The maximum compression of the spring will depend on the spring's elasticity, or its ability to return to its original length after being stretched or compressed which is 2cm
If the same puck hits the spring at a speed of 2v, the spring will compress twice as much as it did when the puck was traveling at v. Thus, the spring's maximum compression will be 2 cm or twice its original compression of 1 cm.
It is important to note that the spring's elasticity will affect the maximum compression. If the spring is relatively stiff and has a low elasticity, it will not compress as far as a spring with a higher elasticity.
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The complete question should be: A hockey puck sliding along frictionless ice with speed v to the right collides with a horizontal spring and compresses it by 1.0 cm before coming to a momentary stop. What will be the spring's maximum compression if the same puck hits it at a speed of 2v?
suppose a basketball player is an excellent free throw shooter and makes 93% of his free throws (i.e., he has a 93% chance of making a single free throw). assume that free throw shots are independent of one another. find the probability that the player misses three consecutive free throws.
4.Chloe and Tino have a combined age of 48. Three years ago Chloe was double the age Tino. Work out the age of Chloe and Tino.
Chloe is 31 years old while Tino is 17 years old.
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
Let x represent Chloe present age and y represent Tino present age. Chloe and Tino have a combined age of 48. Hence:
x + y = 48 (1)
Also, Three years ago Chloe was double the age Tino, hence:
x - 3 = 2(y - 3)
x - 2y = -3 (2)
From both equations:
x = 31, y = 17
Chloe is 31 years old.
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Factor out the greatest common factor from the terms of the polynomial 8x4 − 12x3 + 16x.
A. 4x3(2x − 3) + 18
B. 4x(2x3 − 3x2 + 4)
C. The expression is already fully factored.
D. 8x4 − 4x(3x2 + 4)
The greatest common factor from the terms of the polynomial 8x4 − 12x3 + 16x is 4x(2x3 − 3x2 + 4). Option B
What are algebraic expressions?Algebraic expressions are described as mathematical expressions that are comprised of terms, variables, coefficients, factors and constants.
These algebraic expressions are also composed of mathematical or arithmetic operations, such as;
SubtractionFloor divisionMultiplicationAdditionDivisionBracketParenthesesFrom the information given, we have that;
8x⁴ − 12x³ + 16x
Factor the common terms
4x(2x³ - 3x² + 8)
Hence, the expression is 4x(2x³ - 3x² + 8)
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In a class of 10 , there are 5 students who play soccer. If the teacher chooses 2 students, what is the probability that both of them play soccer?
The probability of choosing 2 students who both play soccer from a class of 10 students, where 5 students play soccer, is 5/6 or 0.83.
The probability of choosing 2 students who both play soccer from a class of 10 students, where 5 students play soccer, can be calculated using the formula for combinations:
[tex]C(5,2) =\frac{5!}{(2! * (5-2)!)}[/tex]
[tex]= \frac{10}{(2 * 3!)} \\ \\=\frac{10}{(2 * 6) } \\\\= \frac{5}{6}[/tex]
So, the probability of choosing 2 students who both play soccer is 5/6 or 0.83.
This means that if the teacher randomly selects 2 students from the class, there is an 83% chance that both of them play soccer.
In conclusion, the probability of choosing 2 students who both play soccer from a class of 10 students, where 5 students play soccer, is 5/6 or 0.83.
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At a local high school, the 40% of the students drink soda regularly, 30% drink coffee regularly, and 10% drink both regularly. If a student was randomly selected from this school, what is the probability that the student drinks soda if we know the student drinks coffee regularly?.
The probability that the student drinks soda, given that they drink coffee, is 0.25.
Let's designate the proportion of students who regularly consume soda as "S," those who frequently consume coffee as "C," and those who regularly consume both as "B."
Since 40% of students frequently consume soda, there are 0.4S kids who do the same.
Additionally, there are 0.3S students who consume coffee because 30% of students do it frequently.
Additionally, since 10% of students consume both beverages, there are 0.1S students who also consume soda and coffee.
Students in the class S = 0.4S + 0.1S = 0.5S either drink soda or both.
The pupils in C = 0.3S + 0.1S = 0.4S either consume coffee or both.
So, given that the student drinks coffee, the probability of drinking soda is:
P(soda | coffee) = P(soda and coffee) / P(coffee)
= 0.1S / 0.4S
= 0.25.
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1. The set of ordered pairs (1, 7), (3, 8), (3, 6), (6, 5), (2, 11), (1, 4)
represents a relation.
