The answer depends on the rank of A.
If the rank of A is less than 4, then the dimension of its null space is greater than or equal to 4-rank(A).
If the rank of A is 4, then the dimension of its null space is 0.
The dimension of the null space of a matrix A is given by the number of linearly independent vectors that satisfy the equation A x = 0,
where x is a column vector.
Since A is a 6x4 matrix, the equation A x = 0 represents a homogeneous system of 6 linear equations in 4 unknowns.
The rank-nullity theorem states that the rank of a matrix plus the dimension of its null space equals the number of columns of the matrix. Therefore, we have:
rank(A) + dim(null(A)) = 4
The rank of A is at most 4, since there are only 4 columns.
If the rank of A is 4, then the dimension of its null space is 0, because there are no linearly independent vectors that satisfy A x = 0. On the other hand, if the rank of A is less than 4, then the dimension of its null space is at least 4-rank(A).
Therefore, the smallest possible dimension of null(A) is:
dim(null(A)) = 4 - rank(A).
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The smallest possible dimension of the null space (nul A) for a 6x4 matrix A is 0.
To determine the smallest possible dimension of the null space (nul A) of a 6x4 matrix A, we need to consider the rank-nullity theorem, which states:
dim(A) = rank(A) + dim(nul A)
Here, dim(A) represents the dimension of the matrix A, rank(A) represents the rank of the matrix A, and dim(nul A) represents the dimension of the null space of A.
For a 6x4 matrix A, the dim(A) is 4 since there are 4 columns. The rank(A) represents the number of linearly independent columns, and it can be at most 4 since there are 4 columns.
To find the smallest possible dimension of the null space, we need to maximize the rank(A). In this case, the maximum possible rank(A) is 4. Now, using the rank-nullity theorem:
4 = 4 + dim(nul A)
Solving for dim(nul A), we get:
dim(nul A) = 4 - 4
dim(nul A) = 0
Therefore, the smallest possible dimension of the null space (nul A) for a 6x4 matrix A is 0.
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If the radius is 3 and LM=2, what is KL?
The calculated value of the length of segment KL is 4 units
Calculating the length of segment KLFrom the question, we have the following parameters that can be used in our computation:
Radius, r = 3
LM = 2
JK = 3
The length KL is calculated as
KL² = JL² - JK²
Where
JL = r + LM = 3 + 2 = 5
Substitute the known values in the above equation, so, we have the following representation
KL² = 5² - 3²
KL² = 16
Take the square roots
KL = 4
Hence, the length is 4 units
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Which of the following is not an equation?
Answer:
Option (3)
Step-by-step explanation:
Option (3) is not an equation. It is an expression. An equation is a mathematical statement where two expressions are equal to each other connected by an equal sign. In option (1), 3+1 is equal to 4+0 so it is an equation. In option (2), x2-2x is equal to 8, so it is also an equation. In option (4), 1+3 is equal to 6, so it is an equation, though it is not a true statement. However, in option (3), there is no equal sign, so it is not an equation. It is an expression that simplifies to 8x+2.
What is the value of the expression below?
(31½ - 93) ÷ (-2.5)
A - 2.5
B-2.3
C 2.3
D 2.5
Answer: the value of the expression is 24.6, which corresponds to option C.
Step-by-step explanation: In order to assess the expression, we must adhere to the sequence of operations (PEMDAS) and execute the computations in the subsequent manner:
Begin by calculating the expression in the parentheses as a priority: (31.5 squared minus 93) equals negative 61.5.
Next, perform the operation of dividing -61.5 by -2.5 which results in 24.6.
The tables represent the points earned in each game for a season by two football teams.
Panthers
14 10 10
10 17 3
28 13 17
32 16 10
14 7 21
Saints
21 12 3
3 10 10
14 3 12
28 40 10
17 20 7
Which team had the best overall record for the season? Determine the best measure of center to compare and explain your answer.
