Find and explain the error in the student’s work below.
Solve 2x² - 5x -12 = 0 using the Quadratic Formula.
Answers
The error made by the student is in simplifying the expression inside the square root.
What is the quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The student made an error in simplifying the expression inside the square root.
The expression should be simplified as follows:
25 + 4(2)(-12) = 25 - 96 = -71
So the correct expression inside the square root is -71, not 121.
Therefore, the correct solution using the Quadratic Formula is:
x = (-(-5) ± √((-5)² - 4(2)(-12)))/(2(2))
x = (5 ± √(25 + 96))/4
x = (5 ± √121)/4
x = (5 ± 11)/4
Hence, the solutions are x = -3 and x = 4/2, which simplifies to x = 2.
Therefore, the error made by the student is in simplifying the expression inside the square root.
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Related Questions
X=4 ?
X=28 ?
How to solve?
Answers
The value of x in the given linear equation of 4x = 28 is determined as 7.
What is the value of x in the linear equation?
To find the value of x in the linear equation 4x = 28, we need to isolate x on one side of the equation.
We can do this by dividing both sides of the equation by 4:
4x/4 = 28/4
Simplifying:
x = 7
Thus, identify the equation and the variable: In this case, the equation is 4x = 28, and the variable we want to solve for is x. Also simplify the linear equation by dividing both sides by 4, we get x = 7, which is the solution.
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The complete question is below:
4x = 28
find the value of x
Find the length of the hypotenuse
on a right triangle with legs of 12
inches and 10 inches.
Answers
Answer:
[tex]2 \sqrt{61} \: in[/tex]
Step-by-step explanation:
Use the Pythagorean theorem (assume, that the length of hypotenuse is x):
[tex] {x}^{2} = {10}^{2} + {12}^{2} = 100 + 144 = 244[/tex]
[tex]x > 0[/tex]
[tex]x = \sqrt{244} = 2 \sqrt{61} [/tex]
Are there two equations below parallel
y = 1/3x +4 and y=-3x - 10
YES
NO
Answers
I don't know but i can help a little
Step-by-step explanation:
But If the slops are the same and the y-intercepts are different, the lines are parallel...
Please help I’ve been stuck on this for daysss
Answers
Therefore , the solution of the given problem of graphs comes out to be a = [P² * G * Ms / [tex](4\pi ^2* Mp)]^(1/3)[/tex]
Explain graph.Graphs are used by theoretical coordinate points physicists to analytically and graphically present assertions rather than values. Typically, a graph point shows the relationship between several distinct objects. A graph is a particular kind of pas de container construction composed of groups and lines. The borders, also known as the channels, should be joined with glue.
Here,
According to Kepler's third law, one can determine the connection between a planet's orbital period and its separation from a star by:
=> P² = (4π² / GM) * a³
where P denotes the orbit's duration in years, a denotes the semi-major axis in astronomical units (AU), G denotes gravity's constant, and M denotes the star's mass in solar masses.
If we rewrite this equation, we obtain:
=> a = [P² * G * Ms / [tex](4\pi ^2* Mp)]^(1/3)[/tex]
We can rewrite this equation as follows since our goal is to estimate the distance from the sun in AU based on the mass of the planet in relation to the sun:
=> a = [P² * G * Ms / [tex](4\pi ^2* Mp)]^(1/3)[/tex]
where Mp is the mass of the planet in relation to the sun and Ms is the mass of the sun.
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if we take a simple random sample from a normal distribution, the probability that the sample mean is equal to the population mean is 1 (i.e., 100%). radio button unchecked false radio button unchecked true submit
Answers
The given statement "if we take a simple random sample from a normal distribution, the probability that the sample mean is equal to the population mean is 1 (i.e., 100%)" is false.
The probability that a sample mean is equal to the population mean is actually zero, since any given sample will differ slightly from the population mean due to sampling error. However, as the sample size increases, the sample mean is likely to be close to the population mean, and the probability of it being equal approaches 1 (i.e., 100%).
To explain further, the population mean is the mean of the entire population and is calculated by adding up all the values of the population and dividing them by the total number of individuals in the population. A sample mean, on the other hand, is the mean of a sample taken from the population and can be calculated by adding up the values of the sample and dividing them by the total number of individuals in the sample. Since the sample size is usually smaller than the population size, the sample mean is likely to be slightly different from the population mean due to sampling error.
