The linear independence of vector sets forms the basis of the space of polynomials of third degree.
In vector space theory, a collection of matrices is said to be heavily dependent if there is a nontrivial concatenation of the vectors that equal the zero vector. If no such linear combination exists, the vectors are said to be linearly independent. These concepts are crucial to the concept of dimension.
The maximum number of nonzero vectors determines whether the dimensions of a vector space are finite or infinite. The capacity to recognize whether a subset of columns in a vector space is dependent, as well as the concept of linear dependence, are crucial for determining a vector space's dimensionality.
If the same vector appears twice in a vector sequence, it must be dependent. The linear dependency of a vector series is independent of the order of the terms. A restricted collection of vectors can have linear independence if the sequence obtained by sorting a finite number of lines is linearly independent. In other words, the following outcome is frequently useful.
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922x81=
783x14=
684x15=
650x22=
2525x37=
615x41=
Please help me
Answer:
1. 922x81=74,682
2. 783x14=10,962
3. 684x15=10,260
4. 650x22=14,300
5. 2525x37= 93,425
6. 615x41=25,215
Step-by-step explanation:
7. Here is an inequality: -7- (3x+2) <-8(x + 1)
Select all the values of x that are solutions to the inequality.
A. x = -0.2
B. x = -0.1
C.x=0
D. x = 0.1
E. x = 0.2
F. x = 0.3
(From Unit 2, Lesson 19.)
Answer:
A,B,C,D
Step-by-step explanation:
-7-(3x+2) <=8(x+1)
-7-3x-2<-8x-8
5x<1
x<1/5
x= -0.2, X=-0.1, X=0, X=0.1
The values of x that are solutions to the inequality are C (x = 0) and D (x = 0.1).
Given inequality: -7 - (3x + 2) < -8(x + 1)
Let's solve the inequality step by step:
Distribute the -8 on the right side:
-7 - 3x - 2 < -8x - 8
Combine like terms on both sides:
-9 - 3x < -8x - 8
Add 8x to both sides to isolate the variable terms on one side:
8x - 3x - 9 < -8
Simplify the left side:
5x - 9 < -8
Add 9 to both sides:
5x < 1
Divide both sides by 5 (since 5 is positive, the direction of the inequality does not change):
x < 0.2
Now, let's compare the solutions to the given options:
A. x = -0.2: Not a solution (not less than 0.2)B. x = -0.1: Not a solution (not less than 0.2)C. x = 0: Solution (0 is less than 0.2)D. x = 0.1: Solution (0.1 is less than 0.2)E. x = 0.2: Not a solution (not less than 0.2)F. x = 0.3: Not a solution (not less than 0.2)So, the values of x that are solutions to the inequality are C (x = 0) and D (x = 0.1).
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can someone please help me figure out what the answer is!!
Answer:
v = 61
Step-by-step explanation:
Hello, of course! These are vertical angles, which means they're equal to each other, so let's set up an equation, shall we? (:
Knowing that they're equal to each other, both sides of the equation should be equal to each other as well, so...
2v + 1 = 123
Now, that we have the equation, we must solve for the variable v!
2v + 1 = 123
- 1 - 1
2v = 122
2v = 122
2 2
v = 61
Therefore, v is 61. Once again, vertical angles are equal to each other, so you set up the equation, where both sides are equal. Hope this helped and best of luck with the rest of your work! <3
(HELP PLEASE ASAP) Lydia wants to purchase guitar lessons. She sees a sign that gives the prices for 7 guitar lessons and 11 guitar lessons. Write a linear equation to find the total cost C for d lessons.
Using the slope and y-intercept, the linear function that model this problem is c = 10d + 12
What is Linear FunctionA linear function is a mathematical function that graphs as a straight line. It is a polynomial of degree one and can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept.