Saints; they have a larger mean value of about 14 points
Panthers; they have a larger mean value of about 14.8 points
Saints; they have a larger median value of 12 points
Panthers; they have a larger median value of 14 points
The team that had the best overall record for the season is Panthers. Therefore the best way to explain the answer B. Panthers; they have a larger mean value of about 14.8 points.
What are the mean values of the score of both team?For panthers, we calculate their mean values by totaling all their scores.
14+10+10+10+17+3+28+13+17+32+16+10+14+7+21 = 222
222/15 scores = 14.8
For Saints, 21+12+3+3+10+10+14+3+12+28+40+10+17+20+7 = 210
210/15 score = 14
This shows that Panthers have a larger mean value. Also, Panthers have a larger median value than saints. We find the median by arranging the scores from small to large and picking the number in between.
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what is the number of permutations of the letters in the word indis- tinguishable such that the strings git, tin, and nab do not appear in the permutation?
The number of permutations of the letters in the word indistinguishable such that the strings git, tin, and nab do not appear in the permutation is
3,172,973,824,000
Let A be the set of stages that contain the string "git",
B be the set of changes that contain the string "tin", and
C be the set of stages that contain the string "nab".
We need to discover the number of stages that don't contain any of these strings, which is the same as finding the measure of the set (A∪B∪C)'.
Utilizing the guideline of inclusion-exclusion, we have:
|A∪B∪C| = |A| + |B| + |C| - |A∩B| - |A∩C| - |B∩C| + |A∩B∩C|
We need to discover |(A∪B∪C)'|, which is the complement of the set A∪B∪C. In this manner:
|(A∪B∪C)'| = n! - |A∪B∪C|
Now we have to discover the measure of the sets A, B, and C, and their convergences.
For set A, able to settle the string "git" in its put in 3! ways, and after that permute the remaining 14 letters in 14! ways. In this manner, |A| = 3!×14!.
Essentially, we will discover |B| = 3!×14! and |C| = 3!×14!.
For the convergences, we are able to settle the comparing strings in their places and permute the remaining 11 letters in 11! ways. In this manner,
|A∩B| = 2!×11!,
|A∩C| = 2!×11!,
and |B∩C| = 2!×11!.
At long last, we have |A∩B∩C| = 1!×11! since we are able to settle all three strings in their places and permute the remaining 11 letters in 11! ways.
Substituting these values into the inclusion-exclusion equation, we get:
|A∪B∪C| = 3(3!×14!) - 3(2!×11!) + 1!×11!
|A∪B∪C| = 13608000
Subsequently:
|(A∪B∪C)'| = 17! - 13608000
|(A∪B∪C)'| = 3172973824000
So there are 3,172,973,824,000 permutations of the letters within the word "indistinguishable" such that the strings "git", "tin", and "nab" don't show up within the stage.
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Factor completely and then place the factors in the proper location on the grid.
20y 2 + 3y - 2
The complete factorization of the quadratic equation, would lead to the factor being (5y + 1)(4y - 1).
How to factor completely ?To factor the quadratic expression 20y² + 3y - 2 completely, we can use the "ac method" (product-sum method).
Rewrite the quadratic expression using these two numbers:
20y² - 5y + 8y - 2
Now, factor by grouping:
5y(4y - 1) + (4y - 1)
Now, we can see that there is a common factor of (4y - 1) in both terms:
(5y + 1)(4y - 1)
So, the factored form of the quadratic expression 20y² + 3y - 2 is (5y + 1)(4y - 1).
In conclusion, the factored form of the quadratic expression 20y² + 3y - 2 is (5y + 1)(4y - 1).
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suppose that 8% of the patients tested in a clinic are infected with hiv. furthermore, suppose that when a blood test for hiv is given, 97% of the patients infected with hiv test positive and that 4% of the patients not infected with hiv test positive. what is the probability that a patient testing positive for hiv with this test is infected with hiv? (enter the value of the probability in decimal format and round the final answer to three decimal places.)
