The given augmented matrix is equivalent to a system of linear equations with 1 equation and 3 variables. The system is underdetermined and the solution to the system is [tex](x, y, z)[/tex]= (0, 0, 0).
The given augmented matrix is in row-reduced form and is equivalent to a system of linear equations. The matrix has 3 columns and 1 row, so there is 1 equation and 3 variables in the corresponding system of linear equations. Since there is only one equation, the system is underdetermined and has infinitely many solutions.
The solution to the system can be stated as: (x, y, z) = (0, 0, 0). The solution is a point where all the variables are equal to zero. Since the matrix is in row-reduced form, this is the only solution to the system. If the augmented matrix was not in row-reduced form, then the solution would be stated as a parameter, such as (x, y, z) = (0, 0, t), where t is a parameter.
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Answer:
1 equation, 3 variablesunderdetermined(x, y, z) = (1 -s +t, 4s, 4t)Step-by-step explanation:
For the given augmented matrix, you want to know the number of equations and variables it represents, whether the system is under- or over-determined, and the solution, using parameters as required.
[tex]\left[\begin{array}{ccc|c}1&\dfrac{1}{4}&-\dfrac{1}{4}&1\\\vphantom{\dfrac{T}{q}}0&0&0&0\end{array}\right][/tex]
Augmented matrixEach column of the augmented matrix is the coefficient of the variable in a linear equation represented by the row. The first row of the matrix represents the equation ...
[tex]1x +\dfrac{1}{4}y-\dfrac{1}{4}z=1[/tex]
The second row of the matrix represents the tautology ...
0x +0y +0z = 0
It contributes no information about the relationships between the variables.
The matrix represents 1 equation in 3 variables.
SolutionFor there to be a unique solution to a linear system, there must be as many consistent and independent equations as there are variables. Here, there are fewer equations than variables. This system is underdetermined.
The solution to an underdetermined system can be written in terms of parameters of free choice. We will need as many parameters as there are missing equations: 2.
Here, the coefficients of y and z suggest we choose parameters that let us represent those values as multiples of 4.
Parameters: s, t
Let y = 4s, z = 4t. Then the equation becomes ...
x +1/4(4s) -1/4(4t) = 1
x +s -t = 1
x = 1 +t -s
Now, the solution can be written as ...
(x, y, z) = (1 +t -s, 4s, 4t)
What is the composition of linear transformation matrix?
A linear transformation matrix is a square matrix that represents a linear transformation of a vector space. The composition of linear transformation matrices is equivalent to the composition of linear transformations they represent.
In general, the composition of two linear transformations A and B can be represented by the matrix product AB. Therefore, the composition of two linear transformation matrices, say A and B, would be the matrix product AB.
Linear transformations are functions that map vectors from one vector space to another in a linear way. These transformations can be represented by matrices, which can be composed to represent the composition of linear transformations.
The composition of two linear transformations represented by matrices involves multiplying the matrices together. To perform this multiplication, we need to ensure that the number of columns in the first matrix matches the number of rows in the second matrix. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.
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Please help with these Formal Logic questions;
8.1 Some cashmere sweaters are fashionable garments, so some cashmere sweaters are not suede jackets, for some suede jackets are not fashionable garments.
Which of the following correctly expresses the form of this argument?
a. Some C are F.
Some C are not S.
Some S are not F.
b. Some S are not F.
Some C are F.
Some C are not S.
c. Some C are not F.
Some C are not S.
Some C are F.
d. Some F are not S.
Some F are C.
Some S are not C.
e. Some C are F.
Some F are not S.
Some S are not S.
8.2 Some cashmere sweaters are fashionable garments, so some cashmere sweaters are not suede jackets, for some suede jackets are not fashionable garments.
Which of the following substitutions proves the argument invalid?
a. C = animals, F = cats, S = mammals.
b. C = dogs, F = animals, S = mammals.
c. C = dogs, F = mammals, S = fish.
d. C = mammals, F = animals, S = dogs.
e. C = cats, F = mammals, S = animals.
8.3 If cell phone companies screen text messages, then freedom of speech is threatened. Thus, freedom of speech is not threatened, because cell phone companies do not screen text messages.
