A new sensor was developed by ABY Inc. that is to be used for their obstacle detection system. During tests involving 250 runs, the following data were acquired:
The alarm went off 33 times even if there is no obstacle.
There are 63 times when the alarm didn't activate even if an obstacle is present.
The alarm went off correctly 62 times.
For the sensor to be commercially produced, it must have an error rate that is lower than 40% and an F-Score that is more than or equal to 70%.
For answers that have decimal places, use four-decimal places.
1. How many times that the alarm didn't activate correctly?
2. How many runs have actual obstacles in place?
3. How often is the sensor correct?
4. How often is the sensor incorrect?
5. What is the hit rate of the sensor?
6. How often does the sensor predict a NO even if it is supposed to be a YES?
7. What is the CSI of the sensor?
8. What is the overall accuracy of the sensor?
9. What is the F-score?
10. Yes or No. Did the sensor pass the expectations?
Answers
A new sensor was developed by ABY Inc. that is to be used for their obstacle detection system. However, the sensor to be commercially produced, it must have an error rate that is lower than 40% and an F-Score that is more than or equal to 70%.
1. The alarm didn't activate correctly 63 times during the tests.
During the tests, it was observed that the alarm failed to activate in the presence of an obstacle 63 times. This means that the sensor missed detecting obstacles in those instances.
2. There were 126 runs with actual obstacles in place.
Out of the 250 runs, the alarm correctly activated 62 times and didn't activate correctly 63 times. Since the alarm failed to activate in the presence of an obstacle 63 times, we can infer that there were 126 runs with actual obstacles.
3. The sensor was correct 156 times out of 250 runs.
To calculate how often the sensor was correct, we need to sum up the number of times the alarm went off correctly (62 times) and the number of times the alarm didn't activate correctly (63 times).
This gives us a total of 125 correct activations. However, we also need to account for the 63 times when the alarm didn't activate even if an obstacle was present. So the sensor was correct 125 + 63 = 188 times out of 250 runs.
4. The sensor was incorrect 62 times out of 250 runs.
The sensor was incorrect when it failed to activate the alarm in the presence of an obstacle (63 times) and when the alarm went off even if there was no obstacle (33 times). Therefore, the sensor was incorrect 63 + 33 = 96 times out of 250 runs.
5. The hit rate of the sensor is 0.4960 or 49.60%.
The hit rate, also known as the True Positive Rate or Sensitivity, measures the proportion of actual positive cases that were correctly identified by the sensor.
It is calculated by dividing the number of correct activations (62) by the total number of runs with actual obstacles (126). Therefore, the hit rate is 62/126 = 0.4960 or 49.60%.
6. The sensor predicted a NO even when it was supposed to be a YES 33 times.
Out of the 250 runs, there were 33 instances where the alarm went off even if there was no obstacle present. This means that the sensor predicted a NO (no obstacle) incorrectly in those cases.
7. The CSI (Critical Success Index) of the sensor is 0.4032 or 40.32%.
The CSI, also known as the Threat Score or True Skill Statistic, measures the effectiveness of the sensor in detecting obstacles while avoiding false alarms.
It is calculated by dividing the number of correct activations (62) by the sum of correct activations, missed detections, and false alarms. So the CSI is 62 / (62 + 63 + 33) = 0.4032 or 40.32%.
8. The overall accuracy of the sensor is 62.80%.
The overall accuracy is calculated by dividing the number of correct activations (62) and correct non-activations (187) by the total number of runs (250). So the overall accuracy is (62 + 187) / 250 = 0.6280 or 62.80%.
9. The F-score is 0.5238 or 52.38%.
The F-score, also known as the F1-score, combines the precision and recall of the sensor's performance. It is calculated using the formula: F-score = 2 * (precision * recall) / (precision + recall).
Precision is the ratio of true positives (62) to the sum of true positives and false positives (33), while recall is the ratio of true positives to the sum of true positives and false negatives (63). Plugging in the values, we get F-score = 2 * (62)
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Related Questions
Find the volume.
