An explicit description of Nul A is given by the set of vectors {[0, 0, 1, 0], [0, 0, 0, 1]}.
What is the explicit description of a null space matrix?
To find an explicit description of the null space of matrix A, we can find a spanning set of vectors that span the null space.
The null space of matrix A, denoted Nul A, is the set of all vectors x that satisfy the equation Ax = 0. In other words, the null space consists of all vectors that are mapped to the zero vector by the matrix A.
To find a spanning set for Nul A, we can use the following steps:
Row reduces the matrix A to a reduced row-echelon form using elementary row operations.
Identify the free variables in the row-reduced matrix.
For each free variable, create a vector with a 1 in the position corresponding to the free variable and 0's in all other positions.
The set of vectors created in step 3 form a spanning set for Nul A.
For example, consider the matrix A = [1, 2, 3, 0; 0, 0, 1, 0]. To find a spanning set for Nul A, we can row reduce the matrix to reduced row-echelon form:
[1, 2, 3, 0] -> [1, 2, 3, 0]
[0, 0, 1, 0] -> [0, 0, 1, 0]
The matrix is already in reduced row-echelon form, so there are no more elementary row operations to perform. The free variables in this matrix are the third and fourth columns, which correspond to the variables x3 and x4, respectively. Therefore, we can create the following vectors:
x3 = [0, 0, 1, 0]
x4 = [0, 0, 0, 1]
These vectors form a spanning set for Nul A, as they are linearly independent and span the null space.
Hence, an explicit description of Nul A is given by the set of vectors {[0, 0, 1, 0], [0, 0, 0, 1]}.
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At the beginning of the year, Kaylee had $60 in savings and saved an additional $12 each week thereafter. Jack started the year with $95 and saved $5 every week. Let K represent the amount of money Kaylee has saved t weeks after the beginning of the year and let J represent the amount of money Jack has saved t weeks after the beginning of the year. Write an equation for each situation, in terms of t, and determine the number of weeks after the beginning of the year until Kaylee and Jack have the same amount of money saved.
After 5 week the savings of both Kaylee and Jack will be same.
The equation for Kaylee's savings, in terms of t, is K = 60 + 12t.
The equation for Jack's savings, in terms of t, is J = 95 + 5t.
To determine the number of weeks after the beginning of the year until Kaylee and Jack have the same amount of money saved, we set K equal to J and solve for t.
K = J
60 + 12t = 95 + 5t
7t = 35
t = 5
Kaylee and Jack have the same amount of money saved after 5 weeks.
What are savings?
The funds one has saved, particularly through a bank or government programme is known as savings.
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A company shipped 3 boxes which each weighed 3.894 pounds and one box which weighed 6.7 pounds. What was the total weight of the 4 boxes?
The total weight of the 4 boxes was - 18.382 pounds.
A company shipped 3 boxes which each weighed 3.894 pounds.
As per the rule, we shall have to multiply the weight of the boxes of similar weight into 3 followed by the addition of the weight of the other box.
Then, we can get the final answer.
one box weighed = 3.894 pounds
Three boxes weighed = 3 * 3.894 pounds
= 11.682 pounds
Another box weighed = 6.7 pounds
The total weight of the 4 boxes was = ( 11.682 + 6.7 ) pounds
= 18.382 pounds
Hence, The total weight of the 4 boxes was - 18.382 pounds.
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What are the vertex and range of y = |2x + 6| + 2?
(0, 2); 2 < y < ∞
(0, 2); −∞ ≤ y < ∞
(−3, 2); 2 < y < ∞
(−3, 2); −∞ ≤ y < ∞
The vertex and the range of y = |2x + 6| + 2 are (c) (-3, 2); 2 ≤ y < ∞
How to determine the vertex and the range?The equation is given as
y = |2x + 6| + 2
The above equation is an absolute value function
An absolute value function represented as
y = a|x - h| + k
Where
Vertex = (h, k)
So, we have
y = |2x + 6| + 2
This gives
y = 2|x + 3| + 2
This means that the vertex is
Vertex = (-3, 2)
Remove the x value
y = 2
Because the leading coefficient is positive, then the vertex is a minimum
i.e.
y ≥ 2
So, the range is 2 ≤ y < ∞
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All fourth grade children on Long Island are given an examination on mathematical achievement. A random sample of 60 fourth graders are selected. Their examination results are summarized in the following stem-and-leaf plot. Find the sample upper quartile.4 6 6 6 88 01 7 7 7 7 7 8 33 445 6667777 8888889 00011111 2233333 4455 66777 8 8 8 8 899 9 001 9 223 45 9
The sample upper quartile of the data set is 91 and the lower quartile is 67 for the students of the given examination.