Which of the following substitutions proves the argument invalid?
a. C = Abraham Lincoln was assassinated, F = George Washington was assassinated.
b. C = Joe Smith was beheaded, F = Joe Smith is dead.
c. C = Abraham Lincoln was beheaded, F = Abraham Lincoln is dead.
d. C = Abraham Lincoln was assassinated, F = Abraham Lincoln is dead.
e. C = Abraham Lincoln was beheaded, F = Abraham Lincoln is not dead.
8.4 If cell phone companies screen text messages, then freedom of speech is threatened. Thus, freedom of speech is not threatened, because cell phone companies do not screen text messages.
Which of the following correctly expresses the form of this argument?
a) If C then F.
C.
F.
b) Not F.
Not C.
If C then F.
c) All C are F.
C.
F.
d) If C then F.
Not C.
Not F.
e) If C then F.
Not F.
Not C.
8.5 All container ships that are ocean-going are air polluters. Hence, all container ships are air polluters.
Which of the following correctly expresses the form of this argument?
a) All C are A.
All C are O.
b) All C are A.
All C that are O are A.
c) All CS are O.
All CS are A.
d) All C are O.
All C are A.
8.6 All container ships that are ocean-going are air polluters. Hence, all container ships are air polluters.
Which of the following substitutions proves the argument invalid?
a. C = husbands, O = married, A = men.
b. C = men, O = humans, A = mammals.
c. C = men, O = married, A = husbands.
d. C = wives, O = divorced, A = women.
e. C = cats, O = animals, A = dogs.
8.17 All A are B. (T) Contrary
a. No A are B. (Und.)
b. All B are A. (Und.)
c. Some A are B. (T)
d. No A are B. (F)
e. No A are non-B. (T)
8.18 Some A are not non-B. (F) Contradiction
a. Some A are non-B. (T)
b. All A are non-B. (T)
c. Some B are not non-A. (F)
d. Some A are non-B. (T)
e. Some A are B. (T)
8.19 Some non-A are not B. (T) Subcontrary
a. Some non-A are B. (Und.)
b. No non-A are B. (Und.)
c. All non-A are B. (F)
d. Some A are B. (T)
e. Some non-B are not A. (T)
The answers for the questions given are mentioned below respectively.
Define the term expression?In mathematics, an expression is a combination of numbers, variables, and mathematical operations that are arranged in a specific way.
It can be a single number or variable, or a combination of them, along with mathematical operations like addition, subtraction, multiplication, division, exponents, and parentheses.
8.1 - The correct expression of the form of this argument is: a. Some C are F. Some C are not S. Some S are not F.
8.2 - The substitution that proves the argument invalid is: b. C = dogs, F = animals, and S = mammals.
8.3 - The substitution that proves the argument invalid is: e. C = Abrahamm Lincoln was beheaded, F = Abraham Lincon is not dead .
8.4 - The correct expression of the form of this argument is: d. If C then F. Not C. Not F.
8.5 - The correct expression of the form of this argument is: b. All C's are A. All C that are O are the A.
8.6 - The substitution that proves the argument invalid is: c. C=men, O=married, A=husbands.
8.17 - The correct truth value of the statement is: c. Some A are B. (T)
8.18 - The correct truth value of the statement is: e. Some A are B. (T)
8.19 - The correct truth value of the statement is: a. Some non-A are B. (Und.)
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1. Find the sine of angle in the triangle below.
3
8
To solve the question asked, you can say: So the other side of the triangle will be as [tex]A = \sqrt73[/tex].
What precisely is a triangle?A triangle is a closed two-dimensional geometric object consisting of three line segments, called edges, that intersect at three places called vertices. Triangles are distinguished by their sides and angles. A triangle can be equilateral (all sides equal), isosceles, or odd, depending on the sides. Triangles are classified as acute (any angle less than 90 degrees), right (angles equal to 90 degrees), or obtuse (any angle greater than 90 degrees). The area of a triangle can be calculated using the formula A = (1/2)bh. where A is the area, b is the base of the triangle, and h is the height of the triangle.
here in the triangle we have sides that are 3 and 8
we can use
[tex]A^2 = B^2 + C^2\\A^2 = 3^2 + 8^2\\A^2 = 9+64\\A^2 = 73\\A = \sqrt73[/tex]
So the other side of the triangle will be as [tex]A = \sqrt73[/tex].
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An art collector buys a replica of a famous sculpture. The replica has exactly the same shape as the original but it is smaller. The replica is 12 cm tall, and the original sculpture is 28 cm tall. If 162 cm^3 of bronze was needed to make the replica, how much bronze was needed to make the original sculpture?