In this problem, we can represent or model the given problem with a set or system of linear equation.
let;
C = cost of lessond = number of lessons.Using y = mx + c and modeling it to suit our given parameter;
m = slope and c = y - intercept
We can take two the two given point and solve for the slope and y - intercept.
m = c₂ - c₁ / d₂ - d₁
m = 122 - 82 / 11 - 7
m = 10
Taking the slope and one point, we can solve for the y - intercept
y = mx + c
82 = 10(7) + c
82 = 70 + c
c = 82 - 70
c = 12
The equation can be written as c = 10d + 12
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what is the answer to [tex]2(10 + n) = 16[/tex]
The initial expression is:
[tex]2(10+n)=16[/tex]So first we can divide by 2 so:
[tex]\begin{gathered} 10+n=\frac{16}{2} \\ 10+n=8 \end{gathered}[/tex]now we rest 10 in bout sides so:
[tex]\begin{gathered} n=8-10 \\ n=-2 \end{gathered}[/tex]what is one hundred three thousand thirty three in standard form?
Answer:
103,033
Step-by-step explanation:
225 words in 5 minutes . what is the unit rate ? at that speed , how many words can be type in 9 minutes
Which point is on the graph of the inverse function h–1(x)?
Solution:
Given:
The graph of the function h(x)
Picking any point on the graph as shown below,
Picking point (0,2) on the graph of the function h(x)
[tex]\begin{gathered} x=0 \\ y=2 \\ \\ \text{Hence, the point of the inverse function is gotten by interchanging the coordinates of the point } \\ ^{}^{} \end{gathered}[/tex][tex]\begin{gathered} \text{If the point of h(x) is }(x,y),thenh^{-1}(x)\text{ is (y,x)} \\ \\ \text{Hence, at (0,2) on h(x)}, \\ h^{-1}(x)\text{ will have the point (2,0)} \\ \\ \text{Also, at (1,0) on h(x),} \\ h^{-1}(x)\text{ will have the point (0,1)} \end{gathered}[/tex]Therefore, a point on the graph of the inverse function of h(x) is (2,0).
Another point on the graph of the inverse function of h(x) is (0,1).
1. (02.06 mc) a car travels 25.0 miles due east for one hour. then it travels another 60.0 miles east for an additional hour. what is the average velocity of the entire trip? (2 points) 17.5 mph east 35.0 mph east 42.5 mph east 85.0 mph east
The average velocity of the entire trip is 42.5 mph east
An object's average velocity is calculated by dividing its total displacement by its total travel time.
It measures how quickly an object shifts from one location to another.
It is a Vector magnitude
For one hour, an automobile travels 25.0 miles due east.
Then it continues for an extra hour and travels another 60.0 miles east.
We must determine his overall journey average speed.
He does the entire journey going straight east.
He travels a total distance of 25 + 60 = 85 miles east.
He takes an hour to get there from here and another hour to get there from there.
The total travel time is 1 + 1 = 2 hours.
Total displacement times total time equals the average velocity.
His average speed = 85 ÷ 2 = 42.5 miles/hour east
The average velocity of the entire trip is 42.5 mph east
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at a certain pizzeria, 1 8 of the pizzas sold in one week were mushroom and 1 3 of the remaining pizzas sold were pepperoni. if n of the pizzas sold were pepperoni, how many were mushroom?
The pizzas sold were (n + 5).
What is the meaning of sold?Past tense and past participle of sales. It is marketed with uncritically related or enthusiastic slang.Sold, for sale. Transfer (goods) to another person or provide (services) for money to another person. Sold to Buyer: He sold me the car for his $1000.If the last sale of the car took place during the talk time or is active, then the statement "This car has been sold 10 times" is correct.But if the last sale of that car happened before the time to speak "Goods Sold" are available. This is passive-past perfect tense means to convince someone that something is good, worthy or useful. Consider the following example:A filmmaker gave me the idea that my book would work on screen.To learn more about sold from the given link :
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a biased coin lands heads with probability 2/3. the coin is tossed three times. a) given that there was at least one head in the three tosses, what is the probability that there were at least two heads? b) use your answer in a) to find the probability that there was exactly one head, given that there was at least one head in the three tosses.
