Depending on the given angle measures of the triangle, the angle measures of triangle ABC are either 30°, 60°, and 90° or 90°, 60°, and 30° or 60°, 90°, and 30°.
Triangle ABC with angle measures ∠A, ∠B, and ∠C given as:
∠A = 30°, ∠B = 60°, ∠C = 90°: This is a special right triangle, known as a 30-60-90 triangle. The angles are in the ratio of 1:2:√3, so ∠A = 30°, ∠B = 60°, and ∠C = 90°.∠A = 90°, ∠B = 60°, ∠C = 30°: This is also a special right triangle, known as a 60-30-90 triangle. The angles are in the ratio of √3:1:2, so ∠A = 90°, ∠B = 60°, and ∠C = 30°.∠A = 60°, ∠B = 90°, ∠C = 30°: This is another special right triangle, which is the same as the previous one, but with the angles labeled differently. So ∠A = 60°, ∠B = 90°, and ∠C = 30°.∠A = 90°, ∠B = 30°, ∠C = 60°: This is not a special right triangle, but the angles still add up to 180°. So m∠A = 90°, m∠B = 30°, and m∠C = 60°.Therefore, depending on the given angle measures of the triangle, the angle measures of triangle ABC are either 30°, 60°, and 90° or 90°, 60°, and 30° or 60°, 90°, and 30°.
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What are the angle measures of triangle abc?
a)∠a = 30 , ∠b = 60, ∠c= 90
b)∠a=90, ∠b= 60, ∠c= 30
c)∠a= 60, ∠b= 90, ∠c=30
d)∠a = 90, ∠b = 30, ∠c = 60
Find the angle between the given vectors to the nearest tenth of a degree
U= (4,-8) V= (-6, -3)
Answer:
90°
Step-by-step explanation:
Given the vectors:
[tex]\displaystyle{\vec v = \langle -6, -3\rangle \ \: \text{and} \ \: \vec u = \langle 4, -8 \rangle}[/tex]
You can find the angle between two vectors by solving for θ in the equation:
[tex]\displaystyle{\vec v \times \vec u = |\vec v | |\vec u| \cos \theta}[/tex]
Where:
[tex]\displaystyle{\vec v \times \vec u = v_xu_x + v_yu_y}\\\\\displaystyle{|\vec v| = \sqrt{v_x^2 + v_y^2}}\\\\\displaystyle{|\vec u| = \sqrt{u_x^2+u_y^2}}[/tex]
Therefore:
[tex]\displaystyle{\vec v \times \vec u = |\vec v | |\vec u| \cos \theta}\\\\\displaystyle{(-6)(4)+(-3)(-8) = \sqrt{(-6)^2+(-3)^2} \cdot \sqrt{4^2+(-8)^2} \cos \theta}\\\\\displaystyle{-24+24=\sqrt{36+9}\cdot \sqrt{16+64}\cos \theta}\\\\\displaystyle{0=\sqrt{45}\cdot \sqrt{80}\cos \theta}\\\\\displaystyle{\dfrac{0}{\sqrt{45}\cdot \sqrt{80}}=\cos \theta}\\\\\displaystyle{0=\cos \theta}\\\\\displaystyle{\theta = 90^{\circ}}[/tex]
Therefore, the angle between two vectors is 90 degrees.
Graph the equation below by plotting the
y-intercept and a second point on the
line. When you click Done, your line will
appear.
1=1/√x-2
Click on the point(s). To change your selection, drag the
marker to another point. When you've finished, click Done.
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Done
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a surveyor determines that the angle of elevation to the top of a building from a point on the ground is . he then moves back 51.3 feet and determines that the angle of elevation is . what is the height of the building?
The height of the building is approximately 62.4369 feet. The solution involves using trigonometry and solving for the opposite side of the triangle using the tangent function.
Let h be the height of the building, and x be the distance between the first point and the base of the building. Then we have:
tan(26.8°) = h/x ----(1)
tan(19.5°) = h/(x + 43.9) ----(2)
From equation (1), we have x = h/tan(26.8°)
Substituting this value of x in equation (2) and solving for h, we get:
h = (43.9 tan(19.5°) tan(26.8°))/(tan(26.8°) - tan(19.5°))
Plugging in the values, we get:
h ≈ 62.4369 feet
Therefore, the height of the building is approximately 62.4369 feet.