Answer:
Yes, the set of ordered pairs (1, 7), (3, 8), (3, 6), (6, 5), (2, 11), (1, 4) represents a relation. This relation is a function since each input (x-value) has a single output (y-value).
Step-by-step explanation:
Please help!
Kyle deposited $7,000 at the end of every six months for 5 years into a 401(k). Given an interest rate of 12% compounded semiannually, find the future value.
A. $92,265. 53
B $97,801. 48
C. $44,469. 95
D. $64,521. 06
Jodie decides to wait until age 70 to begin receiving Social Security benefits. Find the present value of her estimated $31,000 per year in payment assuming 8% per year and payment until her 90th birthday.
A $350,623. 10
B. $310,520. 80
C. $304,362. 65
D. $294,544. 50
Wilma saves $12,000 at the end of every six months for 10 years. Assume 10% compounded semiannually and find the present value.
A. $137,547. 52
B. $149,546. 52
C. $73,734. 84
D. $195,589. 79
(a) The future value is $18,971.06, which is closest to option D) $64,521.06
(b) So the present value of the estimated payments is $317,375, which is closest to option A) $350,623.10
(c) The present value of the savings is $25,620.51, which is closest to option C) $73,734.84
A) The future value of the deposits can be calculated using the formula for compound interest:
FV = PV * (1 + r/n)^(nt)
where
PV = $7,000
r = 12% = 0.12
n = 2 (compounded semiannually)
t = 5 years = 10 semiannual periods
Plugging in these values, we get:
FV = $7,000 * (1 + 0.12/2)^(2 * 10)
FV = $7,000 * (1.06)^20
FV = $7,000 * 2.667532622
FV = $18,971.06
B) The present value of the estimated payments can be calculated using the formula for the present value of an annuity:
PV = PMT * (1 - (1 + r)^(-n)) / r
where
PMT = $31,000
r = 8% = 0.08
n = 20 payments (from age 70 to 90)
Plugging in these values, we get:
PV = $31,000 * (1 - (1 + 0.08)^(-20)) / 0.08
PV = $31,000 * (1 - 0.170811153) / 0.08
PV = $31,000 * 0.83 / 0.08
PV = $31,000 * 10.375
PV = $317,375
C) The present value of the savings can be calculated using the formula for present value of a lump sum:
PV = FV / (1 + r/n)^(nt)
where
FV = $12,000 * 10 (total savings)
r = 10% = 0.1
n = 2 (compounded semiannually)
t = 10 years = 20 semiannual periods
Plugging in these values, we get:
PV = ($12,000 * 10) / (1 + 0.1/2)^(2 * 20)
PV = ($120,000) / (1.05)^40
PV = $120,000 / 4.68
PV = $25,620.51
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How do you solve a graph step by step?
To solve a series of linear equations by graphing them:
1. Visualize the initial equation.
2. Using the same rectangular coordinate system, graph the second equation.
What is a graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
To develop a graph is to make a diagram that depicts the relationship between two or more objects.
Make a sequence of bars on graph paper as an example of a graph. YourDictionary, to express or give the form of using a graph.
To graph a set of linear equations and solve them:
1. Visualize the initial equation.
2. Using the same rectangular coordinate system, graph the second equation.
3. Establish if the lines are parallel, intersect, or are one and the same.
4. Determine the system's remedy. Find the intersection if the lines do indeed meet.
Therefore, to solve a series of linear equations by graphing them:
1. Visualize the initial equation.
2. Using the same rectangular coordinate system, graph the second equation.
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work out the size of angle x
You have a credit card that has a balance of $3,589.90 and has a credit limit of $5,000. How much is the balance over the acceptable debt ratio percentage?
Answer: You have a credit card that has a balance of $3,589.90 and a credit limit of $5,000. How much is the balance over the acceptable debt ratio percentage? $981.88.
Step-by-step explanation:
Answer:
Step-by-step explanation:
the acceptable debt rate would be 43%
(after 2.2) find all values z1 and z2 such that (2, −1, 3), (1, 2, 2), and (−4, z1, z2) do not span r 3 .
The values of z1 and z2 that will satisfy this equation are z1 = −8 and z2 = 6 and the vectors (2, −1, 3), (1, 2, 2), and (−4, −8, 6) do not span R3.
To find these values, we need to understand that for any three vectors to span R3, they must be linearly independent.
This means that none of the vectors can be expressed as a linear combination of the other two vectors.
We can start by finding the determinant of the matrix formed by the three vectors. If the determinant is not equal to 0, then the vectors are linearly independent and span R3.
