The property that should be used to continue simplifying the above equation is A-^1A = 1. So, correct option is C.
We can start with the equation AB = AC and multiply both sides by A^-1 on the left:
A^-1(AB) = A^-1(AC)
Using the associative property of matrix multiplication, we can simplify the left-hand side:
(A^-1A)B = (A^-1A)C
Using the fact that A^-1A = I (the identity matrix), we get:
IB = IC
Simplifying further using the fact that I times any matrix is that matrix itself, we obtain:
B = C
Therefore, the equivalent equation to AB = AC using A^-1 that simplifies to B = C is A^-1(AB) = A^-1(AC), and the property used to continue simplifying the equation is A^-1A = I.
The correct option is (C) A^-1A = 1, which is equivalent to A^-1A = I, since the identity matrix is denoted as 1 in some contexts.
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(Likelihood MC)
A collector has items including baseball cards, gold coins, and stamps in a box. If P(gold coin) 50%, interpret the likelihood of randomly selecting a gold coin from the box.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event
Answer: The likelihood of randomly selecting a gold coin from the box is "Likely."
When the probability of an event is 50%, it means that there is an equal chance of the event happening or not happening. In this case, the probability of randomly selecting a gold coin from the box is 50%, so it is likely to occur.
Step-by-step explanation:
can anyone please help me do this? I need it done asap but nothing makes sense
Answer:
Skip it bro this fin be hard and i can do the next one i tryed to do this and it hard
Step-by-step explanation:
Part C: Charlie designs a square garden. Each side length is 3x + 5.
The perimeter of Charlie's garden is how much larger than the perimeter of Shawn's
garden?i
The requried difference between the perimeters of the two gardens would be, 12x + 20 - 4s.
What is the perimeter?Perimeter is the measure of the figure on its circumference.
Here,
Let's assume that Shawn's garden is also a square with side lengths. Therefore, the perimeter of Shawn's garden would be 4s.
The perimeter of Charlie's garden would be 4(3x + 5), which simplifies to 12x + 20.
The difference between the perimeters of the two gardens would be,
12x + 20 - 4s
We can't simplify this expression any further without knowing the value of s.
Therefore, we can conclude that the difference between the perimeters of the two gardens depends on the side length of Shawn's garden.
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what is 10% of 500000?
Answer:
Step-by-step explanation: the answer is 50000.
3. In one pond in the forest, scientists found that a sample of pond water contained 45 minnows for every 27 tadpoles. How many tadpoles would they expect to find in a sample that contained 315 minnows? Show all work and explain how you got your answer
Answer: 189
Step-by-step explanation:
for every 45 minnow there will be 27
315 minnow is 7 times 45 minnow 27*7 is 189
What is the cost of 0. 85 pound of imported cheese at $7. 90 per pound
Answer:
Step-by-step explanation:
Cost = 0.85 x $7.90
Cost = $6.72
Lucas wants to buy pork to roast cuban sandwhiches. The table below shows how much four local stores charge for different amount of the same type of pork. which store has the lowest price per pound for the pork?
Store A: 2 price dollars: 11.20
Store b: 3 price dollars: 10.95
Store C;4 price dollars : 13.80
Store d : 5 price dollars; 16.25
Mayerlin has xx dimes and yy nickels. She has no more than 20 coins worth no less than $1.30 combined. Solve this system of inequalities graphically and determine one possible solution.
what are the inequalities?
Answer: look at the image for the answers and solutions
Step-by-step explanation:
Graph the line that has a slope of 1/4 and includes the point (0,4).
.
Answer: y = mx+b
y = -1x+1/4
Step-by-step explanation:
what is the solution of the system of equations y=2x+2 y=x
The solution to the two simultaneous linear equations are;
x = -2 and y = -2
How to solve Simultaneous Linear Equations?There are three main ways of solving simultaneous linear equations and they are;
Elimination method
Substitution method
Graphical Method
The two simultaneous equations are;
y = 2x + 2 -----(1)
y = x -----(2)
Plug in eq 2 into eq 1 to get;
x = 2x + 2
x - 2x = 2
-x = 2
x = -2
Thus, y = -2
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The ratio of the number of yellow buttons that Miko had to the number of blue buttons that Miko had was 2: 3. After she had bought 27 more blue buttons, The ratio of the number of yellow buttons to the number of blue buttons became 4:9. How many buttons did Miko have at first?