The likelihood that understanding testing positive for HIV with this test is tainted with HIV is almost 0.104 or 10.4%
To illuminate this issue, we will utilize Bayes' hypothesis. Let's characterize the taking after occasions:
A: the persistent is contaminated with HIV
B: the persistent tests positive for HIV
We need to calculate P(A|B), the likelihood that an understanding is contaminated with HIV given that they tried positive for HIV.
By Bayes' hypothesis:
P(A|B) = P(B|A) * P(A) / P(B)
where
1. P(B|A) is the likelihood of testing positive for HIV given that the persistent is tainted with HIV (97%)
2. P(A) is the predominance of HIV within the clinic (8%)
3. P(B) is the likelihood of testing positive for HIV, which can be calculated utilizing the law of adding up to likelihood:
P(B) = P(B|A) * P(A) + P(B|A') * P(A')
where
1. P(B|A') is the likelihood of testing positive for HIV given that the persistent isn't tainted with HIV (4%)
2. P(A') is the complement of A, i.e., the likelihood of a quiet not being tainted with HIV (1 - 8% = 92%)
Substituting the values we have:
P(B) = 0.97 * 0.08 + 0.04 * 0.92 = 0.0736
P(B) = 0.0736
Hence,
P(A|B) = 0.97 * 0.08 / 0.0736 ≈ 0.104
P(A|B) = 0.104
So the likelihood that understanding testing positive for HIV with this test is tainted with HIV is almost 0.104 or 10.4% (adjusted to three decimal places).
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Last year Liz bought a book for $10. This year the same book is on sale for $5. What was the percent of change?
The percent of change in the price of the book is 50%.
To calculate the percent of change, we first need to find the difference between the original price and the new price. In this case, the original price of the book was $10, and the new price is $5. To find the difference, we can subtract the new price from the original price, which is:
$10 - $5 = $5
Now, we need to express this difference as a percentage of the original price. To do this, we divide the difference by the original price and then multiply by 100. In other words, we need to find the percentage that the original price has changed by. This can be represented mathematically as:
Percent of change = (Difference / Original price) x 100
Plugging in the values we found earlier, we get:
Percent of change = ($5 / $10) x 100
Percent of change = 0.5 x 100
Percent of change = 50%
This means that the price of the book has decreased by 50% from the original price of $10 to the sale price of $5.
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which statement is true about this equation
The equation represents a linear function.
What is quadratic equation?
A quadratic equation is a polynomial equation of degree two which can be written in the form: ax² + bx + c = 0, where x is the variable and a, b, and c are constants with 'a' not equal to 0. The term 'quadratic' comes from the Latin word 'quadratus', which means 'square'.
The equation given in the image is a quadratic equation in standard form, which means it is written in the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.
To determine which statement is true about this equation, we need to analyze its discriminant, which is given by the expression b^2 - 4ac. The discriminant tells us about the nature of the solutions of the quadratic equation.
If the discriminant is positive, then the equation has two distinct real roots.
If the discriminant is zero, then the equation has one real root (also known as a double root).
If the discriminant is negative, then the equation has two complex roots (conjugate pairs).
In the given equation, a = 3, b = -4, and c = 1. Substituting these values into the discriminant formula, we get:
b^2 - 4ac = (-4)^2 - 4(3)(1) = 16 - 12 = 4
Since the discriminant is positive, we know that the quadratic equation has two distinct real roots. Therefore, statement (A) is true.
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Only questions 7, 9, 10, and 11
PLS show how you got the answer and explain
GIVING BRAINLIEST
Answer:
7) .15 + .7 = .85, .1 + .7 = .8
9) Another way to write 44n (44
times n) is 44•n.
Another way to write 44 ÷ n (44
divided by n) is 44/n.
10) $.25 × 7 = $1.75
11) A driver buys d gallons of gas at $3.25 per gallon. How much does the driver spend on gas?