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The preimage shown above is dilated by a scale factor of 4 about the center (-2,-2). What is the coordinate location of the point C'.
Type your answer as an ordered pair, (x,y) with no spaces.
The coordinate location of point C' after the dilation is (-10, 2).
What is coordinate location?
To find the coordinate location of point C' after the dilation by a scale factor of 4 about the center (-2,-2), we can use the following formula:
(x', y') = (k * (x - h) + h, k * (y - k) + k)
where (x, y) are the coordinates of the original point, (h, k) are the coordinates of the center of dilation, k is the scale factor, and (x', y') are the coordinates of the corresponding point after dilation.
For point C, the coordinates are (x, y) = (-2, -1) and the center of dilation is (h, k) = (-2, -2) with a scale factor of k = 4.
Plugging in these values, we get:
(x', y') = (4 * (-2 - (-2)) - 2, 4 * (-1 - (-2)) - 2)
= (-10, 2)
Therefore, the coordinate location of point C' after the dilation is (-10, 2).
What is coordinate?
A coordinate is a set of numbers or values that indicate the position or location of a point or object in a given space or system. Coordinates are often used in mathematics, geometry, physics, and other fields to describe the location of objects or points in a two- or three-dimensional space. The most common type of coordinates are Cartesian coordinates, which are represented by an ordered pair of numbers (x,y) that describe the location of a point on a two-dimensional plane, or an ordered triplet of numbers (x,y,z) that describe the location of a point in a three-dimensional space.
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Complete question is: The preimage shown above is dilated by a scale factor of 4 about the center (-2,-2). the coordinate location of the point C'after the dilation is (-10, 2).
as the size of a sample increases, the mean of the distribution of sample means increases always. (true/false). group of answer choices
As the size of a sample increases, the mean of the distribution of sample means increases always. - False
The mean of the distribution of sample means does not always rise as sample number rises. The population mean is not changed by increasing the sample number because the population mean is equivalent to the mean of the distribution of sample means. The variation of the distribution of the sample means does, however, decline as the sample number rises.
The distribution of sample means approximates normality with a mean equal to population mean and a standard deviation equal to population standard deviation divided by square base of the total sample size. This is known as the central limit theorem. As a result, the distribution of sample means becomes more tightly focused around the community mean and less variable as the sample number rises.
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Which statement is not true for the function notation of the volume of a cube, V(s) = s3?
Answer:
Step-by-step explanation:
The statement that is not true for the function notation of the volume of a cube, V(s) = s3, is not specified. Please provide the statement you are referring to.
Rewrite the expression in terms of sine and cosine and utilize the Fundamental Pythagorean Identity: sin²(x)+cos²(x)=1
Verify the identity using the Pythagorean Identity:
[tex]\frac{1-cos(x)}{sin(x)}=\frac{sin(x)}{1+cos(x)}[/tex]
The identity using the Pythagorean Identity:
[tex]\frac{1-cosx}{sinx}=\frac{sinx}{1+cosx}[/tex] , Hence proved
Trigonometry formulas can be used to address many different kinds of issues. These issues could involve Pythagorean identities, product identities, trigonometric ratios (sin, cos, tan, sec, cosec, and cot), etc. Many formulas, such as those involving co-function identities (shifting angles), sum and difference identities, double angle identities, half-angle identities, etc., as well as the sign of ratios in various quadrants,
the Fundamental Pythagorean Identity: sin²(x)+cos²(x)=1
Verify the identity using the Pythagorean Identity:
[tex]\frac{1-cosx}{sinx}=\frac{sinx}{1+cosx}[/tex]
To prove this take the right-hand side of the given identity.
We know that,
[tex]\frac{sinx}{1+cosx}*\frac{1-cosx}{1-cosx}\\\\=\frac{Sinx(1-cosx)}{1-cos^2x}\\\\=\frac{1-cosx}{sinx}[/tex]
Hence the left-hand sides.
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David is driving on a road with a speed limit of 60 mph. It is possible for him to get a ticket if she goes more than 7mph over the speed limit. Is it possible to David to get a ticket while she is on cruise control.
