In a case whereby longer leg of a right triangle is 3cm longer than the shorter leg and hypotenuse is 6cm longer than the shorter leg then the side lengths of the triangle is 9 inches.
How can the lenght be calculated?The concept that will be used is pythagoras theorem.
We can make s = the length of the shorter leg.
Where the longer leg can be expressedas (s + 3),
Then the hypotenuse is( s + 6).
From pythagoras theorem, a^2 + b^2 = c^2.
then we have s^2 + (s + 3)^2 = (s + 6)^2
[s^2 + (s + 3)(s + 3)] =[ (s + 6)(s + 6) ]
s^2 + s^2 + 6s + 9 = s^2 + 12s + 36
If we collect like terms we have
s^2 - 6s - 27 = 0
Then if we factorize we have
(x - 9)(x + 3) = 0
then
we can set the whole left side to equal 0.
x - 9 = 0, then x = 9
x + 3 = 0, then x = -3.
But we can only have positive value which sis 9, hence shortest side is 9 inches.
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A store sells two sizes of fresh wreaths. An 18-inch wreath costs $15, and a 22-inch wreath costs $30. In one day, the number of 22-inch wreaths sold was FOUR more than TWICE the number of 18-inch wreaths, for a total of $645. How many of each were sold?
The number of 18-inch wreaths is 7, and
the number of 22-inch wreaths is 18.
What is a linear equation?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
Given the cost of an 18-inch wreath = $15
cost of a 22-inch wreath = $30
let the number of 18-inch wreaths be x and the number of 22-inch wreaths is y,
the total cost of both wreaths = $645
cost of x 18-inch wreaths = $15x
cost of y 22-inch wreaths = $30y
equation is,
$15x + $30y = $654
and the number of 22-inch wreaths sold was four more than twice the number of 18-inch wreaths,
y = 4 + 2x
substitute the value of y in the equation
15x + 30y = 645
15x + 30(4 + 2x) = 645
15x + 60x = 645 - 120
75x = 525
x = 525/75
x = 7
and y = 4 + 2x
y = 4 + 2*7
y = 18
Hence store sells 18 22-inch wreaths and 7 18-inch wreaths.
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during the winter season, a prominent newspaper reporter is interested in writing a story about the lack of proper heating of apartment buildings in the city in which he lives. during a particularly frigid weekend, this reporter manages to interview almost everyone in his own apartment building. the reporter finds that everyone, including himself, is satisfied with the heating in the apartment building. identify the type of sampling used in this example. a) Cluster sampling b) Convenience sampling c) Voluntary response sampling d) Systematic sampling 1 e) Attempted census
The type of sampling used in this example is Convenience sampling.
Convenience sampling is a type of non-probability sampling in which the sample is selected based on the ease of access or availability of the subjects. The sample is selected based on the researcher's convenience, and it does not use a random selection process.
In this case, the reporter chose to interview people in his own apartment building because it was convenient for him and he had easy access to them.
The other options you listed are:
a) Cluster sampling, which is a form of probability sampling in which the sample is selected by first dividing the population into smaller groups or clusters, and then selecting a random sample of those clusters.
b) Voluntary response sampling, which is a type of non-probability sampling where individuals choose to participate in the study.
c) Systematic sampling, which is a form of probability sampling in which the sample is selected by choosing a random starting point and then selecting every nth subject from the population.
d) Attempted census, which is when the researcher tries to include all members of a population in the sample.
Therefore, The type of sampling used in this example is Convenience sampling.
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The figure below is a cone with the vertex at A and diameter BC. The cone is cut off along 15 cm B =B 6 cm 49 cm-a)find the base radius of the smaller cone.
b) find the volume of the frustum.
divide the lateral height in half, Height squared lateral height squared is subtracted from height squared, the answer from step three, and find its square root. The radius of the cone is the outcome.
