The columns of the matrix A span R2.
In order to determine if the columns of the matrix A span R2, we need to check if the columns of A can be used to generate all possible linear combinations of the form a1v1 + a2v2, where a1 and a2 are scalars and v1 and v2 are the columns of A.
A = [2 1]
[0 1]
[-3 -1]
The columns of A are [2, 0, -3] and [1, 1, -1]. To check if these columns span R2, we need to see if we can create any vector in R2 by taking linear combinations of the columns. We can see that by taking linear combinations of the columns, we can create any vector of the form (a, b) in R2.
For example, by taking a = 2, b = 1, we can generate the vector (2, 1) by taking
a[2, 0, -3] + b[1, 1]
And by taking a = 3, b = -1, we can generate the vector (3, -1) by taking
a[2,0,-3] + b[1,1,-1].
So the answer would be: The columns of the matrix A span R2.
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plss help me in time!!!
The correct statements are given below.
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: The graph of two functions plotting distance vs time of two Alberto and Bianca
1) Early in the race Alberto runs faster.
2) Alberto maintains a contain speed of 20 km/hr
3) Meanwhile Bianca's Speed is 8.33 km/hr
4) The first person to cross the finish line is Bianca.
Hence, Bianca reached the finished line before Alberto.
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How do you construct a line segment half as long as the given line segment?
To steps to construct a line segment that is 1/2 the length of the given segment is:
Draw a line segment CD of any length.
Fix the compass's end on C and pencil on D. This gives the length of CD.
Now divide the length of CD by 2. That is the 1/2 the length of CD.
Draw a line 1. Mark a point A on line 1. Change compass's setting into 1/3 the length of CD, place the compass at A.
Make an arc on the line l which cuts l at B. Now, AB is a copy of CD which is 1/2 the length of CD.
What is line segment?
A line segment is bounded by two definite points on a line. We also can say a line segment is part of the line which connects two points. A line has no endpoints and extends immensely in both the direction but a line segment has two fixed or distinct endpoints.
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a peer-reviewed (sometimes called refereed) journal article group of answer choices a) has been written by someone with a ph.d. b) is one that has found significant statistical results c) is one for which the author has been paid d) has been evaluated before publication by other researchers in the same field
Peer-reviewed (refereed or scholarly) journals: Before an article is published in a journal, it is examined by a number of other experts in the subject to guarantee that it is of a high caliber. (The paper is more likely to be valid from a scientific standpoint, draw fair conclusions, etc.)
Peer review is conducted on publications in refereed journals.Peer review has been conducted on the publications in a refereed journal. The papers were evaluated for quality by reputable academics or subject-matter experts before being approved for publication, so this tells us that they are of a high caliber. Also known as "scholarly" or "peer-reviewed," these pieces are published in journals.
5 Essential Qualities of writting JournalsAuthors having affiliations or credentials, such as a PhD (e.g. university professor)a particular emphasis on providing fresh, original research in a given field of study (often indicated through a long title)With complicated concepts and arguments, an impartial tone, and an analytical perspective, technical and formal languagematerial that is lengthy (at least 5 pages) and contains a lot of citations and referencesa simple look with barely any color, graphics, or photographs
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A waterwheel has a radius of 4 feet, and the center of the wheel is 1 foot under the waterline. You notice a yellow mark at the top of the wheel. If the wheel rotates radians, how far above the water is the yellow mark?
1 foot
2 feet
3 feet
4 feet
The yellow mark is 1 foot above the water level.
This question can be answered using the concept of trigonometry.
According to the given question
radius of the waterwheel r= 4 feet
let OD is the part of the waterwheel that is submerged in the water and its value is to be determined.
From the figure we can see that
OA=OC=radius= 4 feet
Now
In triangle OAB
cos 60= [tex]\frac{OB}{OA}[/tex]
[tex]\frac{1}{2}= \frac{OB}{OA}[/tex]
OB= 2 feet
which means the length of the yellow mark above water is given by
OB-OD= 2-1= 1 feet.