2052 cm³ volume of bronze was needed to make the original sculpture.
What is volume?Volume is a physical quantity that refers to the amount of space occupied by a three-dimensional object or substance. It is typically measured in cubic units such as cubic meters, cubic centimeters, or cubic feet.
What is Area?Area is a physical quantity that refers to the amount of space within a two-dimensional shape or surface. It is typically measured in square units such as square meters, square centimeters, or square feet.
In the given question,
Since the replica is a scaled-down version of the original sculpture, the ratio of their sizes is the same as the ratio of their volumes.
The ratio of the heights of the original sculpture to the replica is:28 cm / 12 cm = 7/3
Therefore, the ratio of the volumes is:(7/3)³ = 343/27.
This means that the original sculpture is about 12.7 times larger than the replica in terms of volume.
Since 162 cm³ of bronze was needed to make the replica, we can find the amount of bronze needed for the original sculpture by multiplying 162 cm³ by the volume ratio:162 cm³ x 343/27 = 2052 cm³.
Therefore, 2052 cm³ of bronze was needed to make the original sculpture.
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What’s -9.1 times 3.75
7. What is the greatest whole number that satisfies the inequality
3x - 1 < 8 ?
Answer:
2
Step-by-step explanation:
3(2)-1<8
6-1<8
5<8
if you go up to 3 as the whole number then the equation ends up 8<8, and the sign is less than (<) not less than or equal to.
So 2 would be the answer.
At times, the relationship between a dependent and an independent variable is expressed as a logarithmic equation: Given a positive constant € and the two equations below, what is the relationship between X and Y? Equation 1: Log(c) = X/2 Equation 2: Log(c^2) = Y 1 . X Y Submit
The relationship between a dependent and an independent variable expressed as a logarithmic equation is as follows X = Y/2
At times, the relationship between a dependent and an independent variable is expressed as a logarithmic equation. For this question, given a positive constant € and the two equations below, we can find the relationship between X and Y. Equation 1: Log(c) = X/2 Equation 2: Log(c^2) = Y.We can use the basic properties of logarithms to solve this problem. To do so, we need to understand what logarithms are first.Logarithms are the opposite of exponentials. They allow us to find the exponent needed to produce a given value. For instance, log base 2 of 8 is 3 since 2^3 = 8.
A logarithm is represented as log_bx where b is the base and x is the argument or the number being passed to the logarithm.In equation 1, we are given that log(c) = x/2. To isolate x, we need to exponentiate both sides with base e.e^(log(c)) = e^(x/2)This gives us c = e^(x/2).We can rewrite this expression as c^2 = e^x. Now we use equation 2 which states that log(c^2) = y. This is equivalent to 2log(c) = y.Using equation 1, we can substitute log(c) for x/2.2log(c) = y2(x/2) = yx = y/2So the relationship between X and Y is X = Y/2. Therefore, we can conclude that the relationship between a dependent and an independent variable expressed as a logarithmic equation is as follows: X = Y/2.
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QS and TV areparallellines. P Q R S T U V W Which angles are vertical angles?
The required angles ∠SRP and ∠TUW are alternate exterior angles.
What is alternate exterior angles?Alternate exterior angles are a pair of angles that lie on opposite sides of a transversal line that intersects two other lines. Specifically, the angles are exterior to the two intersecting lines and lie on opposite sides of the transversal.
More formally, if two parallel lines are intersected by a transversal, then alternate exterior angles are the pair of angles that are:
On opposite sides of the transversal line.
Outside of the two parallel lines.
Congruent to each other.
These angles are called "alternate" because they are on opposite sides of the transversal and "exterior" because they are outside of the two parallel lines. The congruence of the angles is a result of the parallel lines creating equal corresponding angles.
So,∠SRP and ∠TUW are alternate exterior angles.
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three potential employees took an aptitude test. each person took a different version of the test. the scores are reported below. kaitlyn got a score of 74.5 ; this version has a mean of 68.5 and a standard deviation of 12 . kiersten got a score of 244.8 ; this version has a mean of 210 and a standard deviation of 29 . rebecca got a score of 7.24 ; this version has a mean of 6.7 and a standard deviation of 0.3 . if the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?