Answer:
90 buttons
Step-by-step explanation:
the ratio of yellow : blue = 2 : 3 = 2x : 3x ( x is a multiplier )
after buying 27 more blue buttons
2x : 3x + 27 = 4 : 9
expressing the ratios in fractional form
[tex]\frac{2x}{3x+27}[/tex] = [tex]\frac{4}{9}[/tex] ( cross- multiply )
18x = 4(3x + 27)
18x = 12x + 108 ( subtract 12x from both sides )
6x = 108 ( divide both sides by 6 )
x = 18
number of buttons at first = 2x + 3x = 5x = 5 × 18 = 90
What are four solutions of this equation that are ordered pairs? y=2x+4
Answer: (0,4), (1,6), (2,8), (3,10)
Step-by-step explanation:
you can plug this equation into a graphing calculator (if you don't have a physical one, you can use desmos online graphing calculator) or just graph it on paper.
If you graph it on paper, start at (0,4) because that is the y-intercept. Then go up 2 and right 1 and plot a point there. Up 2 and right 1 and plot a point, etc.
Some points on this line are (0,4), (1,6), (2,8), (3,10)
You have a job with a gross pay of $68282, what is the partially filled tax bracket?
The partial tax bracket is the 24% tax bracket.
How to get Tax Bracket?To determine your tax bracket, you need to know your taxable income, which is your gross pay minus any applicable deductions and exemptions. Based on the information provided, your taxable income is $68,282.
In the United States, the federal tax brackets for the tax year 2022 (for taxes filed in 2023) are as follows:
10% on taxable income from $0 to $9,950 for individuals12% on taxable income from $9,951 to $40,525 for individuals22% on taxable income from $40,526 to $86,375 for individuals24% on taxable income from $86,376 to $164,925 for individuals32% on taxable income from $164,926 to $209,425 for individuals35% on taxable income from $209,426 to $523,600 for individuals37% on taxable income over $523,600 for individualsBased on these tax brackets, you would be in the 24% tax bracket, since your taxable income is between $86,376 and $164,925.
However, it's important to note that the marginal tax rate, which is the rate applied to your last dollar of income, does not reflect the average tax rate you will pay on your entire taxable income. Your actual tax liability will depend on the total amount of your taxable income and any other applicable tax credits or deductions.
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……………Help with 22-27…………
The equations of the lines in slope-intercept form are:
22. y = -1/2x + 3.
23. y = 2x - 3.
24. y = -x
25. y = -2x + 4.
26. y = 3/2x - 2.
27. y = 5/2x - 1/2
28. y = x + 3
29. y = -x + 2
30. y = -1/4x + 9/4
How to Find the Equation of a Line in Slope-intercept Form?The equation of a line is y = mx + b, in slope-intercept form, where:
m = slope = rise/run = change in y / change in x
b = y-intercept or the point where the graph intercepts the y-axis.
22. Slope (m) = rise/run = -1/2
y-intercept (b) = 3
Substitute m = -1/2 and b = 3 into the equation, y = mx + b:
y = -1/2x + 3.
23. Slope (m) = rise/run = 4/2 = 2
y-intercept (b) = -3
Substitute m = 2 and b = -3 into the equation, y = mx + b:
y = 2x - 3.
24. Slope (m) = rise/run = -2/2 = -1
y-intercept (b) = 0
Substitute m = -1 and b = 0 into the equation, y = mx + b:
y = -x + 0
y = -x
25. Slope (m) = rise/run = -2/1 = -2
y-intercept (b) = 4
Substitute m = -2 and b = 4 into the equation, y = mx + b:
y = -2x + 4.
26. Slope (m) = rise/run = 3/2
y-intercept (b) = -2
Substitute m = 3/2 and b = -2 into the equation, y = mx + b:
y = 3/2x - 2.