7 ft
25 ft
18 ft
Answers
Answer:
3150 ft³ or 89.1981 m³ or 116.6667 yd³
Step-by-step explanation:
Determine the area between the curve y = x² + 3x - 28 and the x-axis, from x = -8 to x=0.
Answers
The area between the curve y = x² + 3x - 28 and the x-axis, from x = -8 to x=0 is 64/3 square units.
We want to calculate the integral of the absolute value of the function over the given interval:
Area = ∫[from -8 to 0] |x² + 3x - 28| dx
Since the curve lies below the x-axis between x = -7 and x = 4, we need to split the integral into two parts and change the sign of the function for the interval [-7, 4]
Area = ∫[from -8 to -7] -(x² + 3x - 28) dx + ∫[from -7 to 4] (x² + 3x - 28) dx + ∫[from 4 to 0] -(x² + 3x - 28) dx
We can now integrate each part separately:
Area = -∫[from -8 to -7] (x² + 3x - 28) dx + ∫[from -7 to 4] (x² + 3x - 28) dx - ∫[from 4 to 0] (x² + 3x - 28) dx
Simplifying, we get:
Area = [-1/3 x³ - 3/2 x² + 28x] [from -8 to -7] + [1/3 x³ + 3/2 x² - 28x] [from -7 to 4] - [-1/3 x³ - 3/2 x² + 28x] [from 4 to 0]
Area = [(-1/3(-7)³ - 3/2(-7)² + 28(-7)) - (-1/3(-8)³ - 3/2(-8)² + 28(-8))] + [(1/3(4)³ + 3/2(4)² - 28(4)) - (1/3(-7)³ - 3/2(-7)² + 28(-7))] - [(-1/3(0)³ - 3/2(0)² + 28(0)) - (-1/3(4)³ - 3/2(4)² + 28(4))]
Area = [(343/3 + 147 - 196) - (-512/3 + 96 - 224)] + [(64/3 + 24 - 112) - (-343/3 + 147 - 196)] - [0 - (-64/3 + 24 - 112)]
Area = [(343/3 + 147 - 196) - (-512/3 + 96 - 224)] + [(64/3 + 24 - 112) - (-343/3 + 147 - 196)] - (-64/3 + 24 - 112)
Area = (64/3)
Therefore, the area between the curve y = x² + 3x - 28 and the x-axis from x = -8 to x = 0 is 64/3 square units.
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The base and the height of a triangle are multiplied by 5/4. Which of the following describes the
effect of this change on the perimeter?
Answers
Answer:
The option that describe the effect of the change is;
The perimeter is multiplied by 5/4Step-by-step explanation:
The parameters from the question are;
The (scale) factor by which the base and the height of the triangle are multiplied = 5/4
By the constant proportion of their sides, the triangle before and the triangle obtained after the multiplication are similar
Let 'a' and 'b' represent the length of the base and the height of the triangle respectively, we have;
The area of the triangle, A₁ = 1/2 × a × b = a·b/2
With the application of the scale factor of 5/4, we have;
The area of the scaled triangle, A₂ = 1/2 × (5/4) × a × (5/4) × b = (5/4)² × a·b/2
Therefore, the scale factor of the area = (5/4)²
The scale factor of the perimeter = √(The scale facto of area)
∴ The scale factor of the perimeter = √(5/4)² = (5/4)
The scale factor of the perimeter = (5/4)
Therefore, the perimeter of the scaled triangle is obtained by multiplying the perimeter of the initial triangle by (5/4).
Answer:
The perimeter is multiplied by 5/4.
Step-by-step explanation:
Solve for x. Approximate the result to three decimal places.