Step-by-step explanation:
kaitlyn score is 6 points above the mean
z-score = 6 / 12 = .5
kiersten score is 34.8 above the mean z-score = 34.8/29 = 1.2
rebecca score is .54 above the mean z -score = .54/ .3 = 1.8
rebecca scored the highest percentile (highes z-score) of the three....the best
B = 75*
C = 50*
A = ?*
Answer: A = 55* or 55 degrees
Step-by-step explanation:
The interior angles of a triangle always have a sum of 180 degrees.
75 + 50 + x = 180
Solve for x
FInal answer: 55 degrees
hope i explained it :)
When a researcher draws conclusions about a population based on the results of a test on a sample, he or she is most likely using which of the following? a) inductive statistics b) deductive statistics c) descriptive statistics d) inferential statistics
When a researcher draws conclusions about a population based on the results of a test on a sample, he or she is most likely using inferential statistics. Therefore Option A is correct.
Inferential statistics: It involves using sample data to make inferences or draw conclusions about a population. In this case, the researcher is using the results from the sample to make inferences about the population from which the sample was drawn.
Deductive statistics, inductive statistics, and descriptive statistics are other branches of statistics that are used for different purposes.
Deductive statistics:Deductive statistics involves starting with a general principle or theory and testing it with data, Inductive statistics:Inductive statistics involves starting with data and using it to develop a theory or principle. Descriptive statistics: Descriptive statistics involves summarizing and describing data using measures such as mean, median, and standard deviation.Therefore the researcher draws a conclusion to use inferential statistics about a population based on test of sample.Option A is correct.
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Write the equation of. the circle graphed below
Answer:
[tex](x+2)^{2} +(y+2)^{2} =9[/tex]
Step-by-step explanation:
the equation of circle:
center:(-2,-2)
The distance between the center and the side:3
So, the radius is 3
(x-h)^2+(y-k)^2=r^2
[tex](x - - 2)^{2} +(y- - 2)^{2} =3^{2}[/tex]
[tex](X+2)^{2} +(y+2)^{2} =9[/tex]
In the figure here, a small block is sent through point A with a speed of 6.8 m/s. Its path is without friction until it reaches the section of length L=14 m, where the coefficient of kinetic friction is 0.78. The indicated height are h1=5.4 m and h2=2.8 m. What are the speeds of the block at (a) point B and (b) point C? (c) Does the block reach point D? (d) If, so what is its speed there; if not, how far through the section of friction does it travel?
A small block is sent through point A with a speed of 6.8 m/s. Its path is without friction until it reaches the section of length L=14 m, where the coefficient of kinetic friction is 0.78. The indicated height are h₁ =5.4 m and h₂=2.8 m. The speeds of the block at (a) Point B is 108m/s and (b) Point C is 7.6m/s
The velocity of an object (usually denoted v) is the amount of its position change over time ; therefore it is a scalar quantity. The average speed of an object over a time interval is the distance traveled by the object divided by the duration of the interval; the instantaneous speed remains zero.
(a) At B the speed is :
V = [tex]\sqrt{V^{2}+2gh_1 }[/tex]
⇒ V = [tex]\sqrt{(6.8m/s)+ 2(9.8m/s^2) (5.4)}[/tex]
⇒ V = 108.44 m/s
⇒ V = 108 m/s
(b) Here, matters is the difference in heights (between A and C):
[tex]V = \sqrt{V_0^{2}+2g(h_1+h_2) }[/tex]
⇒ [tex]V = \sqrt{(6.8)+2 (9.8) (5.4- 2.8) }[/tex]
⇒ [tex]V = \sqrt{6.8 +2(9.8)(2.6)}[/tex]
⇒ √57.76 = 7.6m/s
(c) Using the results from part (b), we see that its kinetic energy is just at the beginning of its "rough glide" (horizontally to D) is:
1/2 m(7.6m/s)² = 28.88m (with SI units understood).
We note that this kinetic energy will turn entirely into thermal energy
28.88m = μₙ mgd
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which of the following is most likely a population as opposed to a sample? a) respondents to a newspaper survey. b) the first 5 students completing an assignment. c) every third person to arrive at the bank. d) registered voters in a county.
The option that is most likely a population as opposed to a sample is registered voters in a county. The correct answer is Option D.
A population is a group of individuals, objects, or events whose properties are being studied. A sample is a smaller subset of the population that is selected to represent the whole population.
The four options given in the question are all sets of individuals who are being studied, but the difference is how they were selected. Respondents to a newspaper survey, the first 5 students completing an assignment, and every third person to arrive at the bank are all examples of samples because they are subsets of a larger group.
