The positive divisors of $54$ are $1, 2, 3, 6, 9, 18, 27,$ and $54$.
To find all the positive divisors of a number, we need to list all the factors of that number. In the case of $54$, we can start by listing all the factors of $2$ and $27$, the prime factors of $54$. The factors of $2$ are $1$ and $2$, while the factors of $27$ are $1$, $3$, $9$, and $27$.
To find all the factors of $54$, we can combine these factors in all possible ways. This gives us $1\times 1=1$, $1\times 2=2$, $1\times 3=3$, $1\times 6=6$, $1\times 9=9$, $1\times 18=18$, $1\times 27=27$, $1\times 54=54$, $2\times 1=2$, $2\times 2=4$, $2\times 3=6$, $2\times 6=12$, $2\times 9=18$, $2\times 18=36$, $2\times 27=54$.
Out of these, only the ones where we use each factor at most once are positive divisors of $54$. This gives us $1, 2, 3, 6, 9, 18, 27,$ and $54$ as the positive divisors of $54$.
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Question 2 For the following matrix Then [340]
A= [-127]
[-2-44]
(Please use a comma between two numbers.)
(a) The minors M13, M23, M33= 8,-4,10
(b)The cofactors C13, C23,C33= 8,4,10 (c) The determinant det(A) = 68
For the given matrix A, the minors M13, M23, M33 are 8, -4, and 10 respectively. The cofactors C13, C23, C33 are 8, 4, and 10 respectively. The determinant det(A) is 68.
To find the minors of a matrix, we need to find the determinants of the submatrices obtained by removing the row and column corresponding to the element of interest. In this case, the minors M13, M23, and M33 correspond to the determinants of the 2x2 submatrices obtained by removing the first row and the third column, second row and third column, and third row and third column, respectively.
To find the cofactors, we multiply each minor by a positive or negative sign based on its position in the matrix. The signs alternate starting with a positive sign for the top left element. In this case, the cofactors C13, C23, and C33 correspond to the minors M13, M23, and M33 respectively.
Finally, the determinant of a 3x3 matrix can be found by using the formula det(A) = a11C11 + a12C12 + a13C13, where a11, a12, and a13 are the elements of the first row of the matrix and C11, C12, and C13 are their corresponding cofactors. In this case, the determinant det(A) is 68.
Therefore, the minors M13, M23, M33 are 8, -4, and 10 respectively. The cofactors C13, C23, C33 are 8, 4, and 10 respectively. And the determinant det(A) is 68.
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Calculate the volume of the triangular prism shown below. Give your answer in cm³. 5 cm 7 cm 9 cm 4 cm
The volume of the given triangular prism is 315 cm³.
The volume of a triangular prism, we need to multiply the base area of the triangular base by the height of the prism.
The triangular base has a base length of 5 cm and a height of 7 cm, and the height of the prism is 9 cm.
Calculate the area of the triangular base.
The area of a triangle can be calculated using the formula:
Area = (base length × height) / 2
Plugging in the values, we have:
Area = (5 cm × 7 cm) / 2
Area = 35 cm²
Calculate the volume of the prism.
The volume of a prism can be calculated by multiplying the base area by the height of the prism.
Volume = Base area × Height
Volume = 35 cm² × 9 cm
Volume = 315 cm³
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Please help me!! I have no clue how to start this
Answer:
hypotenuse= AB
Adjacent=AC
Opposite= CB
AB=?
Sol# use Pythagoras theorem {hint}
CA=?
A recipe uses 4 cups of milk to make 24 servings. If the same amount of milk is used for each serving, how many servings can be made from two gallons?
Answer:
768
Step-by-step explanation:
2 gallons is 32 cups. Times 32 by the servings which is 24. 32 times 24 equals 768
of the 35 flavors of ice cream at an ice cream parlor, 25 flavors contain some sort of nuts, 12 are fat-free, and 8 both fat-free and contain nuts. how many of the flavors at the ice cream parlor neither are fat-free nor contain nuts?
The number of ice creams according to the probability, Neither contain nuts nor are fat free is 6.
According to the statement
We have to find that the ice creams that neither are fat-free nor contain nuts.
So, For this purpose, we know that the
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur.