27. Slope (m) = rise/run = 5/2
y-intercept (b) = -0.5 = -1/2
Substitute m = 5/2 and b = -1/2 into the equation, y = mx + b:
y = 5/2x - 1/2
28. Slope (m) = change in y / change in x = (5 - 3) / (2 - 0) = 2/2 = 1
y-intercept (b) = 3
Equation is, y = x + 3
29. Slope (m) = change in y / change in x = (-1 - 4) / (3 -(-2)) = -5/5 = -1
Substitute (x, y) = (3, -1) and m = -1 into y = mx + b, to find b:
-1 = -1(3) + b
-1 = -3 + b
-1 + 3 = b
2 = b
b = 2
The equation would be: y = -x + 2
30. Slope (m) = change in y / change in x = (3 - 2) / (-3 - 1) = 1/-4 = -1/4
Substitute (x, y) = (1, 2) and m = -1/4 into y = mx + b, to find b:
2 = -1/4(1) + b
2 = -1/4 + b
b = 2 + 1/4
b = 9/4
The equation would be: y = -1/4x + 9/4
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What is the equation of this graph
Answer:
[tex]7y {}^{2} = 0[/tex]
Answer:
the correct answer is y = -1/2x + 6
Step-by-step explanation:
A car salesman earns 5% on the sale of a BMW sold for $103,100. What is his take home pay that day?
Answer:
$5155
Step-by-step explanation:
We know
A car salesman earns 5% on the sale of a BMW sold for $103,100.
5% = 0.05
What is his take-home pay that day?
We take
103,100 times 0.05 = $5155
SO he takes home $5155.
Step-by-step explanation:
Looks like we're trying to find out what 5% of 103,100 is. We first need to convert the percent into a decimal and then multiply.
[tex]5\% = 0.05[/tex]
Now we can multiply
[tex](0.05)(103100) = 5155[/tex]
Divide 3x³ - 2x² + 4x - 3 by x² + 3x + 3.
The quotient of the division is 3x - 11 with a remainder of 37x + 21
How to determine the quotientFrom the question, we have the following parameters that can be used in our computation:
Divide 3x³ - 2x² + 4x - 3 by x² + 3x + 3.
Using the long division method of quotient, we have
x² + 3x + 3 | 3x³ - 2x² + 4x - 3
The division steps are as follows
3x - 11
x² + 3x + 3 | 3x³ - 2x² + 4x - 3
3x³ + 9x² + 9
------------------------------------------------
-11x² + 4x - 12
-11x² - 33x - 33
------------------------------------------------
37x + 21
Hence, the quotient is 3x - 11
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Fill the blank! if a residual is negative, then that data point lies _____________ the regression line.
If a residual is negative, then that data point lies below the regression line. In a regression analysis, the goal is to find the line that best describes the relationship between two variables.
The line is determined by finding the values of the slope and intercept that minimize the sum of the squared errors between the observed data points and the predicted values on the line.
The difference between the actual value of the dependent variable and the predicted value on the line is known as the residual. A residual represents the vertical distance between the observed data point and the regression line.
If the residual is positive, it means that the observed value is above the regression line, and if the residual is negative, it means that the observed value is below the regression line.
When a residual is negative, it means that the predicted value on the regression line is higher than the actual value of the dependent variable for that particular data point. In other words, the observed data point is lower than what we would expect based on the relationship described by the regression line.
This situation indicates that the regression line may not fit the data very well at that point, and it may be worth investigating further to see if there are other factors that may be affecting the relationship between the two variables.
In summary, a negative residual means that the observed data point lies below the regression line, and it indicates that the regression line may not be the best fit for that particular data point.
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Leo replaces the strings on some guitars. He puts 6 new strings on Each guitar. He uses 18 strings. How many guitars does leo put Strings on?
Using division, we know that Leo replaces 6 new strings from 3 guitars which are a total of 18 strings.
What is division?One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.
The other operations are multiplication, addition, and subtraction.
On a fundamental level, counting the instances in which one number is included within another is one interpretation of the division of two natural numbers.
When no more full chunks of the size of the second number can be allocated during the computation of the quotient, the division with a remainder or Euclidean division of two natural numbers yields an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains.
So, we know that:
6 new strings are put on each guitar.
He uses 18 strings.
Then, the number of guitars:
⇒ 18/6 = 3
Therefore, using division, we know that Leo replaces 6 new strings from 3 guitars which are a total of 18 strings.
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Please solve this math problem and give an explanation for more points and brainliest
Correct numerical expression is G. 6(18)2 – 27(6)(12).
What is expression?In mathematics, an expression is a combination of numbers, symbols and operations such as addition, subtraction, multiplication and division that may be evaluated to produce a single number, a variable or a set of numbers.
This expression calculates the number of cubic inches of the box filled with packing material by subtracting the volume of the cylinder from the volume of the cube. The volume of the cube is 6(18)2, and the volume of the cylinder is 27(6)(12). Thus, the number of cubic inches of the box filled with packing material is 6(18)2 – 27(6)(12).