The probability that one head in the three tosses, at least two heads is 0.7692, and the probability that exactly one head, at least one head in the three tosses is 0.2308.
What is a toss?
Probability indicates the likelihood of an event.That whenever a coin is tossed, there are only two possible outcomes. Head and Tail are those. In light of the probability formula above, the coin toss probability calculation is as follows:Formula for Probability of a Coin Toss: (Number of Successful Outcomes) (Total occurances of possible outcomes)
It's a binomial distribution with n=3, P=2/3
(a) P(one head in the three tosses, at least two heads)
P(x≥2 | x≥1)=[P(x≥2)∩P(x≥1)]/P(x≥1)
=0.7407/0.9630
=0.7692
(b) P(exactly one head, at least one head in the three tosses)
P(x=1 | x≥1)=[P(x=1∩ (x≥1)]/P(x≥1)
=0.222/0/9630
=0.2308
The probability that one head in the three tosses, at least two heads is 0.7692, and the probability that exactly one head, at least one head in the three tosses is 0.2308.
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If the first differences for a table of values is 3.5 the equation is a
equation and the slope is
When first differences are the same it's a linear equation. First differences are equal to the slope, m. General equation is f(x) = mx + b
To see if a table of values represents a linear function, check to see if there's a constant rate of change. If there is, you're looking at a linear function.
How can one locate an equation?
determine a line's equation from two points:
Using the slope formula, determine the slopeTo find the y-intercept (b), use the slope and one of the points.You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of a line (y = mx +b)To learn more about f(x) = mx + b refer to:
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The price that Abigail paid for her snowboard, $77, is less than what Dan paid by $10. How much did Dan pay for his
snowboard?
The ingredients list for a homemade lemonade recipe is shown below.
Ingredients:
5 lemons
1 cup of brown sugar
3.5 cups of boiling water
Michael wants to use this recipe, but he only has 3 lemons. How many cups of boiling water should he use with only 3 lemons?
Michael should use 2.1 cups of boiling water with 3 lemons.
We are given the list of ingredients for a homemade lemonade recipe.The ingredients include 5 lemons, 1 cup of brown sugar, and 3.5 cups of boiling water.Michael wants to use the above recipe.He has only 3 lemons to make lemonade according to the recipe.He needs the boiling water in the correct proportions.The ratio of the number of lemons to the number of cups of boiling water in the actual recipe is 5/3.5.Let the number of cups of boiling water required now be "x".The ratio of the available number of lemons to the cups of boiling water is 3/x.The ratio should be the same.5/3.5 = 3/xx = (3*3.5)/5x = 2.1Thus, Michael requires 2.1 cups of boiling water.To learn more about ratios, visit :
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Please Help me to answerthe questions and options are in picture
Evelyn has initially $524.96, then she paid $32.50, so she will have less than $500. In order to have at least $500, she needs to deposit the value x.
So the initial value, minus the value paid, plus the deposit needs to be greater than or equal 500, so we have the inequality:
[tex]524.96-32.5+x\ge500[/tex]Solving this inequality for x, we have:
[tex]\begin{gathered} 492.46+x\ge500 \\ x\ge500-492.46 \\ x\ge7.54 \end{gathered}[/tex]Therefore the correct option is the first one (a).
Find the value of 6f + 7g when f= -3 and g = 2
Pls help thanks
Answer: 6f+7g=6*-3+7*2=-4
Step-by-step explanatiomn]]
Answer:
-4
Step-by-step explanation:
6(-3)+7(2)
-18+14
-4
at the kennel there are 6 dogs for every five cats
Answer: I have listed each part below
Step-by-step explanation:
a. The ratio of dogs to cats is 6 to 5
b. The ratio of cats to dogs is 5 to 6
c. For every 6 dogs there are 5 cats
d. The ratio of cats to dogs is 5:6
2ab-ab+2a+3b+2ab simplified
Answer:
3ab + 2a + 3b
Step-by-step explanation:
what will increase the width of a confidence interval? a) increase number in sample b) decrease confidence level. c) decrease variance d) increase variance.
