Answers
It is a proportionate relationship if the ratio remains not constant constant.
What kind of relationship is proportional?As an illustration of a proportionate relationship in real life, let's look at the following: There is a correlation between the number of gallons of gas we put in our car and the price we will have to pay when we fill up the tank. That is to say, the more gas we use, the more we will have to pay.
When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. The "constant of proportionality" is a term used to describe this constant.
Examining the ratios between the two variables will help you determine whether a relationship is proportional. It is a proportionate relationship if the ratio remains constant.
11 $24
36 $39
66 $79
85 $98
It is a proportionate relationship if the ratio remains not constant constant.
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Related Questions
3/5x - 1/3x = 4 find x
Answers
Answer:
x = 15
Step-by-step explanation:
3/5x - 1/3x = 4
9/15x - 5/15x = 4
4/15x = 4
x = 15
(a) (5 pts) prove the following identity: n 1 log n = 2
Answers
This proof by induction shows that n + 1 log n = 2 for all positive integers n. This holds true since S(1) = 2, and S(k + 1) = 2 for any integer k ≥ 1.
Proof:
Let S(n) = n + 1 log n
We will prove S(n) = 2 by induction.
Base Case:
Let n = 1. Then S(1) = 1 + 1(log 1) = 1 + 0 = 1 = 2.
Inductive Step:
Assume S(k) = 2 for some arbitrary integer k ≥ 1. We must show that S(k + 1) = 2.
S(k + 1) = (k + 1) + 1(log(k + 1))
= k + 1 + 1(log k + log 1)
= k + 1 + 1(log k + 0)
= k + 1 + 1(log k)
= k + 1 + log k
= 2 + log k
= 2 (by induction hypothesis)
Therefore, S(n) = 2 for all positive integers n.
This proof by induction shows that n + 1 log n = 2 for all positive integers n. This holds true since S(1) = 2, and S(k + 1) = 2 for any integer k ≥ 1.
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What is a fundamental solution in differential equations?
Answers
The coefficients in the linear combination are determined by the initial or boundary conditions of the problem.
What is the differential equations?
A differential equation is an equation that relates an unknown function to its derivatives. It describes the behavior of a physical, biological, or engineering system in terms of changes in variables over time.
A fundamental solution in differential equations is a particular solution to a differential equation that contains arbitrary constants. It is called "fundamental" because it is a building block for constructing more general solutions to the equation. The general solution to a differential equation can be found by adding a linear combination of several fundamental solutions. The coefficients in the linear combination are determined by the initial or boundary conditions of the problem.
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eval calculates an expression and puts the resulting ____ into a new or existing field.
Answers
Eval is a function that evaluates an expression and puts the resulting value into a new or existing field.
To calculate the value of an expression using Eval, you must use the correct syntax. The syntax for Eval is Eval(expression, optional_parameter). The expression can take the form of a mathematical equation or a logical expression. For example, if you wanted to calculate the sum of two numbers, you would use the following expression: Eval(A + B). The optional parameter allows you to specify a range of values to evaluate the expression against.
For example, if you wanted to calculate the sum of two numbers within a given range, you would use the following expression: Eval(A + B, range). The range parameter can be used to specify the starting and ending values that the expression should be evaluated against.
Using Eval to calculate an expression is a useful tool for quickly getting the desired value. It is also useful for quickly testing the accuracy of a complex expression before implementing it in your code.
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using the squeeze theorem to find the limit of (xy^4)/(x^4 y^4)
Answers
The limit of (xy⁴)/(x⁴y⁴) is 0.
The limit squeeze theorem (also known as sandwich theorem) states that if a function f(x) lies between two functions g(x) and h(x) and the limits of each of g(x) and h(x) at a particular point are equal (to L), then the limit of f(x) at that point is also equal to L. This looks something like what we know already in algebra. If a ≤ b ≤ c and a = c then b is also equal to c. The squeeze theorem says that this rule applies to limits as well. We define the squeeze theorem mathematically as follows:
"Let f(x), g(x), and h(x) are three functions that are defined over an interval I such that g(x) ≤ f(x) ≤ h(x) and suppose lim ₓ → ₐ g(x) = lim ₓ → ₐ h(x) = L, then lim ₓ → ₐ f(x) = L".