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Newton's 2nd law says that when a larger force is applied to an object of mass m, the object will experience a larger acceleration. At the same time, you've learned that all objects experience the same acceleration in a free fall, even if their weights (the forces of gravity acting on them) are different. That sounds like a contradiction: on one hand, from the Newton's 2nd law, a larger force means larger acceleration, on the other hand when applied to motion under gravity - a larger weight (force) means the same acceleration for all objects. How do you reconcile these statements? Why isn't it a contradiction? Does gravity violate the Newton's second law or is there another explanation. Be as thorough and clear in your explanation as possible.
Answers
It is important to understand that the force of gravity acting on an object does not violate Newton's second law. It is an external force that acts on an object and produces an acceleration in it. Therefore, the acceleration due to gravity does not violate Newton's second law.
According to the Newton's second law, a force acting on a body of mass m produces an acceleration a in the body which is directly proportional to the force and inversely proportional to the mass. For instance, If a body of mass m is acted upon by a force F, then the acceleration produced in the body is given by F/m.As per the law, a larger force will produce a larger acceleration in the object.
When a body falls under gravity, it is said to experience weight. The weight of an object is the force of gravity acting on the object. According to Newton's law of gravitation, every object attracts every other object with a force proportional to their masses and inversely proportional to the square of their distance. In general, the weight of an object can be given by the formula weight = mass x acceleration due to gravity.
Therefore, as the acceleration due to gravity is the same for all objects, the weight of an object is proportional to its mass. It implies that a heavier object has more weight, while a lighter object has less weight.As per the above facts, a heavier object would require a larger force to move it than a lighter object. However, when they fall under gravity, both objects fall at the same rate. It appears as a contradiction, but the reason for it is the difference between weight and mass.
The mass of an object is a measure of the amount of matter in it, while the weight of an object is the force exerted on it by gravity.The acceleration produced in an object by an external force is not the same as the acceleration due to gravity. A force F produces an acceleration F/m, whereas the acceleration due to gravity is the same for all objects.
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factor x^2=14x-18=-8x-2
Answers
Answer:
=(x+9)(x+5)
Step-by-step explanation:
Selling price=7950and gain =6% what is the cost price
Answers
The seller purchased the product at a cost of 7500 and sold it for 7950, which resulted in a gain of 6%. So, the cost price is 7500.
In business, it is essential to keep track of cost prices and profit margins to ensure profitability. If the selling price is 7950 and the gain is 6%, we can use the following formula to calculate the cost price:
Cost price = Selling price / (1 + Gain%)
Substituting the given values, we get:
Cost price = 7950 / (1 + 0.06)
Cost price = 7500
Therefore, the cost price of the product is 7500, the gain percentage is calculated based on the cost price and not the selling price.
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Given the data below, which of the following statements correctly describes the relation of the point,(2,2),to the line of best fit?
Answers
The point (2,2) may be considered an anomaly and should be investigated further to determine if it is a valid data point or if it should be excluded from the analysis.
The relation of the point (2,2) to the line of best fit can be determined by analyzing the residual value of this point. The residual value is the difference between the actual y-value and the predicted y-value based on the line of best fit. If the residual value is close to zero, then the point lies on the line of best fit. If the residual value is positive, then the actual y-value is higher than the predicted y-value, and if the residual value is negative, then the actual y-value is lower than the predicted y-value.
Unfortunately, the data necessary to determine the residual value of the point (2,2) is not provided in the question. Therefore, it is impossible to determine the exact relation of this point to the line of best fit.
However, we can make some generalizations based on the location of the point relative to the trend of the data.
If the point (2,2) lies close to the line of best fit, with a residual value close to zero, then it can be said that the point follows the trend of the data and is a typical data point. However, if the point lies far away from the line of best fit, with a large positive or negative residual value, then it can be said that the point is an outlier and does not follow the trend of the data.
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Simplify the following: 2(√12 + 2√3)
Answers
Answer:
[tex]2 \sqrt{2(6 + \sqrt{3} )} [/tex]
Step-by-step explanation:
There's your answer.
BRAINLIEST! HURRY! What is the volume of the prism?
Enter your answer, as a mixed number in simplest form, in the box.