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Jeremy borrowed money from his dad for a car repair. The graph represents the amount
remaining that Jeremy owes his dad.
a. Write an equation to represent the situation.
b. What does the slope mean in the context of
the situation?
c. What does the y-intercept mean in the context
of the situation?
Therefore , the solution of the given problem of equation comes out to be the equation is: y = -700/9 * x + 700.
Explain the equation.Equation construction is the process of connecting two expressions with the equivalent sign. An equation is, for illustration, 7x - 5 = 40. By solving this equation, we can determine that the value of the variable x is 6.
Here,
Given :
Regarding the details provided:
The formula is: y = -700/9 * x + 700
B) The slope represents the amount owned's rate of change.
c) Y-intercept represents the sum borrowed from his father.
thus , the solution is given above
Therefore , the solution of the given problem of equation comes out to be the equation is: y = -700/9 * x + 700.
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Solve the system of equation using elimination.
7x−12y=−3−7x+12y=2
Multiple choice question.
cross out
A)
(−114,112)
cross out
B)
(−1,−13)
cross out
C)
infinitely many solutions
cross out
D)
no solution
The given system of equation has no solution.
What is elimination method?
The elimination method is a way to get rid of one of the variables in a system of linear equations by using multiplication or division of the variable coefficients along with addition or subtraction of the variables and their coefficients.
Substitution, elimination, and augmented matrices are the three approaches that are most frequently used to solve equation systems.
Consider, the given system of equations
7x - 12y = -3 ..(1)
-7x + 12y = 2 ..(2)
Adding equation (1) and (2).
7x - 12y = -3
+ -7x + 12y = 2
___________________
0 = -1
0 = -1 is false.
Hence, the given system of equation has no solution.
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According to government data, 22 percent of children in the United States under the age of 6 years live in households with incomes that are classified at a particular income level. A simple random sample of 300 children in the United States under the age of 6 years was selected for a study of learning in early childhood. If the government data are correct, which of the following best approximates the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level
The best equation that approximates the probability that at least 27 percent of the children in the sample live in households that are classified at a particular income level is [tex]p(z > \frac{0.27-0.22}{\frac{\sqrt{0.22*0.78} }{300} })[/tex] .
What is Probability Sampling?Probability sampling is the process of selecting a sample from a population when the selection is based on the randomization principle, often known as chance or random selection. In general, probability sampling is more difficult, time-consuming, and expensive than non-probability sampling. However, since units from the population are chosen at random and the selection probability for each unit can be determined, accurate estimates can be generated and statistical conclusions about the population may be drawn.Given:
Probability of children who live in households with incomes that are classified at a particular income level,p = 22/100 = 0.22
Number of children in a simple random sample,n = 300
Probability of children who do not live in households with incomes that are classified at a particular income level, q = 1-p = 0.78
The probability of children in the sample living in households that are classified at a particular income level,p₁ = 27/100 = 0.27
Now, we know
[tex]p(z > \frac{p_{1} -p}{\frac{\sqrt{p.q} }{n} } )[/tex]
So,
[tex]p(z > \frac{0.27-0.22}{\frac{\sqrt{0.22*0.78} }{300} })[/tex]
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PLS HELP Choose 2 answers
Answer: C and D
Step-by-step explanation:
Plug in the X and Y from the coordinates into each equation. If both sides are equivalent, that means that the line passes through.
If x is 300 then what is the answer to this equation, 3x plus 10 minus 17x
Answer:
-4190
Step-by-step explanation:
910-5100
probability outcome: toddler triplets whose names are red, green and blue each have a coat whose colour is given by their name, but they aren't clear on which coat belongs to which of them. when they go out, red chooses a coat at random among the three coats, green chooses a coat at random among the remaining two coats and blue is left to take the remaining coat. how many ways are there for exactly one of the toddler triplets to end up with their coat? help
is the answer 3!=6
i dont understand how n! could be the way to go about this, if n! is for If you want to see how many ways you can order a certain number of things: n! (n factorial)
Answer:
There are 3! (3 factorial) ways for the toddler triplets to each choose a coat. However, we are only interested in the ways where exactly one of them ends up with their coat.
