Answer: b) y = negative one fifthx + seven fifths
Step-by-step explanation:
Equation of a line in Slope intercept form : [tex]y=mx+c[/tex] (1)
, where m is slope and c is constant.
Given : The equation of line LM is [tex]5x - y = -4.[/tex]
Convert it into slope- intercept form, we get
[tex]y=5x+4[/tex]
Comparing it to (1) , we get
[tex]m= 5[/tex]
Let [tex]m_1[/tex] be the slope pf the line perpendicular to LM.
Since the product of slopes of two perpendicular lines is -1.
Therefore , [tex]m_1\cdot m=-1\Rightarrow m_1=\dfrac{-1}{m}=\dfrac{-1}{5}[/tex]
Equation of line passing through (-3,2) and having slope [tex]m_1=\dfrac{-1}{5}[/tex] will be :-
[tex](y-2)=\dfrac{-1}{5}(x-(-3))\\\\ y-2=(-\dfrac{1}{5})(x+3)=\dfrac{-1}{5}x-\dfrac{3}{5}\\\\\ y=\dfrac{-1}{5}x-\dfrac{3}{5}+2=\dfrac{-1}{5}x-\dfrac{10-3}{5}\\\\\Rightarrow\ y=\dfrac{-1}{5}x+\dfrac{7}{5}[/tex]
Hence, the equation of a line perpendicular to line LM in slope-intercept form that contains point (−3, 2) is [tex]y=\dfrac{-1}{5}x+\dfrac{7}{5}[/tex].
Hence, the correct answer is b) y = negative one fifthx + seven fifths.
We want to find a line perpendicular to 5x - y = -4 that passes through the point (-3, 2). We will find that the line is: y = (-1/5)*x + 7/5
Perpendicular lines.A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Such that a line is perpendicular to the above one if and only the slope of this other line is the inverse of the opposite of the above slope, so the perpendicular line will be something like:
y = (-1/a)*x + c
Now we start with the line that we know, we need to find its slope:
5x - y = -4
We need to isolate y
y = 5x + 4
Then the slope of this line is a = 5, so the perpendicular line will be:
y = (-1/5)*x + c
Now we need to find the value of c such that the line passes through (-3, 2), this means that x = -3 and y = 2, then we have:
2 = (-1/5)*-3 + c
2 = (3/5) + c
2 - 3/5 = c
10/5 - 3/5 = c
7/5 = c
Then the equation is:
y = (-1/5)*x + 7/5
So the correct option is b.
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A rectangular garden is 2 feet longer than it is wide. If the width is doubled, 50 extra feet of fencing will be needed to keep out the rabbits. What are the dimensions of the original garden?
Answer:
The dimensions of the original garden is [tex]27\times25\ ft[/tex].
Step-by-step explanation:
Let the width of the rectangular garden be 'x'.
Now given:
A rectangular garden is 2 feet longer than it is wide.
so we can say that;
Length of the rectangle = [tex](x+2) \ ft[/tex]
Now to fence the garden we need to find the perimeter of the garden.
Now Perimeter of the garden is equal to twice the sum of the length times width.
framing in equation form we get;
Perimeter of the rectangle = [tex]2(x+x+2)=2(2x+2)=4x+4[/tex]
Now given:
If the width is doubled, 50 extra feet of fencing will be needed
It means that Perimeter of the doubled width rectangle is equal to perimeter of original garden plus 50.
framing in equation form we get;
[tex]2(2x+x+2)=4x+4+50\\\\2(3x+2)=4x+50[/tex]
Now Applying distributive property we get;
[tex]2\times3x+2\times2=4x+54\\\\6x+4=4x+54[/tex]
Combining the like terms we get;
[tex]6x-4x=54-4\\\\2x=50[/tex]
Dividing both side by 2 we get;
[tex]\frac{2x}{2}=\frac{50}{2}\\\\x=25 \ ft[/tex]
Length of the rectangular garden = [tex]x+2=25+2=27\ ft[/tex]
Hence the dimensions of the original garden is [tex]27\times25\ ft[/tex].
Two dice are thrown. Let E be the event that the sum of the dice is
even, let F be the event that at least one of the dice lands on 6 and
let G be the event that the numbers on the two dice are equal. Find
P(E), P(F), P(G), P(EF), P(F G), P(EG).