What is the volume formula of frustum?The following are the conical Frustum formulas in terms of r and h: V = (1/3) * * h * (r12 + r22 + (r1 + r2)) is the formula for a conical frustum's volume.The base's radius is the same as the cylinder's radius. The cylinder's height is equal to the length of the altitude, which is a segment running perpendicular to the planes of each of its bases.Radius = Diameter/ 2 applies when the diameter is known. Radius = Circumference/2 can be calculated after the circumference is known. The radius is calculated using the formula Radius = ((Area of the circle/π).To learn more about radius refer to:
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Therefore , the solution of the given problem of volume comes out to be 9,003.75π cubic cm.
What is the volume formula of frustum?The following are the conical Frustum formulas in terms of r and h: V = (1/3) * * h * (r12 + r22 + (r1 + r2)) is the formula for a conical frustum's volume. The base's radius is the same as the cylinder's radius. The cylinder's height is equal to the length of the altitude, which is a segment running perpendicular to the planes of each of its bases.
Here,
Given :
=> 15 cm is the AB
=> radius = 49/2 = 24.5 cm
The radius of base is 24.5 cm
and
the volume of frustrum:
=> π(24.5)(24.5)(15)
=> 9,003.75π cubic cm
Therefore , the solution of the given problem of volume comes out to be
9,003.75π cubic cm.
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fraction numerator dover denominator d x end fraction open square brackets in parentheses 4 x minus 7 close parentheses to the power of 4 open parentheses 7 x plus 8 close parentheses to the power of 5 close square brackets.
Differentiating the expression [tex]\frac{d}{dx} [(4x-7)^4(7x+8)^5 ][/tex] with respect to x will be [tex]16(4x-7)^3(7x+8)^5 + 35(4x-7)^4(7x+8)^4[/tex]
We are given with
[tex]\frac{d}{dx} [(4x-7)^4(7x+8)^5 ][/tex]
Here we will be using the chain rule. According to the chain rule, we will first have to solve the parentheses as a variable. Then we will have to solve the expression within the parenthesis
First, we will differentiate [tex](4x-7)^4[/tex] keeping [tex](7x+8)^5[/tex] constant. Here we will first assume [tex](4x-7)[/tex] as one variable and differentiate using the formula d/dx[x^n] then we will differentiate 4x - 7 to get just 4. They would be multiplied by one another
Hence we get
[tex]4 X4(4x-7)^3(7x+8)^5[/tex]
[tex]16(4x-7)^3(7x+8)^5[/tex]
Now, we will keep [tex](4x-7)^4[/tex] constant and differentiate [tex](7x+8)^5[/tex] and adding it up we get
[tex]16(4x-7)^3(7x+8)^5 + 5X7(4x-7)^4(7x+8)^4[/tex]
[tex]= 16(4x-7)^3(7x+8)^5 + 35(4x-7)^4(7x+8)^4[/tex]
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Complete Question
[tex]\frac{d}{dx} [(4x-7)^4(7x+8)^5 ][/tex]
A ball is thrown from an initial height of 2 meters with an initial upward velocity of 5 m/s.
h=2+5t-5t^2
The ball's height of (in meters) after seconds is given by the following. Find all values of for which the ball's height is 3 meters.
Answer: The height of the ball (in meters) after t seconds is given by the equation h = 2 + 5t - 5t^2. We can use this equation to find the values of t for which the ball's height is 3 meters.
We need to find the values of t that make h = 3, so we can substitute 3 for h in the equation:
3 = 2 + 5t - 5t^2
Then we can solve for t by moving all the terms to one side of the equation and factoring it:
-5t^2 + 5t - 1 = 0
And we can use the quadratic formula to find the solutions of this equation:
t = (5 +/- sqrt(5^2 - 4*(-1)(-1)))/ 2(-1)
t = (5 +/- sqrt(25 + 4))/ -2
t = (5 +/- sqrt(29))/ -2
The solutions of this equation are t = (5 +/- sqrt(29))/ -2
Since the time, t, is a real value the square root of 29 should be positive.
The values of t for which the ball's height is 3 meters are not real values, so there's no time when the ball's height is 3 meters.