However, registered voters in a county are most likely a population because they are the entire group that is being studied, and there is no need for a subset of this group since the entire population is available. Therefore, option d) registered voters in a county is the most likely population as opposed to a sample.
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rita received a $80 gift card for a coffee store. she used it in buying some coffee that cost $7.37 per pound. after buying the coffee, she had $57.89 left on her card. How many pounds of coffee did she buy?
Answer:
3 pounds of coffee.
Step-by-step explanation:
Equation
y = -7.37x + 80
substitute 57.89 for y
57.89 = -7.37 + 80 Subtract 80 from both sides
57.89 - 80 = -7.37 + 80 - 80
-22.11 = -7.37x Divide both sides by -7.37
3 = x
3 pound of coffee
Helping in the name of Jesus.
Answer:
rita received a $80 gift card for a coffee store. she used it in buying some coffee that cost $7.37 per pound. after buying the coffee, she had $57.89 left on her card. How many pounds of coffee did she buy?
Step-by-step explanation:
Let's first find out how much money Rita spent on coffee:
$80 (initial balance) - $57.89 (remaining balance) = $22.11 spent on coffee
Now, let x be the number of pounds of coffee that Rita bought. Since the coffee costs $7.37 per pound, we can set up the equation:
$7.37x = $22.11
Solving for x, we can divide both sides by $7.37:
x = 3
Therefore, Rita bought 3 pounds of coffee.
13x • 4x^2y
Does it equal 52x^2y? Or can you not combine them?
We can simplify the expressiοn tο [tex]52x^3y,[/tex] nοt [tex]52x^2y[/tex].
In math, hοw dο yοu sοlve expressiοns?Yοu must substitute a number fοr each variable and perfοrm arithmetic οperatiοns tο evaluate an algebraic expressiοn. Because 6 + 6 = 12, the variable x in the preceding example is equal tο 6. We can evaluate the expressiοn after replacing the variables with their values if we knοw their values.
We can use expοnent prοperties tο simplify the expressiοn [tex]13x[/tex]• [tex]4x^2y[/tex]:
[tex]13x[/tex]•[tex]4x^2y = 13[/tex] • [tex]x^1[/tex]• 4 • [tex]x^2[/tex]•[tex]y^1[/tex]
[tex]= 52[/tex]• [tex]x^3[/tex]•[tex]y^1[/tex]
As a result, we can simplify the expressiοn tο [tex]52x^3y[/tex] rather than[tex]52x^2y.[/tex]
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16 A function is given.
f(x)= (2x-2)(x − 3)
-
Use the Add Point tool to plot the zeros and the maximum or minimum value of the function.
The zeros of the function are x=1 and x=3, and the minimum value of the function is at x=2.
What is the polynomial function?
A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.
To find the zeros, we set the function equal to zero and solve for x:
(2x-2)(x-3) = 0
This equation is true when either 2x-2=0 or x-3=0. Solving for x in each case, we get:
2x-2=0 => x=1
x-3=0 => x=3
So the zeros of the function are x=1 and x=3.
To find the maximum or minimum value of the function, we can take the derivative of the function and set it equal to zero:
f'(x) = 4x - 8
4x - 8 = 0 ----> x = 2
So the critical point of the function is x=2. To determine if this point is maximum or minimum, we can use the second derivative test:
f''(x) = 4
Since f''(2) > 0, the function has a minimum at x=2.
Therefore, the zeros of the function are x=1 and x=3, and the minimum value of the function is at x=2.
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Sgr A has a diameter of about 27.3 million miles; that's roughly the same distance from Mercury to:
Venus
Jupiter
Earth
The Sun
Sgr A has a diameter of about 27.3 million miles; that's roughly the same distance from Mercury to The Sun.
What is distance?Distance is a measurement of how far apart two objects or points are, either numerically or rarely qualitatively. Distance can relate to a physical length in physics or to an estimate based on other factors in everyday language (e.g. "two counties over"). The term is frequently used metaphorically to refer to a measurement of the difference between two similar objects (such as statistical distance between probability distributions or edit distance between strings of text) or a degree of separation, as spatial cognition is a rich source of conceptual metaphors in human thought (as exemplified by distance between people in a social network). The concept of a metric space is used in mathematics to formalize the majority of these ideas of distance, both literal and figurative.