Answer:
P(E) = 1/2P(F) = 11/32P(G) = 1/6P(EF) = 5/52P(FG) = 1/32P(EG) = 1/6Step-by-step explanation:
For the sum to be even, both dice can be odd, or both even. The probability of a dice being odd is 1/2 and the same is for it to be even. Since the result of the dices are independent, we have that
P(E) = (1/2)² + (1/2)² = 1/2
Out of the 36 possible outcomes for the dice (assuming that you can distinguish between first and second dice), there are 11 cases in which one dice is a 6 (if you fix 1 dice as 6, there are 6 possibilities for the other, but you are counting double 6 twice, so you substract one and you get 6+6-1 = 11). Since all configurations for the dices have equal probability, we get that
P(F) = 11/32
The probability for the second dice to be equal to the first one is 1/6 (it has to match the same number the first dice got). Hence
P(G) = 1/6
for EF, you need one six and the other dice even. For each dice fixed as 6 we have 3 possibilities for the other. Removing the repeated double six this gives us 5 possibilities out of 32 total ones, thus
P(EF) = 5/32
If one dice is 6 and both dices are equal, then we have double six, as a result there is only one combination possible out of 32, therefore
P(FG) = 1/32
If both dices are equal, in particular the sum will be even, this means that G= EG, and as a consecuence
P(EG) = P(G) = 1/6
The probabilities are P(E) = 1/2, P(F) = 11/36, P(G) = 1/6, P(EF) = 1/6, P(FG) = 1/12, and P(EG) = 1/4.
Explanation:To find the probabilities, we need to use the concept of counting outcomes.
P(E):There are 36 equally likely outcomes when two dice are thrown. Out of these, 18 outcomes result in an even sum. So, P(E) = 18/36 = 1/2.
P(F):There are 11 outcomes where at least one die lands on 6 out of the 36 total outcomes. So, P(F) = 11/36.
P(G):There are 6 outcomes where both dice show the same number, out of the 36 possible outcomes. So, P(G) = 6/36 = 1/6.
P(EF):There are 6 outcomes where at least one die shows 6 and the sum is even. So, P(EF) = 6/36 = 1/6.
P(FG):There are 3 outcomes where both dice show 6 and at least one of them shows 6. So, P(FG) = 3/36 = 1/12.
P(EG):Out of the 36 outcomes, 9 outcomes result in both dice being the same and the sum being even. So, P(EG) = 9/36 = 1/4.
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Ken drives a taxi cab and receives $100 a day plus $0.50 for every mile he drives. He is saving up for a new television that costs about $2500. If Ken drives an average of 400 miles per day, how many days will he have to drive to save enough money to buy the television? In a inequality statment
Answer:
i got 8.33 so I would say about 9. Im not sure about inequality statements but I know that's about how many days since he makes 300 per day, and you divide that by 2500
Step-by-step explanation:
Knowing that 9 is closer to 10 than to 1 and understanding that 2 plus 1 equals 3 demonstrates a basic understanding of
a. reversibility.
b. intelligence.
c. whole number skills.
d. seriation.
Answer: C: Whole number skills
Step-by-step explanation: The question involves simple understanding of whole numbers from counting 1 to 10, and also addition of these whole numbers, which makes its a basic understanding of whole number skills
If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact.
f(x) = -16x^5 - 7x^4 - 6
Degree: -16; leading coefficient: 5
Degree: 5; leading coefficient: -16
Not a polynomial function.
Degree: 9; leading coefficient: -16
Degree: 5; leading coefficient: –16
Explanation:
Given polynomial function is [tex]f(x)=-16x^5-7x^4-6[/tex]
The degree of the polynomial is a highest value of the exponent in one variable in the given polynomial.
Here, highest value of the exponent = 5
So, degree of the polynomial = 5
Leading coefficient is the value before the highest degree of the variable in the polynomial.
Here, leading coefficient = –16
Hence, the answer is Degree: 5; leading coefficient: –16.
Working his way through school, Joe works two part-time jobs for a total of 18 hours a week. Job A pays $5.70 per hour, and Job B pays $6.80 per hour. How many hours did he work at each job the week that he made $111.40?