Step-by-step explanation:
A small town surveyed 250 adults one Haiti of whom were parents about whether a Park should be expanded the results showed that 150 of adults who were parents and 40 of the adult who were not parents thought the park should be expanded useless information to complete the two way table
Based on the information, we can infer that of the 250 adults surveyed, 190 wanted the park to be expanded and 60 did not want the park to be expanded.
How to complete the table?To complete the table we must take into account the available information. In this case, they are only referring to the adults who wanted the park to be expanded:
40 non-parent adults wanted it expanded.150 adult parents wanted it expanded.40 + 150 = 190According to the above, if we add these two values we would have a group of 190 adults who want the park to be expanded. So the number of adults who do not want the park to be expanded would be 60.
250 - 190 = 60Finally, if there are 60 people who do not want the park to be expanded, we can infer that there may be 30 who are parents and 30 who are not parents.
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Which expression is equivalent to -63y² +27y?
O-9y(7y-3)
O9y(7y-3)
O-9y(7y + 3)
9y(7y + 3)
Answer:
[tex]9y\left(-7y+3\right)[/tex]Step-by-step explanation:
[tex]-63y^2+27y[/tex]
[tex]-63yy+27y[/tex]
[tex]-9\cdot \:7yy+9\cdot \:3y[/tex]
[tex]9y\left(-7y+3\right)[/tex]
six friends met for a book club at a local coffee shop. Each person ordered a small cup of coffee and a muffin. The total for the order, including taxes, was $38.10, if the cost of a small coffee is $3.79 after taxes find the cost of one muffin after taxes
Please help me
The cost of one muffin after taxes is $2.56. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
For all the real numbers, there are four basic mathematical operations which are:
1. Addition(‘+’) wherein the sum of the numbers is obtained.
2. Subtraction(‘-’) wherein the difference of the numbers is obtained.
3. Multiplication(‘×’) wherein the product of the numbers is obtained.
4. Division(‘÷’) wherein the quotient of the numbers is obtained.
Let cost of one muffin after taxes be 'x'
We are given that there were six friends and each person ordered a small cup of coffee and a muffin.
The total for the order, including taxes, was $38.10
Also, the cost of a small coffee is $3.79 after taxes.
So, we get
⇒ 6(3.79 + x) = 38.10
⇒ 22.74 + 6x = 38.10
⇒ 6x = 15.36
⇒ x = $2.56
Hence, the cost of one muffin after taxes is $2.56.
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AC=A, C, equals Round your answer to the nearest hundredth. A right triangle A B C. Angle A C B is a right angle. Angle A B C is twenty-five degrees. Side A C is unknown. Side B C is five units.
The unknown side AC will be equal to 2.33.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that a right triangle ABC. Angle ACB is a right angle. Angle ABC is twenty-five degrees. The side AC is unknown. Side BC is five units.
The unknown side will be calculated as:-
tan(25) = P / B
tan(25) = AC / BC
AC = BC x tan(25)
AC = 5 x tan(25)
AC = 2.33
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which of the following is equivalent to the probability of less than 50% democrats in a sample size of
Probability of less than 50 % democrats for the example based on sample proportion is equal to 0.1562.
Sample size 'n' = 100
Registered voters 'p' = 55%
= 0.55
σ = √ p( 1- p )/ n
= √0.55( 0.45)/ 100
= 0.04975
Mean 'μ' = 55%
= 0.55
Probability of getting less than 50% democrats in a sample size of 100 voters
X = 0.5
Z = ( X - μ ) / σ
= ( 0.5 - 0.55) / 0.4975
= -1. 005
= -1.01
p-value pf -1.01 is equal to 0.156248
Therefore, the probability of getting 50% democrats for the given sample size id equal to 0.1562. The given example represents sample proportion.
The above question is incomplete , the complete question is :
In a congressional district, 55% of the registered voters are Democrats. Which of the following is closest to the probability of getting less than 50% Democrats in a random sample of size 100?
Is this an example of a sample proportion OR a sample mean?