This is a inequality problem.
It is possible for her to exceed the speed limit and get a ticket if she is not paying attention or if the road conditions change.
What is speed?
she should always be aware of her speed and adjust it as necessary to stay within the legal limit.
Yes, this is an inequality problem. We can use an inequality to represent the situation:
David's speed ≤ Speed limit + 7 mph
Let's substitute the given values:
David's speed ≤ 60 mph + 7 mph
David's speed ≤ 67 mph
If David's speed is less than or equal to 67 mph, then she will not get a ticket, because she is within the allowable limit of going 7 mph over the speed limit. However, if David's speed is greater than 67 mph, then she will be going too fast and is at risk of getting a ticket.
Since David is driving on cruise control, it is possible for her to exceed the speed limit and get a ticket if she is not paying attention or if the road conditions change. Therefore, she should always be aware of her speed and adjust it as necessary to stay within the legal limit.
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joy is giving ice cream cones to some children at a carnival. she has 8 chocolate ice cream cones, 10 vanilla ice cream cones, and 6 strawberry ice cream cones. if joy selects an ice cream cone randomly without looking, what is the probability that she will give a chocolate ice cream cone to the first child and then a vanilla ice cream cone to the second child?
The required probability that Joy will give a chocolate ice cream cone to the first child and then second child get a vanilla ice cream cone is equal to 3/16.
Number of chocolate ice cream cones = 8
Number of vanilla ice cream cones = 10
Number of strawberry ice cream cones = 6
Total number of ice cream cones = 8+10+6
= 24 cones,
The probability of Joy giving a chocolate ice cream cone to the first child is 8 cones,
P(chocolate) = 8/(8+10+6) = 8/24 = 1/3
Now,
Assuming that Joy gave away a chocolate ice cream cone to the first child,
There are 8-1=7 chocolate ice cream cones left.
Similarly, there are 10-1=9 vanilla ice cream cones left.
Probability of Joy giving a vanilla ice cream cone to the second child,
given that she gave a chocolate ice cream cone to the first child, is,
P(vanilla | chocolate)
= 9/(7+9)
= 9/16
Probability of Joy giving a chocolate ice cream cone to the first child and a vanilla ice cream cone to the second child is,
P(chocolate and vanilla)
= P(chocolate) × P(vanilla | chocolate)
= (1/3) × (9/16)
= 3/16
Therefore, the probability that Joy will give a chocolate ice cream cone to the first child and then a vanilla ice cream cone to the second child is 3/16.
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Lola has 4 1/2 cups of rice. She uses 3/4 of the rice to make sushi rolls for dinner. She uses the rest of the rice to make rice pudding for dessert. How much rice does Lola use for the rice pudding?
Based on the given information, Lola used 9/8 cups of rice for the rice pudding.
What is a fraction?A fraction is a mathematical expression that represents a part of a whole or a division of one quantity by another. It consists of two numbers separated by a horizontal line called a fraction bar or a vinculum. The number above the fraction bar is called the numerator, and the number below the fraction bar is called the denominator.
Lola has 4 1/2 cups of rice, which is equivalent to 9/2 cups of rice.
She uses 3/4 of the rice to make sushi rolls for dinner. So, the amount of rice she uses for the sushi rolls is:
(3/4) x (9/2) = 27/8 cups of rice
To find the amount of rice she uses for the rice pudding, we need to subtract the amount she used for the sushi rolls from the total amount she had:
9/2 - 27/8 = 36/8 - 27/8 = 9/8
So Lola used 9/8 cups of rice for the rice pudding.
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a part of a population chosen in such a way that every member had an equal chance of being selected.
This is called random sampling.
What is random sampling?
Random sampling is commonly used in research and statistical analysis, as it helps to reduce the potential for bias in the sample selection process. There are several techniques for conducting random sampling, such as simple random sampling, stratified random sampling, and cluster sampling, each with its own specific method of selection.
Random sampling is an important tool in statistical inference and research. By selecting a random sample from a population, researchers can obtain an estimate of the population parameters (such as the mean or proportion) with a known level of precision and confidence.