Answer:
A = 14.2/1.1 hours
B = 5.091 hours
Step-by-step explanation:
Formulate 2 simultaneous equations
5.7A + 6.8B = 111.40..........(1)
A +B =18...............................(2)
Multiply each item in (2) by 5.7 to get
5.7A + 5.7B = 97.2............(3)
subtract (1) - (3) on each side
5.7A -5.7A + 6.8B - 5.7B = 111.40 -97.2
1.1B = 14.2
B = 14.2 /1.1
to get A use equation (2)
A = 18 - B
A = 18 - 14.2/1.1 = 5.091
Answer:in the week , he worked 10 hours at Job A and 8 hours at job B
Step-by-step explanation:
Let x represent the number hours that Joe worked at job A in a week.
Let y represent the number of hours that Joe worked at job B in a week.
Working his way through school, Joe works two part-time jobs for a total of 18 hours a week. This means that
x + y = 18
Job A pays $5.70 per hour, and Job B pays $6.80 per hour. He made a total of $111.4 working at each job during the week. It means that
5.7x + 6.8y = 111.4 - - - - - - - - - -1
Substituting x = 18 - y into equation 1, it becomes
5.7(18 - y) + 6.8y = 111.4
102.6 - 5.7y + 6.8y = 111.4
- 5.7y + 6.8y = 111.4 - 102.6
1.1y = 8.8
y = 8
x = 18 - y = 18 - 8
x = 10
(c+5)^3 solve using binomial theorem
Answer:
c^3+15c^2+75c+125
Step-by-step explanation:
If the businesswoman randomly selects one of the possible itineraries and Denver and San Francisco are two of the cities that she plans to visit, what is the probability that she will visit Denver before San Francisco?
Answer: The probability that she will visit Denver before San Francisco is [tex]\dfrac{1}{2}[/tex] .
Step-by-step explanation:
Given : The businesswoman randomly selects one of the possible itineraries and Denver and San Francisco are two of the cities that she plans to visit.
The possible itineraries = (First Denver and then San Francisco , First San Francisco and then Denver)
i.e. Total outcomes =2
If she visit Denver before San Francisco , then the favorable outcome = 1
Now , the probability that she will visit Denver before San Francisco = [tex]=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{1}{2}[/tex]
Hence, the probability that she will visit Denver before San Francisco is [tex]\dfrac{1}{2}[/tex] .
Which system is represented by the graph?
Answer:
The answer to your question is the first option
Step-by-step explanation:
Process
1.- Identify the y-intercepts of the lines
blue line y-intercept = -1
brown line y-intercept = -2
With this information, we can discard the last option because those lines don't have those y-intercepts.
2.- We observe in the graphs that the lines are increasing so the slopes are positive. From this information, we can discard the second option.
3.- Calculate the slopes of the lines of options 1 and 3
Blue line Points (0, -1) (1, 2)
m = [tex]\frac{2 + 1}{1 - 0} = \frac{3}{1} = 3[/tex]
Brown line Points (0, -2) (1, 1)
m = [tex]\frac{1 + 2}{1 - 0} = 3[/tex]
As the slopes are 3, we conclude that the answer is the first option.
Mr. Abed tries a new mathematics game to help his third grade students learn their multiplication tables and records the results. This would best be described as which of the following?
Group of answer choices
A. true experiment
B. one-shot case study
C. one-group
D. pretest–posttest design
E. correlational research
Answer: D Pretest–posttest design
Step-by-step explanation:
According to the question, Mr Abed is just designing the game and the purpose is to help the grade 3 students learn their mutiplication table, upon completion of the game design, the students are to use (play) it - all this makes up the pretest stage
The result of the game will then be evaluated by Mr Abed to Know if the game is effective or not, if the students have actually learnt their multiplication table by playing the game, if there is need for modification - all this makes the posttest stage.
Henry mixes 1 cup grape concentrate with 4 cups water to make his favorite drink. How much water will he need to mix if he uses 5 cups grape concentrate
Answer:he will need to mix 20 cups of water if he uses 5 cups grape concentrate.
Step-by-step explanation:
Henry mixes 1 cup grape concentrate with 4 cups water to make his favorite drink. It means that the number of cups of grape concentrate that henry requires to mix 1 cup of water would be
1/4
Therefore, the number of cups of water that he needs to mix if he uses 5 cups grape concentrate would be
5/(1/4) = 20 cups of water
The value of a baseball card in dollars has been found to be 0.15y + 0.35, where y is the number of years since it was released. By how much is the baseball card's value increasing per year?