What is the sum and the product of x^2-9x+8
Answer:
Step-by-step explanation:
This is a trinomial quadratic equation
x^2-9x+8
= x^2 -x-8x+8
= (x-1)(x-8)
A rectangle has a length of 9 cm and width of (3x-y)cm the area of the rectangle is 72cm^2
PQRS is a kite where PQ = 4xcm and QR = ycm
The perimeter of the kite PQRS IS 33cm
Calculate the values of x and y
You must show your working
Do not use a trial and improvement method.
Answer:
the value of x ia 7/2 and y is 5/2
Andre, Bilal, Glenna, and Juanita are all friends. They have given each other nicknames as well. The four nicknames are Boss, Buzz, Cosmo, and Tiger. The following clues, determine the nickname of each of the friends. friends are competing in the track and field day at their school. Using the Clues: 1. Juanita beat Tiger in the 400 m race, but Juanita lost to Buzz in the high jump. 2. Glenna and Tiger tied in the long jump, but Boss beat Glenna in the 1500 m 3. Cosmo, Tiger and Andre found the water station together after the first event. 4. Cosmo and Juanita ran separate legs on the relay race. race. Problem A Track and Field be helpful in solving this problem. The table below, with a column for each name and a row for each nickname, may Boss Buzz Cosmo Tiger Andre Bilal Glenna Juanita
Answer:vvv
Step-by-step explanation:
Boss's nickname is Boss because they beat Glenna in the 1500m race.
Buzz's nickname is Buzz because they beat Juanita in the high jump.
Cosmo's nickname is Cosmo because they were with Tiger and Andre at the water station.
Tiger's nickname is Tiger because they lost to Juanita in the 400m race and tied with Glenna in the long jump.
Andre's nickname is not given, but we know they ran a leg of the relay race with Bilal.
Bilal's nickname is not given, but we know they ran a leg of the relay race with Andre.
Glenna's nickname is not given, but we know they tied with Tiger in the long jump.
Juanita's nickname is not given, but we know they lost to Buzz in the high jump and beat Tiger in the 400m race, and ran a leg of the relay race with Cosmo.
On a piece of paper, use a protractor to construct a triangle with angle measures of 40° and 60º.
What is the measure of the third angle?
Responses
60°
80°
100°
180°
The measure of the third angle in the triangle is 80 degrees.
What is the measure of the third angle?The sum of the angles in a triangle is always 180 degrees.
Therefore, to find the measure of the third angle in the triangle with angle measures of 40° and 60°,
We can subtract the sum of these two angles from 180°:
180° - (40° + 60°) = 180° - 100° = 80°
Therefore, the measure of the third angle in the triangle is 80 degrees.
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Two amateur marathoners were running a marathon. The first marathoner kept a steady pace and was able to finish in four hours. The second marathoner was keeping 4 the speed of the speed of the first runner. Then he was tired and his speed for the 3
second half of the distance was only 3 4 the speed of the first runner. How much did it
take the second runner to finish the distance?
It takes the second marathoner 4 hours and 40 minutes to complete the marathon.
Let's assume the distance of the marathon is "d" miles.
The first marathoner runs at a constant speed for 4 hours, so we can find their speed as:
speed = distance / time = d / 4
The second marathoner starts by running at 4 times the speed of the first marathoner, so their speed is:
speed = 4(d / 4) = d
For the second half of the race, the second marathoner's speed drops to 3/4 of the first marathoner's speed. Let's assume it takes "t" hours for the second marathoner to complete the second half of the race. Then, we can write:
d / 2 = (3/4)(d / 4)(t)
Simplifying this equation, we get:
t = (2/3) hours
So the total time it takes the second marathoner to finish the race is:
4 + (2/3) = 4 2/3 hours = 4 hours and 40 minutes.
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If the area of a triangle is 72 square inches and the height is 6 inches, what is the length of the base
Answer: 24 inches.