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suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. if the population grows to 500 after one year, what will the population be after another three years?
Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, the population will be 852.78 after another three years.
What is the logistic model?A logistic model, also known as the Verhulst-Pearl model, is a type of function used to describe population growth that is limited. It’s a form of exponential growth that takes into account the carrying capacity of an environment.
Population growth that is limited and slows down as the population approaches its carrying capacity is modeled using the logistic model. It is given by this equation:
[tex]P(t) = K / (1 + Ae^{-rt})[/tex]
where P(t) is the population at time t, K is the carrying capacity, A is the constant of proportionality, and r is the growth rate.
Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, substitute this information into the logistic model: [tex]P(1) = 500[/tex], [tex]K = 2000[/tex], and [tex]P(0) = 200[/tex].
[tex]500 = 2000 / (1 + Ae^{-r(1)})[/tex]
Now, solve for A by dividing both sides by 2000 / (1 + A):
[tex]1 + A = 4A = 3[/tex]
Substitute the value of A back into the logistic model equation:
[tex]P(t) = 2000 / (1 + 3e^{-rt})[/tex]
Solve for r by using the data provided in the problem for the first year (t = 1) and second year (t = 4):
[tex]P(1) = 500 = 2000 / (1 + 3e^{-r(1)})[/tex]
[tex]P(4) = ? = 2000 / (1 + 3e^{-r(4)})[/tex]
Solve the first equation for r:
[tex]500 = 2000 / (1 + 3e^{-r})\\1 + 3e^{-r} = 4e^{-r}\\1 + 3e^r = 4e[/tex]
Solve for e using the quadratic formula to get:
e = 0.4274 and e = 1.1713
Let e = 0.4274:
[tex]1 + 3e^{-r} = 4e^{-r}\\1 + 3(0.4274)^{-r} = 4(0.4274)^{r}\\1 + 0.5746^r = 1.7166^r[/tex]
Take the natural logarithm of both sides:
[tex]ln(1 + 0.5746^r) = ln(1.7166^r) - lnr\\ln(1 + 0.5746^r) = rln(1.7166) - lnr[/tex]
Use a graphing calculator to solve for r:
[tex]ln(1 + 0.5746^r) = rln(1.7166) - lnr[/tex]; -0.1568 < r < 0.7534
Solve for r using the second year’s data:
[tex]2000 / (1 + 3e^{-r(4)}) = P(4)\\2000 / (1 + 3(0.4274)^{-r(4)}) = P(4)\\P(4) = 852.78[/tex]
Thus, the population will be 852.78 after another three years.
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You construct three 88% confidence intervals as follows: A) A t-interval with 6 degrees of freedom. B) A t-interval with 2 degrees of freedom. C) A z-interval Assuming the mean and standard deviation are the same for all three intervals, write the three intervals (A, B, and C) in order, from narrowest to widest.
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. A low standard deviation means data are clustered around the mean, and a high standard deviation indicates data are more spread out.
A) A t-interval with 6 degrees of freedom: Mean +/- 0.76 * Standard Deviation
B) A t-interval with 2 degrees of freedom: Mean +/- 1.82 * Standard Deviation
C) A z-interval: Mean +/- 1.645 * Standard Deviation
Therefore, the intervals in order from narrowest to widest are:
A) A t-interval with 6 degrees of freedom,
C) A z-interval, and
B) A t-interval with 2 degrees of freedom.
The order from narrowest to widest is:
C) z-interval
A) t-interval with 6 degrees of freedom
B) t-interval with 2 degrees of freedom
Also,
The z-interval will be the narrowest because the z-distribution has a smaller variance than the t-distribution. The t-interval with 6 degrees of freedom will be wider than the z-interval because the t-distribution has a larger variance than the z-distribution.
Finally, the t-interval with 2 degrees of freedom will be the widest because the t-distribution has the largest variance when degrees of freedom is low.
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Thabo and his friend Amon shared a Job of cleaning Thabo's uncle yard He paid both of them R400. Thabo worked three hours and Amon worked for two hours. Use the information above to answer the questions that follow: 1.1 Determine the amount Thabo will receive, if they decide to share the R400 in a ratio of 3.2. 12 Thabo used 1/5 of his money towards a second hand video game. Calculate the cost of the video game. 13. Thibo's transport fare to school has increased from R800 to R1150. 1.3.1 Write R1150 in words. 1.3.2 Determine the percentage increase of the transport fare. You may use the formula: Percentage increase New amount-Old amount * 100% (2)
1.1) If Thabo and Amon decide to share the R400 in a ratio of 3.2, the amount Thabo will receive is R240.