However, if the determinant is equal to 0, then the vectors are linearly dependent and do not span R3.
Let's consider the matrix formed by the three vectors:
[tex]= > \begin{bmatrix}2 & 1 & -4 \\-1 & 2 & z1 \\3 & 2 & z2\end{bmatrix}[/tex]
The determinant of this matrix is equal to:
=> 2 * (2 * z2 - 2 * z1) - (-1) * (1 * z2 - 2 * -4) + 3 * (1 * z1 - 2 * -4)
=> 2z2 - 2z1 + 7z1 + 24 - 2z2 + 8z1 - 24
=> 9z1 + 2z2 - 24
So, the vectors will not span R3 if 9z1 + 2z2 - 24 = 0.
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An office opens at 9 a.m. and closes at 5 p.m. with a lunch interval of 30 minutes. What is the ratio of lunch interval to the total period in office?
The ratio is 1:16 or (30 minutes:480 minutes).
What is the ratio of lunch interval to the total period in office?
The theory used in this question is the ratio of two numbers.
A ratio is a comparison of two numbers, usually expressed as a fraction or as a decimal. Ratios can be used to compare two numbers and identify relationships between them.
In this case, the ratio is being used to compare the lunch interval (30 minutes) to the total time the office is open (450 minutes).
Given:
The total time the office is open in minutes: 9 am - 5 pm = 8 hours = 8 x 60 minutes = 480 minutes.
Divide the lunch interval (30 minutes) by the total time the office is open (450 minutes): 30 minutes / 480 minutes.
= 1: 16
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Does the equation Ax = b have a solution for each b in R4? O A. No, because each b in R4 is a linear combination of the columns of A. B. Yes, because the columns of A do not span R4. ос C. No, because A does not have a pivot position in every row. D. Vos hecause the reduced echelon form of a does not have a row of the form Co on Twith h nonzero Use the following vectors to answer parts (a) and (b). 3 5 V= 4 V2 = 12 V3 6 3 -9 h (a) (b) For what values of his vz in Span{V1, v}? For what values of his {V1, V2, V3} linearly dependent? (a) For what values of h is vz in Span{v1, v2}? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. h= (Use a comma to separate answers as needed.) OB. All values of h O C. No values of h
The equation Ax = b has a solution for each b in R4 if and only if the columns of A span R4.
The equation Ax = b is a linear equation that is commonly used in linear algebra. This equation is used to find the solution of a system of linear equations. The equation consists of a matrix A and a vector b.
Spanning refers to the ability of a set of vectors to generate all other vectors in a given space. If the columns of A span R4, then for each vector b in R4, there exists a unique solution x in R4 such that Ax = b.
On the other hand, if the columns of A do not span R4, then there are some vectors in R4 that cannot be generated by the columns of A and thus the equation Ax = b will not have a solution for each b in R4.
In conclusion, the set of vectors in the matrix A must be able to generate all other vectors in R4 for the equation to have a solution for each b in R4.
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Julia had a bag filled with gumballs. There were 1 lemon-lime, 2 watermelon, and 3 grape gumballs. What is the correct sample space for the gumballs in her bag?
Sample space = 1, 2, 3
Sample space = 1, 2, 3, 4, 5, 6
Sample space = lemon-lime, watermelon, grape
Sample space = lemon-lime, watermelon, watermelon, grape, grape, grape
the correct sample space for the gumball in her bag is option (D) Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape
What is sample space?The sample space S of a random experiment is defined as the set of all possible outcomes of an experiment. In a random experiment, the outcomes, also known as sample points, are mutually exclusive
Given, Julia had a bag filled with gumballs. There were 1 lemon-lime, 2 watermelon, and 3 grape gumballs.
The number of lemon limes in the bag = 2 lemon-lime
Number of watermelons in the bag = 3 watermelon
Number of grape gumballs in the bag = 5 grape gumball
Sample space is the set of all the possible outcomes of the experiment
Here there are 2 lemon-lime, 3 watermelons, and 5 grape gumball
Hence, if Julia had a bag filled with gumballs and there were 2 lemon-lime, 3 watermelon, and 5 grape gumballs, then the correct sample space for the gumball in her bag is an option (D) Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape
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watermelon,lemon lime,lemon lime,grape,grape,grape
sarah is a marine biologist. of the coral she observes at a dive site, 30% is healthy, 40% is unhealthy, and 30% is dead. she estimates that 30% of the dead coral died in the past 12 months. what percentage of the coral that she observes is dead coral that died more than 12 months ago?
