The chance of an IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 16-year period. Assume each year is independent.
Find the probability that a person is audited more than twice. (Round your answer to four decimal places.)
Answers
Answer:
The probability that a person is audited more than twice is 0.0037 .
Step-by-step explanation:
We are given that The chance of an IRS audit for a tax return with over $25,000 in income is about 2% per year.
We are interested in the expected number of audits a person with that income has in a 16-year period
Now we are supposed to find the probability that a person is audited more than twice.
So, We will use binomial distribution
So, Probability of success =p= 2% = 0.02
So, Probability of failure = q=1-0.02=0.98
n = 16
Now we are supposed to find the probability that a person is audited more than twice i.e. \(P(x \geq 2)\)
So, \(P(x \geq 2)= 1-(P(x=0)+P(x=1)+P(x=2)\)
Formula :\(^nC_x p^x q^{n-x}\)
So,\(P(x \geq 2)= 1-(^{16}C_0 {(0.02)}^0 {(0.98)}^{16-0}+^{16}C_1 {(0.02)}^1 {(0.98)}^{16-1}+ ^{16}C_2 {(0.02)}^2 {(0.98)}^{16-2})\)\(P(x \geq 2)= 1-(\frac{16!}{0!(16-0)!} {(0.02)}^0 {(0.98)}^{16-0}+\frac{16!}{1!(16-1)!} {(0.02)}^1 {(0.98)}^{16-1}+\frac{16!}{2!(16-2)!} {(0.02)}^2 {(0.98)}^{16-2})\)
\(P(x \geq 2)= 1-(0.9963)\)
\(P(x \geq 2)= 0.0037\)
Hence the probability that a person is audited more than twice is 0.0037 .
Related Questions
When looking for interesting facts, avoid using
A. Lists of statistics
B. Quotes from famous people
C. Reliable sources
D. Humor
Answers
Answer:
D: humor.
Step-by-step explanation:
it's just common sense. I am not a gen z so I should know.
I really need help with this question
Answers
The length of each side of the wood is 5 centimetres.
How to use quadratic equation to find the length of each side of the wood?Doug has 8 square pieces of wood. Each piece of wood have a side length of s cm. The total area of all 8 pieces of wood is 200 cm².
Hence, using quadratic equation let's find the length of each side of the wood.
Therefore,
8s² = 200
Hence,
8s² = 200
divide both sides of the equation by 8
s² = 200 / 8
s² = 25
s = √25
s = 5 centimetres
learn more on quadratic equation here: https://brainly.com/question/22364785
#SPJ1
Select the correct answer. In which direction must the graph of f(x) = x be shifted to produce the graph oSelect the correct answer.
In which direction must the graph of f(x) = x be shifted to produce the graph of g(x) = f(x) - 4?
A.
left and down
B.
right and up
C.
down
D.
upf g(x) = f(x) - 4? A. left and down B. right and up C. down D. up
Answers
Answer:
A. down
Step-by-step explanation:
The parent graph is
f(x)=x
If this graph is transformed to obtain
g(x)=f(x)−4
The subtracttion means the graph will shift downward vertically
The graph of g(x) is obtained by shifting f(x) down by 4 unit.
Therefore the direction is down.
Mark this as brainliest please.
The product of two negative integers is a negative integer.
Answers
Answer:
False. The product of two negative integers is a positive integer.
Write a sentence of the form “–––––––––––––– is a function of –––––––.”
Type your response in the space below.
Answers
"Distance traveled is a function of time." In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.
Distance is a fundamental concept in physics and mathematics that measures the extent or length between two points.
It represents the amount of ground covered or space traveled. When we say that distance is a function of various factors, it means that different variables or parameters can influence the distance traveled.
In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.
The sentence "Distance traveled is a function of time" expresses this relationship, indicating that the distance traveled can be determined or calculated based on the value of time.
Thus, it implies that as time changes, the corresponding distance traveled also changes, establishing a functional relationship between the two variables.