There are 3 ways for the first toddler to get their coat, 2 ways for the second toddler to get their coat, and 1 way for the third toddler to get their coat.
Therefore, there are 3*2*1 = 6 ways for exactly one of the toddler triplets to end up with their coat.
In other words, there are 6 possible scenarios in which exactly one of the toddler triplets get their coat.
For example, Red getting his coat, Green getting the wrong coat and Blue getting the wrong coat.
a piece of clothes was 5 m long,after washing it srank to 4.2m long find the percentage decrease in length
The length of the piece of clothing decreased by 16% after washing.
What is the percentage decrease?
To compute a percentage drop, first determine the difference (decrease) between the two values being compared. Then, divide the reduction by the original number and multiply the result by 100. The percentage change is expressed as a result of the alteration.
The percentage decrease in length of the piece of clothing can be calculated as follows:
Percentage decrease = (original length - new length) / original length * 100
Percentage decrease = (5 - 4.2) / 5 * 100
Percentage decrease = 0.8 / 5 * 100
Percentage decrease = 16%
Hence, the length of the piece of clothing decreased by 16% after washing.
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8.04 Rotations Assignment
The angle of rotations are 90° , 180° and 270° counterclockwise
What is Rotation?The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.
90° clockwise rotation: (x,y) becomes (y,-x)
90° counterclockwise rotation: (x,y) becomes (-y,x)
180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
270° clockwise rotation: (x,y) becomes (-y,x)
270° counterclockwise rotation: (x,y) becomes (y,-x)
Given data ,
Let the point be represented as A
Now , the value of A is
a)
Let the coordinates of the point be A = A ( 4 , 1 )
Now , the rotation angles are 90° , 180° and 270° counterclockwise
90° counterclockwise = A' ( -1 , 4 )
180° counterclockwise = A'' ( -4 , -1 )
270° counterclockwise = A''' ( 1 , -4 )
b)
Let the coordinates of the point be A = A ( 0 , -7 )
Now , the rotation angles are 90° , 180° and 270° counterclockwise
90° counterclockwise = A' ( 7 , 0 )
180° counterclockwise = A'' ( 0 , 7 )
270° counterclockwise = A''' ( -7 , 0 )
c)
Let the coordinates of the point be A = A ( -2 , 9 )
Now , the rotation angles are 90° , 180° and 270° counterclockwise
90° counterclockwise = A' ( -9 , -2 )
180° counterclockwise = A'' ( 2 , -9 )
270° counterclockwise = A''' ( 9 , 2 )
d)
Let the coordinates of the point be A = A ( -12 , -4 )
Now , the rotation angles are 90° , 180° and 270° counterclockwise
90° counterclockwise = A' ( 4 , -12 )
180° counterclockwise = A'' ( 12 , 4 )
270° counterclockwise = A''' ( -4 , 12 )
Hence , the rotation of coordinates are solved
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Central High School plays Eastern High School in a basketball game. Eastern had double the score of Central
before Central scored a three-pointer as the game ended.
The variable, c, represents Central's score before the three-pointer. Express the total points scored in the game as a
variable expression. Check all that apply.
2c + c
3c + 3
2c +3
2c + c-3
2c-c+3
2c +c+ 3
Answer:
Step-by-step explanation:
The total points scored in the game is a sum of the points scored by both teams.Given that Eastern had double the score of Central before Central scored a three-pointer as the game ended, Eastern's score can be represented as 2c.So the total points scored in the game is:Central's score before the three-pointer + Eastern's score before the three-pointer + the points scored by Central in the last three-pointer.So the total points scored in the game can be represented as:c + 2c + 3 = 2c + 3So the correct answer is C) 2c +3
Is 0 positive real number?