There are several techniques for conducting random sampling:
Simple random sampling: In this technique, each member of the population has an equal chance of being selected. This can be done by assigning each member of the population a unique number and using a random number generator to select the sample.
Stratified random sampling: In this technique, the population is divided into subgroups (strata) based on some characteristic (such as age or gender). A random sample is then selected from each stratum.
Cluster sampling: In this technique, the population is divided into clusters (such as neighborhoods or schools). A random sample of clusters is then selected, and all members within those clusters are included in the sample.
Random sampling has several advantages over non-random sampling methods, such as convenience sampling or purposive sampling. First, it helps to ensure that the sample is representative of the population, reducing the potential for bias in the sample selection process. Second, it allows for the calculation of sampling error, which is the degree of error that is inherent in any sample due to chance variation. Finally, random sampling allows for the use of inferential statistics, which enables researchers to make inferences about the b based on the sample data.
However, random sampling also has some limitations. It can be expensive and time-consuming to select a truly random sample from a large population. Additionally, it may be difficult to ensure that all members of the population are included in the sampling frame, which could result in some members being excluded from the sample. Finally, the sample size must be large enough to ensure a sufficient level of precision in the estimates of the b parameters.
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Can I have some help with this math problem
The answer is A. 1/4.
the waiting time at a drive-through window has an exponential distribution with a mean of 6 minutes. what is the probability that the waiting time is greater than 5 minutes? enter your answer as a percentage accurate to two decimal places. for example, a probability of 0.4567 is 45.67%, so it should be entered as 45.67.
The probability that the waiting time is greater than 5 minutes is 0.3012
Given that the waiting time at a drive-through window has an exponential distribution with a mean of 6 minutes.
The probability density function of an exponential distribution is given by
f(x) = (1/μ) × e^(-x/μ)
where μ is the mean of the distribution.
Therefore, the probability that the waiting time is greater than 5 minutes is
P(X > 5) = ∫[5, ∞] f(x) dx
= ∫[5, ∞] (1/6) × e^(-x/6) dx
= [-e^(-x/6)]_[5, ∞]
= e^(-5/6)
Using a calculator, e^(-5/6) is approximately 0.3012.
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The volume of a rectangular prism is 768 ft3. What is the volume of the same shape if the width is changed by a scale factor of 1/3?
The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height of the prism, respectively. If the width is changed by a scale factor of 1/3, then the new width is (1/3)w. The length and height remain the same. Therefore, the new volume of the rectangular prism is:
V' = l(1/3w)h
Multiplying both sides by 3 to simplify the expression, we get:
3V' = lw(3h)
Since the original volume of the rectangular prism is 768 ft3, we have:
V = lwh = 768
Multiplying both sides by 3 to simplify the expression, we get:
3V = lw(3h)
Substituting 3V for lw(3h), we get:
3V' = 3V(1/3w) = Vw
Therefore, the new volume of the rectangular prism is:
V' = Vw = (768 ft3)(1/3) = 256 ft3
So, the volume of the same shape if the width is changed by a scale factor of 1/3 is 256 ft3.
a mosaic table top has triangular and rectangular peices for every 8 rectangular pieces there are 12 triangular pieces there are a total of 80 pieces how many of each shape are used
It is $150 to rent a room at local skating rink, and it is $5 extra per child for pizza, drink, and a party bag. Write the equation in slope intercept form for the situation above
A) x+y=1050
B) y=150
C) y=150x+5
D) y=5x+150
Answer:
Let's start with the fixed cost, which is the cost to rent the room: $150. This is the y-intercept of the equation. Now, for each child attending the party, there is an additional cost of $5. We can represent the number of children attending with the variable x. Therefore, the equation in slope-intercept form is: y = 5x + 150 So the correct answer is D) y = 5x + 150
Which number should be added to
both sides of this quadratic equation
to complete the square?
The number that should be added to both sides of this quadratic equation to complete the square is (-3/2)² .
Explain about the completing square:When a square is complete, a quadratic is written in the shape of a squared bracket, and if necessary, a constant is added. Finding the function's highest or minimum value and the time it happens is one use for the square-root method.
We can solve quadratic equations that lack a factor by completing the square.