For more details regarding distance, visit:
https://brainly.com/question/13034462
#SPJ1
which is the correct expression for 1 /3 (log x - log y )
Answers
As according to rule of logarithm:
\(\log (a)-\log (b)=\log (\frac{a}{b})\)And
\(a(\log b)=\log (b^a)\)Now applying both rules in given question:
\(\begin{gathered} \frac{1}{3}(\log x-\log y)=\frac{1}{3}(\log \frac{x}{y}) \\ \frac{1}{3}(\log \frac{x}{y})=\log (\frac{x}{y})^{\frac{1}{3}} \\ \log (\frac{x}{y})^{\frac{1}{3}}=\log (\sqrt[3]{\frac{x}{y}}) \end{gathered}\)What is the additive inverse of the polynomial? -7y^2+x^2y-3xy-7x^2
Answers
The additive inverse of the polynomial is +7y²-x²y+3xy+7x².
What is Additive inverse?The additive inverse can be defined as when we add a number to some number and get result as zero.
Given polynomial:
-7y²+x²y-3xy-7x²
As, the value of additive inverse is same as of the number but the sign of the additive inverse is opposite.
So,
= +7y²-x²y+3xy+7x²
Check:
-7y²+x²y-3xy-7x² + 7y²-x²y+3xy+7x²
= -7y²+ 7y² +x²y -x²y -3xy +3xy -7x² +7x²
=0
Hence, the additive inverse of the polynomial is +7y²-x²y+3xy+7x².
Learn more about this additive inverse here:
https://brainly.com/question/12092863
#SPJ1
solve the given triangle by finding the missing angle and other side lengths
Answers
Answer:
angle B=122degree
Step-by-step explanation:
straight line AC =180degree, then 180-(21+37)=122 degree
a=b*sinA/sinB=84.5
c=b*sinC/sinB=141.9
Sarah predicted that she could text 80 words
per minute on her phone. However, she only
texted 52 words per minute. What was Sarah's
percent error?
Prediction Actual |
| Actual |
Round to the nearest percent.
Hint: Percent error =
-
x 100
Answers
Answer:
20
Step-by-step explanation:
percentage error = predictions - actual ÷actual × 100
error
\( \frac{82 - 52 \\ }{52} \times 100\)
=
20
Austin correctly answered 92% of the questions on a geography quiz.Liz answered 47 of the 50 questions correctly
Answers
Answer:
Liz did
Step-by-step explanation:
because if you multiply 47 to 2, then you get 94 and that's higher than 92, not sure but i hope this works
-
First, rewrite
13 9
and
30 20
so that they have a common denominator.
13 9
Then, use <, =, or > to order and
30 20
13
9
<
D>
30
20
Х
?
13
9
30
20
Answers
Answer:
18/14=64+7%×r try it out
The values shows 13/30 < 9/20.
What is fraction?Fractions are the components of a collection or whole. Two parts make up a fraction. The numerator is the number at the top of the line. It indicates the number of equal portions taken from the collection or whole. The term "denominator" refers to the number below the line. It indicates the total number of identical parts that make up a collection or the total number of parts that make up the whole.
The number of parts we take is a fraction when the whole is divided into equal parts.
Given 13/30 and 9/20
to make the common denominator,
multiply by 20 in numerator and denominator of 13/30
(13 x 20)/(20 x 30) = 260/600
multiply by 30 in numerator and denominator of 9/20
(9 x 30)/(20 x 30) = 270/600
the terms with same denominator are
260/600 and 270/600
as we can see that 270/600 > 260/600
so 13/30 < 9/20.
Hence 13/30 is less than 9/20.
Learn more about fraction;
https://brainly.com/question/10354322
#SPJ2
Find the exact value of (7\pi )/(6)) by using the unit circle.
Answers
To find the exact value of (7π/6) using the unit circle, locate the angle (π/6) on the unit circle in the second quadrant, determine the coordinates, and adjust the y-coordinate to be negative. The final answer is (√3/2, -1/2). This answer is obtained by understanding the reference angle and using the coordinates of the point where the angle intersects the unit circle.
To find the exact value of (7π/6) using the unit circle, follow these steps:
1. Start by understanding the reference angle. The reference angle for (7π/6) is (π/6).
2. Locate the angle (π/6) on the unit circle. This angle lies in the second quadrant.
3. Determine the coordinates of the point where the angle intersects the unit circle. For (π/6), the x-coordinate is √3/2 and the y-coordinate is 1/2.
4. Since (7π/6) lies in the second quadrant, the x-coordinate will remain the same, but the y-coordinate will be negative. Therefore, the coordinates for (7π/6) are (√3/2, -1/2).