From the given information:
There are 35 flavors of ice cream at an ice cream parlor, 25 flavors contained ice creams.
Contain nuts = 25
Are fat free = 12
Are both = 8
Then
Contain nuts or are fat free = 25+12-8 = 29
Total = 35
Neither contain nuts nor are fat free = 35-29 = 6.
So, The number of ice creams according to the probability, Neither contain nuts nor are fat free is 6.
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Solve each equation. log 5x+1=-1
Answer:
\(5x = - 1 - 1 = 5x \div 5 = - 2 \div 5 = 2 \div 5\)
Find the values of the six trigonometric functions for angle θ, when AC = 26 and BC = 24.
Answer:
See below
Step-by-step explanation:
The first step is to find the length of AB. By the Pythagorean Theorem:
\(AB=\sqrt{26^2-24^2}=\sqrt{676-576}=\sqrt{100}=10\)
Now, you can proceed:
\(\sin \theta= \dfrac{24}{26}=\dfrac{12}{13} \\\\\\\cos \theta= \dfrac{10}{26}=\dfrac{5}{13} \\\\\\\tan \theta= \dfrac{24}{10}=\dfrac{12}{5} \\\\\\\csc \theta= \dfrac{13}{12} \\\\\\\sec \theta=\dfrac{13}{5} \\\\\\\cot \theta=\dfrac{5}{12}\)
If the first and the last term of an arithmetic progression, with common difference
\(1 \times 1\frac{1}{2} \)
, are
\(? \times 2\frac{1}{2} \)
and 19 respectively, how many term has the sequence?
The number of terms in the given arithmetic sequence is n = 10. Using the given first, last term, and the common difference of the arithmetic sequence, the required value is calculated.
What is the nth term of an arithmetic sequence?The general form of the nth term of an arithmetic sequence is
an = a1 + (n - 1)d
Where,
a1 - first term
n - number of terms in the sequence
d - the common difference
Calculation:The given sequence is an arithmetic sequence.
First term a1 = \(1\frac{1}{2}\) = 3/2
Last term an = \(2\frac{1}{2}\) = 5/2
Common difference d = 1/9
From the general formula,
an = a1 + (n - 1)d
On substituting,
5/2 = 3/2 + (n - 1)1/9
⇒ (n - 1)1/9 = 5/2 - 3/2
⇒ (n - 1)1/9 = 1
⇒ n - 1 = 9
⇒ n = 9 + 1
∴ n = 10
Thus, there are 10 terms in the given arithmetic sequence.
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Disclaimer: The given question in the portal is incorrect. Here is the correct question.
Question: If the first and the last term of an arithmetic progression with a common difference are \(1\frac{1}{2}\), \(2\frac{1}{2}\) and 1/9 respectively, how many terms has the sequence?
Please help.
Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.
Answer:
question 12 is answer B
question 13 is -8x^3
Step-by-step explanation:
exponent rule \(\frac{a^m}{a^n} = a^(^m^-^n^)\)
Find the Total Surface Area and the Volume of these shapes:
TSA =
וחרון 18
וחות 36
וחוון 45
Answer:
6156
Step-by-step explanation:
formula is TSA=2LW+2LH+2HW
Find sin(B) in the triangle.
Answer:
4/5
Step-by-step explanation:
The sin of B is equal to opposite/hypotenuse
So, the equation would be 4/5 because 4 is equal to the opposite side length of B and 5 is equal to the hypotenuse of the triangle.
So, the answer would be 4/5
(-5
If m
+ 7 = 39, what is the value of m?
Answer:
m=32
Step-by-step explanation:
solve for m by subtracting 7 by both sides. Then you get m = 32
(can i get brainliest please)
Which of the following statement/s is/are correct? I. A statistic can never be larger than a parameter II. A statistic can never be equal to zero III. A statistic can never be smaller than a parameter IV. A statistic can be calculated whereas a parameter can never be established V. A statistic can never be equal to a parameter A. I, II, III and IV B. V Only c. None of these D. IV and V E. IV Only
A statistic can never be larger than a parameter is not a correct statement. The correct statement among the following is as follows: IV Only. The statement "A statistic can be calculated whereas a parameter can never be established" is the correct statement.