In order to make the left side of the formula a perfect square trinomial, the equation's form must be adjusted.
The given quadratic equation:
1 = x² - 3x
This can be written as:
x² - 3x - 1 = 0
a = 1, b = -3 and c = -1.
using the formula: (b/2)² = (-3/2)²
The number added both side is:
(-3/2)² + 1 = x² - 3x + (-3/2)² (required equation);
On simplification:
9/4 + 1 = (x -3/2)²
13/4 = (x -3/2)²
Thus, the number that should be added to both sides of this quadratic equation to completing square is (-3/2)² .
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Ms. Collins recently got an aquarium that is 3 ft tall, 3 feet wide, and 6 ft. long. She needs to fill her aquarium with water but she already put .5 ft of gravel in the bottom.
How much more room is left for the water?
There is 53.5 cubic feet of space left for water in the aquarium.
what is volume ?The volume of three-dimensional space occupied by an object or substance alone is referred to as volume.
The aquarium's total volume can be found by multiplying its dimensions:
Volume = Length x Width x Height
Volume = 6 ft x 3 ft x 3 ft
Volume = 54 cubic feet
However, Ms. Collins has already filled the bottom of the tank with gravel that takes up 0.5 ft of space. Therefore, the remaining space for water is:
Remaining space = Total volume - Gravel volume
Remaining space = 54 cubic feet - 0.5 cubic feet
Remaining space = 53.5 cubic feet
So, there is 53.5 cubic feet of space left for water in the aquarium.
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a chair is normally $30.00. it's now on sale for 10% off. what is the sale price?
- ugly person
Answer:27
Step-by-step explanation:First you find 10% of 30 which is 3 then you subtract 30-3=27
what's the answer The area of a square is A = s², where s is the length of one side of the square.
What is the side length s for each square?
Drag the answer into the box to match each description.
The square with A = 225 in²
The side length of each square is √225 in = 15 inches so the option B is correct
What do you mean by term Square root ?The square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol √. For example, the square root of 9 is 3 because 3 multiplied by 3 equals 9. The square root of 16 is 4 because 4 multiplied by 4 equals 16. The square root of a number is always a positive number, although it can be irrational (a non-repeating, non-terminating decimal) for some numbers.
The formula to find the length of one side of a square, s, when given the area, A, is:
s = √(A)
So, for the square with A = 225 in², the side length would be:
s = √(225) in
s = 15 inches
Therefore, the side length of the square with an area of 225 in² is 15 inches.
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What is the result when the number 94 is decreased by 50%?
Answer:
47
Step-by-step explanation:
Given: 94 decreased by 50%
First, we will change the percentage to a decimal, by moving the decimal two nodes to the left.
50% = .50
Next, we will multiply the decimal with the number.
94 · .50 = 47
check attached image for further explanation
3n + 9 = 11n -23 Please
Answer: N=4
Step-by-step explanation:
Answer: n = 4
Step-by-step explanation:
subtract 9 from both sides simplify subtract 11n from both sides then combine like terms, simplify, divide both sides by the same factor, then simplify then boom :)
last month alex sold his bike for 50.00 and deposited 80 percent of the money into his savings account he made the tqo other deposits of 24 and 35 before he withdrew 2/3 of the total to buy a used skate board write the amounts of alex transmission in order as inergets
The amounts of Alex's transactions in order are $50.00, $40.00, $24.00, $35.00, $149.00, and $98.67.
The amounts of Alex's transactions can be listed in the following order:
The amount he received from selling his bike: $50.00
The amount he deposited into his savings account, which is 80% of $50.00: $40.00
The first deposit he made of $24.00
The second deposit he made of $35.00
The total amount he had in his account before withdrawing 2/3 of it: $149.00 (which is the sum of $50.00, $40.00, $24.00, and $35.00)
The amount he withdrew to buy the used skateboard, which is 2/3 of $149.00: $98.67
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Find the approximate area of the lake whose shape is overlaid on the grid below. Each
square of the grid represents one square mile. (3 points)
Thus, the approximate area of lake whose shape is taken on the square of the grid is 8 sq. unit.
Explain about the area on grid:A grid area is a rectangular area just on grid that is made up of one or more grid cells. When you define an area using named grid areas or when you place an object using line-based placement, grid areas are produced.