_ cm³
Answers
Answer:
331/2
Step-by-step explanation:
5 1/2= 11/2
3 1/2 = 7/2
11/2x7/2x6=115 1/2 = 331/2
Answer:
115.5 cm^3
Step-by-step explanation:
Volume=LengthxWidthxHeight
The values from the diagram are 3.5, 6, and 5.5
Multiply!
3.5x6x5.5=115.5
(1) if the number of bacteria in a culture is 5 million at the end of 6 hours and 8 million at the end of 9 hours, how many were present initially?
Answers
There were initially 4 million bacteria in the culture.
To determine the initial number of bacteria in the culture, we can follow these steps:
Step 1: Identify the given data.
At the end of 6 hours, there are 5 million bacteria.
At the end of 9 hours, there are 8 million bacteria.
Step 2: Find the rate of bacterial growth.
Since the number of bacteria increased by 3 million (8 million - 5 million) over 3 hours (9 hours - 6 hours), the rate of bacterial growth is 1 million per hour (3 million ÷ 3 hours).
Step 3: Calculate the initial number of bacteria.
The number of bacteria increased by 5 million over the 6 hours. Therefore, if we divide this number by the rate of growth, we can determine the initial number of bacteria. Divide 5 million by 1 million per hour, which results in 5 hours.
Step 4: Subtract the time from the initial time.
Since we know that the culture was growing for 5 hours before reaching 5 million, we can subtract 5 hours from 6 hours, which equals 1 hour.
Step 5: Calculate the initial number of bacteria at 1 hour.
Since the bacteria grow at a rate of 1 million per hour, at the end of the 1st hour, there would be 1 million bacteria. Subtracting this number from the 5 million at the end of 6 hours will give us the initial number of bacteria: 5 million - 1 million = 4 million bacteria.
So, there were initially 4 million bacteria in the culture.
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emme takes a quiz for her anthropology 401e course. there are 9 multiple-choice questions on the test with 4 answer choices, only one of which is correct. emme has not studied for the test, so she just randomly guesses the answers. what is the probability that emme answers exactly 3 questions correctly? enter your answer as a decimal with four significant digits
Answers
The probability that Emme answers exactly 3 questions correctly is 0.1961.
Since each question has four answer choices and only one is correct, the probability of Emme randomly guessing the correct answer for each question is 1/4 = 0.25. Emme needs to answer exactly 3 out of the 9 questions correctly, so we use the binomial distribution with n = 9 and p = 0.25 to calculate the probability:
P(X = 3) = (9 choose 3) * (0.25)^3 * (0.75)^6
Using a calculator, we get:
P(X = 3) = 0.1961
Therefore, the probability that Emme answers exactly 3 questions correctly is 0.1961.
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Help please, I will give brainiest
Type the correct answer in each box. Round your answers to the nearest hundredth.
City Cat Dog
Lhasa Apso Mastiff Chihuahua Collie
Austin 24. 50% 2. 76% 2. 86% 3. 44% 2. 65%
Baltimore 19. 90% 3. 37% 3. 22% 3. 31% 2. 85%
Charlotte 33. 70% 3. 25% 3. 17% 2. 89% 3. 33%
St. Louis 43. 80% 2. 65% 2. 46% 3. 67% 2. 91%
Salt Lake City 28. 90% 2. 85% 2. 78% 2. 96% 2. 46%
Orlando 37. 60% 3. 33% 3. 41% 3. 45% 2. 78%
Total 22. 90% 2. 91% 2. 68% 3. 09% 2. 58%
The table gives the probabilities that orphaned pets in animal shelters in six cities are one of the types listed.
The probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is ______%. The probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is ______%
Answers
The probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is 11.71%. The probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is 29.37%.
The probability that a haphazardly chosen vagrant pet in a creature covered in Austin is a canine is 11.71%.
The probability that a haphazardly chosen stranded canine in a similar creature cover in Austin is a Chihuahua is 29.37% .
2.76% + 2.86% + 3.44% + 2.65% = 11.71%
11.71/3.44 = .2937
.2937 = 29.37%
Probability is just the way that logical something is to occur.
Whenever we're uncertain about the result of an occasion, we can discuss the probabilities of specific results — how likely they are. The investigation of occasions represented by probability is called statistics.
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A rocket is launched from the top of a 90 foot cliff with an initial velocity of 160 feet per second. The height, h, of the rocket after t seconds is given by the equation h=-16t^2+160t+90. How long after the rocket is launched will it be 30 feet from the ground?