Here:
The function f lies between g and h and hence they are lower and upper bounds of f respectively.
'a' doesn't necessarily need to be within I.
We have to find the limit of (xy⁴)/(x⁴y⁴).
After applying the limit squeeze theorem, we get
[tex]\lim_{x \to \infty} \frac{xy^{4} }{x^{4}y^{4} }\\ = \lim_{x \to \infty} \frac{1}{x^{3} } \\= 0[/tex]
Thus, the limit of (xy⁴)/(x⁴y⁴) is 0.
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add parentheses to the regular expression to remember the street number (which is: 613) and apartment number (which is: apt 57), but not remember the street name.
Answers
Adding parentheses to a regular expression can be used to capture specific information, such as the street number and apartment number in this example.
A regular expression is a pattern used to match and search for specific strings. To remember the street number "613" and apartment number "apt 57" but not the street name, we can add parentheses to the regular expression to create capturing groups. The parentheses will capture the desired information and allow us to reference it later if needed.
The regular expression would look something like this: (613) (apt 57)
The parentheses indicate that the information inside should be captured as a group. This regular expression will match a string that contains the street number "613" and the apartment number "apt 57", and capture these values in two separate groups.
For example, if we have the following address: "613 Main St, apt 57"
We can use the regular expression to match the desired information:
(613) (apt 57)
In this case, the two groups captured are "613" and "apt 57". The information inside the parentheses can be accessed and used for various purposes, such as formatting or validation.
In summary, adding parentheses to a regular expression can be used to capture specific information, such as the street number and apartment number in this example. This allows for more precise and flexible matching and extraction of information from strings.
Therefore, Adding parentheses to a regular expression can be used to capture specific information, such as the street number and apartment number in this example.
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if l is parallel to m find x
Answers
The correct answer fort parallel angles is x = 33° and y = 10°.
What is an example of a similar angle?The angles created when a transversal intersects two parallel lines are known as corresponding angles. Opening and shutting a lunchbox, completing a Rubik's cube, and an infinite stretch of parallel train lines are common examples of identical angles.
Angle 3y + 20° and angle 5y are parallel angles.
3y + 20° = 5y
2y = 20°
y = 10°
Angles 2x - 16° and 3y + 20° are in direct opposition to one another.
3y + 20° = 2x - 16°
Put the value of angle y in the equation.
3(10) + 20 = 2x - 16
30 + 20 = 2x - 16
50 = 2x - 16
2x = 66
x = 33
As a result, the angles are 33° for x and 10° for y.
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Question:
Find the value of x for which l is parallel to m. The diagram is not to scale. Lines l and m are parallel.
A medical clinic is randomly selecting three staff members to attend a conference. The clinic employees include 7 nurses, 3 doctors, and 4 office staff. What is the probability that three nurses are selected to attend the conference?
0.10
0.13
0.42
0.50
Answers
Answer:
50%
Step-by-step explanation:
7 nurses
3 doctors
4 offices
14 in total
7/14 or 50% is the probability
Answer:
0.50
Step-by-step explanation:
[tex]7 + 3 + 4 = 14[/tex]
So, the probability that the nurses are selected to attend the conference is,
[tex] \frac{7}{14} = \frac{1}{2} [/tex]
[tex] \frac{1}{2} = 0.50[/tex]
Which of the following would be classified as categoricalâdata?
Choose the correct answer below.
Hair color
Number of suitcases on a plane
Tree height
Amount of rainfall
Answers
Categorical data is data that can be divided into different categories. Examples of categorical data include hair color, number of suitcases on a plane, tree height, and amount of rainfall.
Hair color would be classified as categorical data because it can be divided into categories such as black, brown, blonde, and red. Number of suitcases on a plane would also be classified as categorical data because the amount of suitcases can be divided into categories such as 0, 1, 2, 3, etc. Tree height would be classified as categorical data as it can be divided into categories such as small, medium, and large. Amount of rainfall would also be classified as categorical data as it can be divided into categories such as light rainfall, moderate rainfall, and heavy rainfall.
