [tex]0.9^3[/tex] × 0.1 + (4 choose 4) × [tex]0.9^4[/tex] × [tex]0.1^0[/tex] = 0.2916
P(X = 4) = P(N = 4) = (4 choose 4) × [tex]0.9^4[/tex] × [tex]0.1^0[/tex] = 0.6561
Therefore, the probability that the system can decode the correct message is:
P(X >= 3) = P(X = 3) + P(X = 4) = 0.2916 + 0.6561 = 0.9477.
So the probability that the system can decode the correct message is approximately 0.9477.
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Masks are $5.18 for a box of 50, how much does each mask cost?
Answer: .1036
Step-by-step explanation:
Admission to a circus is $16 for adults and $8 for children Select the numerical expression that shows the total cost of 3 adults and 8 children.
24
⋅
11
24⋅11
16
⋅
3
+
8
⋅
8
16⋅3+8⋅8
16
+
8
⋅
3
⋅
8
16+8⋅3⋅8
Answer:b or 2 option
Step-by-step explanation= $16x3=48 and $8x8=64 adding those together equals $112 and that is what answer b says i would really apreaciate branliest.
Jason spent $15.75 on art supplies.
This is $3.90 more than Andreas spent on art supplies.
Which equations represent this situation, including the amount that Andreas spent on art supplies?
1. a +3.90 15.75
a=19.65
2. 3.90 + a 15.75
a = 11.85
3. 3.90 + a = 15.75
a = 11.85
4. a 3.90 15.75
a = 19.65
Answer:
11.85 (3)
Step-by-step explanation:
The correct equation that represents this situation is:
3.90 + a = 15.75
where "a" represents the amount that Andreas spent on art supplies.
To solve for "a", we can subtract 3.90 from both sides:
a = 15.75 - 3.90
a = 11.85
Therefore, Andreas spent $11.85 on art supplies.
Discuss the costs and benefits of overdraft protection and lines of credit.
When you sign up for overdraft protection, checks, and other bank features, debit transactions clear even if there is not enough money in the account. The bank may charge large fees for overdraft protection. Instead of paying a fee, some people choose to have a line of credit tied to their checking account.
Kevin is opening a new checking account and is trying to decide if he should sign up for overdraft protection, a line of credit, or neither. Research both options and then discuss the advantages and disadvantages of each option.
Overdraft protection and lines of credit are two financial tools that can be used to cover unexpected expenses or short-term financing needs. Some of their costs and benefits are shown below.
What are overdraft protection and lines of credit ?Overdraft protection is a service offered by banks to protect their customers from overdraft fees. If a customer tries to withdraw more money than is available in their account, the bank will cover the transaction and charge a fee.
The cost of overdraft protection is usually a fee charged by the bank for each overdraft transaction, which can add up over time. The benefit of overdraft protection is that it can help customers avoid overdraft fees and the embarrassment of declined transactions.
Lines of credit are a type of loan that allows borrowers to access funds up to a certain limit. They are typically unsecured, meaning that they do not require collateral, and are often used for short-term financing needs such as home improvements, car repairs, or unexpected expenses.
The cost of a line of credit is usually an interest rate on the amount borrowed. The benefit of a line of credit is that it provides access to funds when they are needed, without having to apply for a loan each time.
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please help me im doing pre alg and i cant figure out wether i shade up or to the side; graph x > 1
The representations of the inequality is an open circle is at 1 and a bold line starts at 1 and is pointing to the right.
How to graph an inequality?An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.
Since our answer is x > 1. An open circle will be at 1 and a bold line starts at 1 and is pointing to the right (>). Check the attached image.
Note: You only shade up if you have ≤ (less than or equal) or ≥ (greater than or equal).
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you are given the following probability distribution for a stock probability outcome 5 6 5 18 1 a compute the expected return 0.5 0.06 0.5 0.18 6 2 b compute the standard deviation 3 c compute the coefficient of variation
If probability distribution for a stock probability outcome is 5, 6 ,5 ,18, 1.
a) The expected return is 1.56
b) The standard deviation is 5.1715
c) The coefficient of variation is 331.25%.