The median and quartiles of a data set:
The data set's median, or 50th percentile, separates the bottom half from the higher half.
The first quartile is the median of the data set's first half.
The third quartile is the median of the data set's second half.
Because there are an even number of items 60, the median is the mean of the31st element elements, with the first half consisting of 30 elements ranging from 1 to 29, and the second half consisting of 12 elements ranging from 31 to 60.
The first quartile is the mean of the elements, 67 and 68, respectively, therefore Q1 = 60/4 =15th element = 67
The third quartile is defined as the mean of the sixth and seventh elements of the second half, hence Q3 = 3×60 / 4 = 91.
Hence the quartiles are at 67 and 91 respectively.
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Rachel has \frac{7}{15}
15
7
of her project done. If she can finish \frac{7}{45}
45
7
of her project each day, how many more days will it take her to complete it?
Answer:
4 days
Step-by-step explanation:
If Rachel has 7/15 of her project done, then she has 8/15 of her project left to complete.
Convert 8/15 and let it have a denominator of 45, and you get 24/45. If she can finish the rest of her project 7/45 each day, and she has 24/45 left to go, then divide 24 by 7, and you get 3 R3.
Afterwards round that to 4, because Rachel can't leave 3/45 of her project unfinished, she just doesn't have as much work the last day.
So then Rachel can finish her project in 4 days.
Hope this helps!
Answer:
4 days
Step-by-step explanation:
7/15 done ...then 8/15 to go
8/15 = 24 / 45 if she can do 7/45 per day, she will need 4 more days
(24/7) = 3.4 =~ 4 days
Twelve percent of the manufactured parts were defective and had to be pulled from the assembly line. Forty-eight defective parts
were pulled from the line. How many total parts were manufactured during this run?
O d) 126
O a) 400
O c) 383
Ob) 48
Answer:
a) 400---------------------------
Let the number of total parts be x.
12% of x were defective and it is 48 in number.
Find x:
0.12x = 48x = 48/0.12x = 400Correct choice is A.
At a water park, 42 out of 56 tickets sold were child tickets. What percentage of the tickets
were child tickets?
Write your answer using a percent sign (96).
Answer:
75%
Step-by-step explanation:
42/56 * 100% = 0.75 * 100
= 75%
a 50.0 cmcm, uniform, 50.0 nn shelf is supported horizontally by two vertical wires attached to the sloping ceiling (figure 1). a very small 20.0 nn tool is placed on the shelf midway between the points where the wires are attached to it.
the tension in each wire will be equal. The tension in each wire, T ,the tension in each wire is 85.36 N with its weight.
Assuming that the tool has negligible mass so that its weight does not contribute to the tension in the wires, the tension in each wire will be equal. The tension in each wire, T, can be calculated using the equation:
T = (W/2) + (L/2)*sin(θ),
where W is the weight of the shelf and L is the length of the shelf. The angle θ is the angle between the ceiling and the shelf.
In this case, W = 50 N, L = 50 cm and θ = 45°. Therefore, T = (50/2) + (50/2)*sin(45) = 50 + 35.36 = 85.36 N.
So, the tension in each wire is 85.36 N.
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A speech class has eight freshmen and five sophomores. Three people are selected at random to give speeches in sequence. Find the probability that
(a) the first is a sophomore, the second is a freshman, and the third is a sophomore.
(b) all three are freshmen.
(c) the first is a sophomore and the other two are freshmen.
1716 is the probability that a sophomore, the second is a freshman, and the third is a sophomore.
What is probability explained with an example?
A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty. The likelihood that an event will occur increases with its probability.
The flip of a fair (impartial) coin serves as a straightforward illustration. The probability of an event occurring, or P(E), is defined as the ratio of the number of favorable outcomes to the total number of outcomes in the probability formula.
The total number of ways in which 3 students can be arranged for speech out of total 13 students is,
P(13,3) = 13 * 12 * 11
= 1716
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Marcus worked 45 hours this week. His hourly rate of pay is $9.00. What was the pay
for Overtime hours only?