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Dennis is 55 5/6 inches tall. Dwight is 1 1/3 inches shorter than Dennis and Jane is 1 1/4 inches shorter than Dwight. How tall is Jane?
Answers
Answer:
53 1/4
Step-by-step explanation:
55 5/6 - 1 1/3 - 1 1/4 Rewrite with a common denominator
55 10/12 - 1 4/12 - 1 3/12
55 10/12 - 1 4/12 = 54 6/12
54 6/12 - 1 3/12
53 3/12
53 1/4
Which expression is equivalent to this expression?
3/4(4h – 6)
Answers
The equivalent expression is 12h - 18/4
How to determine the equivalent expressionIt is important to note that algebraic expressions are mathematical expression comprising of factors, constants, coefficients, variables and terms.
These algebraic expressions are also known to be made up of mathematical to arithmetic operations, such as;
Floor divisionSubtractionAdditionDivisionBracketParenthesesMultiplicationFrom the information given, we have that;
3/4(4h – 6)
To simply this, we need to expand the bracket, we get;
12h - 18/4
Hence, the expression is 12h - 18/4
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Hazma’s Logo wants to create a bumper sticker with his design.
Bumper stickers usually have a height of 3 1/2 inches.
What will the width of his sticker be?
Answers
The width of the sticker will be 8 3/4 inches.
What is a scale factor?The scale factor defines a variable in a ratio of two different measurements.
Sometimes drawings of large models are represented in a scale factor of a smaller unit.
Given, The given logo has a height of 2 inches and a width of 5 inches.
Bumper stickers usually have a height of 3 1/2 inches which has a
= (7/2)/2 = 7/4 scale factor.
Therefore, The width of the sticker will be,
= 5×(7/4).
= 35/4.
= 8 3/4 iches.
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in fall 2020, the department has a cohort of 100 mds juniors. students in the class are enrolled in various classes including stor 435 (undergraduate probability), math 547 (linear algebra for applications) and comp 401 (foundations of programming). to simplify notation below i will denote these as prob., la and comp. assume the classes are not taught at the same time so there can be students who are taking all 3 courses. further there can also be students who are taking none of these 3 courses. 65 of these students are in prob, 45 in la and 40 in comp. there are 25 students that are in both prob. and comp, 20 that are in both la and comp, and 30 that are in both prob. and la. in addition, there are 10 students taking all 3 classes. how many students are taking none of the classes? (you can use venn diagrams for this problem.)
Answers
30 students are taking none of the classes.
We can use the Principle of Inclusion-Exclusion (PIE) to determine the number of students taking none of the classes. The PIE states that the total number of elements in the union of several sets is equal to the sum of elements in each set, minus the sum of elements in the pairwise intersections, plus the sum of elements in the three-way intersections, and so on.
In this case, we want to find the number of students taking none of the classes, which is equal to the total number of students (100) minus the number of students taking at least one class.
So, we can apply PIE as follows:
students taking none of the classes = 100 - (students in prob. + students in la + students in comp - students in prob. & comp - students in la & comp - students in prob. & la + students in prob., comp & la)
Using the given information, we have:
students taking none of the classes = 100 - (65 + 45 + 40 - 25 - 20 - 30 + 10)
students taking none of the classes = 100 - (95 - 25)
students taking none of the classes = 100 - 70
students taking none of the classes = 30
Hence, 30 students are taking none of the classes.
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30 students are taking none of the classes.
We can use the Principle of Inclusion-Exclusion (PIE) to determine the number of students taking none of the classes. The PIE states that the total number of elements in the union of several sets is equal to the sum of elements in each set, minus the sum of elements in the pairwise intersections, plus the sum of elements in the three-way intersections, and so on.
In this case, we want to find the number of students taking none of the classes, which is equal to the total number of students (100) minus the number of students taking at least one class.