Step-by-step explanation:
We can use the formula for the area of a triangle to solve for the length of the base:
A = (1/2)bh
where:
A = the area of the triangle (in this case, 72 square inches)
b = the length of the base (what we're trying to find)
h = the height of the triangle (in this case, 6 inches)
Plugging in the values we know, we get:
72 = (1/2)b(6)
72 = 3b
b = 24
Therefore, the length of the base of the triangle is 24 inches.
How to do substitution
A polynomial p(x) has a relative maximum at (-2, 4), a relative minimum at (1,1), and a relative maximum at (5,7) and no other critical points. How many real zeros does p(x) have?a) oneb) twoc) threed) foure) five
The polynomial p(x) has option (c) three real zeros because it has a relative maximum at (-2, 4), a relative minimum at (1,1), a relative maximum at (5,7), and a negative leading coefficient.
Since p(x) has a relative maximum at (-2, 4), a relative minimum at (1,1), and a relative maximum at (5,7), it means that the degree of the polynomial must be odd and at least three.
Moreover, we know that p(x) has no other critical points. This means that p(x) does not change sign between these relative extrema, which in turn implies that there are no real zeros between these extrema.
Therefore, the number of real zeros of p(x) is either one or three. To determine the answer, we need to consider the leading coefficient of p(x).
If the leading coefficient is positive, then p(x) must eventually increase on both ends, since the degree is odd. This means that there is exactly one real zero.
If the leading coefficient is negative, then p(x) must eventually decrease on both ends. In this case, since there are three relative extrema, there must be three real zeros.
Thus, we need to find the sign of the leading coefficient of p(x). This can be done by looking at the relative extrema.
Since p(x) has a relative maximum at (-2, 4), we know that the leading coefficient is negative.
Therefore, the correct option is (c) three.
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A polynomial with n turning points has a degree of at least n + 1. Therefore, the polynomial p(x) must have a degree of at least 4. Since a polynomial of degree 4 can have up to 4 real zeros, the answer is d) four real zeros.
A polynomial p(x) has a relative maximum at (-2, 4), a relative minimum at (1, 1), and a relative maximum at (5, 7), with no other critical points. This means there are turning points at these coordinates. Since there are two relative maxima and one relative minimum, the polynomial must have at least 3 turning points.
A polynomial with n turning points has a degree of at least n + 1. Therefore, the polynomial p(x) must have a degree of at least 4. Since a polynomial of degree 4 can have up to 4 real zeros, the answer is d) four real zeros.
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I NEED HELP ON THIS ASAP!!!
The horizontal asymptote of the function f(x) = 2ˣ is y = 0.
What is a horizontal asymptote?In Mathematics and Geometry, a horizontal asymptote can be defined as a horizontal line (y = b) where the graph of a function approaches the line as the input values (domain or independent value) approach negative infinity (-∞) to positive infinity (∞).
In this context, the line passing through the ordered pair (0, 1) on the graph of this exponential growth function represents a horizontal asymptote and it has an equation of y = 0, as shown in the image attached above.
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Question 7 of 8
Which variable is most important to the following problem?
Ralph and Patrick play on a basketball team. Ralph played the whole first
quarter and the first 4 minutes of the second quarter. Patrick played the rest
of the second quarter and all of the third quarter. Ralph played the whole
fourth quarter. Each quarter is 10 minutes long. How long did Patrick play?
O A. the number of minutes Patrick played
B. the number of substitutions between Patrick and Ralph
C. the number of players on the team
OD. the length of a quarter
Answer:
D. the length of the quarter
Step-by-step explanation:
Given Patrick started playing 4 minutes into the 2nd quarter, and played until the end of the 3rd quarter, you want to know how long Patrick played.
QuarterIf q is the length of a quarter, Patrick's playing time is ...
2q -4 . . . . minutes
In order to give this a numerical value, we need to know the value of q.
The most important variable to the problem is ...
D. the length of a quarter.
<95141404393>
answer the last one plss i give brain
The complete sequence are 2, 3, 5, 8, 12, 17, 23, 30 38, 47, 1024, 512, 256, 128, 64 and 32.