To calculate the expected return, we multiply each possible outcome by its probability and then sum the results. For example, the expected return from a 5% return is calculated as 0.5 x 5%, or 0.025. We do this for each possible outcome and then sum the results to get the expected return for the investment.
In this case, the expected return is 1.56, which means that over the long run, we can expect to earn an average return of 1.56% on this investment.
The standard deviation is a measure of how much the possible outcomes of an investment vary from the expected return. A higher standard deviation means that the possible returns are more spread out, while a lower standard deviation means that the possible returns are more tightly clustered around the expected return.
To calculate the standard deviation, we first need to calculate the variance, which is the average of the squared deviations from the expected return.
To calculate the variance, we first calculate the deviation of each possible outcome from the expected return. For example, the deviation of a 5% return from the expected return of 1.56% is 5% - 1.56% = 3.44%.
We then square each deviation and multiply it by the probability of that outcome. We do this for each possible outcome, and then sum the results to get the variance. In this case, the variance is 26.7424, which means that the possible returns are quite spread out.
The coefficient of variation is a measure of the risk per unit of return. It is calculated by dividing the standard deviation by the expected return and then multiplying by 100% to get a percentage. In this case, the coefficient of variation is 331.25%, which means that the investment is quite risky relative to its expected return.
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A line passes through the point (-4, 6) and has a slope of 5/4. Write and equation in slope-intercept form for this line
In slope-intercept form, the equation of the line is y = (5/4)x + 6 1/2.
What is equation?An equation in mathematics is a statement that two expressions are equal. An equation can be written in the form of a mathematical expression on the left side equal to a value or another mathematical expression on the right side. There are different types of equations, including linear equations, quadratic equations, and exponential equations, among others. Equations can be solved for a specific variable, and the solution is the value of the variable that makes the equation true. The process of solving an equation involves isolating the variable on one side of the equation and finding its value.
Here,
The slope-intercept form of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point at which the line intersects the y-axis. To find the equation of a line in slope-intercept form given its slope and a point on the line, we can use the following steps:
Use the point-slope form of a line: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Plug in the slope and the point: y - 6 = (5/4)(x + 4).
Solve for y: y = (5/4)x + (26/4).
Simplify the equation: y = (5/4)x + 6 1/2.
So, the equation of the line in slope-intercept form is y = (5/4)x + 6 1/2.
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boy can row a boat at a constant rate of 5 mi/hr in still water, as indicated in the figure. He rows upstream for 15 minutes and then rows downstream, returning to his starting point in another 10 minutes.
(a) Find the rate of the current. mi/hr
(b) Find the total distance traveled. mi
The rate of the current is 10 mi/hr and the total distance traveled is 100 mi.
Let S be the speed of the current, R be the speed of the boat in still water, t1 be the time taken to row upstream and t2 be the time taken to row downstream. The total distance traveled is given by the formula [tex]d = R(t1 + t2)[/tex]. In this case, [tex]d = 5(15 + 10) = 100 mi[/tex].
To calculate the rate of the current, we can use the formula[tex]d = (R + S)t1 = (R - S)t2[/tex]. In this case, 100[tex]= (5 + S)15 = (5 - S)10[/tex], which can be simplified to [tex]S = (100 - 50)/5 = 10 mi/hr[/tex].
Therefore, the rate of the current is 10 mi/hr and the total distance traveled is 100 mi.
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PLEASE HELP
“Simplify the following using the properties of exponents”
A). (3x^-3y^5)^4
B). 5x^0
Answer:
[tex]A) 81x^{-12}y^{20}[/tex]
B) 5
Step-by-step explanation:
[tex]A) (3x^{-3}y^5)^4=(3)^4 \,\cdot\, (x^{-3})^4\,\cdot\,(y^5)^4=81x^{-12}y^{20}\\\\B) 5x^0=5(1)=5[/tex]
Math help needed, within 30 minutes please :)
34.) If a fruit punch is made using 3 parts strawberries, 2 parts blueberry, 2 parts lime juice, 3 parts simple syrup, and 6 parts I’ve. How many ounces of each ingredient do you need to make five gallons? (Note: 1 gal=128 oz.)