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AE and CD intersect at point B. Find m
Answer:
m∠ABD = 111
Step-by-step explanation:
69 + x = 180
x = 111
Answer:
< ABD = 111 °
Step-by-step explanation:
< ABD and < DBE form a straight line which is 180 degrees
< ABD + < DBE = 180
< ABD + 69= 180
< ABD = 180 -69
< ABD = 111
Two airplanes leave Philadelphia for Rochester. The first airplane to leave travels at an average speed of 590 kilometers per hour. The second airplane, which leaves 3 hours later, travels at an average speed of 650 kilometers per hour. How long does it take the second airplane to overtake the first?
it would take 29.5 hours the second airplane to overtake the first.
What is Speed?speed is described as. the pace at which an object's location changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar quantity because it just has a direction and no magnitude.
Given, Two airplanes leave Philadelphia for Rochester. The first airplane to leave travels at an average speed of 590 kilometers per hour. The second airplane, which leaves 3 hours later, travels at an average speed of 650 kilometers per hour.
So, in 3 hours first airplane will reach at;
Distance = speed *time
Distance = 590 * 3
Distance travels by first airplane in 3 hours will be = 1770 km
Since, Relative speed of given two planes = 650 - 590
Relative speed of given two planes = 60 km/hour
To reach 1770 km it would take = 1770/60 hours
Thus,
To reach 1770 km it would take = 29.5 hours
therefore, it would take 29.5 hours the second airplane to overtake the first.
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a) Estimate the initial and final amounts of water contained in the pool.
The initial amount of water contained in the pool was __ thousands of gallons.
The required initial and final amounts of water contained in the pool are 46 ans 26 gallons of water.
Explain about Graph?A graph is made up of vertices, or points, and edges, or lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and uncorrected graphs, and simple graphs, there are many other forms of graphs.
According to question:As graph says
The initial amount of water contained in the pool is
at t = 0
= 46 gallons of water
And at t = 5, is final amount of water in pool
= 26 gallon of water
Thus, there are 46 ans 26 gallons of water.
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Give f(x) = 3x^3+kx-13, and x-1 is a factor of f(x), then what is the value of k?
Answer: If x-1 is a factor of f(x) = 3x^3+kx-13, then f(x) can be written as (x-1)g(x) for some polynomial g(x). This means that f(1) = 0.
We can substitute x = 1 into f(x) to get f(1) = 3(1)^3 + k(1) - 13 = 3 + k - 13 = 0.
Therefore k - 10 = 0, so k = 10
So the value of k is 10.
Step-by-step explanation:
please help! giving 20 points for this answer please!
Answer:
6 divided by 2/3 = 9
Step-by-step explanation:
Steven cuts the 6 ft long rope by 2/3 to make 9 pieces and the answer is mathematically correct, via calulcator
standard form y-100=-50x-3
Answer:
Answer in attached photo.
Step-by-step explanation:
SolutionSolution in attached photo, do take note the standard form of an equation is:
y = mx + c,
where m is the gradient and c is the y-intercept.
Answer: (x– 8)2= 4(1)(y+ 3); vertex: (8, –3); opens upward
As of summer 2020, Voyager 1 is about 13.8 billion miles from Earth. Express this distance in AU,
using scientific notation, with two significant figures.
Answer:
1.478 x 10^2 AU
Step-by-step explanation:
To convert this distance to astronomical units (AU), we can use the fact that 1 AU is approximately equal to 93 million miles.
So, 13.8 billion miles is approximately:
13.8 billion miles / 93 million miles/AU = 147.8 AU
In scientific notation, this distance would be written as: 1.478 x 10^2 AU
Meredith plays softball, she gets a hit about 35% of the time. Write this as a fraction.
A 1/4
B 2/5
C 1/35
D 7/20
The depiction of 35% as a fraction is 7/ 20, and option D is the correct answer.
What are percentages?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given that the chance of getting hit by the ball is 35%.