Answers
The rocket will be 30 feet from the ground approximately 0.4 seconds or 9.6 seconds after it is launched.
To solve this problem, we need to find the value of t for which the height of the rocket is 30 feet. We can use the given equation to set up an equation for this as follows:
-16t² + 160t + 90 = 30
Simplifying and rearranging, we get:
-16t² + 160t + 60 = 0
Dividing by -4, we get:
4t² - 40t - 15 = 0
Using the quadratic formula, we get:
t = [40 ± √(40² - 4(4)(-15))] / (2×4)
t = [40 ± √(1840)] / 8
t = [40 ± 2×√(460)] / 8
t = 5 ± (1/2)×√(460)
Therefore, the rocket will be 30 feet from the ground at t = 5 - (1/2)×√(460) seconds or t = 5 + (1/2)×√(460) seconds. These are the two possible solutions to the equation. We can simplify them as follows:
t = 0.4 seconds or t = 9.6 seconds
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54 is what percent of 90? Question 9 options: 60% 65% 55% 52%
Answers
Answer:
The answer to your problem is, A. 60%
Step-by-step explanation:
54 of 90 can be written as: [tex]\frac{54}{90}[/tex]
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
[tex]\frac{54}{90} * \frac{100}{100}[/tex]
= [tex]\frac{( 54 * 100)}{90} * \frac{1}{100} = \frac{60}{100}[/tex]
Thus the answer to your problem is, A. 60%
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Answer:
x = 60%
Step-by-step explanation:
Let the unknown percentage be x.
We can make an expression using the given information.
[tex]\sf90*\frac{x}{100} =54[/tex]
Solve for x to find the percentage.
[tex]\sf\frac{90x}{100} =54\\90x=54*100\\\\90x=5400\\\\\frac{90x}{90}=\frac{5400}{90}\\\\ x=60[/tex]
Find the are 22ft 37ft 38. 09ft 109degrees 138degrees
Answers
Answer:
B.
Step-by-step explanation:
I just took the test
pls help me with both of them
Answers
The year that saw 164 billion dollars being spent on advertising, given the function for the advertising would be c. 1994
The dimensions of the rectangle, given the area of the rectangle would be:
Length : 12. 8 meters Width : 6.9 meters How to find the year ?The function is given by y = 0.93x² + 2.2x + 130, where y is the amount of money spent (in billions of dollars) and x is the number of years since 1990. We need to find the value of x when y = 164.
164 = 0.93x² + 2.2x + 130
0.93x² + 2.2x + 130 - 164 = 0
0.93x² + 2.2x - 34 = 0
x = 2.5
Now, we'll find the year by adding the value of x to 1990:
Year = 1990 + 2.5 = 1992.5
= 1994 which is the closest year in options
How to find the dimensions of the rectangle ?The area of the rectangle is given by:
Area = width × length
91 = (x + 2)(2x + 3)
91 = 2x² + 3x + 4x + 6
91 = 2x² + 7x + 6
2x² + 7x - 85 = 0
When solved differently:
x = 4.9
x = -3.5
Using the positive values:
Width = x + 2 ≈ 4.9 + 2 = 6.9 meters
Length = 2x + 3 ≈ 2(4.9) + 3 ≈ 9.8 + 3 = 12.8 meters
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PLS HELP (SORRY I KEEP ASKING QUESTIONS I HATE MATH SO I DONT RLLY PAY ATTENTION THAT WELL)
Answers
The graph shows that the rise is 3 and the run is 3, and the hypotenuse is the length between the two points.
let hypotenuse = x
using Pythagorean theorem:
x^2= 3^2 + 3^2
x^2 = 9 + 9
x= sqrt 18
x = 4.2426....
rounding to the nearest 10th:
x = 4.2
Solve the equation by completing the square.
x^2−12x+35=0
After completing the square, the equation is _____, and the solution is x=5,x=7
Answers
Answer:
x:5,x:7
x^2-12x+35
x^2-12x=-35
x^2-12x+6^2=-35+36
(x+6)^2=1
insert a radical anywhere
x+6=1
x=1-6
x=-5. x=5
x=-1-6
x=-7. x=7
Ian went to dinner last night and remembers leaving a 6.50 tip. The tip was 20% of the cost of dinner. What was the cost of dinner before tip?