Answer:
The value of the baseball increase $0.15
Step-by-step explanation:
we have
The expression above represent a linear equation in slope intercept form
where
The slope or unit rate is equal to
The y-intercept is equal to ----> original value of a baseball card
therefore
The value of the baseball increase $0.15 per year
Final answer:
The value of the baseball card is increasing by $0.15 per year. For the bat and ball problem, the ball costs $0.05 and the bat costs $1.05.
Explanation:
To find out how much the baseball card's value is increasing per year, we look at the formula given for the value of the baseball card: 0.15y + 0.35. In this formula, y represents the number of years since the card was released. The coefficient of y is 0.15, which indicates the yearly increase in the value of the card.
Therefore, the value of the baseball card is increasing by $0.15 per year.
Now let's look at the classic bat and ball problem. The total cost of the bat and the ball is $1.10, and the bat costs $1.00 more than the ball. If we denote the cost of the ball as x, then the cost of the bat is x + $1.00. Setting up the equation x + (x + $1.00) = $1.10, we combine like terms to get 2x + $1.00 = $1.10. Solving for x, we subtract $1.00 from both sides to get 2x = $0.10. Dividing both sides by 2 yields x = $0.05. So, the ball costs $0.05, and the bat costs $1.05.
7. In a state lottery, a player must choose 8 of the numbers from 1 to 40. The lottery commission then performs an experiment that selects 8 of these 40 numbers. Assuming that the choice of the lottery commission is equally likely to be any of the 40 8 combinations, what is the probability that a player has (a) all 8 of the numbers selected by the lottery commission
Answer:a) P(8 of the players numbers are drawn)=1.3×10^-8
b) P(7 of the players number are drrawn)=3.33×10^-c) P(at least 6 of the players number were drawn)=1.84×10^-4
Step-by-step explanation:
Players has 8 combinations of numbers from 1-40. The outcome S contains all the combinations of 8 out of 40
a) P(8 of the players numbers are drawn)= 1/40/8= 1.3×10^-8
There are one in hundred million chances that the draw numbers are precisely the chosen ones.
b) Number of ways of drawing 78 selected numbers from 1-40=8×(40-7)
8×32
P(7 of the players number are drawn)=8×32/40 =3.33×10^-6.
There are approximately 300,000 chances that 7 of the players numbers are chosen
c) P(at least 6 players numbers are drawn)= 32/2×(8/6) ways to draw.
P(at least 6 players numbers are drawn)=P(all 8 chosen are drawn)+P(7 players numbers drawn)+P(6 chosen are drawn) = 1+ 8 x32/40/8 +[8\6 ×32/2]
P(at least 6 players numbers are drawn) = 1.84×10^-4.
There are approximately 5400chances that at least6 of the numbers drawn are chosen by the player.
The probability that a player has all 8 of the numbers selected by the lottery commission
Explanation:To find the probability that a player has all 8 numbers selected by the lottery commission, we need to determine the favorable outcome and the total possible outcomes. The favorable outcome is 1 because the player needs to match all 8 numbers. The total possible outcomes can be calculated using the combination formula. There are 40 numbers to choose from and the player must choose 8, so the total possible combinations is C(40,8). Therefore, the probability of a player matching all 8 numbers is:
P(all 8 numbers matched) = 1 / C(40,8)
Help! Will give brainliest.
Answer:
Step-by-step explanation:
[tex]g(x)=log_{2}( x+4) -1\\let g(x)=y\\y=log_{2}(x+4)-1 \\x+4=2^{y+1} \\when y=0\\x+4=2^1=2\\x=2-4=-2\\when x=0\\4=2^{y+1}=2^y*2^1=2*2^y\\2^y=\frac{4}{2}=2=2^1\\so~y=1\\x -intercept=-2\\y-intercept=1[/tex]4. it is a transformation of 4 units left and 1 unit down.
Simplify the radical expression and shows steps
Answer: [tex]4\sqrt{2}+10[/tex]
=============================================
Let [tex]x = \sqrt{8}[/tex]
We can replace every square root of 8 with x, since we have that equation above. We end up with 3-x+7+3x. This simplifies to 2x+10 after combining like terms.