35 % = 35/100
Simplifying the fraction:
35/100 = 7/ 20
Hence, depiction of 35% as a fraction is 7/ 20, and option D is the correct answer.
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Select the 2 fractions that are equivalent to 1
Answer: Anything that has the same two numbers
Step-by-step explanation:
You don't have a picture, so I'm basing this off of what I know. A number over another number that is the same is equivalent to one.
Kathy and Mark Smith believe investing in their retirement is critical. Kathy began investing 20% of each paycheck in a retirement account when she was 20 years old. She has saved four times more than Mark who began saving when he was 35. If their total retirement savings equals $1,560,000, how much are Kathy’s and Mark's investments worth?
Kathy’s and Mark's investments worth will be $1248000 and $312000.
How to calculate the worth of each individual?From the information, Kathy and Mark Smith believe investing in their retirement is critical. Kathy began investing 20% of each paycheck in a retirement account when she was 20 years old. She has saved four times more than Mark who began saving when he was 35.
Let Mark = x
Kathy = 4 × x = 4x
The equation to represent this will be:
4x + x = 1560000
5x = 1560000
Divide
x = 1560000 / 5
x = 312000
Mark contributed $312000
Kathy contributed
= 312000 × 4
= 1248000
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For the function f(x) given in the table, find the average rate of change over each specified interval.
x 0 2 2.5 3 3.8 4 5
f(x) 15 16 20 23 19 17 24
(a) [2, 5]
(b) [3.8, 4]
(a) The average rate of change over the interval [2, 5] is given by (f(5) - f(2)) / (5 - 2), which is equal to (24 - 16) / (5 - 2) = 8 / 3 = 2.67.
(b) The average rate of change over the interval [3.8, 4] is given by (f(4) - f(3.8)) / (4 - 3.8), which is equal to (19 - 19.6) / (4 - 3.8) = -0.6 / 0.2 = -3.
The average rate of change over a given interval [a, b] is a measure of how much the value of a function changes on average as the input changes over that interval. It is calculated as the difference between the value of the function at the endpoints of the interval divided by the difference of the corresponding inputs.
Formally, the average rate of change over the interval [a, b] is given by:
f_avg = (f(b) - f(a)) / (b - a)
where f is the function being evaluated and f_avg represents the average rate of change.
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Jacob has a smart phone data plan that costs $25 per month that includes 5 GB of data, but will charge an extra $20 per GB over the included amount. How much would Jacob have to pay in a month where he used 4 GB over the limit? How much would Jacob have to pay in a month where he used went over by � x GB?
The amount Jacob has to pay in a month where he used x GB over the limit is y=25+20x.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Jacob has a smart phone data plan that costs $25 per month that includes 5 GB of data, but will charge an extra $20 per GB over the included amount.
Amount Jacob has to pay in a month where he used 4 GB over the limit is
25+4×20
= $105
Amount Jacob has to pay in a month where he used x GB over the limit is
y=25+20x
Where, y is total amount of money
Hence, the amount Jacob has to pay in a month where he used x GB over the limit is y=25+20x.
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Answer:
Step-by-step explanation:
I don’t know just 5 point
Tyler's brother earns $14 per hour. The store offers him a 5% increase in wages per hour. After the raise, how much will tyler's brother make per hour?
After the raise, Tyler's brother will make $14 x 1.05 = $14.70 per hour.
Answer:
14 x 1.05 = 14.70
Step-by-step explanation:
IS 1.5 MORE OR LESS THAN -1.5
Answer:
1.5 is more than -1.5
Step-by-step explanation:
Positive numbers, like 1.5, are always greater than negative numbers, like -1.5
An instructor asked her students how much time to the nearest hour) they spent studying for the midterm. The data are displayed in the following histogram: What percentage of students study to or more hours for the midterm? 3 % Round your answer to the nearest whole number
Based on the data displayed in the histogram, the percentage of students who study 2 or more hours for the midterm is 88%.