Marcus' overtime pay for the week is $67.50.
How is the overtime pay determined?The overtime pay is paid at the hourly rate and a half.
This translates to the regular rate of pay x 1.5 x overtime hours worked.
The total hours worked this week = 45 hours
Normal working hours per week = 40 hours (5 days x 8 hours)
Overtime hours = 5 hours (45 - 40)
Hourly rate = $9.00
Overtime rate = $13.50 ($9 x 1.5)
Overtime pay = $67.50 ($13.50 x 5)
Thus, for this week, Marcus has earned overtime pay of $67.50 above his normal weekly pay of $360.
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1. Assume that there is a party consisting of people between the ages of 18 and 24 inclusive. How many people would have to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year? Note: assume the range of birth years include 2 leap years. (10 points)
at least 24 people must be in the party to guarantee that at least 3 people have the same date of birth, date of birth, date of birth.
To warrant that at least three people have the same date, month, and year of birth, we need to find the minimum number of people such that there is a probability that at least three people have the same date, month, and year. there is. Birth year she is 1 or more. Non-leap years have 365 days, and leap years have her 366 days. The birth year range includes two leap years, so there are 3652 + 3662 = 2,922 possible births. This means that the probability that a particular person's birthday is unique is (2922-1)÷2922 = 1÷2922.
Now we can use the birthday puzzle to calculate the probability that at least three people have the same birthday. The probability that no one has the same birthday is (1 - 1÷2922)^n, where n is the number of people in your party. At least he has 1-(1-1÷2922)^n probability that 3 of them have the same birthday. You can set this probability to 1 or more and solve for n.
1 - (1 - 1÷2922)^n >= 1
(1 - 1÷2922)^n <= 0
n >= log(0) ÷ log(1 - 1÷2922)
The logarithm of 0 is not defined, so you can use a small value on the right hand side instead. B. 10^-6. This will tell you:
n >= log(10^-6) ÷ log(1 - 1/2922)
n >= log(10^-6) ÷ log(2921/2922)
n >= log(10^-6) ÷ log(2921) - log(10^-6) / log(2922)
n >= log(10^-6) × log(2922) ÷ log(2921) - log(10^-6)
n >= log(10^-6) × log(2922) ÷ log(2921) - log(10^-6)
n >= 23.
Hence, at least 24 people must be in the party to guarantee that at least 3 people have the same date of birth, date of birth, date of birth.
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One week gas was $1.75 per gallon. The next week gas was $2.10 per gallon. By what percentage did the price increase or decrease? % (increase or decrease)
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse.
If b = 16 units and c = 20 units, what is the perimeter? If necessary, round your answer to the nearest tenth.
Answer: 48
Step-by-step explanation: Use this to help you!
Write an equation for a parabola with x-intercepts (-1,0) and (3,0) ehich pass the point (1,-16)
The equation for a parabola with x-intercept is y = 4/3x² + 8/3x - 20.
What is equation?
In arithmetic, an equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.
Main body:
The equation has the form y = Ax² + Bx + C
Since (3,0), (-1,0), (1,-16) are points on the graph, we get the following system of equations:
9A + 3B + C = 0
A - B + C = 0
A + B + C = -16
Subtracting the first 2 equations and subtracting the 3rd equation from the first, we obtain:
8A - 4B = 0
8A + 2B = 16
Since 8A - 4B = 0, 8A = 4B. So, A = 1/2B.
Therefore, 8A + 2B = 16
6B = 16 So , B = 8/3 and A = 8/6
Since A + B + C = -16 and A = 8/6 , B = 8/3, we have 4 + C = -16. So, C = -20.
An equation of the parabola is y = 4/3x² + 8/3x - 20
Hence , the equation for a parabola with x-intercept is y = 4/3x² + 8/3x - 20.
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$5400 is invested, part of it at 11% and part of it at 9%. For a certain year, the total
yield is $546.00. How much was invested at each rate?
Answer:$2400 invested at $9% $3000 invested at $11%
Step-by-step explanation:
The equation for line g can be written as y–1= – 1/10 (x+8). Parallel to line g is line h, which passes through the point ( – 5,5). What is the equation of line h?