The percentage of the corals at the dive site that Sarah observes died more than 12 months ago is 21%.
What is a percentage?A percentage is a specification of the quantity of an item in a collection per 100 of all items in the collection.
The observations of the corals are;
The percentage of the corals that are healthy = 30%
Percentage of the corals that are unhealthy = 40%
Percentage of the corals that are dead = 30%
Percentage of the dead corals that died in the past 12 months = 30%
The percentage of corals Sarah observed died more than 12 months ago; required.
The 30% of the dead corals that died in the last 12 months, indicatesa that the percentage of the dead corals that died more than 12 months ago = 100% - 30% = 70%
The percentage of the dead corals that died more than 12 months ago = 70%
Therefore, the percentage of the population of corals at the dive site that died more than 12 months ago = 70% × 30% = 21%
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4/7 i ubtracted from a poitive number and the reult i multiplied by 7 to obtain the
Q3. Original number. What i the number?
The fraction of the given equation would be 2/3.
locating the Original number.
The outcome is one less than the original number when a two-digit number with its digits reversed is subtracted from the same number. The number itself can be obtained by adding three times the tens digit and four times the units digit of the original integer.
Suppose that x is the initial or positive number.
(x - 4/7)* 7 = x
7(x) - 7(4/7) = x
7x - 4 = x
7x-x = 4
6x = 4
x = 4/6 = 2/3
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how many times as many burglaries were there actually in year 4 compared to year 1? round your answer to 2 decimal places.
Based on the graph, in year 4 there were 1.16 times more burglaries if compared to year 1.
How many burglars were there in years 1 and 4?Based on the graph, the number of burglaries these years was:
Year 1: 220 burglariesYear 4: 255 burglariesThis shows a growing trend in the number of burglaries over the years.
How many times as many burglaries were there in year 4 compared to year 1?number in year 4/ 1
255/220 = 1.159 which can be rounded to 1.16
Based on this, year 4 had 1.16 times more burglaries than year 1.
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Given the lines shown here what are two possible equation for this system of equations?
y=x+1 and y=x-5 are the equations of the lines in the given graph.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Considering the two lines are parallel, they both have the same slope.
let m be the slope of the two lines:
y=mx+y₀
y=mx+y₁
y₀, y ₁ are the value on y axis where the two lines cross the axis.
Because the lines are parallel, there exists no point that lies on both lines, therefore the system has 0 solution.
Hence, y=x+1 and y=x-5 are the equations of the lines in the given graph.
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7x (9 x 2) = (7x [?]) × 2
Solve for ?
Answer:
9
Step-by-step explanation:
7 x (9 x 2) = (7 x 9) x 2 This is the associative property.
7 x ( 18) = (63) x 2
126 = 126
Multi-Step Equation!!
Can someone please explain how to get this step by step?
Answer:
[tex]\boxed{\mbox \large a = \dfrac{9}{10} = 0.9}[/tex]
Step-by-step explanation:
Equation to be solved is
[tex]\dfrac{5}{3}a + \dfrac{4}{5} = a + \dfrac{7}{5}[/tex]
Step 1
Get rid of those annoying denominators by multiplying throughout 15. We choose 15 because it is the lowest common multiple of 3 and 5. Since 3 and are prime numbers the LCM is 3 x 5 = 15
[tex]15 \cdot \dfrac{5}{3}a +15 \cdot \dfrac{4}{5} = 15\cdot a + 15\cdot \dfrac{7}{5}}[/tex]
==> [tex]25a + 12 = 15a + 21}\\[/tex]
Step 2
Subtract 15 from both sides:
==> [tex]25a -15a + 12 = 15a -15a + 21}\\\\\\ 10a + 12 = 21}\\[/tex]
Step 3
Subtract 21 from both sides
[tex]10a + 12 -12 = 21 - 12\\\\[/tex]
[tex]10a = 9[/tex]
Step 4
Divide by 10 both sides
[tex]\dfrac{10a}{10} = \dfrac{9}{10}\\\\\implies a = \dfrac{9}{10} = 0.9[/tex]
The ratio of orange to green in a bag of colored marble i 6:1. Which tatement mut be true about thi bag of marble
There are six orange marbles for every one green marble in the bag.
How many days will it take for 125 people to contract the virus?Step 1: Understand the question.
The question asks us to determine which statement must be true about a bag of colored marbles with a ratio of orange to green marbles of 6:1.