5. The exact value of (7π/6) is (√3/2, -1/2).
For more questions on the circle
https://brainly.com/question/28162977
#SPJ8
Everv goat has eaten a wolf: There is a wolf who has eaten every goat; Every goat is eaten by a wolf Some goat was eaten by wolf: Question 6 (1 point) Let A - { 1,2,3 and B = { 5,4,2,3 }. Select all that are true from below: A U B = {5,3,2,4] A 0 B = { 2 , 3 } A - B = { 1,3 } B - A = {4,5 }'
Answers
All of the statements are true.
Here is a breakdown of the set operations:
A U B (the union of A and B) is the set of all elements that belong to either A or B or both. In this case, the elements that belong to
A U B are {5, 3, 2, 4}, as these are the elements that belong to either A or B.A ∩ B (the intersection of A and B) is the set of all elements that belong to both A and B. In this case, the elements that belong to
A ∩ B are {2, 3}, as these are the elements that belong to both A and B.A - B (the difference between A and B) is the set of all elements that belong to A but not to B. In this case, the elements that belong to
A - B are {1}, as 1 belongs to A but not to B.B - A (the difference between B and A) is the set of all elements that belong to B but not to A. In this case, the elements that belong to
B - A are {4, 5}, as these elements belong to B but not to A.Learn more about Set operations here:
https://brainly.com/question/9025420
#SPJ4
A 10-sided fair die, a 20-sided fair die, and a 6-sided fair die are rolled. What is the probability of all three happening:
Showing 8 on the first die
Showing 21 on the second die
Showing an odd number on the third die
Probability =
(Enter your answer as a reduced fraction.)
Answers
three fair dies are rolled. The first die is a 10-sided fair die and it shows 8.The second die is a 20-sided fair die and it shows 21.The third die is a 6-sided fair die and it shows an odd number. the probability is 1/400.
The probability that all three are occurring is given by the probability of the first die multiplied by the probability of the second die multiplied by the probability of the third die
Probability = P(first die shows 8) * P(second die shows 21) * P(third die shows an odd number)
The probability of the first die showing 8 is 1/10The probability of the second die showing 21 is 1/20The probability of the third die showing an odd number is 3/6 (as there are 3 odd numbers out of 6 numbers)Therefore, the probability of all three happening is:
Probability = P(first die shows 8) * P(second die shows 21) * P(third die shows an odd number) = (1/10) * (1/20) * (3/6) = 1/400
Thus, the probability is 1/400.
For more question sided fair die
https://brainly.com/question/2410543
#SPJ8
4. Calculate the estimated cost of constructing the following house in New
Orleans, Louisiana: a two-story home of 950 ft2 on the first floor and 800 ft²
on the second floor.
O A. $113,750
O B. $67,600
O C. $61,750
O D. $52,000
Answers
The estimated cost for constructing the house in New Orleans, Louisiana of the given square feet is option A. $113,750.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
Given that, construction rate per square feet is $65.
We have to find the estimated cost for a two-story home of 950 ft2 on the first floor and 800 ft² on the second floor.
Total area of the plot = 950 ft² + 800 ft²
= 1750 ft²
Estimated cost can be calculated by multiplying total area with the construction rate per square feet.
Estimated cost = 1750 ft² × $65
= $113,750
Hence the estimated cost is $113,750.
Learn more about Multiplication here :
https://brainly.com/question/29452737
#SPJ1
Find to value of a if you knew the perimeter was 250 inches long
Answers
Answer:
To find the value of "a" when you know the perimeter of a shape, you need to know the specific shape you're referring to. Please provide more information about the shape in question, such as whether it's a rectangle, triangle, or another geometric figure. Additionally, if you have any specific measurements or relationships between the sides of the shape, please provide them as well.
the graph of a certain quadratic function has no x-intercepts. Which of the following are possible values or the disriminant?
Answers
The possible values for the discriminant include the following:
A. -1
D. -18
What is the x-intercept?In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).
Since the graph of this quadratic function has no x-intercepts, we can logically deduce that the zeros, roots, or x-intercepts of this quadratic function must be an imaginary number.
Discriminant, D = b² - 4ac
In conclusion, we can reasonably infer and logically deduce that negative numbers such as -1 and -18 are possible values for the discriminant.