Now we can reintoduce the square root back in
[tex]2x+10 = 2\sqrt{8}+10[/tex]
The use of x is optional as you can combine like terms directly. However, it might help to make the temporary replacement.
-------------
Now simplify the square root
[tex]\sqrt{8} = \sqrt{4*2}[/tex]
[tex]\sqrt{8} = \sqrt{4}*\sqrt{2}[/tex]
[tex]\sqrt{8} = 2\sqrt{2}[/tex]
--------
Therefore,
[tex]2\sqrt{8}+10[/tex]
turns into
[tex]2*2\sqrt{2}+10[/tex]
[tex]4\sqrt{2}+10[/tex]
Answer:
10 + 4sqrt(2)
Step-by-step explanation:
3 - sqrt(8) + 7 + 3sqrt(8)
3 - 2sqrt(2) + 7 + 6sqrt(2)
10 + 4sqrt(2)
sqrt: square root
If the graph f(x)= 9x^2+36x+41/3x+5 has an oblique asymptote at y=3x+k what is the value of k
Answer:
The value of k is 7.Explanation:
To find the oblique asymptote of a rational function you divide the numerator by the denominator and take the quotient (not the remainder).
Such quotient (without the remainder) is the equation of the line that is the oblique asymptote of the rational function.
The rational function is:
[tex]\frac{9x^2+36x+41}{3x+5}[/tex]
You can see the long division in the picture attached. The quotient is 3x + 7.
Hence, by comparison with y = 3x + k, k = 7.
Answer:
7
Step-by-step explanation:
Correct on EDGE
Consider a= ⟨−2,5,1⟩, b= ⟨−5,2,−5⟩ and c= ⟨−1,−5,4⟩. Find the angles between the following vectors: The angle between a and b is:
Answer:
[tex]cos^{-1}(\frac{\sqrt 5}{6})[/tex]
Step-by-step explanation:
We are given that
[tex]a=<-2,5,1>,b=<-5,2,-5>[/tex] and c=<-1,-5,4>
We have to find the angles between a and b .
[tex]\mid a\mid=\sqrt{(-2)^2+(5)^2+(1)^2}=\sqrt{30}[/tex]
[tex]\mid b\mid=\sqrt{(-5)^2+(2)^2+(5)^2}=3\sqrt{6}[/tex]
[tex]a\cdot b=<-2,5,1>\cdot <-5,2,-5>=10+10-5=15[/tex]
Angle between two vectors a and b is given by
[tex]cos\theta=\frac{a\cdot b}{\mid a\mid \mid b\mid }[/tex]
Using the formula
[tex]cos\theta=\frac{15}{\sqrt{30}\times 3\sqrt{6}}[/tex]
[tex]cos\theta=\frac{5}{6\sqrt{5}}[/tex]
[tex]cos\theta=\frac{5\times \sqrt 5}{6\times (\sqrt 5)^2}=\frac{\sqrt 5}{6}[/tex]
[tex]\theta=cos^{-1}(\frac{\sqrt 5}{6})[/tex]
Hence, the angle between a and b=[tex]cos^{-1}(\frac{\sqrt 5}{6})[/tex]
Fortuna worked 39.5 hours this week at $8.18 an hour.
What was her gross pay?
$327.20
$323.90
$323.11
$319.02
Answer:
c
Step-by-step explanation:
because 39.5 hours makes 8.18
Fortuna's gross pay is $323.11
What is unit rate?A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
Given that, Fortuna worked 39.5 hours this week at $8.18 an hour.
Since, she is being paid $8.18 for 1 hour, that mean her unit rate is $8.18
To find total rate we will multiply her unit rate with total hours she worked.
Therefore,
The total pay = 39.5 × 8.18 = $323.11
Hence, Fortuna's gross pay is $323.11
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Christilla and her friends purchased tickets for the factory that costs $13 each and bottled water that costs $1.50 each. Write an algebraic expression for the total cost of their night out
Answer:
An algebraic expression for the total cost of their night out is [tex]T=13x+1.5y[/tex].
Step-by-step explanation:
Given:
Cost of per person ticket to factory = [tex]\$13[/tex]
Cost of each bottled water = [tex]\$1.50[/tex]
we need to write an algebraic expression for the total cost of their night out
Solution:
Let the number of persons visiting the factory be 'x'.