Show with steps please! It’s a practice problem and I’m trying to learn. :)
120 ounce of strawberry, 80 ounce of blueberry, 80 ounce of lime juice, 120 ounce of simple syrup and 240 ounce of sugar is needed to make five gallons (640 ounces) of fruit punch
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
1 gal = 128 oz. Hence:
5 gal = 5 gal * 128 oz. per gal = 640 ounces
If a fruit punch is made using 3 parts strawberries, 2 parts blueberry, 2 parts lime juice, 3 parts simple syrup, and 6 parts sugar. Hence. of 5 gallons:
Amount of strawberry = [3/(3 + 2 + 2 + 3 + 6)] * 640 ounces = (3/16) * 640 = 120 ounces
Amount of blueberry = [2/(3 + 2 + 2 + 3 + 6)] * 640 ounces = (2/16) * 640 = 80 ounces
Amount of lime juice = [2/(3 + 2 + 2 + 3 + 6)] * 640 ounces = (2/16) * 640 = 80 ounces
Amount of simple syrup = [3/(3 + 2 + 2 + 3 + 6)] * 640 ounces = (3/16) * 640 = 120 ounces
Amount of sugar = [6/(3 + 2 + 2 + 3 + 6)] * 640 ounces = (6/16) * 640 = 240 ounces
120 ounce of strawberry, 80 ounce of blueberry, 80 ounce of lime juice, 120 ounce of simple syrup and 240 ounce of sugar is needed
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lo . Madison hace un mantel individual. Lo divide en 6 partes iguales para colorearlo. ¿Cómo se llaman las partes?
The scale factor of for the given scaled reproduction of figure {P} to figure {Q} is 7/10.
What is scale factor?Scale factor is a constant value that is used to dilate (enlarge or reduce) the image size. Mathematically, for the scale factor -
{K} > 1 : Enlargement
{K} < 1 : Shrinking
{K} = 1 : Preserved
Given is figure {Q} is a scaled reproduction of figure {P}.
We can write the ratio of their corresponding sides as constant. So, we can write, the scale factor as -
K = 14/20
K = 7/10
Therefore, the scale factor of for the given figure {P} to figure {Q} is 7/10.
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{QUESTION IN ENGLISH -
Figure Q is a scaled reproduction of Figure P. What is the number by which the measurement of Figure Q must be multiplied to obtain Figure P?
Figure P
20cm
Figure Q
14cm
Solve and explain how you would use ratios and proportions to answer
the following two questions:
If Layla paid $48 for 4 movie tickets, how much would it cost her to
purchase 7 tickets? How much does each ticket cost? !USE RATIOS AND PROPORTIONS IN YOUR ANSWER!
Answer:
1/ $12 for each ticket
2/ $84 for 7 tickets
Step-by-step explanation:
We know
Layla paid $48 for 4 movie tickets
How much does each ticket cost?
48 / 4 = $12 for each ticket
So, each ticket cost $12
How much would it cost her to purchase 7 tickets?
12 x 7 = $84
So, it cost her $84 to purchase 7 tickets.
Consider the curve C parametrized by x= t and y (`6-t^2)^1/2 for -4≤ t ≤ 4 write an equation relating x and y but without t and without square roots. write it so variable terms are on one side and any constant on the other side.
An equation relating x and y but without t and square roots is represented by x² + y² = 16, here variable terms are present on one side and any constant on the other side.
A function is represented in the cartesian form, such as, f(x,y)=0 or expressed in the form of parametric equations, written as
r(t) = ⟨x(t),y(t)⟩, α ≤ t ≤ β
the position vector, x(t) and y(t) helps to determine the location of a particular point on the curve with respect to a third independent parameter or varible t. We have, a curve C with parametrized equation, x = t and y = √(6-t²) for -4≤ t ≤ 4. We have to write eqution related to x and y without t and square roots. So,
substitute t = x in y
=> y = √(16 − x²)
squaring on both sides
=> y² = (16 - x²)
=> x² + y² = 16
Hence, the required equation is x² + y² = 16.
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in terms of the function s, the limit we would have to evaluate in order to calculate the slope of the tangent line to s at t=1 is
It is not possible to give an exact answer to this question without knowing the specific function s. However, in general, the slope of the tangent line to a function s at a specific point t can be found by taking the derivative of the function s at that point.