Answer:
point-slope form: [tex]y+5=-\frac{1}{10}(x-5)[/tex]
slope-intercept form: [tex]y = -\frac{1}{10}x - \frac{9}{2}[/tex]
Step-by-step explanation:
Point-Slope Form:We can express any one-variable linear equation as: [tex]y-y_1=m(x-x_1)[/tex], where "m" is the slope, and [tex](x_1, y_1)[/tex] is some point on the graph.
We're given the equation in point-slope form: [tex]y-1=-\frac{1}{10}(x+8)[/tex], and if we want to make a line parallel to this line, we just need the slopes to be the same. So let's just look at the value in front of the parenthesis. This is given to be: [tex]-\frac{1}{10}[/tex]
We can use this same form, to develop an equation parallel to the given line, and passing through: [tex](-5, 5)[/tex]
Plugging the values into the point-slope formula, we get:
[tex]y-(-5)=-\frac{1}{10}(x-5)\\\\y+5=-\frac{1}{10}(x-5)[/tex]
From here we can also convert this into slope-intercept form, where "y" is isolated.
[tex]\\y+5=-\frac{1}{10}(x-5)\\\\y+5=-\frac{1}{10}x + \frac{5}{10}\\\\y + \frac{10}{2} = -\frac{1}{10}x + \frac{1}{2}\\\\y + \frac{10}{2} - \frac{10}{2} = -\frac{1}{10}x + \frac{1}{2} - \frac{10}{2}\\\\y = -\frac{1}{10}x - \frac{9}{2}[/tex]
Find a positive and a negative coterminal angle for each given angle.
A positive and a negative co - terminal angle for each given angle is 1) -π/2 and -9π / 2 and 2) 7π / 2 and -π / 2 .
Given :
a positive and a negative co - terminal angle for each given angle
1 )
= -5π / 2
To find positive and negative co - terminal angle we need to add and subtract by 2π .
= -5π / 2 + 2π
= -5π + 4π / 2
= -π/2
= -5π / 2 - 2π
= -5π - 2 * 2π / 2
= -5π - 4π / 2
= -9π / 2
or =
2 )
= 3π / 2
= 3π / 2 + 2π
= 3π + 2 * 2π / 2
= 3π + 4π / 2
= 7π / 2
= 3π / 2 - 2π
= 3π - 4π / 2
= -π / 2
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Find the circumference of a circle with a radius of 5 inches
Answer: The answer should be 31.42 in
Justin was out at a restaurant for dinner when the bill came. His dinner came to $35. After adding in a tip, before tax, he paid $44.10. Find the percent tip.
Justin paid a tip that was 26% of his bill.
Step-by-step explanation:1. Form the expression.[tex]\frac{44.10-35}{35}[/tex]
2. Calculate.[tex]\frac{44.10-35}{35}=0.26[/tex]
3. Conclude.Justin paid a tip that was 26% of his bill.
Find the volume of the composite solid
Mona's school tennis team is running a car wash this weekend. They will charge $13 per car, and they are hoping to
aise $200. How much money will the team have left to raise once they have washed 10 cars?
Write and solve an equation to find the answer.
Answer:
$70
Step-by-step explanation:
x = 200 - 10 · 13
x = 200 - 130
x = 70
Find the value of x from the figure
Answer:
x = 20
Step-by-step explanation:
the figure is a parallelogram, therefore the sum of angle A and angle B is 180°, we solve with an equation
180 = 5x + 5 + 4x - 5
180 = 9x
x = 180 : 9
x = 20
------------------------
check
180 = 5x + 5 + 4x - 5
180 = 5 × 20 + 5 + 4 × 20 - 5 (remember PEMDAS)
180 = 180
the answer is good
Answer:
The angle x is equal to 20 degrees
In ΔA B G, if m ∠C is nine less than m ∠A and m ∠B is fifteen less than four times m ∠A, find the measure of ∠B
A) 125° hula hooping
B) 121° doing the Nae Nae
C) 57° finger painting
D) 34° playing clarinets
The measure of angle B is 121°
The correct option is B) 121° doing the Nae Nae
"Information available from the question"
In the question:
In ΔA B C, if m ∠C is nine less than m ∠A and m ∠B is fifteen less than four times m ∠A,
To find the measure of ∠B.