So, we can apply PIE as follows:
students taking none of the classes = 100 - (students in prob. + students in la + students in comp - students in prob. & comp - students in la & comp - students in prob. & la + students in prob., comp & la)
Using the given information, we have:
students taking none of the classes = 100 - (65 + 45 + 40 - 25 - 20 - 30 + 10)
students taking none of the classes = 100 - (95 - 25)
students taking none of the classes = 100 - 70
students taking none of the classes = 30
Hence, 30 students are taking none of the classes.
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dried apricots with 3.25 were mixed with dried prunes worth 4.79 to produce a mixture of dried fruit, how much each kind of fruit was used to produce 25 ponds
Answers
14.84 pounds of dried apricots were used and 10.16 pounds of dried prunes were used to produce 25 pounds of the dried fruit mixture.
Let's call the weight of dried apricots used in the mixture "x" (in pounds). Then the weight of dried prunes used in the mixture is 25 - x (in pounds).
The cost per pound of dried apricots is 3.25, and the cost per pound of dried prunes is 4.79. So the total cost of the mixture is:
3.25x + 4.79(25 - x) = 3.25x + 119.75 - 4.79x
Expanding both sides:
119.75 = 8.04x
Dividing both sides by 8.04:
x = 14.84 pounds
So 14.84 pounds of dried apricots were used in the mixture, and 25 - 14.84 = 10.16 pounds of dried prunes were used in the mixture.
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14.84 pounds of dried apricots were used and 10.16 pounds of dried prunes were used to produce 25 pounds of the dried fruit mixture.
Let's call the weight of dried apricots used in the mixture "x" (in pounds). Then the weight of dried prunes used in the mixture is 25 - x (in pounds).
The cost per pound of dried apricots is 3.25, and the cost per pound of dried prunes is 4.79. So the total cost of the mixture is:
3.25x + 4.79(25 - x) = 3.25x + 119.75 - 4.79x
Expanding both sides:
119.75 = 8.04x
Dividing both sides by 8.04:
x = 14.84 pounds
So 14.84 pounds of dried apricots were used in the mixture, and 25 - 14.84 = 10.16 pounds of dried prunes were used in the mixture.
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What is 333333+(5+6)-657-(564-3)
Answers
Answer:
332126
Step-by-step explanation:
333333+(5+6)-657-(564-3)=332126
There are two ducks in front of a duck, two ducks behind a duck and a duck in the middle. How many ducks are there?
Answers
Answer:
There are 5 ducks
Step-by-step explanation:
2 ducks behind
1 duck in the middle
2 ducks infront
Which system of equations is represented by this graph?
Answers
The system of equations is given by: y = -2/5x +2 and y = -3x - 4.
How is a three-way system of equations solved?Choose two equation pairs at random from the system. Apply the Addition/Subtraction technique to each pair to remove the same variable. Use the Addition/Subtraction method to solve the two new equations as a system. Reintroduce the solution into one of the original equations and find the third variable there.
equations is:-
y = -2/5x +2 and y = -3x - 4.
when x=0
y= -2/5(0) +2 = 2
y = -3(0) - 4= 4
when y=0
0= -2/5x +2
x=.80
0= -3x - 4
x=13.33
so from the above value we come to conclusion that system of equations is given by: y = -2/5x +2 and y = -3x - 4.
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Ahmad owes $382. 45 on his Visa account. He returns two items costing $25. 10 & $34. 50 for credit. Then he makes purchases of $45 & $98. 17.
A) how much should his payment be if he wants to pay off the balance on the account?
B) Instead of paying off the balance, he makes a payment of $300 and then incurs a finance charge of $24. 66. What is the balance on his account?
Answers
By applying the debt concept, it can be concluded that:
A. He should pay $466.02 to pay off the balance on the account.
B. The balance on his account is $190.68
Debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor.
We have the following information:
Ahmad owes $382.45, and because he owes, it means this value is the debt, and we write it:
D = $382.45
Then he returns two items ($25. 10 & $34. 50) so that their values get credited into his accounts.
D = $382.45 - $25.10 - $34.50 = $322.85
Now after this, he makes another two purchases of $45 and $98.17, which increase his debt and makes:
D = $322.85 + $45 + $98.17 = $466.02
Part A: Since the debt or the account balance is $466.02, then he should pay $466.02 to pay off the balance on the account.