If we let f(t) be the function s, then the derivative of f(t) at t=1 would give us the slope of the tangent line to s at that point. This can be written mathematically as:
s'(1) = lim(h->0) [s(1+h) - s(1)]/h
Here, s'(1) represents the derivative of s at t=1, and h represents a small change in t. By taking the limit as h approaches 0, we can find the instantaneous rate of change of s at t=1, which is the slope of the tangent line to s at that point.
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1
2
3
4
5
6
7
8
9
4
1 point
Find AC.
A
O
B
3√2
3√3
3
6
Previous
3
C
Answer:
the answer is 3√3
Step-by-step explanation:
seven high school teachers want to schedule exams for their classes next week in such a way that no student has to take more than one exam each day. the teachers have consulted with each other, and found that their students overlap as follows:
The problem of scheduling exams for the high school students can be solved by using graph theory. We can represent the overlap of students in the form of a graph where each teacher is a node and the edges represent the students who belong to both the teachers classes.
To ensure that no student has to take more than one exam each day, we need to find a coloring of the graph such that no two adjacent nodes have the same color. This is equivalent to scheduling exams such that no two exams on the same day have any common students.
Using a greedy approach, we may overcome this issue by starting with any node and assigning it a color.. We then recursively color the neighbors of the node with a different color and so on. This algorithm will always produce a valid coloring since we are guaranteed to find a valid color for every node, given that we have not run out of colors.
In this case, we have seven teachers so we need at least seven colors. However we can find a valid coloring with fewer colors, depending on the structure of the graph. This problem can also be extended to more general situations, where we have more than one exam per day or where we have more complex constraints on the scheduling of exams.
The answer is general as no additional data is given.
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Which choice shows 25.367 written in expanded form?
(2 × 1) + (5 × 1) + (3 × 0.1) + (6 × 0.001) + (7 × 0.001)
(2 × 10) + (5 × 1) + (3 × 0.1) + (6 × 0.001) + (7 × 0.001)
(2 × 10) + (5 × 1) + (3 × 0.1) + (6 × 0.01) + (7 × 0.001)
(2 × 10) + (5 × 1) + (6 × 0.01) + (3 × 0.001) + (7 × 0.001)
Answer:
the third one
Step-by-step explanation:
(2 × 10) + (5 × 1) + (3 × 0.1) + (6 × 0.01) + (7 × 0.001)
20+5+0.3+0.06+0.007=25.367
Answer:
the third number will be correct answer
a statistics professor asks each of the students in an introductory statistics class to fill out a survey. there are only 10 students in the class, and each one filled out the survey. one of the questions asked students to state their age. the data are included below. use a ti-83, ti-83 plus, or ti-84 to calculate each of the population standard deviation and the population variance. round your answers to one decimal place. do not use rounded intermediate values to calculate either parameter. age of students 24 34 18 26 23 35 25 24 19 helpcopy to clipboarddownload csv provide your answer below:
Based on the provided data, the population standard deviation is 6.0 and the population variance is 36.0.
To calculate the population standard deviation and variance using a TI-83, TI-83 Plus, or TI-84 calculator, follow these steps:
1. Press the "STAT" button, and then select "Edit" to enter the data.
2. Enter the ages of the students into a list. For example, you could enter the ages into list L1.
3. Once you have entered the data, press the "STAT" button again, and then select "CALC."
4. Choose "1-Var Stats" and enter the list name that contains the data (L1 in this case). Press "ENTER" to see the result.
5. The calculator will display a list of statistics, including the population standard deviation (σx) and the population variance (σx²). Round these values to one decimal place.
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The equation shown is used to find the force of gravity, F, between tow objects
The equation shown is used to find the force of gravity, F = G(m₁m₂)/R², between two objects.
What is gravitational force?All physical things with mass are drawn to the gravitational force, which can be thought of as an attractive force. The strongest known natural force is actually this one.
The attracting force F has a magnitude equal to G. (the gravitational constant, a number the size of which depends on the system of units used and which is a universal constant) multiplied by the product of the masses (m₁ and m₂) and divided by the square of the distance R:
F = G(m₁m₂)/R².
Newton’s Law would imply an infinite gravitational force when two very small objects touch, that is, when their centers of mass are so close that "r" is effectively zero.