Now, According to the question:
We know that:
The sum of the measures of the angles of a triangle are 180
m<A + m<B + m<C = 180°
m<C = m<A - 9
m<B = 4*m<A - 15
m<A + 4*m<A - 15 + m<A - 9 = 180°
6m<A - 24 = 180°
6m<A = 204
m<A = 34°
Now, To find the measure of ∠B
m<B = 4*m<A - 15
m<B = 4* 34 - 15
m<B = 121°
The correct option is B) 121° doing the Nae Nae
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For the 2009 regular season, the MLB batting leaders in number of hits were Ichiro Suzuki and Derek Jeter. These two players had a total of 437 hits. Suzuki had 13 more hits than Jeter. How many hits did each player have?
34 In the appeal of the People v. Collins case (see Exercise 4.1.28), the counsel for the defense argued as follows: Suppose, for example, there are 5,000,000 couples in the Los Angeles area and the probability that a randomly chosen couple fits the witnesses’ description is 1/12,000,000. Then the probability that there are two such couples given that there is at least one is not at all small. Find this probability. (The California Supreme Court overturned the initial guilty verdict.)
The probability that there are two such couples given that there is at least one is 1 - (4999999/12000000) = 4/12 = 1/3.
What is probability?Probability is the measure of the likelihood that a given event will occur. It is expressed as a number between 0 and 1 (or 0% to 100%). A probability of 1 indicates that the event is certain to occur, while a probability of 0 indicates that it is impossible for the event to occur. Probability is used in a wide range of disciplines including mathematics, science, engineering, finance, and philosophy. Probability can be used to make predictions and help inform decision-making. By understanding probability, we can better understand the chances of certain outcomes and make more informed decisions.
This is because the probability that the first couple matches the description is 1/12000000, and the probability that the second couple matches the description, given that the first couple does, is 1/(12000000-1). Since there are 4999999 other couples, the probability that the second couple matches the description is (4999999/12000000). Thus, the probability that there are two such couples is 1 minus the probability that the second couple does not match the description, which is 1 - (4999999/12000000) = 4/12 = 1/3.
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what is an expression equivalent to 5 1/4d - 5?
Answer:
Step-by-step explanation:
23
√3ab
rewrite the equation in radical form
Answer:
√3√ab
Step-by-step explanation:
Please look in the attachment! Hope this helps! :D
Graph g(x) = −2x − 8 and identify its x-intercept.
(−8, 0)
(−4, 0)
(0, −4)
(0, −8)
Based on the graph of the function g(x) = −2x − 8, the x-intercept is equal to -4.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.
What is the x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" is equal to zero (0).
By critically observing the graph of g(x) = −2x − 8, the x-intercept is -4. This ultimately implies that, the function g(x) = −2x − 8 would cross the x-coordinate (x-axis) at point (-4, 0.
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a sales manager analyzed the sales, in dollars, y, of snow shovels compared to the outside temperature, in degrees fahrenheit, x. the manager calculated the correlation coefficient of r
The correlation coefficient of r measures how closely the two variables, x and y, are related. If the coefficient is close to 1, it means that the two variables are strongly related, whereas if it is close to 0, it means that there is no relation between them.
The correlation coefficient of r is a measure of how closely related two variables are to each other. It is calculated by taking the covariance of the two variables and dividing it by the product of their standard deviations. The coefficient ranges from -1 to +1, with -1 indicating a perfectly negative linear relationship, 0 indicating no relationship, and +1 indicating a perfectly positive linear relationship. In the case of the sales manager analyzing the sales of snow shovels compared to the outside temperature, the correlation coefficient of r can be used to measure the strength of the relationship between the two variables. If the coefficient is close to 1, it indicates that the two variables are strongly related, while a coefficient close to 0 indicates that there is no relation between them.
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Suppose f(x)is a continuous differentiable function and you are given that f"(x) is always positive. Which of the following statements must be true? f(x) is always increasing. f'(x) is always increasing. f"(x) is always increasing. None of the above must be true.
According to the facts provided in the question and we know that the derivative of the function f(x) is f'(x) which refers to the slope at the point. The answer is f(x) is always increasing.
What do you mean by derivative?The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative. The rate at which a function changes in relation to a variable Calculus and differential equations issues must be solved using derivatives.
What do you mean by slope of the line?A line's steepness can be determined by looking at its slope. The ratio of the change in the y-value to the change in the x-value can also be used to determine slope.
f(x) is the function.
f'(x) is the derivative of the function.
f'(x) is always positive which explains that the line has positive slope that is moving upwards in graph.
So, f(x) is always increasing.
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