Read more on x-intercept here: brainly.com/question/6240745
#SPJ1
Complete Question:
The graph of a certain quadratic function has no x-intercepts. Which of the following are possible values for the discriminant? Check all that apply.
A. -1
B. 3
C. 0
D. -18
Here are the shopping times (in minutes) of ten shoppers at a local grocery store.
Complete the grouped frequency distribution for the data.
In the distribution, the frequency of a class is the number of shopping times in that class.
(Note that we are using a class width of 5.)
Answers
The frequency which is to filled in the table is 1, 4, 2 and 4.
Given that;
All shopping time of ten shopkeeper:
25, 29, 25, 18, 24, 28, 36, 25, 33, 37
We have to complete the frequency in the table. Frequency of something is the number of times that number is coming.
Since, Shopping time is given as ,
25, 29, 25, 18, 24, 28, 36, 25, 33, 37
And, Intervals for which frequency is given is ,
18 to 22, 23 to 27, 28 to 32, 33 to 37.
Hence, WE get;
Numbers in the range 18 to 22 = 18 therefore 1
Numbers in the range 23 to 27 = 25, 25, 24, 25 therefore 4
Numbers in the range 28 to 32 = 29, 28 therefore 2
Numbers in the range 33 to 37 = 36, 33, 37, therefore 3
Hence, the frequency which is to filled are 1, 4, 2 and 4.
Learn more about frequency visit:
brainly.com/question/254161
#SPJ1
need help can't figure it out
Answers
Answer:
415
Step-by-step explanation:
What is the answer please?
Answers
Answer:
omg that question is impossible to answer
Answer:
I don't know complicated for me. sorry I could not help
PLS HELP ASAP.!
THANK YOU, WILL MARK BRAINLIEST
Answers
Answer:
Explanation:
The volume of the triangular prism:
The base area of the prism = 1/2 x 4 x 6 = 12 ft2
Height = 6 ft
The volume of the triangular prism = 12 x 6 = 72 ft3
The volume of the rectangular prism:
The base area of the prism = 4 x 6 = 24 ft2
Height = 12 ft
The volume of the triangular prism = 12 x 24 = 288 ft3
Volume of the composite figure = (288 + 72)ft3 = 360 ft3
Step-by-step explanation:
Write the "to prove" statement for the following theorem.
If one angle of a triangle is 90°, then the other two add to 90°.
Answers
To prove: If one angle of a triangle is 90°, then the sum of the other two angles is equal to 90°. is sum of angles on a triangle is 180 degrees
What is sum of angles on a triangle?In a triangle, the sum of the interior angles in the triangle is 180 degrees
For right triangle, that is angle that has one side as 90 degrees, the sum of the other two sides will be 90 degrees
Assuming the other angles are x and y, then a side is 90 degrees
x + y + 90 = 180 (sum of interior angles on a triangle)
x + y = 180 - 90
x + y = 90 degrees
hence the sum of the interior angles is 90 degrees
Learn more about angles at:
https://brainly.com/question/25716982
#SPJ1
In a newspaper, it was reported that the number of yearly robberies in Silringfield in 2013 was 180, and then went down by 40% in 2014. How many robberies were there in Springfield in 2014?
Answers
Answer:
The number of robberies in Springfield 2014 was 108
Explanation:
Given that the number of yearly robberies in Springfield in 2013 was 180
In 2014, this number went down by 40%
That is, the number is 60% of 180 in 2014
60% = 60/100 = 0.6
60% of 180 = 0.6 * 180
= 108
This is the number of robberies in 2014
∠C and ∠D are complementary.
Let m∠C=(5x)° and m∠D=(7x−6)°.
What is the value of x?
Enter your answer in the box.
x =
Answers
Complementary angles have sum 90°
\(\\ \rm\Rrightarrow 5x+7x-6=90\)
\(\\ \rm\Rrightarrow 12x-6=90\)
\(\\ \rm\Rrightarrow 12x=96\)
\(\\ \rm\Rrightarrow x=8\)
Answer:
x = 8
Step-by-step explanation:
Complementary angles are two angles with measures that sum to 90°
Given:
m∠C = (5x)° m∠D = (7x − 6)°⇒ m∠C + m∠D = 90°
⇒ 5x + 7x - 6 = 90
⇒ 12x - 6 = 90
⇒ 12x = 96
⇒ x = 8
The function f(1) = 60,000(2)
00(2) 410 gives the number
of bacteria in a population & minutes after an initial
observation. How much time, in minutes, does it
take for the number of bacteria in the population to
double?