In reality, this would only take place at the subatomic scale, but at the time of Newton, they were unaware of subatomic particles, the Quantum Theory, or Einstein's reinterpretation of gravity, which would have allowed them to rule out infinite or extremely strong gravitational forces. The least powerful force is gravity.
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Which relation is a function?
The relation that is a function is D (see image below).
How to Determine if a Relation is a Function Using the Vertical Line Test?If any vertical line passes through more than one point on a graph, then the relation is not a function. Conversely, if every vertical line intersects the graph at most one point, then the relation is a function.
Applying the vertical line test, if we place a vertical line across each graph given, only the graph in option D (as shown in the image below) will have the the vertical line intersects it at most one point.
Therefore, the correct option is D. (see image below).
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An investment firm offers its customers municipal bonds that mature after varying number of years. Given that the cumulative distribution function of t, the number of years to maturity for a randomly selected bond is:f(x) = { 0 t < 1{ 1/4 1 ≤ t < 3{ 1/2 3 ≤ t < 5{ 3/4 5 ≤ t < 7{ 1 t ≥ 7Find:a) P(T = 5)b) P(T > 3)c) P(1.4 < T < 6)d) P(T ≤ 5 | T ≥ 2)
The cumulative distribution function of t, the number of years to maturity for a randomly selected bond is a. 1/4, b. 3/4, c. 1/2, d. 1/3.
The probability of a randomly selected bond maturing exactly after 5 years is 1/4. The probability of a randomly selected bond maturing after more than 3 years is 3/4. The probability of a randomly selected bond maturing between 1.4 and 6 years is 1/2.
a) P(T=5) = F(5) - F(4) = 3/4 - 1/2 = 1/4
b) P(T>3) = 1 - P(T≤3) = 1 - F(3) = 1 - 1/4 = 3/4
c) P(1.4 < T < 6) = F(6) - F(1.4) = 3/4 - 1/4 = 1/2
d) P(T≤5 | T≥2) = P(2 ≤ T ≤ 5) / P(T≥2) = (F(5) - F(2)) / (1 - F(2)) = (3/4 - 1/4) / (1 - 1/4) = 1/3
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The question is -
An investment firm offers its customers municipal bonds that mature after varying numbers of years. Given that the cumulative distribution function of t, the number of years to maturity for a randomly selected bond is:
f ( x ) = ⎧ 0 t < 1
⎪ 1 / 4 1 ≤ t < 3
⎪ 1 / 2 3 ≤ t < 5
⎨ 3 / 4 5 ≤ t < 7
⎩ 1 t ≥ 7
Find: a) P(T = 5) b) P(T > 3) c) P(1.4 < T < 6) d) P(T ≤ 5 | T ≥ 2)
convert 10111.011 base 2 to binary
Answer:
Step-by-step explanation:
The number 10111.011 in base 2 is already in binary, so no conversion is necessary.
The Melbourne Formula 1 track is 5.303 km in length.
The track record is 1 minute and 24 seconds. What is
the average speed (km/h) for the lap record? Answer
correct to two decimal places.
To calculate the average speed of the lap record, we need to know the distance covered and the time taken.
Distance = 5.303 km
Time = 1 minute and 24 seconds = 84 seconds
To convert seconds to hours, we divide by 3600 (the number of seconds in an hour):
[tex] \frac{84 \: seconds \:}{3600} = 0.02333 \: hours[/tex]
Now we can calculate the average speed:
[tex]Average \: speed = \frac{d}{t} = \frac{5.303km}{0.02333} [/tex]
Average speed = 227.59 km/h
Li Marie's water tables are evenly spaced along the 5,000-meter (or 5-kilometer) course, including one at the beginning and one at the end. What is the distance between each pair of tables that are next to each other? Hint: There are not 9 sections between tables.
The distance between each of the 9 tables is given as follows:
625 meters.
How to obtain the distance?The distance is obtained applying the proportions in the context of the problem.
A proportion is applied as the distance is calculated by the division of the total distance by the number of spaces, which is one less than the number of tables.
The parameters for this problem are given as follows:
Total distance of 5000 meters.Eight spaces.Hence the distance between each of the 9 tables is obtained as follows:
5000/8 = 625 meters.
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