Answers
Answer:
$32.50
Step-by-step explanation:
20% * y = 6.5 =>
y =6.5 ÷ 20% =
6.5 ÷ (20 ÷ 100) =
(100 × 6.5) ÷ 20 =
650 ÷ 20 =
32.5
Percentage of 20% of what number = 6.5?
20% × ? = 6.5
20% of 32.5 = 6.5
9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, 9 1/2 make a line plot that displays the lengths of the books on the bottom shelf
Answers
The line-plot of the the given data 9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, 9 1/2 that displays the lengths of the books on the booom shelf is attached.
What is line plot?
A line plot is a type of graph that represents the kind of data representation. It is line plot or a line chart shows the data in a visual form or visual representation. The graph is plotted with help of straight lines and points or dots. The x-axis is represented by straight lines or the it is labelled about the data. The y-axis is represented by the dots or frequency of the data. It is generally used to represent the small data set. This graph uses symbols to show or represent the frequency of the observations.
The data represented here is 9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, 9 1/2
we can make the frequency table using the above values, after which it can be plotted on the line-plot graph.
1-9 1/4--1 dot
2-9 1/2--1 dot
3-9 1/2--1 dot
4-10 1/4-2 dots
5-10 1/2--1 dot
6-11--1 dot
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Attached is a line-plot of the given data showing the lengths of the books on the book shelf: 9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, and 9 1/2.
What is line plot?An example of a graph that shows this sort of data representation is a line plot. The data is presented visually in the form of a line plot or a line chart. With the aid of straight lines, points, or dots, the graph is drawn. Straight lines or labels that describe the data are used to depict the x-axis. The dots or frequency of the data are used to depict the y-axis. It often serves as a representation for a tiny group of data. The frequency of the observations is shown or represented by symbols on this graph.
9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, and 9 1/2 are the numbers shown.
Using the aforementioned variables, we can create the frequency table, which can then be plotted on the line-plot graph.
1-9 1/4--1 dot
2-9 1/2--1 dot
3-9 1/2--1 dot
4-10 1/4-2 dots
5-10 1/2--1 dot
6-11--1 dot
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the clock on the wall at the aops office has an hour hand that's 4 cm long and a minute hand that's 8 cm long. at exactly 2:00, at what rate, in centimeters per minute, is the distance between the tips of the two hands changing?
Answers
At exactly 2:00, the distance between the tips of the two hands is changing at the rate of 4 cm/min.Therefore, at exactly 2:00, the distance between the tips of the two hands is changing at the rate of [tex]2\sqrt{13}[/tex] cm/min.
What is meant by "at exactly 2:00"?The phrase "at exactly 2:00" means that at 2:00:00, the hour hand and the minute hand overlap. Both hands are together pointing upwards in the vertical direction. At this moment, the angle between the minute hand and the hour hand is 0 degrees.How do we determine the rate of change of the distance between the tips of the two hands?We start by calculating the angle between the two hands. The angle is given by:
θ(t) = 30h - 11/2m
where h is the number of hours past midnight and m is the number of minutes past the most recent hour. At exactly 2:00, h = 2 and m = 0. Thus:
θ(t) = 30(2) - 11/2(0) = 60 degrees
Next, we use the formula for the distance between two points (the tips of the two hands). Let the hour hand be at the point (0,0) and let the minute hand be at the point (x,y).
The distance between the two points is given by:
[tex]d(t) = \sqrt{(x^2 + y^2)}[/tex]
To find x and y, we use the formulas:
x(t) = r cos θ(t)y(t) = r sin θ(t)
where r is the length of each hand. At exactly 2:00:
[tex]r = 4 cmx(t) = 4 cos 60 = 2 my(t) = 4 sin 60 = 2\sqrt{(3) m}[/tex]
Therefore: [tex]d(t) = \sqrt{(x^2 + y^2)} = \sqrt{(2 m)^2 + (2sqrt(3) m)^2)} = 2\sqrt{(13) m}[/tex]
Finally, we differentiate with respect to time t to find the rate of change of [tex]d(t):d'(t) = 2\sqrt{13}[/tex] cm/min
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6,7,7,8,9,10,10,10,10,13,13,14,14,15,15 box and whisker plot
Answers
The box and whisker plot can be created by :
Minimum value - 6
Maximum Value - 15
Median - 10
Quartiles - Q1 - 7.5, Q2 - 10, Q3 - 13.5
To create a box and whisker plot for the given data set {6,7,7,8,9,10,10,10,10,13,13,14,14,15,15}, we need to first find the minimum value, maximum value, median, and quartiles.