Zero is not a real number that is positive. Because it lies between positive and negative real numbers. Therefore, it is considered neither a positive nor negative real number.
Real numbers are founded on the idea of the number line: the positive numbers to the right of zero and the negative numbers to the left of zero. Any number that fits on this number line can be considered real.
All numbers that are either rational or irrational are also referred to as real numbers. A real number that is positive and bigger than zero is known as a positive real number. Any real number that is not a positive integer is either zero or negative. Therefore, 0 is neither positive nor negative.
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Is it possible to construct a triangle with 2cm 3cm 7cm justify your answer?
It is not possible to construct a triangle with 2cm, 3cm, and 7cm.
The sides measure 2 cm, 3 cm, and 7 cm in length.
Only when the third side is greater than the sum of any two sides can a triangle be drawn. This the condition.
Let's verify the rule now.
2 + 3 > 7 Not true
2 + 7 > 3 True
3 + 7 > 2 True
As 2 + 3 > 7 does not satisfy the condition.
Hence, it is not possible to construct a triangle having 2cm, 3cm, and 7cm in length.
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two hikers start at a ranger station and leave at the same time. one hiker heads due west at 3 miles/hour. the other hiker heads due north at 4 miles/hour. how far apart are the hikers after 2 hours of hiking?
The hikers will be 8 miles apart after 2 hours of hiking.
The formula used to calculate the distance apart is the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the distance between the two hikers, and the other two sides are the distances each hiker has traveled in the two directions: 3 miles to the west, and 4 miles to the north. The formula is written as a^2 + b^2 = c^2, where a and b represent the side lengths, and c represents the hypotenuse. Plugging in the values, 3^2 + 4^2 = c^2, or 9 + 16 = c^2. Solving for c, c^2 = 25, so c = 5. Therefore, the distance between the two hikers is 5 miles after two hours of hiking.
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1. the probability you'll see a falling star in the sky over the course of one hour is 0.44. what's the probability you'll see one over half an hour? (asked by citadel)
The probability you'll see one over half an hour is 0.26
The term probability in math is defined as the possibility of the outcome of any random event
Here we have given that the probability you'll see a falling star in the sky over the course of one hour is 0.44.
Then in an hour can be taken as two half hours so we can write the probability to see a falling star as
Then it can be written as,
=> (1-P)*(1-P) = 1 - 0.44
When we simplify this one then we get
=> (1 - P)² = 0.56
Here we need to value of p then it can be written as,
=> 1 - P = √0.56
Then the value of P is calculated as,
=> -P = 0.74 - 1
=> P = 0.26
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A race is made up of 4 separate stages. Round each stage’s distance to the nearest thousand|:
Stage Name Distance Rounded Distance
Le Start 30,060 m m
The Uphill 21,111 m m
The Downhill 33,501 m m
Le Finish 49,840 m m
According to the round off rule, the resulting value of the total distance is 135,000
As we al know that if the rounded number increases then the given number is said to be rounded up on the other hand if the rounded number decreases then it is said to be rounded down.
Here we have given the details about the race is made up of 4 separate stages.
Now, we need to find the total distance, that can be calculated by adding all the given distance, then we get,
=> 30,060 + 21,111 + 33,501 + 49,840
=> 134512.
Now, we have to round off the value to the nearest thousandth term, then it can be written as,
Here we need rounded to the nearest thousands place. The 4 in the thousands place rounds up to 5 because the digit to the right in the hundreds place is 5.
=> 135,000
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The large rectangle below represents one whole.
What percent is represented by the shaded area?
%
Grace is making cookies. She has 6 tablespoons of baking soda left in the container. If she uses 2 teaspoons of baking soda for her recipe, how many teaspoons of barking soda will be left??
Answer: 16 Teaspoons
Hope this helps! :)
Step-by-step explanation:
1 Tablespoon= 3 Teaspoons
6 Tablespoons= (6*3) 18 Teaspoons
18 - 2= 16 tsp
PLEASE HELP!!! The seventh grade teachers want to buy the principal a giant stuffed tiger for his office costing $50.00 However the store is having a 10% off sale. Tax is 6% . What is the total cost of the tiger? If we pay $60.00 how much change do we have left?