1.2) If Thabo used 1/5 (a fraction) of his money towards a secondhand video game, the cost of the secondhand video game is R48.
1.3.1) If Thabo's transport fare to school has increased from R800 to R1,150, R1,150 written in words, is One Thousand, One Hundred and Fifty rupees.
1.3.2) If Thabo's transport fare to school has increased from R800 to R1,150, the percentage increase in the transport fare is 43.75%.
What is the ratio?The ratio refers to the relative size of one quantity compared to another.
Ratios are formally written using the ratio standard form (:). Ratios can also be expressed as decimals, percentages, and fractions.
The total amount received from the cleaning job = R400
The number of hours Thabo worked = 3 hours
The number of hours Amon worked = 2 hours
1.1) Sharing ratio = 3:2
The sum of ratios = 5
Thabo's share of R400 = R240 (R400 x 3/5)
1.2) The cost of the video game = R48 (R240 × ¹/₅)
1.3) Transport Fare:Old transport fare = R800
Current transport fare = R1,150
Increase in transport fare = R350 (R1,150 - R800)
Percentage increase in transport fare = 43.75% (R350/R800 x 100)
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Can you help me with this question
The length of the side x is equal to √22 using the trigonometric ratio of sin45° for the isosceles triangle.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
The triangle is an isosceles so the other two angles are the same and each equal to 45°
using the trigonometric ratio of sin 45°
{recall that sin 45°° = √2/2}
sin 45° = √11/x {opposite/hypotenuse}
√2/2 = √11/x
x = (√11 ×2)/√2 {cross multiplication}
x = 2√11/2 × √2/√2 {rationalize}
x = 2√22/2
x = √22
Therefore, the length of the side x is equal to √22 using the trigonometric ratio of sin 45° for the isosceles triangle.
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Reggie is rolling a block with the number 1,2,3,4, and 5 on it. Kaitlyn is drawing one desk from a basket of three disks: one blue, one red, and one yellow. use the tree diagram below to answer the question. What is the probability that they end up with a yellow disk
The probability of getting an even number and a yellow disc is 1/6 1/3 = 1/18. This is due to the fact that there is only one method to obtain an even number and a yellow disc.
What is probability?Probabilistic theory is a branch of mathematics that calculates the chance of an event or a claim being true. A risk is a number between 0 and 1, where 1 represents certainty and a probability of about 0 shows how likely an event appears to be to occur. Probability is a mathematical term for the likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1, or as percentages ranging from 0% to 100%. The proportion of occurrences among equally likely choices that result in a certain event in compared to all possible outcomes.
the answers to the questions:
a) The chance of getting a yellow disc is 1/6 + 1/6 = 1/3. This is because there are two methods to acquire a yellow disc: receive an even number and then choose the yellow disc, or get an odd number and then choose the yellow disc.
b) The chance of getting a blue disc is 1/6 + 1/6 = 1/3. This is because there are two methods to receive a blue disc: get an even number and then choose the blue disc, or get an odd number and then choose the blue disc.
c) The chance of getting an odd number with a red disc is (1/6 + 1/6) 1/3 = 1/18. This is because there are two ways to acquire an odd number, and there is only one way to get a red disc for each of those two methods.
d) The chance of getting an even number and a yellow disc is 1/6 1/3 = 1/18. This is due to the fact that there is only one method to obtain an even number and a yellow disc.
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Select the reason why these triangles are
similar. If they are not, select "Not similar."
A. SAS
C. Not similar
B. AA
D. SSS
109⁰
41°
30⁰
30°
The triangles are similar by the AA similarity criterion since they have two pairs of congruent angles (41° and 109°, and 30°). Therefore, the answer is B. AA.
What is triangle?A triangle is a polygon that has three sides, three vertices, and three angles. It is the simplest polygon in Euclidean geometry and one of the most studied shapes in mathematics. The sum of the three angles in a triangle is always 180 degrees, and the length of one side of a triangle is always less than the sum of the other two sides. There are many different types of triangles, including equilateral triangles (where all sides are equal), isosceles triangles (where two sides are equal), and scalene triangles (where no sides are equal). Triangles are used in many areas of mathematics and science, including trigonometry, geometry, and physics.