Minimum value: 6
Maximum value: 15
Median: To find the median, we need to first arrange the data set in ascending order:
6,7,7,8,9,10,10,10,10,13,13,14,14,15,15
The median is the middle value in the data set, which is 10.
Quartiles: To find the quartiles, we need to divide the data set into four equal parts.
First quartile (Q1): The first quartile is the median of the lower half of the data set. In our case, the lower half of the data set is:
6,7,7,8,9,10
The median of this set is (7+8)/2 = 7.5.
Second quartile (Q2): The second quartile is the median of the entire data set, which we already found to be 10.
Third quartile (Q3): The third quartile is the median of the upper half of the data set. In our case, the upper half of the data set is:
10,10,10,10,13,13,14,14,15,15
The median of this set is (13+14)/2 = 13.5.
Now, we can use the above information to create the box and whisker plot.
The horizontal line inside the box represents the median (10). The bottom of the box represents the first quartile (7.5), and the top of the box represents the third quartile (13.5). The whiskers extend from the box to the minimum value (6) and maximum value (15).
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How long is each side of the box if the volume is 1,000,000?
Answers
Step-by-step explanation:
[tex]volume = {x}^{3 \\} \\ so \: 1000000 = {x}^{3 \\} \\ x = \sqrt[3]{1000000} \\ x = 100[/tex]
Help please Hurry
Brenda throws a dart at this square shaped target: Part A: Is the probability of hitting the black circle inside the target closer to 0 or 1? Explain your answer and show your work. (5 points)
Part B: Is the probability of hitting the white portion of the target closer to 0 or 1? Explain your answer and show your work. (5 points)
Answers
The probability of hitting the black circle is closer to 0 and the probability of hitting the white portion of the target is closer to 1.
What is probability?
Probability refers to the numerical measure of the likelihood or possibility of a specific event taking place. It is a mathematical concept that involves calculating the ratio of the number of desired outcomes to the total number of possible outcomes. Probability ranges from 0 (representing an impossible event) to 1 (representing a certain event), with values in between indicating the degree of likelihood. Probability is widely used in various fields, including mathematics, statistics, science, engineering, finance, and social sciences, to make predictions, analyze data, and make decisions under uncertainty.
Explanation of the given questions :
Part A: The black circle has a radius of 1 unit and its center is the same as that of the square. Therefore, its diameter is 2 units, which is much smaller than the side length of the square, which is 11 units. This means that the area of the circle is much smaller than the area of the square.
Therefore, the probability of hitting the black circle is closer to 0.
Part B: The white portion of the target is the area of the square minus the area of the black circle. The area of the square is [tex]11 x 11 = 121[/tex] square units.
The area of the circle is [tex]\pi \times r^2 = \pi\times 1^2 = \pi[/tex] square units, which is approximately 3.14 square units. Therefore, the area of the white portion of the target is [tex]121 - 3.14 = 117.86[/tex] square units.
Since this is much larger than the area of the black circle, the probability of hitting the white portion of the target is closer to 1.
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a supply container dropped from an aircraft by parachute hits a target with a probability of 0.37. (a) what is the expected number of container drops needed to hit a target?
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The given probability is 0.37 which is the probability of a supply container dropped from an aircraft by a parachute hitting a target. So the expected number of container drops needed to hit a target is approximately 2.7027.
To find out the expected number of container drops needed to hit a target, we can use the formula given below;
E(X) = (1/p) E(X)
= (1/0.37)E(X)
= 2.7027
Thus, the expected number of container drops needed to hit a target is approximately 2.7027.
An expected value is a statistical concept that represents the theoretical average value of a random variable. It is represented as E(X).
The expected value is calculated by multiplying each possible value of the random variable by its probability and then adding all of the products.
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Jason worked for 14/3 hours on Monday, and his friends Sheldon worked for 25/6 hours.How many more hours did Jason work than Sheldon?