Step 2: Determine the ratio of orange to green marbles.
The ratio of orange to green marbles is 6:1, which means that for every one green marble, there are six orange marbles.
Step 3: Determine the statement that must be true.
Therefore, the statement that must be true about this bag of marbles is that there are six orange marbles for every one green marble in the bag.
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If f(x) = {x and g(x)=x? - 8, simplify the expressions (fog)(4), (f of)(8), (gof)(x), and (fog)(x). (fog)(4)=0 (f of)(8)= (gof)(x)= (fog)(x) = 0
For given functions, f(g(4)) = 2, f(f(8)) = ∛2 and f(g(x)) = ∛ ( x² - 8 ).
Describe a function.A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range and a co-domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
In math, various function types exist. Among the crucial kinds are:
When there is a mapping for a range for each domain between two sets, this is known as an injective function or one to one function.
When more than one element is mapped from domain to range, the function is said to be surjective or to be an onto function.
a polynomial function is a function made by of polynomials
Now,
For functions f(x) = ∛ x and g(x) = x²-8
f(g(x)) = ∛ (x²-8)
f(f(x)) = ∛ ∛ x
g(f(x)) = ( ∛ x ) ² - 8
Therefore,
f(g(4))=∛4²-8= ∛16 - 8
= ∛8 = 2
f(f(8)) = ∛ ∛ 8 = ∛2
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Right function are
f(x)=∛x and g(x)=x^2-8
What is the linear function equation that best fits the data set? 15 14 13 + 12 + 11 + 10 9 ŷ = -x +9 o ŷ = 3x + 15 ŷ = -3x + 15 ŷ= - 4/3x + 10 8 7+ 6. 5+ 4+ 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
The equation ŷ = -3x + 15 best fits the given data sets.
The word linear function in mathematics refers to two separate but related concepts: A linear function in calculus and related fields is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
The linear function equation that best fits the data set is likely to be the one that minimizes the differences (or residuals) between the observed y-values (the data points) and the predicted y-values (calculated from the equation).
To find this equation, you can use the method of least squares, which involves finding the line that minimizes the sum of the squared residuals.
In this case, the equation ŷ = -3x + 15 minimizes the sum of the squared residuals and is therefore the best fit for the data set.
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Alyssa just accepted a job at a new company where she will make an annual salary of $68000. Alyssa was told that for each year she stays with the company, she will be given a salary raise of $2000. How much would Alyssa make as a salary after 9 years working for the company? What would be her salary after
t
t years?
a) Using the linear equation 68000 + 2000t, Alyssa would make a salary of $86,000 after 9 years of working for the company.
b) Based on the same linear equation, Alyssa's salary after t years would be 68000 + 2000t.
What is a linear equation?A linear equation is a mathematical equation written in the form of y=mx+b.
Linear equations involve a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
The offered annual salary of Alyssa = $68,000
Annual salary raise = $2,000
The number of years Alyssa would work for the company = t years
The number of years Alyssa worked in the company = 9 years
Equation:68000 + 2000t
68000 + 2000(9)
68000 + 18000
= 86,000
= $86,000
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How many feet? Plsss help
The length of the fabric is 15cm.
What is Pythagoras' theorem?
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Here, we have
Given: Elijah takes a rectangular piece of fabric and makes a diagonal cut from one corner to the opposite corner. The cut he makes is 17 inches long and the width of the fabric is 8 inches.
We have to find the fabric's length.
We apply here Pythagoras theorem and we get
a² + b² = c²
a² + (8)² = (17)²
a² +64 = 289
a² = 289 - 64
a² = 225
a = 15
Hence, the length of the fabric is 15cm.
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explain why s is not a basis for r2. s = {(−5, 7)}
s = {(-5, 7)} cannot be a basis for R^2 because it does not satisfy the three requirements of a basis: having at least two linearly independent vectors, containing only linearly independent vectors, and spanning the entire vector space.
The set s = {(-5, 7)} is not a basis for R^2 (the two-dimensional real vector space) for several reasons:
Cardinality: A basis for a vector space must contain at least two linearly independent vectors. Since s contains only one vector, it cannot be a basis for R^2, which has dimension 2.
Linear independence: A basis must contain linearly independent vectors. If a vector in the basis can be written as a linear combination of the other basis vectors, it is not linearly independent, and the set cannot be a basis.
Spanning: A basis must span the entire vector space, meaning that every vector in the vector space can be written as a linear combination of the basis vectors. The set s = {(-5, 7)} does not span R^2 because it contains only one vector, and not every vector in R^2 can be written as a scalar multiple of this vector.