Statistics and parameters are two fundamental concepts in statistical analysis. Both of these concepts are widely used in various researches and surveys.
A statistic is a numerical value that represents a particular characteristic of the sample and is used to estimate an unknown parameter. A parameter is a numerical value that represents a particular characteristic of a population.Statistics can be larger, smaller, or equal to parameters. A statistic is a value that is calculated from a sample, whereas a parameter is a value that represents a population characteristic and is estimated from the sample.A parameter can be established, but it is only possible if the entire population is considered for analysis. In contrast, a statistic is calculated from a sample of the population and represents only the characteristics of the sample.
:A statistic can never be larger than a parameter is not a correct statement. The correct statement is IV Only. The statement "A statistic can be calculated whereas a parameter can never be established" is the correct statement.
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Find mZABD.
D
20°
B
С
o
mZABD
Answer:
The answer is 20.
Step-by-step explanation:
#>×==×
what is the equation of a line that passes through point (-2,1) and is perp to y= -5x 2
The equation of the line that passes through (-2,1) and is perpendicular to y = -5x² is y = -10x + 21
The equation of a line is a mathematical representation of the relationship between its x and y values.
In this case, we are given a line that passes through the point (-2,1) and is perpendicular to y = -5x².
To find the equation of this line, we first need to find the slope of the line that is perpendicular to y = -5x².
The slope of a line can be found by finding the derivative of the original equation.
In this case, the derivative of
=> y = -5x² is -10x,
which gives us the slope of -10x.
Since we know that the line passing through (-2,1) is perpendicular to
y = -5x²,
we can use the point-slope form of the equation of a line.
The point-slope form of the equation is given by
=> y - y1 = m(x - x1),
where m is the slope and (x1, y1) is a point on the line.
Plugging in the values, we have
=> y - 1 = -10(x + 2).
We can simplify this equation further by distributing the -10 and combining like terms.
This gives us
=> y - 1 = -10x - 20,
which we can then rearrange to get
=> y = -10x + 21.
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MAX POINTS + BRAINLY CROWN!
whats n if \(n\sqrt{256}\) = 8 1/3 X 8 1/3
Answer:
n=4 49/144 or n=625/144
Step-by-step explanation:
to rent a popcorn machine, it costs 35$ plus $6.95 for each hour. write and evaluate an expression to find the total cost of renting the popcorn machine for 5 hours. then make a table showing the cost for 5, 6, 7, and 8 hours
Answer:
y=6,95x+35
Step-by-step explanation:
y=6,95x+35
y=6,95*5+35=69,75 for 5 hours
for 6 hours y=76,7
for 7 hours y=83.65
for 8 hours y=90,6
lemme know if its right <3.
schedules the processor in the order in which they are requested. question 25 options: first-come, first-served scheduling round robin scheduling last in first scheduling shortest job first scheduling
Scheduling the processor in the order in which they are requested is "first-come, first-served scheduling."
The scheduling algorithm that schedules the processor in the order in which they are requested is known as First-Come, First-Served (FCFS) scheduling. In FCFS scheduling, the processes are executed based on the order in which they arrive in the ready queue. The first process that arrives is the first one to be executed, and subsequent processes are executed in the order of their arrival.
FCFS scheduling is simple and easy to understand, as it follows a straightforward approach of serving processes based on their arrival time. However, it has some drawbacks. One major drawback is that it doesn't consider the burst time or execution time of processes. If a long process arrives first, it can block the execution of subsequent shorter processes, leading to increased waiting time for those processes.
Another disadvantage of FCFS scheduling is that it may result in poor average turnaround time, especially if there are large variations in the execution times of different processes. If a long process arrives first, it can cause other shorter processes to wait for an extended period, increasing their turnaround time.
Overall, FCFS scheduling is a simple and fair scheduling algorithm that serves processes in the order of their arrival. However, it may not be the most efficient in terms of turnaround time and resource utilization, especially when there is a mix of short and long processes. Other scheduling algorithms like Round Robin, Last In First Scheduling, or Shortest Job First can provide better performance depending on the specific requirements and characteristics of the processes.
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Find the indefinite integral. (use c for the constant of integration.)
e2x 25 e4x dx.