Answers
[tex]\log_7x=\dfrac{1}{2}\\\\x=7^{1/2}\\\\x=\sqrt{7}\approx2.646[/tex]
x-y=3
work out the value of 5(x-y)
work out the value of 2x-2y
k
work out the value of y-x
Answers
If x - y = 3
Work out the value of 5(x - y)
Answer:-x - y = 3 ( Given )
[tex] \therefore [/tex] 5(x - y) = 5 × 3 = 15 [ as x - y = 3 ]
_____________________________________
Question:-If x - y = 3
Work out the value of 2x - 2y
Answer:-x - y = 3 ( Given )
[tex] \therefore [/tex] 2x - 2y = 2(x - y) = 2 × 3 = 6 [ as x - y = 3 ]
_____________________________________
Question:-If x - y = 3
Work out the value of y - x
Answer:-x - y = 3 ( Given )
[tex] \therefore [/tex] y - x = -3 [ as x - y = 3 ]
_____________________________________
Answer:
1
Step-by-step explanation:
PLEASE HELPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
(a) 6688 divided by 88 = 76
(b) 312 - 73 = 239
What is the volume of this sphere?
Use ≈ 3.14 and round your answer to the nearest hundredth.
8 yd
cubic yards
Answers
Step-by-step explanation:
First step
Formula: Number of Cubic Yards = Length, Width, and Depth divided by 27.
Second step
Simply multiply the three dimensions together to find the number of cubic feet, then divide by 27 to find the number of cubic meters.
Suppose you have a standard deck of 52 cards. What is the probability that if you select a card at random that it does not have a face value of 9?
Answers
The probability that a randomly selected card does not have a face value of 9 is approximately 0.9231 or 92.31%.
In a standard deck of 52 cards, there are 4 cards of each face value (Ace through 10) for each of the four suits (hearts, diamonds, clubs, and spades). Since the face value of 9 is one of the possible values, there are 4 cards with a face value of 9.
To find the probability that a randomly selected card does not have a face value of 9, we need to determine the number of cards that do not have this particular value. There are 52 cards in total, and we subtract the 4 cards with a face value of 9:
52 - 4 = 48
So, there are 48 cards that do not have a face value of 9. Therefore, the probability of selecting a card without a face value of 9 is:
P(not 9) = number of favorable outcomes / total number of outcomes
= 48 / 52
= 12 / 13
≈ 0.9231
The probability that a randomly selected card does not have a face value of 9 is approximately 0.9231 or 92.31%.
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Solve this please!!!!!
Answers
328 hope this helps
Pls mark brainliest!Ricky wants a carrier so that he can take his pet to the veterinarian. He chooses one in the shape of a right rectangular prism that is 4 feet deep, 3 feet tall, and 2 feet wide. What is the surface area of the carrier?
A. 26ft^2
B. 36ft^2
C. 40ft^2
D.52ft^2
Answers
Answer:
its c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
great job mate
Can someone help me with this question. Need answer and explanation/work. Thank you. Will make brainliest.
Answers
Answer:
y = - 3 x - 5
Step-by-step explanation:
find the negative reciprocal of the slope of the original line use the point slope formula y - y 1 = m ( x - x 1 ) to find the line perpendicular to 3 y = x + 6
hope this helps
Which ordered pair will be solution for the function y = 12 - x?
(4, 9)
(6, 6)
(2, 14)
(7, 4)
( if u steal my points ill steal yours)
(no links or ill report u and get u band , I am not bluffing)
(also ill give 100 brianlist after if its right)
Answers
Answer:
(6, 6)
Step-by-step explanation:
ordered pair (6, 6) will be solution for the function y = 12 - x.
When x = 6
y = 12 - 6
y = 6
(x, y) = (6, 6)
Answer:
6,6
Step-by-step explanation:
Creating a discrete probability distribution: A venture capitalist, willing to invest $1,000,000, has three investments to choose from.
The first investment, a social media company, has a 20% chance of returning $7,000,000 profit, a 30% chance of returning no profit, and a 50% chance of losing the million dollars.
The second company, an advertising firm has a 10% chance of returning $3,000,000 profit, a 60% chance of returning a $2,000,000 profit, and a 30% chance of losing the million dollars.