Also Let the number of bottled water be 'y'.
Also Let the total cost be 'T".
So we can say that;
total cost is equal to Cost of per person ticket to factory multiplied by the number of persons visiting the factory plus Cost of each bottled water multiplied number of bottled water.
framing in equation form we get;
[tex]T=13x+1.5y[/tex]
Hence an algebraic expression for the total cost of their night out is [tex]T=13x+1.5y[/tex].
If the square root of p2 is an integer greater than 1, which of the following must be true? I. p2 has an odd number of positive factors II. p2 can be expressed as the product of an even number of positive prime factors III. p has an even number of positive factors?
Answer:
Option | and Option || is True
Step-by-step explanation:
Given:
If the square root of [tex]p^{2}[/tex] is an integer greater than 1,
Lets p = 2, 3, 4, 5, 6, 7..........
Solution:
Now we check all option for [tex]p^{2}[/tex]
Option |.
[tex]p^{2}[/tex] has an odd number of positive factors.
Let [tex]p=2[/tex]
The positive factor of [tex]2^{2}=4=1,2,4[/tex]
Number of factor is 3
Let [tex]p=3[/tex]
The positive factor of [tex]3^{2}=9=1,3,9[/tex]
Number of factor is 3
So, [tex]p^{2}[/tex] has an odd number of positive factors.
Therefore, 1st option is true.
Option ||.
[tex]p^{2}[/tex] can be expressed as the product of an even number of positive prime factors
Let [tex]p=2[/tex]
The positive factor of [tex]2^{2}=4=1,2,4[/tex]
[tex]4=2\times 2[/tex]
Let [tex]p=3[/tex]
The positive factor of [tex]3^{2}=9=1,3,9[/tex]
[tex]9=3\times 3[/tex]
So, it is expressed as the product of an even number of positive prime factors,
Therefore, 2nd option is true.
Option |||.
p has an even number of positive factors
Let [tex]p=2[/tex]
Positive factor of [tex]2=1,2[/tex]
Number of factor is 2.
Let [tex]p=4[/tex]
Positive factor of [tex]4=1,2,4[/tex]
Number of factor is 3 that is odd
So, p has also odd number of positive factor.
Therefore, it is false.
Therefore, Option | and Option || is True.
Option ||| is false.
Determine if the statement is true or false, and justify your answer. Suppose A is a matrix with n rows and m columns. If n < m, then the columns of A span Rn.
Answer:
The question is incomplete as there are given options ;
Q:
Determine if the statement is true or false , and justify your answer . Suppose A is a matrix with n rows and m columns . If n < m, then the columns of A span R True, since there are more columns than rows. O False, since there are not enough columns to span R". True, since every column of A must be a nonzero column, False, since every column of A may be a zero column, True, since every column of A must be a non zero column, False, since every column of A may be a zero column
Step-by-step explanation:
Considering a matrix A with n-rows and m-columns,
given that n is less than m i.e the rows is less than the columns
then the columns of A span Rn? TRUE OR FALSE?
the matrix is of nxm as n is less than m, hence from linear transformation, T will span : Rm towards Rn
the concept of ranking of a matrix is applied here as ranking entails the number of linearly independent rows or columns vectors in a matrix, in this case
the order is n x m where n is less than m, as such the rank of the matrix is n
So, Rank of MATRIX A is n
To prove if the rows vectors are linearly independent or not since n is the rank of the matrix
In this case, m columns vector will be considered with respect to n which is the rank and which is also less than m from the conditions, as such there exist a linearly independent relationship between them which R may be spanned since we know that from ranking, reduction to echelon form comes into play by trying to reduce every element of the column A to zero.
Trying to reduce to echelon form implies all the element of column A may or may not zero.from the foregoing, the last option is the correct answer ; False, since every column of A may be a zero column
The statement 'If n < m, then the columns of A span R^n' is false because it implies a guarantee without considering the linear independence of the columns, which is necessary for them to span the space.
Explanation:Determining whether the statement 'If n < m, then the columns of A span Rn' is true or false involves understanding linear algebra concepts. For a matrix A with more columns than rows (m > n), it is possible that the columns of A could span Rn, since there are enough vectors to possibly cover the entire n-dimensional space. However, without more information about the vectors, such as whether they are linearly independent, we cannot definitively conclude that they span the space.