A histogram is a graphical representation of data that shows the distribution of a dataset. It is used to show the frequency or the relative frequency of different values within a set of data. It is a bar chart that displays the data in a continuous format, with the bars touching each other.
Based on the histogram, the number of students studying 2 or more hours for the exam are:
= 9 + 6 + 3 + 2 + 1 + 1
= 22 students
While the total number of students studying is :
= 3 + 9 + 6 + 3 + 2 + 1 + 1
= 25 students
The percentage of students study to or more hours can be determined by dividing the number of students studying 2 or more hours with the total number of students studying multiply by 100.
percentage = 22/25 x 100
percentage = 0.88 x 100
percentage = 88%
Therefore, 88% of students study to or more hours for the midterm.
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For which of the following sets of data should a stacked bar chart be used?
The total number of planes landing at O’Hare Airport categorized by type
The number of white cars vs, the number of white trucks
The average age of male high school grads vs. the age of female graduates
The average golfers vs the average age of tennis players
Answer:
The total number of planes landing at O’Hare Airport categorized by type.
The following data show the miles per gallon of small SUVs. Sketch a box plot. Calculate the smallest, Q1, median, Q3, largest value, range, and the interquartile range for a box plot. 19 22 22 26 23 24 21 16 16
Smallest = 16, median=22, largest value of data=26 , interquartile range=Q3-Q1=23-19=4.
In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.
We have the data 19 22 22 26 23 24 21 16 16, and we have to calculate smallest, Q1, median ...
First rearrange the data 16,16,19,21,22,22,23,24,26
So, Smallest = 16
Median of the data = middle number of data=22
Q1=middle of smallest and median=19
Q3=23
largest value of data=26
range= 19-26
interquartile range=Q3-Q1=23-19=4
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segment ac is called a diagonal. on your paper, put a mark on it to indicate that it is congruent to itself. now, look at all of the markings on your paper. you should see that triangle abc is congruent to triangle cda. based on your markings, why are these triangles congruent?
The triangles abc and cda are congruent by sss congruence criteria.
The full form of CPCT is Corresponding parts of Congruent triangles. After proving triangles congruent, the remaining dimension can be predicted without actually measuring the sides and angles of a triangle. Different rules of congruency are as follows. SSS (Side-Side-Side)
SAS (Side-Angle-Side)ASA (Angle-Side-Angle)AAS (Angle-Angle-Side)RHS (Right angle-Hypotenuse-Side)SSS (Side-Side-Side)SSS (Side-Side-Side) :-If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.
so, sides
AB=CD
BC=DA
AC=CA
Hence by SSS (Side-Side-Side) the triangles are congruent.
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Help me please!!!!!!!
Answer:
Yes, one gallon is enough
Step-by-step explanation:
16ft x 12ft = 192ft
If one gallon covers 250 square feet then she will have enough for another 58ft remaining
Which of the following is (are) true concerning the confusion matrix? [select all that apply]
a. It is so named because it is traditionally confusing to read
b. It is a matrix that tabulates correct and incorrect predictions of the choice categories
c. It is useful to determine the predictive accuracy of a choice model
d. None of the above
It is useful to determine the predictive accuracy of a choice model and hence option c is correct for confusion matrix
the misclassification error rate for the following xlminer confusion matrix and the accuracy value of the confusion matrix is 10.82% .
In the field of machine learning, specifically the problem of statistical classification (in unsupervised learning, it is typically referred to as a matching matrix), a confusion matrix, also known as an error matrix, is a specific table structure that enables visualizing the performance of an algorithm.
The literature describes both iterations of the matrix, where each row represents instances in an actual class and each column represents instances in a predicted class. Since it is straightforward to tell whether the system is combining two classes, the name was chosen (i.e. commonly mislabeling one as another).
accuracy is given by the formula :
Accuracy(%) = (true positive + true negative)/(positive + negative)
Here TP true positive =10
and TN true negative is 8.2
hence accuracy = (10+8.2) / (1+0) %
Accuracy = 10.82%
Therefore the accuracy value of the confusion matrix is 10.82% .
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