The third company, a chemical company has a 40% chance of returning $3,000,000 profit, a 50% chance of no profit, and a 10% chance of losing the million dollars.
a. Construct a Probability Distribution for each investment. This should be 3 separate tables (See the instructors video for how this is done) In your table the X column is the net amount of profit/loss for the venture capitalist and the P(X) column uses the decimal form of the likelihoods given above.
b. Find the expected value for each investment.
c. Which investment has the highest expected return?
d. Which is the safest investment and why?
e. Which is the riskiest investment and why?
Answers
a) the venture capitalist has three investment options: a social media company, an advertising firm, and a chemical company.
b) The advertising firm has the highest expected return, making it the most profitable choice.
c) The investment with the highest expected return is Investment 2 (the advertising firm) with an expected value of $1,200,000.
d) The safest investment is Investment 3 (the chemical company) because it has the highest probability (50%) of not incurring any loss (no profit, but no loss either).
e) The riskiest investment is Investment 1 (the social media company) because it has a 50% chance of losing the entire $1,000,000 investment, which is the highest probability of loss among the three investments.
a. Probability Distribution for each investment:
Investment 1 (Social Media Company):
X (Profit/Loss) P(X)
$7,000,000 0.20
$0 0.30
-$1,000,000 0.50
Investment 2 (Advertising Firm):
X (Profit/Loss) P(X)
$3,000,000 0.10
$2,000,000 0.60
-$1,000,000 0.30
Investment 3 (Chemical Company):
X (Profit/Loss) P(X)
$3,000,000 0.40
$0 0.50
-$1,000,000 0.10
b. Expected value for each investment:
Expected value (Investment 1):
E(X) = ($7,000,000 × 0.20) + ($0 × 0.30) + (-$1,000,000 × 0.50)
= $1,400,000 + $0 - $500,000
= $900,000
Expected value (Investment 2):
E(X) = ($3,000,000 × 0.10) + ($2,000,000 × 0.60) + (-$1,000,000 × 0.30)
= $300,000 + $1,200,000 - $300,000
= $1,200,000
Expected value (Investment 3):
E(X) = ($3,000,000 × 0.40) + ($0 × 0.50) + (-$1,000,000 × 0.10)
= $1,200,000 + $0 - $100,000
= $1,100,000
c. Investment with the highest expected return:
The investment with the highest expected return is Investment 2 (the advertising firm) with an expected value of $1,200,000.
d. Safest investment:
The safest investment is Investment 3 (the chemical company) because it has the highest probability (50%) of not incurring any loss (no profit, but no loss either).
e. Riskiest investment:
The riskiest investment is Investment 1 (the social media company) because it has a 50% chance of losing the entire $1,000,000 investment, which is the highest probability of loss among the three investments.
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3 7 of the total computer files were infected by a virus. A engineer later managed to restore 2 15 of the infected files. What fraction of the total files were restored?
Answers
Answer:
2/35
Step-by-step explanation:
[tex]\frac{3}{7}[/tex] × [tex]\frac{2}{15}[/tex]
[tex]\frac{1}{7}[/tex] x [tex]\frac{2}{5}[/tex]
= 2/35
The null hypothesis is that the laptop produced by HP can run on an average 120 minutes without recharge and the standard deviation is 25 minutes. In a sample of 50 laptops, the sample mean is 125 minutes. Test this hypothesis with the alternative hypothesis that average time is not equal to 120 minutes. What is the p-value?
Answers
The p-value for testing the hypothesis that the average runtime of HP laptops is not equal to 120 minutes, based on a sample mean of 125 minutes from a sample of 50 laptops, cannot be determined without additional information.
To calculate the p-value, we need the population standard deviation or the t-value associated with the sample mean and the degrees of freedom. The p-value represents the probability of observing a sample mean as extreme or more extreme than the observed sample mean, assuming the null hypothesis is true.
However, since the population standard deviation is not provided in the question, we cannot directly calculate the p-value. Similarly, the degrees of freedom for the t-distribution depend on the sample size and are not given.
To determine the p-value, we would need either the population standard deviation or the t-value associated with the sample mean and the degrees of freedom. With this information, we could look up the p-value from the t-distribution table or use statistical software to obtain the p-value.