The statement assumes that because there are more columns than rows, the columns automatically span the space. This could be true if the columns are linearly independent and cover the space. However, it's possible for a matrix to have redundant vectors that do not contribute to spanning the space, even if m > n. Therefore, the statement as given is false because it suggests a guarantee without consideration of linear independence.
What is the sum of the infinite geometric series?
120 + 20+ 10/3 + 5/9+...
Answer:
for an infinite geometric series the formula for the sum of the infinite geometric series when the common ratio is less than one is given by
[tex]\frac{a_{1} }{1 - r}[/tex] = [tex]\frac{120}{1 - \frac{1}{6} } = \frac{120}{\frac{5}{6} } =[/tex] [tex]\frac{120 \times 6}{5}[/tex] = 144.
Step-by-step explanation:
i) from the given series we can see that the first term is [tex]a_{1 }[/tex] = 120.
ii) let the common ratio be r.
iii) the second term is 20 = 120 × r
therefore r = 20 ÷ 120 = [tex]\dfrac{1}{6}[/tex]
iv) the third term is [tex]\frac{10}{3}[/tex] = 20 × r
therefore r = [tex]\dfrac{10}{3}[/tex] ÷ 20 = [tex]\dfrac{1}{6}[/tex]
v) for an infinite geometric series the formula for the sum of the infinite geometric series when the common ratio is less than one is given by
[tex]\frac{a_{1} }{1 - r}[/tex] = [tex]\frac{120}{1 - \frac{1}{6} } = \frac{120}{\frac{5}{6} } =[/tex] [tex]\frac{120 \times 6}{5}[/tex] = 144.
Answer:
C. 144
Step-by-step explanation:
Find a counterexample to show that the following conjecture is false.
The quotient of any two integers is always less than 1.
Answer:
4/2 = 2 > 1
Step-by-step explanation:
The quotient of any two integers of the same sign and the dividend having the larger magnitude will be greater than 1:
-88/-11 = 8 > 1
4/2 = 2 > 1
Hence the conjecture is false.
Trilobites to concert tickets from her friend she pays $90 for the two tickets she looks at the tickets and see that each ticket has a space value of 52. 50. How much of a markdown did her friend give Shelia. Explain how you know.
Answer:
Her friend gave Sheila a markdown of $15.
Step-by-step explanation:
Given;
Amount paid for 2 tickets = $90
Actual amount for each ticket = $52.50
we need to find the markdown value did her friend gave to Shelia.
Solution:
each ticket = $52.50
2 tickets = Cost of 2 tickets.
By using unitary method we get;
Cost of 2 tickets = [tex]52.50\times 2 =\$105.00[/tex]
Now To find the markdown we will subtract the Amount paid for 2 tickets from the actual Amount of 2 tickets.
framing in equation form we get;
Markdown [tex]105-90 =\$15[/tex]
Hence her friend gave sheila a markdown of $15.
Complete the table for the following function (Image down below)
y=3^x
Graph the function and describe what the graph looks like.
a.
Increases in Quadrant III
b.
Increases from left to right
c.
Decreases from left to right
d.
Decreases in Quadrant II
Answer:
b
Step-by-step explanation:
The graph of the given function will increase from left to right.
What are the needs for graphs in mathematics?Graphs are a popular tool for visually illuminating data relationships. A graph serves the objective of presenting data that are either too many or complex to be fully expressed in the text while taking up less room.
Given, a function y = 3ˣ. graph of this function is attached below. as we can see in the attached graph that it will increase from left to right.
For x = -3
y = 3⁻³ = 1/27
For x = -2
y = 3⁻² = 1/9
for x = 2
y = 3² = 9
For x = 3
y = 3³ = 27
Therefore, The supplied function's graph will rise from left to right.
Learn more about graphs here:
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A mini-golf course is determining the par score for each of its holes. The dot plot shows the number of strokes required to place a ball in the ninth hole for a sample of 31 players. A number line going from 1 to 9. 2 dots are above 1. 3 dots are above 2. 4 dots are above 3. 5 dots are above 4. 5 dots are above 5. 3 dots are above 6. 2 dots are above 7. 0 dots are above 8. 1 dot is above 9. Which measure of center is best to use to determine the expected number of strokes required for the ninth hole? a. The mean is the best choice because the data is nearly symmetrical. b. The median is the best choice because data is clustered. c. The mean is the best choice because the data is skewed to the right. d. The median is the best choice because the data is skewed to the left.