The width of a confidence interval decreases as the sample size increases and increases as the confidence level increases.
What is a confidence interval?A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a certain confidence level; the 95% confidence level is the most commonly used, although other levels, such as 90% or 99%, are also employed.So, we know that smaller samples result in narrower intervals.
With a higher sample size, we can more precisely estimate a population proportion.Therefore, a confidence interval narrows as the sample size grows and widens as the level of confidence rises.
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pls help A rectangle has a length of 4.3 cm and a perimeter of 14.8 cm. Find the width of the rectangle.
cm
A rectangle has a length of 4.3 cm and a perimeter of 14.8 cm. The width of the rectangle is 3.1 cm.
What is a rectangle?A rectangle is a shape that has four right angles and whose adjacent lengths are not the same.
Given, the length L is 4.3 cm
The perimeter of the rectangle is 14.8 cm.
To calculate the perimeter = 2(l + w)
Putting the values:
14. 8 = 2(4.3) + 2w
Expand the bracket
14. 8 = 8. 6 + 2w
Collect like terms
2w = 14. 8 - 8.6
2w = 6. 2
Divide through by the coefficient of w
w = 6.2/2
w = 3.1 cm
Therefore, the width of the rectangle is 3.1 cm.
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HELP ASAP
Use what you know about trapezoid properties to solve for x. Confirm the angle measure.
83⁰
X =
Angle (-x +33) =
(-x +33)
degrees.
8 9
10
11
Answer:
the answer is x = -50° and the angle measures 83°
Step-by-step explanation:
in this trapezoid, the angles adiacent to each base have se same amplitude, so:
-x + 33 = 83°. this means the answer is -50 because
-(-50) + 33 = 50 + 33 = 83
Machine A makes 12.75 ounces of popcorn in 3 minutes. Machine B makes 18 ounces of popcorn in 4 minutes.
If each machine makes popcorn for 10 minutes, will there be enough popcorn for eight 9-ounce bags? Explain.
a) Yes; Machine A and Machine B make 77.5 ounces in 10 minutes. 77.5 > 72, so there will be enough popcorn.
b) Yes; Machine A and Machine B make 87.5 ounces in 10 minutes. 87.5 > 72, so there will be enough popcorn.
c) No; Machine A and Machine B make 67.5 ounces in 10 minutes. 67.5 < 72, so there will not be enough popcorn.
d) No; Machine A and Machine B make 30.75 ounces in 10 minutes. 30.75 < 72, so there will not be enough popcorn.
If each machine makes popcorn for 10 minutes, there will be enough popcorn as machine A and machine B make 87.5 ounces in 10 minutes.
According to the question,
We have the following information:
Machine A makes 12.75 ounces of popcorn in 3 minutes.
So, we will find the ounces of popcorn in 1 minute:
3 minutes = 12.75 ounces
1 minute = 12.75/3 ounces
1 minute = 4.25 ounces
So, in 10 minutes machine A will make:
10 minutes = (4.25*10) ounces
10 minutes = 42.5 ounces
Machine B makes 18 ounces of popcorn in 4 minutes.
So, we will find the ounces of popcorn in 1 minute made by machine B:
4 minutes = 18 ounces
1 minute = 18/4 ounces
1 minute = 4.5 ounces
So, in 10 minutes machine B will make:
10 minutes = (4.5*10) ounces
10 minutes = 45 ounces
Now, the total amount of popcorn made by both the machines will be:
Popcorn made by machine A in 10 minutes + Popcorn made by machine B in 10 minutes
42.5 + 45
87.5 ounces
Now, the eight 9-ounce bags mean that there will be 72 ounces of popcorn.