How do we get the last numbers?Looking at the pattern, we can find the next two numbers in the sequence. All we need to do is notice that each term in the sequence is obtained by dividing the previous term by 2.
To get term after 128, we cam divide 128 by 2 which will give us:
= 128 / 2
= 64
To get term after 64, we divide 64 by 2 which give us:
= 64 / 2
= 32
Therefore, the last two numbers in the sequence are 64 and 32.
Full question: Find the last 2 numbers after the sequence of "2, 3, 5, 8, 12, 17, 23, 30 38, 47, 1024, 512, 256, 128, __ and ___.
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Carrington had a checking account balance of $800 at the
beginning of the month. She deposited $2,800 and used her debit
card for purchases of $310, $88, and $35.50. She also wrote
checks for $150 and $375.
What is her balance now?
Her current checking account balance is $2,641.50.
Account balance calculation.
To find Carrington's current checking account balance, we need to add up all the deposits and subtract all the withdrawals from her starting balance.
Starting balance = $800
Deposits = $2,800
Withdrawals = $310 + $88 + $35.50 + $150 + $375 = $958.50
Therefore, Carrington's current checking account balance is:
$800 + $2,800 - $958.50 = $2,641.50
Her current checking account balance is $2,641.50.
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Factor ax-2bx + ay-2by
Use the image to determine the type of transformation shown.
Reflection across the x-axis
90' clockwise rotation
Horizontal translation
Vertical translation
C
B
Which trapezoid is not isosceles
Answer:
D) a trapezoid with congruent diagnols
Explanation:
When none of the sides of a trapezoid are congruent, then it is a non isosceles trapezoid or a scalene trapezoid.
solve cos^2x = (power reducing formula)
[tex]cos^2(x) = cos^2(x)[/tex].
This equation is true for all values of x, so the solution is:
x ∈ ℝ (x is any real number).
To solve the equation[tex]cos^2(x)[/tex]= (power reducing formula),
we need to replace [tex]cos^2(x)[/tex] with the power reducing formula.
The power reducing formula for [tex]cos^2(x)[/tex] is:
[tex]cos^2(x) = (1 + cos(2x)) / 2[/tex]
Now, let's solve the equation:
[tex](1 + cos(2x)) / 2 = cos^2(x)[/tex]
We want to find x when this equation is true.
Since the left side is the power reducing formula for [tex]cos^2(x)[/tex],
we can simply write:
[tex]cos^2(x) = cos^2(x)[/tex].
The power reducing formula is a trigonometric identity that allows you to express a trigonometric function of a higher power in terms of a trigonometric function of a lower power.
It is most commonly used for reducing the power of the sine and cosine functions.
The power reducing formula for cosine is:
[tex]cos^2(x) = (1 + cos(2x))/2[/tex]
The power reducing formula for sine is:
[tex]sin^2(x) = (1 - cos(2x))/2[/tex]
These formulas can be derived using the Pythagorean identity, which states that [tex]sin^2(x) + cos^2(x) = 1.[/tex]
By solving for either [tex]sin^2(x) or cos^2(x)[/tex] in terms of the other, and then using the double angle formula for cosine [tex](cos(2x) = cos^2(x) - sin^2(x)),[/tex]we can arrive at the power reducing formulas.
The power reducing formulas can be used to simplify trigonometric expressions and make them easier to work with.
For example, if you have an expression such as [tex]sin^4(x)[/tex], you can use the power reducing formula for sine to express [tex]sin^4(x)[/tex] in terms of [tex]sin^2(x),[/tex]and then use the power reducing formula for cosine to express [tex]sin^2(x)[/tex]in terms of cos(2x).
This can make the expression simpler and easier to integrate or differentiate.
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Simplify (2x3y)(3x4y2).