By dividing the supplied figure in square grids and counting how many of these there are, it is easiest to determine the area of a typical two-dimensional shape.
For the following question:
The area of 1 complete grid is taken 1 sq. unit.Area greater than half but less then 1 is taken as 1/2 sq. unit.Area less than half units is not taken:Thus,
Total area = 4*1 + 8*(1/2)
Total area = 4 + 4
Total area = 8 sq. unit
Thus, the approximate area of the lake whose shape is taken on the square of the grid is 8 sq. unit.
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Pablo is mailing packages. Each small package costs him $2.80 to send. Each large package costs him $3.80. How much will it cost him to send 5 small packages and 4 large packages?
Step-by-step explanation & Answer
———-———-———-———-———-———-———-———-———-———-———-——
Page 1
So first we need to multiply the small packages by 5 because he needs to said 5 of them which is:
5 x 2.80 = 14 Which is our answer for the first part of the question.
Next we need to multiply the big/large packages by 4 because he is going to send 4 of them.
4 x 3.80 = 15.2 / ( money terms ) = 15.20
[tex]\left \{ {{small= 14} \atop {big=15.20}} \right.[/tex]
———-———-———-———-———-———-———-———-———-———-———-——
Page 2
We can them add them up or we can leave it at this but just in case lets add them up:
15.20 + 14 = 29.20 Which is the answer.
[tex]\left[\begin{array}{ccc}An&sw&r\\&=&\\22&.&9\end{array}\right][/tex]
formula to find area of acircle
A = π r² is the formula
r is the radius
Hope it helps ✨
Answer:
Step-by-step explanation:
[tex]A=\pi \times r^2[/tex] where r is the circle's radius
the daily high temperature in a town in Alaska has been colder than -4f for three weeks
This statement implies that the daily high temperature in the town in Alaska has been below -4°F (minus four degrees Fahrenheit) for three consecutive weeks.
Which of the following is a valid application of the distributive property?
A. 5 x 2 + 3 = 5 X (2 + 3)
B. 5 x 2 + 3 = 5 x (2) + 5 x (3)
B only
A only
Neither A nor B
Both A and B
Answer:
B only
Step-by-step explanation:
The correct answer is B only.
The distributive property states that a multiplication of a number by a sum or difference can be rewritten as the sum or difference of the products of the number with each term in the sum or difference. In other words, a(b + c) = ab + ac and a(b - c) = ab - ac.
Option A, 5 x 2 + 3 = 5 X (2 + 3), does not use the distributive property correctly. It tries to distribute the 5 over the sum 2 + 3, which is not possible.
Option B, 5 x 2 + 3 = 5 x (2) + 5 x (3), correctly applies the distributive property by distributing the 5 over each term in the sum 2 + 3.
Therefore, the valid application of the distributive property is B only.
after running a classification model, we have the following confusion matrix: confusion matrix what is this model's overall accuracy ?
The overall classification accuracy of this model on the test set is 0.179
The overall classification accuracy of the model can be calculated by dividing the number of correctly classified instances (the sum of true positives and true negatives) by the total number of instances in the test set
Accuracy = (TP + TN) / (TP + TN + FP + FN)
where TP = True Positives, TN = True Negatives, FP = False Positives, and FN = False Negatives.
From the confusion matrix given
True Positives (TP) = 124
True Negatives (TN) = 116
False Positives (FP) = 77
False Negatives (FN) = 851
Plugging these values into the formula, we get
Accuracy = (124 + 116) / (124 + 116 + 77 + 851)
Accuracy = 0.179
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The given question is incomplete, the complete question is:
The following classification confusion matrix shows the results of a model's classifications on a test set: Test Set Results Model Prediction FALSE TRUE FALSE 116 TRUE 77 124 851 (The rows refer to the model's classifications, and the columns to the actual results in the test set.) a. What is the overall classification accuracy of this model on the test set?
WILL GIVE BRAINLIEST TO THE CORRECT ANSWER
Find the value of x.
Let a = 10, b = 6, c = 12, and d = x
ab=cd
x = ab/c
x = 10(6)/12
x = 5