Answer:
A
Step-by-step explanation:
The mean is a good measure of central tendency because it takes into account all of the data compared to other. One of the instance where the mean is not good measure is when there are outliers ( extreme values) in the data in this case the median is better. In the scenario in the question the data set is nearly symmetrical therefore the mean is best central tendency measure to use
Answer:
Option A - The mean is the best choice because the data is nearly symmetrical.
Step-by-step explanation:
Given : A mini-golf course is determining the par score for each of its holes. The dot plot shows the number of strokes required to place a ball in the ninth hole for a sample of 25 players.
To find : Which measure of center is best to use to determine the expected number of strokes required for the ninth hole?
Solution :
To determine the expected number of strokes required for the ninth hole the best measure of center is the mean of the data as the data is nearly symmetrical about the center point 4 and 5.
We can also find the mean of the data,
Mean is defined as the sum of observation divided by number of observation.
i.e, Sum of observation is
Referring the dot plot of ninth hole strokes
Total number of observation n= 25
Therefore, Option A is correct.
The mean is the best choice because the data is nearly symmetrical.
The length of a rectangle is 4 meters less than twice the width. If the area of the rectangle is 240 square meters, find the dimensions.How many meters is the length? How many meters is the width?
Step-by-step explanation:
Let L be the length and W be the width.
The length of a rectangle is 4 meters less than twice the width.
That is
L = 2W - 4
The area of the rectangle is 240 square meters
That is
L x W = 240
(2W - 4) x W = 240
2W² - 4W = 240
W² - 2W - 120 = 0
(W -12 ) (W+10) = 0
W = 12 m or W = -10 m
So width of rectangle is 12 meter
Length = 2 x 12 - 4 = 20 m
Length is 12 meter and width is 20 meter.
The median is:
a. the second quartile
b. the 50th percentile
c. the observation with half of the data on either side of it
d. all of the above
The median is all of the above: the second quartile, the 50th percentile, and the observation with half of the data on either side. It represents the central point of a data set where 50% of the values are below and 50% are above it.
Explanation:The question asks to identify what the median represents in statistical terms. The median is:
a. the second quartile b. the 50th percentile c. the observation with half of the data on either side of it d. all of the aboveThe correct answer is d. all of the above. The median or second quartile (Q₂) is the value that divides the ordered dataset in half. It is also known as the 50th percentile since it implies that 50% of the data lies below this point and 50% lies above it. For example, in a dataset 1, 1, 2, 2, 4, 6, 6.8, 7.2, 8, 8.3, 9, 10, 10, 11.5, the median is 7, meaning that half of the values are smaller than 7 and half of the values are larger than 7.
Four houses in a row are each to be painted with one of the colors red, blue, green, and yellow. In how many different ways can the houses be painted so that no two adjacent houses are of the same color? There are possible ways to paint the houses.
Answer:
Possible ways to paint the house is 108
Step-by-step explanation:
Total number of houses to be painted=4
Total number of colours to b used(red,blue,green and yellow)=4
Number of ways to paint the first house=4
Number of ways to paint the second house=3
Number of ways to paint the third house=3
Number of ways to paint the fourth house=3
Total number of ways to paint the 4 houses=4×3^3=108 ways.
Final answer:
There are 24 different ways to paint the houses so that no two adjacent houses are of the same color.
Explanation:
To solve this problem, we can use the concept of permutations. Since there are 4 houses and 4 colors to choose from, we can start by selecting a color for the first house. We have 4 options for the first house. Next, we need to choose a color for the second house, but we must ensure that it is different from the color chosen for the first house. We have 3 options for the second house. For the third house, we have 2 options, and for the fourth house, we have only 1 option.
Therefore, the total number of ways to paint the houses without any two adjacent houses being the same color is calculated as:
4 x 3 x 2 x 1 = 24
Which of the following can be derived from other assumptions about numbers. A. Subtraction. B. Multiplication. C. Division D. All of the above. E. B and C above.
Answer: D All of the above
Step-by-step explanation:
Addition,subtraction,multiplication and division are basic mathematical operations used in the determination and assumption of numbers.
Without them,there will be no theorems .