Therefore, without the necessary information, the p-value for the hypothesis test cannot be determined.
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I WILL GIVE 10 POINTS AND BRAINLIEST WHO EVER ANSWERS FIRST The space capsule is moving up at a speed of 80 miles per hour a few seconds after launch. What is the space capsule's velocity per hour
Answers
.................
The Willis Tower In Chicago is 1,451 FEET tall. The Transamerica Pyramid is San Francisco is 10,236 INCHES tall. How do these two compare?
Answers
Answer:
Willis Towers is 1.7 times bigger than the Transamerica pyramid
Step-by-step explanation:
The Willis Tower In Chicago is 1,451 FEET tall. The Transamerica Pyramid is San Francisco is 10,236 INCHES tall. How do these two compare?
Note that
1 foot = 12 inches
We convert the height of willis tower to inches
1 foot = 12 inches.
1,451 feet = x inches
Cross Multiply
x = 1451 × 12 inches
x = 17412 inches
Comparing the two buildings
Willis Tower : Transamerica pyramid
1,7412 inches : 10,236 Inches
= 1.7010550996 : 1
Therefore,
Willis Towers is 1.7 times bigger than the Transamerica pyramid
Which expression has a solution of 6, if r = 4?
1. r + 2
2. 4 - r
3. 10 + r
4. r - 10
Answers
Answer:
1.
Step-by-step explanation:
1. 4 + 2 = 6
2. 4 - 4 = 0
3. 10 + 4 = 14
4. 4 - 10 = -6
number 1 is the right answer
Answer:
1.
Step-by-step explanation:
Using your calculator, construct a normal probability plot for the octane data from problem 1, and make a sketch of that plot below. From the plot you sketched, does it seem reasonable to assume that octane rating is normally distributed?
Answers
Based on the normal probability plot constructed for the octane data, it does not appear reasonable to assume that the octane rating is normally distributed. The plot deviates significantly from a straight line, indicating a departure from normality.
A normal probability plot is a graphical tool used to assess whether a dataset follows a normal distribution. In a normal plot, the observed data points are plotted against the corresponding quantiles of a theoretical normal distribution. If the data points fall approximately along a straight line, it suggests that the data can be reasonably modeled as normally distributed.
In this case, when constructing the normal probability plot for the octane data, if the plot deviates significantly from a straight line, it indicates a departure from normality. If the points on the plot show a distinct curvature or exhibit systematic patterns, it suggests that the data does not follow a normal distribution.
By examining the sketch of the normal probability plot for the octane data, if it shows substantial deviations from a straight line, with points deviating from the expected pattern, it implies that the octane rating is not normally distributed. This departure from normality could be due to various factors, such as skewness, outliers, or a different underlying distribution that better fits the data. Therefore, based on the sketch of the plot, it is reasonable to conclude that the octane rating is not normally distributed.
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[tex]8 \times \frac{3}{4} [/tex]
Answers
Answer:
6
Step by step explanation:
8 × ¾ = ²⁴⁄₄ = 6
Answer:
6
Step-by-step explanation:
You can solve this equation in multiple ways:
1) Change [tex]\frac{3}{4}[/tex] into a decimal
[tex]\frac{3}{4} = .75[/tex][tex]8[/tex] × [tex].75 = 6[/tex]2) Change [tex]8[/tex] into a fraction, and multiply that way.
[tex]8 = \frac{8}{1}[/tex][tex]\frac{8}{1}[/tex] × [tex]\frac{3}{4} = \frac{24}{4}[/tex][tex]\frac{24}{4} = 6[/tex]An airplane is preparing to land at an airport. It is 42,000 feet above the ground and is descending at the rate of 3,300 feet per minute. At the same airport, another airplane is taking off and will ascend at the rate of 2,700 feet per minute. When will the two airplanes be at the same altitude and what will that altitude be?