Answers
Answer:
Step-by-step explanation:
To find out how many more hours Jason worked than Sheldon, we need to subtract the number of hours Sheldon worked from the number of hours Jason worked:
Jason's hours = 14/3
Sheldon's hours = 25/6
Jason's hours - Sheldon's hours = (14/3) - (25/6)
To subtract fractions, we need to have a common denominator, which in this case would be 6:
(14/3) - (25/6) = (28/6) - (25/6) = 3/6
Simplifying the result, we get:
3/6 = 1/2
Therefore, Jason worked 1/2 more hours than Sheldon.
Jason worked 1/3 more hours than Sheldon.
To find out how many more hours Jason worked than Sheldon, we need to subtract the number of hours Sheldon worked from the number of hours Jason worked.
Jason worked for 14/3 hours, which can be simplified to 4 and 2/3 hours. Sheldon worked for 25/6 hours, which can be simplified to 4 and 1/6 hours.
Subtracting the hours Sheldon worked from the hours Jason worked, we get: 4 and 2/3 - 4 and 1/6 = 2/3 - 1/6 = 1/3.
Therefore, Jason worked 1/3 more hours than Sheldon.
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|x-3|\ge11 ∣x−3∣≥11 please anwser quickly
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The given inequality is [tex]|x-3|/11 \geq 1[/tex]and the solution to the inequality is [tex]x \leq -8[/tex] or [tex]x \geq 14.[/tex]
We want to solve for [tex]x[/tex], which means we want to find all possible values of [tex]x[/tex] that satisfy the inequality.
To start, we multiply both sides of the inequality by 11, which gives us:
[tex]| x - 3 | \geq 11[/tex]
Now we have an inequality without any fractions. The absolute value sign means that we need to consider two cases: one where [tex]x-3[/tex] is positive, and one where [tex]x-3[/tex] is negative.
Case 1: [tex]x-3[/tex] is positive
If [tex]x-3[/tex] is positive, then [tex]| x - 3 |[/tex] is equal to [tex]x-3[/tex]. So we can rewrite the inequality as:
[tex]x - 3 \geq 11[/tex]
Adding 3 to both sides, we get:
[tex]x \geq 14[/tex]
This means that if [tex]x[/tex] is greater than or equal to 14, then the inequality is satisfied.
Case 2: [tex]x-3[/tex] is negative
If [tex]x-3[/tex] is negative, then [tex]| x - 3 |[/tex] is equal to [tex]-(x - 3)[/tex]. So we can rewrite the inequality as:
[tex]-(x - 3) \geq 11[/tex]
Multiplying both sides by -1, we get:
[tex]x - 3 \leq -11[/tex]
Adding 3 to both sides, we get:
[tex]x \leq -8[/tex]
This means that if [tex]x[/tex] is less than or equal to -8, then the inequality is satisfied.
Putting these two cases together, we get:
[tex]x \leq -8[/tex] or [tex]x \geq 14[/tex]
These are all the possible values of [tex]x[/tex] that satisfy the inequality.
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The complete question is:
Solve the equation: | x - 3 | / 11 ≥ 11 and determine the type of solution.
two angles are supplementary. if one angle is two times the sum of other angle and 3, find the two angle
Answers
The answer of the given question based on the supplementary angle is the two angles are 58° degrees and 122° degrees.
What is Angle?An angle is a geometric figure that is formed by two rays or lines that share a common endpoint, called the vertex. The rays or lines are called sides or arms of angle. Angles are typically measured in the degrees or the radians.
The measure of an angle is determined by the amount of rotation needed to bring one of its sides into coincidence with the other side. A full rotation is 360° degrees, so an angle that is half of a full rotation is 180 degrees, an angle that is a quarter of a full rotation is 90° degrees, and so on.
Let's call the two angles "x" and "y". We know that they are supplementary, which means that their sum is 180° degrees:
x + y = 180
We also know that one angle (let's say "x") is two times the sum of the other angle (y) and 3:
x = 2(y + 3)
Now we can substitute the second equation into the first equation to eliminate "x":
(2(y + 3)) + y = 180
Simplifying the equation, we get:
3y + 6 = 180
Subtracting 6 from both sides, we get:
3y = 174
Dividing both sides by 3, we get:
y = 58
Now that we know "y", we can substitute it back into the equation for "x" to find its value:
x = 2(y + 3) = 2(58 + 3) = 122
Therefore, the two angles are 58° degrees and 122° degrees.
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