5x7y3
6x7y2
6x7y3
6x12y2 -------------------------------- (69 points ill follow you thank the question and
account if its right)
The expression[tex](2x^3y)(3x^4y^2)[/tex] simplifies to [tex]6x^7y^3[/tex]. The coefficients are multiplied, and the variables are combined by adding their exponents. Option C.
To simplify the expression [tex](2x^3y)(3x^4y^2),[/tex] we can multiply the coefficients and combine the variables with the same base by adding their exponents.
Multiplying the coefficients, we have:
2 * 3 = 6
For the variables, we multiply the x terms by adding their exponents (3 + 4 = 7), and the y terms by adding their exponents (1 + 2 = 3).
Therefore, simplifying the expression [tex](2x^3y)(3x^4y^2)[/tex] gives us:
[tex]6x^7y^3[/tex]
Hence, the simplified form of[tex](2x^3y)(3x^4y^2)[/tex] is[tex]6x^7y^3[/tex]. Option c is correct.
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Answer:
C:6x7y3
Step-by-step explanation:
i took the test and got it right
Can a binomial probability distribution with p =.10 and n = 40 be approximated by the normal probability distribution? If so, what are the mean and standard deviation for the normal approximation?
The normal approximation for the given binomial distribution with p = 0.10 and n = 40 has a mean of 4 and a standard deviation of 1.93.
The binomial probability distribution can be approximated by the normal distribution when certain conditions are met, such as a large sample size and a probability of success not too close to 0 or 1.
In this case, n = 40 and p = 0.10. To determine if the normal approximation is appropriate, we can check if both np and n(1-p) are greater than or equal to 10
np = 40 x 0.10 = 4
n(1-p) = 40 x 0.90 = 36
Both np and n(1-p) are greater than or equal to 10, so the normal approximation is appropriate.
The mean of the binomial distribution is given by μ = np = 4, and the standard deviation is given by σ = √(np(1-p)) = √(40 x 0.10 x 0.90) ≈ 1.93.
To find the mean and standard deviation of the normal approximation, we use the same mean and standard deviation values
μ = np = 4
σ = √(np(1-p)) ≈ 1.93
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a person who works from home in sales earned an average of $2,350 per month over the past 12 months with a standard deviation of 175. calculate 90% confidence interval for the true mean income per month. round to 2 decimal places.
After calculating the 90% confident true mean income per month of a person who works from home in sales falls between $2146.47 and $2553.53.
To calculate the 90% confidence interval for the true mean income per month of a person who works from home in sales, we can use the following formula:
[tex]CI = X' ± Z\frac{a}{2}[/tex] * (σ/√n)
here:
X' = sample mean
Zα/2 = z-score that corresponds to the desired level of confidence (in this case, 90%)
σ = population standard deviation
n = sample size
Placing the values
CI = 2350 ± 1.645 * (175 / √12)
= [2146.47, 2553.53]
After calculating the 90% confident true mean income per month of a person who works from home in sales falls between $2146.47 and $2553.53.
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How does sample variance influence the estimated standard error and measures of effect size such as r2 and Cohen's d?
A) Larger variance increases both the standard error and measures of effect size.
B) Larger variance increases the standard error but decreases measures of effect size.
C) Larger variance decreases the standard error but increases measures of effect size.
D) Larger variance decreases both the standard error and measures of effect size.
The estimated standard error and measures of effect size such as r2 and Cohen's d larger variance increases the standard error but decreases measures of effect size. B.
Larger variance increases the standard error but decreases measures of effect size.
The standard error is a measure of how much the sample mean is likely to vary from the true population mean.
It is calculated as the standard deviation of the sample divided by the square root of the sample size.
If the sample variance is large, the standard deviation of the sample will also be large, resulting in a larger standard error.
Measures of effect size, such as r2 and Cohen's d, indicate the strength of the relationship between variables or the size of the difference between groups, respectively.
Larger sample variances indicate greater variability in the data, which can make it more difficult to detect significant effects.
This can result in smaller effect sizes, as the magnitude of the effect is reduced relative to the variability in the data.
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