Therefore, s = {(-5, 7)} cannot be a basis for R^2 because it does not satisfy the three requirements of a basis: having at least two linearly independent vectors, containing only linearly independent vectors, and spanning the entire vector space.
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An audio treaming ervice ubcriber pay $16. 99 per month for unlimited muic and podcat treaming. The ubcriber pay for the ervice uing a credit card with a 27. 999 APR. If the balance i paid off after one month of interet charge, how much more will have been paid intead of uing cah? • $0. 40 O $0. 26 O $1. 27 O $4. 75
The subscriber will pay $0.40 more if they pay using a credit card with a 27.999 APR instead of using cash.
Credit Card Monthly Cost DifferenceHere are the steps to calculate the amount paid more when paying using a credit card instead of cash:
Calculate the monthly interest:Take the annual percentage rate (APR) of 27.999 and divide it by 12 to get the monthly interest rate.
Multiply the monthly interest rate by the balance ($16.99) to get the monthly interest charge.
Calculate the total amount paid after one month:Add the monthly interest charge to the balance ($16.99).
This gives you the total amount paid after one month of interest charges.
Calculate the difference between the total amount paid and the original balance:Subtract the original balance ($16.99) from the total amount paid after one month of interest charges.
This gives you the amount paid more due to the interest charges.
The final answer would be the amount paid more, which is $0.40 in this case.
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suppose that limx→3f(x)=12 and limx→3g(x)=−7. find the following limits. a.limx→3[f(x)g(x)] b. limx→3[3f(x)g(x)] c. limx→3[f(x) 8g(x)] d. limx→3
expression by 8 in the third case, giving us 12*(-7)*8 = -672. Finally, we divide the expression by g(x) to find the fourth limit, giving us 12/(-7) = -1.714.
a. limx→3[f(x)g(x)] = limx→3[12*(-7)] = -84
b. limx→3[3f(x)g(x)] = limx→3[3*12*(-7)] = -252
c. limx→3[f(x) 8g(x)] = limx→3[12*(-7)*8] = -672
d. limx→3[f(x)/g(x)] = limx→3[12/(-7)] = -1.714
The given limits are limx→3f(x)=12 and limx→3g(x)=−7. We can calculate the following limits by substituting x=3 in the given expressions: limx→3[f(x)g(x)] = -84, limx→3[3f(x)g(x)] = -252, limx→3[f(x) 8g(x)] = -672 and limx→3[f(x)/g(x)] = -1.714. To find these limits, we first multiply the two expressions, f(x) and g(x). This gives us 12*(-7) = -84 in the first case. In the second case, we multiply this expression by 3, giving us 3*12*(-7) = -252. We then multiply this expression by 8 in the third case, giving us 12*(-7)*8 = -672. Finally, we divide the expression by g(x) to find the fourth limit, giving us 12/(-7) = -1.714.
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1. Let X = {a} and Y = {a,b}, do the following. (8 points, 4 each) (a). Use the set-roster notation to write set (XXX) XY. (b). Find two functions and two non-function relations from X x Y to Y.
Two non-functions could be (a,a) -> a and (a,b) -> a and (a,a) -> b and (a,b) -> b, meaning that both inputs can result in either a or b.
A set is a collection of distinct objects, which can be anything, such as numbers, letters, or even other sets.
The set-roster notation is a way to write a set by listing its elements inside curly brackets {}.
(a) To write the set (XXX) XY, we need to repeat the set X three times, which would be X = {a,a,a}.
Then we can join it with the set Y to form (XXX) XY = {a,a,a,a,b}.
(b) To find two functions and two non-function relations from X x Y to Y, we need to understand what a function and a relation are. A function is for every element in the domain (X x Y), there is exactly one corresponding element in the codomain (Y) where as a non-function, or a relation, is a set of ordered pairs where the same input can have different outputs.
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What is 30 degrees Celsius in Fahrenheit?
30 degrees Celsius in Fahrenheit is 86
What is 30 degrees Celsius in Fahrenheit?
30 degrees Celsius to Fahrenheit30 degrees Celsius are equal to 86 degrees Fahrenheit:
30ºC = 86ºF
30 degrees Celsius to Fahrenheitcalulation:
The temperature T in degrees Fahrenheit (ºF) is equal to 30 degrees Celsius (ºC) times 9/5 plus 32:T(ºF) = 30ºC × 9/5 + 32 = 86ºF
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