Answers
Answer:
7 minutes
Step-by-step explanation:
From the question :
Descent = ascent
Initial height * descent rate = initial position * ascent rate
Plane on ground is at an initial position or height of 0
42000 - 3300t = 0 + 2700t
Where, t = time
-3300t - 2700t = 0 - 42000
-6000t = - 42000
t = 42000 / 6000
t = 7 minutes
Which term of the AP 21, 18, 15, ... is 0?
Answers
Answer:
Solution : Let Tn=0. Then,21+(n-1)×(-3)=0⇒n=8. So, 8th term is zero.
Step-by-step explanation:
Yeah, I need help again. IM NOT GOOD AT MATH
Answers
Answer:
21
Step-by-step explanation:
7 * 3 =21
Write an expression for the phrase. Jessica is eight inches less than twice Parkers height. Use P to represent parker.
Answers
Answer:
P = Parker
According to the question,
Equation for Jessica's height = 8 - 2P
PLEASE HELP!!!!!! I WILL MARK!!!
Answers
can you help me solve this?
6 ÷ 2(1+2) = ?
Answers
Answer:
9
Step-by-step explanation:
it just is
For a random sample of 60 overweight men, the mean of the number of pounds that they were overweight was 32. The standard deviation of the population is 3.9 pounds.The best point estimate of the mean is pounds.
Answers
The most accurate estimate of the population mean is 32 pounds, based on the sample data.
The best point estimate of the mean can be obtained by using the sample mean as an estimate for the population mean.
Given that the sample mean of the number of pounds that the 60 overweight men were overweight is 32, the best point estimate of the mean is also 32 pounds.
Therefore, the best point estimate of the mean is 32 pounds.
Mean: The term "mean" refers to a measure of central tendency. It is often referred to as the average of a set of numbers. The mean is calculated by adding up all the values in the set and dividing the sum by the total number of values.
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PLEASE HURRY ILL GIVE BRAINLIEST Emma is going to invest in an account paying an interest rate of 3.7% compounded continuously. How much would Emma need to invest, to the nearest dollar, for the value of the account to reach $1,130 in 18 years?
Answers
Answer:
581
Step-by-step explanation:
Kristy dad makes 3 times as much per hour as she does. If he makes $48 per hour, how much per hour, how much per hour does kristy make
Answers
Answer:
Kristy makes 16 per hour.
Step-by-step explanation: Divded 48 by 3.
Evaluate ∫ (3z + 1) / (z^2 + 2) dz, where C is the contant.
Answers
The value of the integral ∫(3z + 1) / (z^2 + 2) dz, where C is the constant is ln|z^2 + 2| + 3/√2 arctan(z/√2) + C.
To evaluate the given integral, we first need to break it down using partial fraction decomposition. Therefore, we have:
(3z + 1) / (z^2 + 2) = (Az + B) / (z^2 + 2)
Multiplying both sides by (z^2 + 2), we get:
3z + 1 = (Az + B)
We now need to find the values of A and B. Setting z = 0, we get:
1 = B
Setting z = 1, we get:
3 + 1 = A + B
A = 2
Therefore, the integral becomes:
∫ (2z + 1) / (z^2 + 2) dz
We can now integrate using substitution, with u = z^2 + 2 and du/dz = 2z. This gives us:
∫ (2z + 1) / (z^2 + 2) dz = ∫ (1/u) du
= ln|u| + C
= ln|z^2 + 2| + C
Using trigonometric substitution, we can also evaluate the integral in terms of arctan:
Let z = √2 tanθ, dz = √2 sec^2θ dθ. Then the integral becomes:
∫ (3z + 1) / (z^2 + 2) dz = ∫ (3√2 tanθ + 1) / (2tan^2θ + 3) √2 sec^2θ dθ
= 3/√2 ∫ (tanθ) / (tan^2θ + (3/2)) d(tanθ) + 1/√2 ∫ (1) / (tan^2θ + (3/2)) dθ
= 3/√2 ln|tan^2θ + (3/2)| + 3/√2 arctan(tanθ/√2) + C
= 3/√2 ln|z^2 + 2| + 3/√2 arctan(z/√2) + C
Thus, we get the same result as before.
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