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7:31 PM Wed Feb 8
S÷
7
9
for s=4.
ixl.com
Write your answer as a fraction or as a whole or mixed number.
Submit
The expression S÷7 when s = 4 is simplified to 4/7
What is a fraction?
A fraction can be described as the part of a whole variable, number or element
There are several types of fractions which includes;
Mixed fractionsSimple fractionsProper fractionsImproper fractionsComplex fractionsFrom the information given, we have that;
S÷7 is the given expression as a quotient.
For s = 4, we have to substitute the value of s as 4 in the expression, we have;
4/7
Hence, it is an example of a proper fraction where the denominator is greater than the numerator.
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Which one of the following best defines the notion of the P-value of a hypothesis test? a. The probability of rejecting H_o, whether it's true or not b. The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true c. The probability of the type I error d. The probability of the type II error
P-value of a hypothesis test is an important measure of the strength of evidence against the null hypothesis and helps us make informed decisions about rejecting or failing to reject the null hypothesis.
A hypothesis test is a statistical method used to test the validity of an assumption or a hypothesis about a population based on a sample data.
The correct answer is b. The P-value of a hypothesis test is the probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true.
In hypothesis testing, we start with a null hypothesis, which is usually denoted as H_0, that represents the status quo or the default assumption. The alternative hypothesis, denoted as H_a, represents the opposite of the null hypothesis.
The P-value is the probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true. A low P-value indicates that the sample data provides strong evidence against the null hypothesis, and we reject the null hypothesis.
A high P-value indicates that the sample data does not provide strong evidence against the null hypothesis, and we fail to reject the null hypothesis.
In mathematical terms, the P-value is calculated as the probability of observing a test statistic Z that is more extreme than the one actually obtained, assuming the null hypothesis is true.
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A spherical tank with radius 3 m is half full of a liquid that has a density of 900 kg/m3. The tank has a 2 m spout at the top. Find the work W required to pump the liquid out of the spout. (Use 9.8 m/s2 for g.)
Answer:
3.0549 MJ
Step-by-step explanation:
You want to know the work done to empty a half-full spherical tank of radius 3 m containing liquid of density 900 kg/m³ through a 2 m spout at the top of the tank.
MassThe mass of the liquid is the product of its volume and its density. The volume of the hemisphere is ...
V = 2/3πr³ = 2/3π(3³) = 18π . . . . . . cubic meters
Then the mass of the liquid is ...
m = ρV = (900 kg/m³)(18π m³) = 16200π kg
HeightThe centroid of the liquid is 3/8r below the center of the tank. The mass of liquid must be moved from that location to a point 2 m above the top of the tank. The total height the liquid must be moved is ...
3/8(3 m) + 3m + 2m = 6.125 m
WorkThe work done to lift the liquid is ...
W = Fd = (m·g)d = (16200π kg)(9.8 m/s²)(6.125 m) = 972405π J
W ≈ 3,054,900.4 J ≈ 3.0549 MJ
The work required is about 3.0549 megajoules.
__
Additional comment
We could find the incremental work to move a layer of liquid dy thick to the necessary height, then integrate over the depth of liquid. It is much easier to look up the centroid location for a hemisphere, and use that in the calculation.
We have used "m" to represent both mass and meters. We trust you can determine which is which from the context.
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The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
0 5
1 0, 3, 7
2 4, 6, 8
3 2
4
5 8 Key: 5|8 means 58
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.
For the given data, the best measure of variability is the interquartile range (IQR) and its value is 18.5.
What is variability?
The extent to which data points in a statistical distribution or data collection diverge or vary from the average value, as well as the extent to which these data points differ from one another, is practically by definition the concept of variability.
The given stem and leaf plot is:
stem leaf
0 5
1 0, 3,7
2 4,6,8
3 2
5 8
The value in the stem is the ten's place and the value in the leaf is the one's place.
So the scores are 05, 10, 13, 17, 24, 26, 28, 32 and 58.
Because extreme values and outliers have a smaller impact on the interquartile range than the complete data range, statisticians prefer using them to measure variability. To understand the centre and spread of your data, utilise the IQR along with a measure of central tendency, like the median.
Range for this data = 58 - 5 = 53.
To find the Inter Quartile Range (IQR), we first find the median.
Median = 24
So Q1 is the first quartile.
This is the median of the first half of the scores(5,10,13,17).