Answers
It takes 10 minutes for the number of bacteria in the population to double.
To determine the time it takes for the number of bacteria in a population to double, we need to find the value of t when the function f(t) equals twice the initial number of bacteria.
The given function is f(t) = 60,000 * 2^(t/10).
To find the time it takes for the number of bacteria to double, we set f(t) equal to twice the initial number of bacteria, which is 2 * 60,000 = 120,000:
120,000 = 60,000 * 2^(t/10).
Next, we can simplify the equation by dividing both sides by 60,000:
2 = 2^(t/10).
Since both sides of the equation have the same base (2), we can equate the exponents:
t/10 = 1.
To solve for t, we multiply both sides by 10:
t = 10.
Therefore, it takes 10 minutes for the number of bacteria in the population to double.
This result is obtained by setting the growth rate of the bacteria population in the given function. The exponent t/10 determines the rate of growth, and when t is equal to 10, the exponent becomes 1, resulting in a doubling of the initial number of bacteria.
For more scuh questions on population visit:
https://brainly.com/question/31243583
#SPJ8
Which is the better deal? [You must show your work in order to receive full credit (2 points).]
12 packs of fruit snacks for $9.12 or 9 packs of fruit snacks for $6.99
Answers
Answer:
i think it is 12 packs of fruit snacks for $9.12
Step-by-step explanation:
find the odds in favor of drawing a red marble whyen a marble is selected at random from a bag containing 2 yellow, 5 red and 6 green marbles
Answers
Answer:
The odd in favor of drawing a red marble is 5:8
Step-by-step explanation:
Let’s calculate the probability of selecting a red marble
That would be;
number of red marbles/Total number of marbles
Total number of marbles = 2 + 5 + 6 = 13
So the probability of drawing a red marble is 5/13
The probability of not drawing a red marble = 1-5/13 = 8/13
So the odd in favor of drawing a red marble is 5:8
This is just a question I had.
If Denny (random name) left to another country and he left the Tuesday of this week (June 20) and he left for a month, what day would he be back on? I though July 18 but I’m not sure. Pls help?
Answers
Answer:
Step-by-step explanation:
Well, since the length of a month can vary in the number of days, this answer can also vary.
For example, February is only 28 days long, while December is 31 days long.
That being said, the average length of all 12 months is 30.436875 days, so if Denny left to another country on June 20th, he would most likely be back July 19th of July 20th.
I hope this helps!
A phone company offers two monthly plans. Plan A costs $17 plus an additional $0.09 for each minute of calls. Plan B costs $9 plus an additional $0.11 for each minute of calls.For what amount of calling do the two plans cost the same?What is the cost when the two plans cost the same?
Answers
Answer:
Step-by-step explanation:
100 POINTS PLEASE HELP FAST
Select the correct answer.
The weight of a radioactive isotope was 96 grams at the start of an experiment. After one hour, the weight of the isotope was half of its initial weight. After two hours, the weight of the isotope was half of its weight the previous hour. If this pattern continues, which of the following graphs represents the weight of the radioactive isotope over time?
Answers
The top left graph represents the weight of the radioactive isotope over time.
How to define an exponential function?An exponential function has the definition presented according to the equation as follows:
\(y = ab^x\)
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The parameter values for the function in this problem are given as follows:
a = 96, b = 0.5.
Hence the function is given as follows:
\(y = 96(0.5)^x\)
Two points on the graph of the function are given as follows:
(1,48) and (2, 24).
Hence the top left graph represents the weight of the radioactive isotope over time.
More can be learned about exponential functions at brainly.com/question/2456547
#SPJ1
Answer:
Graph W
Step-by-step explanation:
The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.
Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).
The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.
Initial weight: 96 grams
After 1 hour: 96 / 2 = 48 grams
After 2 hours: 48 / 2 = 24 grams
After 3 hours: 24 / 2 = 12 grams
After 4 hours: 12 / 2 = 6 grams
After 5 hours: 6 / 2 = 3 grams
So, the points on the graph would be:
(0, 96), (1, 48), (2, 24), (3, 12), (4, 6), (5, 3)Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.