To find the indefinite integral of the given expression, we can use the power rule for integration. The power rule states that for any function of the form xⁿ, the integral is (1/(n+1)) * x^(n+1) + c, where c is the constant of integration.
The given expression is e²ˣ + 25e⁴ˣ dx. Using the power rule, we can integrate each term separately.
For the first term, e²ˣ, the power is 2. Applying the power rule, we get ∫e²ˣ. dx = (1/(2+1))e²ˣ = (1/3) e²ˣ.
For the second term, 25e⁴ˣ, the power is 4. Applying the power rule, we get ∫25e⁴ˣ. dx = (1/(4+1)) × 25e⁴ˣ = (1/5) × 25e⁴ˣ = 5e⁴ˣ.
Therefore, the indefinite integral of ∫(e²ˣ + 25e⁴ˣ) dx is (1/3)e²ˣ + 5e⁴ˣ + c, where c is the constant of integration.
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✨I NEED A SMART PERSON✨ (math)
Answer:
A and E.
Step-by-step explanation:
Using the math from 7th grade, 6 rooted is 36/9=4+10 is 14. Everything else you must multiply everything in parenthesis, by the outside number, then you add them. E is right because -15+35=20-6=14. Yw.
An exact location in space is called a _______ALineBPointCCircleDLine segment
Option B is Correct. An specific place in space is called a point. A dot indicates a point.
A point in space is a location. No length, width, or thickness exist in a point. In geometry, a dot stands in for a point. We typically use a (capital) letter to name a point. The simplest basic geometric object is a point. It is named with a capital letter and symbolised by a dot.
A point has no size and solely represents position (that is, zero length, zero width, and zero height). In a line, a line segment has two distinct endpoints. The line segment's length, which is the separation of two fixed points, is constant.
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Correct Question:
An exact location in space is called a _______
A. Line
B. Point
C. Circle
D. Line segment
Total Surplus The sum of consumer surplus and producer surplus is called the total surplus; it is one measure economists use as an indicator of the economic health of a society. Total surplus is maximized when the market for a good is in equilibrium. A camera company estimates that the demand function for its new digital camera is and the supply function is estimated to be here is measured in thousands. Compute the maximum total surplus.
The total surplus at the equilibrium point is: $200,000
This is the maximum total surplus that can be achieved in the market for the digital camera.
To compute the maximum total surplus, we need to find the equilibrium quantity and price in the market for the digital camera, and then calculate the consumer and producer surplus at that point.
First, we need to set the demand and supply functions equal to each other to find the equilibrium quantity:
50 - 2P = 2P - 10
4P = 60
P = 15
Substituting this equilibrium price into either the demand or supply function, we can find the equilibrium quantity:
Q = 50 - 2(15) = 20
So the equilibrium price is $15, and the equilibrium quantity is 20,000 digital cameras.
Next, we can calculate the consumer and producer surplus at the equilibrium point. Consumer surplus is the difference between the maximum price a consumer is willing to pay for a good and the market price, summed over all consumers in the market. Producer surplus is the difference between the market price and the minimum price a producer is willing to accept for a good, summed over all producers in the market.
The demand function gives us the maximum price consumers are willing to pay for each quantity of digital cameras:
P = 25 - 0.5Q
So at the equilibrium quantity of 20,000 digital cameras, the maximum price consumers are willing to pay is:
P = 25 - 0.5(20) = 15
This is exactly the same as the market price, so there is no consumer surplus at the equilibrium point.
The supply function gives us the minimum price producers are willing to accept for each quantity of digital cameras:
P = 0.5Q - 5
So at the equilibrium quantity of 20,000 digital cameras, the minimum price producers are willing to accept is:
P = 0.5(20) - 5 = 5
The market price is $15, so the producer surplus is:
(15 - 5) * 20 = $200,000
Therefore, the total surplus at the equilibrium point is:
$200,000
This is the maximum total surplus that can be achieved in the market for the digital camera.
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If there is a negative relationship between the temperature and coat sales, it is safe to say that ________.
A negative relationship between temperature and coat sales suggests that as temperature increases, coat sales tend to decrease, but other factors and analysis would be needed for a more conclusive understanding.