So, we have:
87.5 ounces is greater than 72 ounces.
Hence, the correct option is B.
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What is the slope of the line shown below?
(-1,-4)
(2, 2)
Answer:
2
Step-by-step explanation:
To find the slope, you need to use the term y2-y1/x2-x1
To do this, first do:
-4-2:
-6
Now, do -1-2=
-3
Now, since -6/-3 has two negatives, the fraction will turn into
6/3
Now simplify
2.
The slope of the line is two.
5) How can we guarantee that a polynomial is not a perfect square, considering just the constant term? For instance, in 4, the constant term is -121, in 2, the constant term is 36. Which of them cannot be a perfect square and why, based only on the constant term?
Polynomials with a negative constant term are not perfect squares, hence polynomial 4, with constant term of -121, is not a perfect square.
What are perfect square expressions?Perfect square expressions are formed in two ways, either with the square of the sum or the square of the subtraction, as follows:
Square of the sum: (a + b)² = a² + 2ab + b².Square of the subtraction: (a - b)² = a² - 2ab + b².The constant term is the final term. Since this term is squared, it will always be positive for perfect squares, hence if the constant term is negative, it will guarantee that the polynomial is not a perfect square.
For the expressions in this problem, we have that:
The expression with a constant term of 36 can be a perfect square, as 36 is a positive number.The expression with a constant term of -121 cannot be a perfect square, as -121 is a negative number.More can be learned about perfect squares at https://brainly.com/question/14584348
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whats the G.C.F for 25 and 40 help me
Answer:
5
Step-by-step explanation:
G.C.F means greatest common factor
this means the highest number that will go into both 25 and 40
5 is the highest number that will divide into both
Which expressions are equivalent to the given expression? square root of 40
Answer:
Step-by-step explanation:
√40 = √4*√10
= 2√10 is one equivalent expression
Help pls............................
Answer:
the 2nd, 3rd, 5th
i hope this helps :)
If my grade is an 85 and i make a 67 on an assignment, what is my final grade
The percentage of your grade based on the final grade is 78.8%.
How to calculate the percentage?The information given is incomplete and the complete question is attached below. This was illustrated as "If my grade is an 85 and i make a 67 on an assignment, what is the percentage of my final grade?"
The following can be deduced based on the information illustrated:
Total grade = 85
Your grade = 67
It should be noted that the percentage will be:
= Your grade / Total grade × 100
= 67/85 × 100
= 78.8%
The percentage is 78.8%.
Note that the complete question is given below.
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If my grade is an 85 and i make a 67 on an assignment, what is the percentage of my final grade
What is 5 & 2/5 as a mixed fraction Halp brainlest to correct answer
Answer: 27/5.
Step-by-step explanation: 5 and 2/5 is already a mixed fraction, so I think you mean a improper fraction. If not, then its 5 and 2.5. Hope this helps.
The current student population of Memphis is 2900. If the population increases at a rate of 10.7% each year. What will the student population be in 10 years?Write an exponential growth model for the future population P(x) where x is in years:P(x)=What will the population be in 10 years? (Round to nearest student)
Given:
Current population = 2900
rate of increase = 10.7% each year
The exponential growth formula is defined as:
[tex]\begin{gathered} P\text{ = P}_0e^{rt} \\ Where\text{ P}_0\text{ is the initial population} \\ r\text{ is \% growth rate} \\ and\text{ t is time in years} \end{gathered}[/tex]Substituting the given values:
[tex]P(x)\text{ = 2900e}^{0.107x}[/tex]Hence, the exponential model is:
[tex]P(x)\text{ = 2900e}^{0.107x}[/tex]The population in 10 years
We substitute 10 for x in the equation above and solve:
[tex]\begin{gathered} P(x=10)\text{ = 2900e}^{0.107\times10} \\ =\text{ 8454.6005} \\ \approx\text{ 8455 students} \end{gathered}[/tex]Hence, the population of the students after 10 years would be 8455 students