Part B: However, instead of paying off the balance, Ahmed makes a payment of $300 and he has to be charged $24.66. It means that his debt is not paid off:
D = $466.02 - $300 + $24.66 = $190.68
So, the balance on his account is $190.68.
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PLEASE HELP TIME LIMIT - 100 POINTS
Use Graph For Reference
Answers
The line of best fit gives a general outlook on the data while the correlation is the exact points showcased to calculate or show for a data set or table.
How to explain the informationIt should be noted that between the two variables it is a positive correlation because they both increase in the same direction.
Positive correlation is a relationship between two variables in which both variables move in tandem that is, in the same direction.
In order to find the residual one would subtract the predicted value from the measured value.
The diagram is attached.
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Five items x increased by5gives55
Answers
Answer:
x=10
Step-by-step explanation:
5x+5=55
5x=55-5
5x=50
x=10
hth
the sum of squared errors (deviations) is 20 for a sample of 5 scores. what is the variance for this sample?
Answers
The variance for this sample of 5 scores with the sum of squared errors (deviations) 20 is 5.
Variance is a measure of the spread of the data around the mean. It can be calculated from the sum of squared deviations (SSE) as follows:
Variance = SSE / (n - 1)
where n is the number of scores in the sample.
In this case, n = 5 and SSE = 20, so the variance is:
Variance = 20 / (5 - 1) = 20 / 4 = 5
So the variance for this sample is "5".
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Let u= [-12, 36, 8] and A= [ 5 -2 1 -3 6 1]. Is u in the plane in ℝ3 spanned by the columns of A? Why or why not?
Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or decimal for each matrix element.)
A.No, the reduced echelon form of the augmented matrix is which is an inconsistent system.
B.Yes, multiplying A by the vector writes u as a linear combination of the columns of A.
Answers
Since n•u is not equal to 0, we conclude that the vector u is not in the plane spanned by the columns of A.
Why plane spanned by the columns of A?A vector u is in the plane spanned by the columns of a matrix A if and only if the dot product between u and the normal vector of the plane is equal to 0.
In this case, let A = [5 -2 1; -3 6 1]. To determine if u = [-12, 36, 8] is in the plane spanned by the columns of A, we can calculate the dot product between u and the normal vector of the plane, which can be found by taking the cross product of the two columns of A.
Since the cross product of two columns in A gives the normal vector of the plane spanned by the columns, we have:
According to question:n = (5, -2, 1) × (-3, 6, 1) = (18, -26, -11)
Next, we calculate the dot product of n and u:
n•u = (18, -26, -11) • [-12, 36, 8] = 18 * -12 - 26 * 36 - 11 * 8 = -816 - 936 - 88 = -1840
Since n•u is not equal to 0, we conclude that the vector u is not in the plane spanned by the columns of A. In other words, u is not orthogonal to the normal vector of the plane and therefore, is not in the plane.
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How much fencing does she need?
Answers
Answer: 24 feet
Step-by-step explanation:
Perimeter: 2(length+width)
2(7+5)
14+10=24
voter sentiment: one of the questions rasmussen reports included on a 2018 survey of 2.500 likely voters asked if the country is headed in the right direction. representative data are shown in the file rightdirection. a response of yes indicates that the respondent does think the country is headed in the right direction. a response of no indicates that the respondent does not think the country is headed in the right direction. respondents may also give a response of not sure. a. what is the point estimate of the proportion of the population of likely voters who do think that the country is headed in the right direction? b. at 95% confidence, what is the margin of error? c. what is the 95% confidence interval for the proportion of likely voters who do think that the country is headed in the right direction? d. what is the 95% confidence interval for the proportion of likely voters who do not think that the country is headed in the right direction? e. which of the confidence intervals in parts c and d has the smaller margin of error? why?
Answers
Margin of Error is 0.0245, 0.8209 <= p <= 0.8264 and CI in (C) is 0.1291 to 0.1781 and in (d) is 0.8209 to 0.8264.
(a) The point estimate of the proportion of the population of respondents who do think that the country is headed in the right direction is 384 / 2500 = 0.1536.