If there is a negative relationship between temperature and coat sales, it means that as the temperature increases, coat sales tend to decrease, and vice versa. However, it is important to note that correlation does not imply causation, and other factors could be influencing coat sales.One possible explanation for this negative relationship could be that people are less likely to purchase coats when the temperature is higher because they do not perceive the need for warm outerwear. In warmer climates, people may rely more on lighter clothing options or may not require coats at all.
It is safe to say that the negative relationship between temperature and coat sales suggests a pattern or trend in the data, but it does not provide a complete understanding of all the factors at play. Other factors, such as seasonal changes, fashion trends, marketing strategies, and economic conditions, may also impact coat sales.
To draw more definitive conclusions, further analysis, including controlling for confounding variables and considering a larger dataset, would be necessary.
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The Johnson family's budget was $3,200 in September. If they spend 8% of their monthly budget on entertainment. How much money did they spend on entertainment in September?
Answer:
256
Step-by-step explanation:
3200 x 0.08 = 256
If a figure is a square, its diagonals divide it into isosceles triangles.
p: A figure is a square.
q: A figure's diagonals divide into isosceles triangles.
Which represents the converse of this statement? Is the converse true?
The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:
"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."
The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.
Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.
In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.
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Given g(x)=30-6x, find g(-4)=____?
Answer:
g(-4)=54
Step-by-step explanation:
g(-4)=30-6(-4)
g(-4)=30+24
g(-4)=54
In January, a toy store sold 846 puzzles. Each puzzle cost $5, including tax. What was the total cost of the puzzle sold, including tax? *
$4, 320
$4, 230
$4, 302
$4, 203
Answer:
$4,230
Step-by-step explanation:
There are 846 puzzles sold and including tax, it is $5 per puzzle. Multiply the amount of puzzles by cost and you get the total cost of all puzzles sold including tax.
What is the constant of variation if y varies inversely as x and y = 3 when x = 6? PLZ HELP ME I DONT UNDERSTAND
Answer:
k = 18
Step-by-step explanation:
Given that y varies inversely as x then the equation relating them is
y = \(\frac{k}{x}\) ← k is the constant of variation
To find k use the condition y = 3 when x = 6, that is
3 = \(\frac{k}{6}\) ( multiply both sides by 6 )
18 = k
The constant of variation is k = 18
Given that g(x)=x2−2x−9 find
(g∘g)(−2)=
To find the value of (g∘g)(−2) for the function g(x) = x^2 - 2x - 9, we need to evaluate the composition of g with itself at x = -2. This involves substituting the output of g(-2) into the function g.
First, let's find the value of g(-2) by substituting -2 into the function g(x):
g(-2) = (-2)^2 - 2(-2) - 9
= 4 + 4 - 9
= -1
Now, we can substitute this value back into the function g(x) to evaluate (g∘g)(−2):
(g∘g)(−2) = g(g(-2))
= g(-1)
Substituting -1 into the function g(x):
g(-1) = (-1)^2 - 2(-1) - 9
= 1 + 2 - 9
= -6
Therefore, the value of (g∘g)(−2) for the given function g(x) = x^2 - 2x - 9 is -6.
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Find the value for k for which y= 2x+k is a tangent to the curve y=2x^2-3 and determine the point of intersection
Answers:
k = -3.5
Intersection point is (0.5, -2.5)
================================================
Explanation:
Apply the derivative to y=2x^2-3 and you should get dy/dx = 4x
The derivative helps determine the slope of the tangent at any point on the curve.
The slope of the tangent line y = 2x+k is 2.
We want the slope of the tangent to be 2, so we'll replace the dy/dx with 2 and solve for x.
dy/dx = 4x
2 = 4x
x = 2/4
x = 0.5
Plug this into the curve's original equation.
y = 2x^2 - 3
y = 2(0.5)^2 - 3
y = -2.5
Therefore, the tangent line y = 2x+k and the curve y = 2x^2-3 intersect at the point (0.5, -2.5). This is the point of tangency.
We'll use the coordinates of this point to determine k.
y = 2x+k
-2.5 = 2(0.5) + k
-2.5 = 1 + k
k = -2.5-1
k = -3.5
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