Q1 = 10+13 / 2 = 11.5
Q3 is the third quartile.
This is the median of the second half of the scores (26, 28, 32 58).
Q3 = 28+32 / 2 = 30
Now,
IQR = Q3 - Q1 = 30 - 11.5 = 18.5
Therefore for the given data, the best measure of variability is the interquartile range (IQR) and its value is 18.5.
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Answer:
Step-by-step explanation:
For the given data, the best measure of variability is the interquartile range (IQR) and its value is 18.5.
What is variability?
The extent to which data points in a statistical distribution or data collection diverge or vary from the average value, as well as the extent to which these data points differ from one another, is practically by definition the concept of variability.
The given stem and leaf plot is:
stem leaf
0 5
1 0, 3,7
2 4,6,8
3 2
5 8
The value in the stem is the ten's place and the value in the leaf is the one's place.
So the scores are 05, 10, 13, 17, 24, 26, 28, 32 and 58.
Because extreme values and outliers have a smaller impact on the interquartile range than the complete data range, statisticians prefer using them to measure variability. To understand the centre and spread of your data, utilise the IQR along with a measure of central tendency, like the median.
Range for this data = 58 - 5 = 53.
To find the Inter Quartile Range (IQR), we first find the median.
Median = 24
So Q1 is the first quartile.
This is the median of the first half of the scores(5,10,13,17).
Q1 = 10+13 / 2 = 11.5
Q3 is the third quartile.
This is the median of the second half of the scores (26, 28, 32 58).
Q3 = 28+32 / 2 = 30
Now,
IQR = Q3 - Q1 = 30 - 11.5 = 18.5
Therefore for the given data, the best measure of variability is the interquartile range (IQR) and its value is 18.5.
I totally didnt copy - 0
What is the prime factorization of 51?
The prime factorization of 51 is 3 * 17.
please help!! Describe an octant's main features
An octant's main features are :
Axes Positive and negative regions Quadrants What are the main features of an octant ?An octant is formed by three perpendicular axes, labeled X, Y, and Z. These axes intersect at a common point called the origin. Each octant contains both positive and negative values along the X, Y, and Z axes. The positive region is located on one side of each axis, while the negative region is on the other side.
Each of the three axes divides an octant into two quadrants. These quadrants are numbered from 1 to 8, with quadrant 1 being in the positive X, Y, and Z regions and quadrant 8 being in the negative X, Y, and Z regions.
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20. A popular pizza parlor charges $12 for a large cheese pizza plus $1.50 for each additional topping. The
total cost, C, of a pizza with T toppings can be represented by C = 1.50T + 12. What is the domain in
the context of the problem situation?
Answer:
efgdfhncdrt gguhd r g sixtieth sex
E = (children who go to the park),
T = {children who play tennis) ,
G = {children who play golf}
120 children go to the park. 50 play tennis. 75 play golf. 25 do not play tennis or golf.
(a) Show this information in the Venn diagram.
(b) How many children play both golf and tennis?
Answer:
125 children play tennis and golf
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What is the value of (2^(2014)+2^(2012))/(2^(2014)-2^(2012))? (A) -1 (B) 1 (C) (5)/(3) (D) 2013 (E) 2^(4024)
The value of the exponential equation is A = 5/3
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = [ 2²⁰¹⁴ + 2²⁰¹² ] / [ 2²⁰¹⁴ - 2²⁰¹² ] be equation (1)
On simplifying the equation , we get
Taking the common factor as 2²⁰¹² , we get
A = 2²⁰¹² [ 2² + 1 ] / 2²⁰¹² [ 2² - 1 ]
On further simplification , we get
A = ( 2² + 1 ) / ( 2² - 1 )
A = ( 4 + 1 ) / ( 4 - 1 )
A = 5/3
Therefore , the value of A is 5/3
Hence , the equation is A = 5/3
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the scale of a map is 1:50000 find the area in square km of a square field 4cm² on the map.
The area in square km of a square field 4 cm² is given as follows:
1 km².
How to obtain the area?The area is obtained applying the proportions in the context of the problem.
The scale is of:
1 cm : 50000 cm -> 1 cm = 0.5 km, as 1 cm = 10^-5 km.
Hence, for the areas, in square units, the scale is obtained squaring both sides, as follows:
(1 cm)² = (0.5 km)²
1 cm² = 0.25 km².
Meaning that the area of the square field is of:
4 x 0.25 = 1 km².
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