(b) To find the margin of error for the proportion, we use the formula:
ME = 1.96 * sqrt(p * (1 - p) / n), where p is the point estimate and n is the sample size.
ME = 1.96 * sqrt(0.1536 * (1 - 0.1536) / 2500) = 0.0245
(c) The 95% confidence interval for the proportion of respondents who do think that the country is headed in the right direction is:
0.1536 - 0.0245 <= p <= 0.1536 + 0.0245
0.1291 <= p <= 0.1781
(d) To find the 95% confidence interval for the proportion of respondents who do not think that the country is headed in the right direction, we subtract the proportion from 1:
1 - 0.1536 - 0.0245 <= p <= 1 - 0.1536 + 0.0245
0.8209 <= p <= 0.8264
(e) The confidence interval in part (c) has a smaller margin of error because the sample proportion of respondents who do think that the country is headed in the right direction is closer to 0.5 (the midpoint of the interval) than the sample proportion of respondents who do not think that the country is headed in the right direction.
Confidence interval in part (c): 0.1291 to 0.1781
Confidence interval in part (d): 0.8209 to 0.8264
Therefore, Margin of Error is 0.0245, 0.8209 <= p <= 0.8264 and CI in (C) is 0.1291 to 0.1781 and in (d) is 0.8209 to 0.8264.
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Margin of Error is 0.0245, 0.8209 <= p <= 0.8264 and CI in (C) is 0.1291 to 0.1781 and in (d) is 0.8209 to 0.8264.
(a) The point estimate of the proportion of the population of respondents who do think that the country is headed in the right direction is 384 / 2500 = 0.1536.
(b) To find the margin of error for the proportion, we use the formula:
ME = 1.96 * sqrt(p * (1 - p) / n), where p is the point estimate and n is the sample size.
ME = 1.96 * sqrt(0.1536 * (1 - 0.1536) / 2500) = 0.0245
(c) The 95% confidence interval for the proportion of respondents who do think that the country is headed in the right direction is:
0.1536 - 0.0245 <= p <= 0.1536 + 0.0245
0.1291 <= p <= 0.1781
(d) To find the 95% confidence interval for the proportion of respondents who do not think that the country is headed in the right direction, we subtract the proportion from 1:
1 - 0.1536 - 0.0245 <= p <= 1 - 0.1536 + 0.0245
0.8209 <= p <= 0.8264
(e) The confidence interval in part (c) has a smaller margin of error because the sample proportion of respondents who do think that the country is headed in the right direction is closer to 0.5 (the midpoint of the interval) than the sample proportion of respondents who do not think that the country is headed in the right direction.
Confidence interval in part (c): 0.1291 to 0.1781
Confidence interval in part (d): 0.8209 to 0.8264
Therefore, Margin of Error is 0.0245, 0.8209 <= p <= 0.8264 and CI in (C) is 0.1291 to 0.1781 and in (d) is 0.8209 to 0.8264.
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Determining class width. Below are some pieces of information you may need to help you compute a class width. Using the formula introduced in class, please find the class width. EXPLAIN how you arrived at your answer, and write your answer below.
Number of desired classes: 5
Largest value in the dataset: 273
Smallest number in the dataset: 17
Number of data in the data set: 84
Answers
5-3x
From this you add
5-3x+6
A car travels from X to Y at an average speed of 60km/h and returns to X at a speed of 40kph. What is its average speed for the whole journey?
Answers
The average speed of the whole journey is 24 kilometres per hour.
How to find the average speed of the journey?The average speed is the total distance travelled by the object in a particular time interval.
A car travels from X to Y at an average speed of 60km/h and returns to X at a speed of 40km/h.
Therefore, the average speed for the whole journey can be calculated as follows:
The total distance travelled is 120 km.
Hence,
total time = 120 / 60 + 120 / 40
total time = 2 + 3 = 5 hours
Therefore,
average speed = total distance / total time taken
average speed = 120 / 5
average speed = 24 km/hr
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determine whether s is a basis for m2,2. s = 4 0 0 3 , 1 0 4 1 , 0 1 4 1 , 0 2 2 0
Answers
The set S is linearly dependent and the matrix A has rank 3.