Answer:
i think 48.00
Step-by-step explanation:
10% of 50 is 5 while 6% of 50 is 3 so 50-5+3 is 48
PLEASE HELP ASAP THERE ARE 3 QUESTIONS!!!!!! CORRECT ANSWER GETS BRAINLLEST!!! WORTH 100 POINTS. PLEASE HELP!!!!!!!!!!!!!!!!!!!!
Case 2
The quadratic equation x² - 14 · x + 48 = 0 have the following roots: x₁ = 6 and x₂ = 8. (Correct choice: B)
Case 3
We need to add + 64 to both sides. (Correct choice: B)
Case 4
We need to add + 16 to both sides. (Correct choice: C)
How to use completing the square method
In this problem we find three cases of quadratic equation that are not perfect square trinomials, these equations can be rewritten partially in that form by algebra properties. Completing the square offers a quick method to determine the roots of quadratic equations with integer coefficients. Now we proceed to determine the solutions corresponding to each case:
Case 2
x² - 14 · x + 48 = 0
x² - 14 · x + 49 = 1
(x - 7)² = 1
x - 7 = ± 1
x = 7 ± 1
The roots of the quadratic equation x² - 14 · x + 48 = 0 are x₁ = 6 and x₂ = 8, respectively.
Case 3
x² - 16 · x = - 21
x² - 16 · x + 64 = 64 - 21
(x + 8)² = 43
The first step consists in adding both sides by + 64.
Case 4
x² - 8 · x = 0
x² - 8 · x + 16 = 16
(x - 4)² = 16
The first step consists in adding both sides by + 16.
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a small bag of 10 identical apples weighs n ounces, and a large bag of n of these apples weighs less than 40 ounces, where n is an integer. in ounces, what is the greatest possible weight of the large bag? express your answer as a mixed number.
The greatest possible weight of the large bag is 1.9n ounces.
How do you get a mixed number?Divide the numerator by the denominator of an improper fraction to get a mixed number. The mixed number is represented by the answer's whole number, and the fractional portion of the mixed number is represented by the answer's remaining fractional component. No change is made to the denominator.Given:
Weight of 10 apples = n ounces
Weight of 1 apple = n/10 ounces
Weight of n apples = n²/10 ounces
It is given that a large bag of n of these apples weighs less than 40 ounces,
= n²/10 < 40
= n²< 400
= n < 20
So, the large bag contains at most 19 apples.
Hence, the weight of the large bag is at most 1.9n ounces, or (19/10)(n) ounces.
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you are choosing between two different cell phone plans. the first plan charges a rate of 23 cents per minute. the second plan charges a monthly fee of $34.95 plus 12 cents per minute. how many minutes would you have to use in a month in order for the second plan to be preferable? give the exact number of minutes (do not approximate).
In order for the second plan to be preferable, a greater amount of 249.6 minutes would have to be used in one month.
Let
x -----> the number of minutes in a month
y ----> the charge monthly
we know that
First Plan
y= 0.23 x ----> equation A
Second Plan
y= 0.12x+34.95 ----> equation B
Equate the equations A and B and solve for x
so x= 249.6
For x< 249.6 ----> is preferable the first plan
For x> 249.6 ----> is preferable the second plan
therefore
In order for the second plan to be preferable, a greater amount of 249.6 minutes would have to be used in one month.
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IF THE PROBABILITY OF WINNING IS 0.3 THEN WHAT IS THE PROBABILTY OF NOT LOSE?
Answer:
0.7
Step-by-step explanation:
if we set the total race of win and lose is 1
then we use 1-0.3=0.7
(c) Suppose that L is a line tangent to the boundary of the golf green and parallel to the path of the ball. Let Q be the point where the line is tangent to the circle. Notice that there are two possible positions for Q. Find the possible x-coordinates of Q:
The value x-coordinates which is required is found out to be as Q = -19.41 and +19.41.