Here,
To determine whether the two triangles are similar using AA similarity, we need to compare the angles of both triangles.
Triangle 1 has angles 41°, 30°, and 109°.
Triangle 2 has angles 30°, 41°, and 109°.
We see that the two triangles have two pairs of congruent angles, namely 41° and 41°, and 109° and 109°. Therefore, the two triangles are similar by the AA similarity criterion.
Note that the order of the angles does not matter when comparing triangles for similarity.
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a circular piece of glass has a radius of 2.1 meters the glass sells for $7.10 per square meter what is the cost of the glass
Answer:
Step-by-step explanation:
The area of a circle is given by the formula:
A = πr^2
where A is the area and r is the radius.
Substituting the given values, we get:
A = π(2.1 m)^2 = 13.85 m^2
So the total cost of the glass with a price of $7.10 per square meter is:
Cost = Price per square meter x Total area
Cost = $7.10/m^2 x 13.85 m^2 = $98.24
Therefore, the cost of the glass is $98.24.
Identify the circumference of a circle with a diameter of 34 feet. Use 3.14 for π.
Circumference= diameter × 3.14
C= 34 feet× 3.14= 106.76 feet
The population of a slowly growing bacterial colony after t hours is given by p(t)=3t^2+24t+200. Find the growth rate after 2 hours.
The growth rate of a bacterial colony after a 2 hours is given by the derivative of its population function with respect to time is 36 .
The growth rate of a bacterial colony is given by the derivative of its population function.
Thus, we need to find the derivative of the population function p(t) with respect to time t, and then evaluate it at t = 2 to get the growth rate after 2 hours.
p(t) = 3t² + 24t + 200
Taking the derivative of p(t) with respect to t, we get:
p'(t) = 6t + 24
Now, evaluating p'(t) at t = 2, we get:
p'(2) = 6(2) + 24 = 36
Therefore, the growth rate of the bacterial colony after 2 hours is 36.
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The simple interest on a certain sum at 5% per annum for 3 years and 4years differ by rupees 82 find the sum
The principal sum is Rs. 1640 if the difference in simple interest between 3 years and 4 years is Rs. 82 at a rate of 5% per annum.
Let x be the principal sum. According to the problem, the difference in simple interest between 3 years and 4 years is Rs. 82. This means that the interest earned in the fourth year is Rs. 82 more than the interest earned in the third year.
Using the formula for simple interest, we can calculate the interest earned in each year:
Simple interest for 3 years = (x * 5% * 3) = 0.15x
Simple interest for 4 years = (x * 5% * 4) = 0.2x
The difference between the two is:
0.2x - 0.15x = 0.05x
We are given that this difference is equal to Rs. 82, so:
0.05x = 82
Solving for x, we get:
x = 82 / 0.05 = 1640
Therefore, the principal sum is Rs. 1640.
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12x + 376; 15x + 280.
When would they have the same amount
Answer: 32,760
Step-by-step explanation
12x+376
15x+280
when you put it in demos both of the line cross and you can see you answer when you click were the lines cross.if you use the giving value it would be 750
Polynomial question
I don't understand this working
Why is b = d = 0 if the function is even?
Please explain the steps to solve a question like this.
To understand why b = d = 0 if the function is even, we need to consider the definition of an even function.Therefore If P(x) is an even function, then b = d = 0.
What is Polynomial?A polynomial is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication. It can have one or more terms and can be of any degree.
An even function is a function that satisfies the condition f(x) = f(-x) for all x in the domain of the function.
If P(x) is an even function, then we have P(x) = P(-x) for all x. Substituting -x for x in the expression for P(x), we get:
P(-x) = a(-x)⁴ + b(-x)³ + c(-x)² + d(-x) + e
= a(x⁴) - b(x³) + c(x²) - d(x) + e
Since P(x) = P(-x), we can equate the two expressions for P(x) and P(-x) to get:
a(x⁴) + b(x⁴) + c(x²) + d(x) + e = a(x⁴) - b(x³) + c(x²) - d(x) + e
Simplifying this equation, we get:
2b(x³) + 2d(x) = 0
Since this equation holds for all values of x, we can set x = 0 to get:
2d(0) = 0
which implies that d = 0. Similarly, setting x = 1, we get:
2b(1³) + 2d(1) = 0
2b = 0
b = 0
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