Sets are groups of well-defined objects or components in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.
Set A, for instance, is a collection of all the natural numbers, with the form A = 1, 2, 3, 5, 6, 7, 8, etc.
The maximum number of linearly independent columns (or rows ) of a matrix is called the rank of a matrix. The rank of a matrix cannot exceed the number of its rows or columns.
Thus, The set S is linearly dependent and the matrix A has rank 3.
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a tent has the shape pictured below, where the cross sections are triangles. (the height of each triangle is equal to the base for that triangle.) what is the interior volume of the tent? (all distances are in feet.)
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The interior volume of the tent where the cross sections are triangles is given is 120ft³.
There are two cross sectional triangles
The one smaller triangle with the height and base of 2ft
The other bigger triangle has a base and height of 4 ft
And the total length of the Tent is given as 6 ft.
Therefore,
Area of smaller triangle = 2 x 2 = 4m²
Area of bigger triangle = 4 x 4 = 16 ft²
So the Volume of the tent is given by ,
Total length x (Area of smaller triangle + Area of bigger triangle)
= 6 x ( 4 + 16 )
=6 x ( 20 )
= 120 ft ³
A measurement of three-dimensional space is volume. Numerous imperial or US customary units, as well as SI-derived units (such the cubic metre and litre), are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship. The capacity of a container is typically regarded to be its volume.
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Let P and Q be equivalent propositional forms. Explain why P ↔ Q is a tautology. Hint: it might be helpful to consider truth tables for a simple example like P = (~ R) VT and Q = ~ (R^(~T)). However you must argue in general, not just for a specific example. =N
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P ↔ Q is a tautology because if P and Q are equivalent propositional forms, they have the same truth value in every possible interpretation, making the bi-conditional proposition P ↔ Q always true.
A tautology is a proposition that is always true, regardless of the truth values of its component propositions.
When two propositions, P and Q, are equivalent, it means that they have the same truth value in every possible interpretation. That is, P and Q are logically equivalent.
Therefore, if P and Q are equivalent propositional forms, then P ↔ Q, the bi-conditional proposition, is a tautology. This is because the truth value of P ↔ Q will always be true, as both P and Q have the same truth value in every possible interpretation.
This can be shown through the truth table for P ↔ Q. The bi-conditional proposition is true if and only if both P and Q have the same truth value. If P and Q are equivalent, then they will always have the same truth value, and so P ↔ Q will always be true.
In general, for any equivalent propositions P and Q, P ↔ Q will always be a tautology.
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from a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed. how many different committees are possible if (a) 2 of the men refuse to serve together?
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The total number of different committees possible is 6 * 3 * 2 * 56 = 3456.
If 2 of the men refuse to serve together, then we have to choose the first man for the committee first and then choose the other two men one by one, making sure that the two men who refuse to serve together are not chosen together.
There are 6 possible choices for the first man. After the first man is chosen, there are 4 remaining men, and we have to choose 2 more men from these 4. However, one of these 2 men must be the one who refused to serve with the first man. So, there are only 3 possible choices for the second man. After the second man is chosen, there are only 2 possible choices for the third man.
Next, we have to choose 3 women from 8. There are C(8,3) = 56 ways to do this.
So, the total number of different committees possible is 6 * 3 * 2 * 56 = 3456.
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The total number of different committees possible is 6 * 3 * 2 * 56 = 3456.
If 2 of the men refuse to serve together, then we have to choose the first man for the committee first and then choose the other two men one by one, making sure that the two men who refuse to serve together are not chosen together.
There are 6 possible choices for the first man. After the first man is chosen, there are 4 remaining men, and we have to choose 2 more men from these 4. However, one of these 2 men must be the one who refused to serve with the first man. So, there are only 3 possible choices for the second man. After the second man is chosen, there are only 2 possible choices for the third man.
Next, we have to choose 3 women from 8. There are C(8,3) = 56 ways to do this.
So, the total number of different committees possible is 6 * 3 * 2 * 56 = 3456.
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