The given values are,
radius , r = 35 feet
speed of ball = 11 ft./sec
location of the cup = (0, 0)
starting location the ball = (-40. -50)
In order to find the possible x-coordinates of Q,
The coordinates of the rightmost edge of the golf course = (35, 0)
slope = m = ( y2 - y1)/ ( x2 - x1)
now , the equation for a circle is known as , (x - h)² + (y - k)² = r²
and the center of the course is given as , (h, k) = (0, 0)
Therefore the equation becomes (x - 0)² + (y - 0)² = x² + y² = 35²
equation of tangent , y = -3x/2
putting this value in the tangent = x² + ( -3x/2 )² = 35²
13x² /4 = 35²
x = √ ( 35² x 4 )/ 4 = 35²
x = 70/13√ 13 = 19.41
Therefore, the coordinates of Q are found out to be as -19.41 and +19.41
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write the expression as a single real number. Do not use decimal approximations
sin(pie/6)cos(pie/2)-cos(pie/60)sin(pie/2)
The expression as a single real number is [tex]\frac{1-\sqrt{3} }{2}[/tex] .
What is trignomentry ?
Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. It is used to study the properties of triangles and to solve problems involving angles and distances in two-dimensional space.
sin(π/6)cos(π/2) - cos(π/60)sin(π/2)
The first term in the expression, sin(π/6)cos(π/2), can be simplified as follows ,
sin(π/6) = √(3)/2, cos(π/2) = 0
so sin(π/6)cos(π/2) = (√(3)/2) * 0 = 0
The second term in the expression, -cos(π/60)sin(π/2) , can be simplified as follows ,
sin(π/2) = 1, cos(π/60) = sqrt(3)/2 - 1/2
so -cos(π/60)sin(π/2) = -(sqrt(3)/2 - 1/2) * 1 = -sqrt(3)/2 + 1/2
Now we can substitute the simplified values back into the original expression ,
0 - (-sqrt(3)/2 + 1/2)
and combining like terms, [tex]\frac{1-\sqrt{3} }{2}[/tex],
Hence , The expression as a single real number is [tex]\frac{1-\sqrt{3} }{2}[/tex] .
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all of marcy's marbles are blue, red, green, or yellow. one third of her marbles are blue, one fourth of them are red, and six of them are green. what is the smallest number of yellow marbles that macy could have?
According to the concept of probability, the smallest number of yellow marbles that Marcy could have is 24
The term probability is known as the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.
Here we have given that all of Marcy's marbles are blue, red, green, or yellow. one third of her marbles are blue, one fourth of them are red, and six of them are green.
Here we know that the 6 green marbles and yellow marbles form is calculated as,
=> 1 - 1/3 - 1/4 = 5/12 of the total marbles.
Here let us consider that the total number of marbles is x.
And here we know the number of yellow marbles is is written as,
=> 5/12x - 6 and a positive integer.
Now, we have to divide 12 by x, then we get,
Then we get the value of x as 24.
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(PLEASE HELP ASAP)
Solve the given system using your choice of either graphically or algebraically. Show and explain all work.
-4x + 9y = 14
12x - 10y = - 8
Answer:
w
Step-by-step explanation:
6. A family's income amount is $25,000. They budget out of their income:
Food: 20%
Shelter: 25%
Clothing: 15%
How much money is allotted for each of these items?
Food
Shelter
Clothing
Answer:
To find out how much money is allotted for each of these items, we can multiply the percentage of the income allocated to each item by the total income.
Food: 20% of $25,000 = $25,000 x 0.20 = $5000
Shelter: 25% of $25,000 = $25,000 x 0.25 = $6250
Clothing: 15% of $25,000 = $25,000 x 0.15 = $3750
So the family has $5000 for food, $6250 for shelter and $3750 for clothing.
