The probability of completing the exam in one hour or less is 0.0228.
We are given that the time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. We need to find the probability of completing the exam in one hour or less, i.e., in 60 minutes or less.
Now, we need to convert this value into the standard normal variable z, by using the formula
z = (x - μ) / σ
where, x is the given value, μ is the mean and σ is the standard deviation. Putting the given values in the formula, we get
z = (60 - 80) / 10z = -2
We need to find the probability of completing the exam in 60 minutes or less. This can be represented as P(X ≤ 60). We know that P(Z ≤ z) can be found out from the standard normal table. Therefore, we need to look at the standard normal table to find the probability P(Z ≤ -2). From the standard normal table, we get
P(Z ≤ -2) = 0.0228
Therefore, the probability of completing the exam in one hour or less is 0.0228 (rounded to four decimal places).
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assume that 20% of criminal suspects who agree to take lie detector tests are actually guilty while 80% of those who agree to take the test are innocent. of those who are guilty, 70% fail the lie detector test. of those who are innocent, only 15% fail the test. suppose a person is arrested and takes a lie detector test. given that the person fails the test, what is the probability that the person is actually innocent?
The probability that the person is actually innocent given that they have failed the test is 0.4615... or approximately 0.462.
The question asks us to calculate the probability that the person is actually innocent given that they have failed the test. The probability that the person is actually innocent is given by the formula: P(innocent | fails test) = P(innocent and fails test) / P(fails test).
Now we need to calculate the values of the probabilities on the right-hand side of this equation. P(fails test) is equal to the sum of the probabilities that a guilty person fails the test and that an innocent person fails the test. Hence, P(fails test) = P(guilty and fails test) + P(innocent and fails test). P(guilty and fails test) = 0.2 × 0.7 = 0.14P(innocent and fails test) = 0.8 × 0.15 = 0.12. Therefore, P(fails test) = 0.14 + 0.12 = 0.26.
Finally, we can calculate the probability that the person is actually innocent given that they have failed the test: P(innocent | fails test) = P(innocent and fails test) / P(fails test)= 0.12 / 0.26= 0.4615 (rounded to four decimal places).
Therefore, the probability that the person is actually innocent given that they have failed the test is 0.4615... or approximately 0.462.
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What is the order of rotational symmetry of
each of the shapes below?
a)
Equilateral triangle
b)
Isosceles triangle
The order of rotational symmetry of an equilateral triangle is 3.
The order of rotational symmetry of the isosceles triangle is 1.
What is an equilateral triangle?
An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.
When an object is rotated around its own axis, its shape stays the same, which is explained by the rotational symmetry of a shape.
All sides of an equilateral triangle are equal.
When an equilateral triangle rotates 120⁰, then its shape remains the same.
The order of rotational symmetry of an equilateral triangle is 360⁰/120⁰ =3.
All sides of an isosceles triangle are not equal.
When an isosceles triangle rotates 360⁰, then its shape remains the same.
The order of rotational symmetry of an isosceles triangle is 360⁰/360⁰ =1.
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the probability that the splices in a rope splicing shop are weak is 1/1000 and the probability that the splices are ugly is 1/20. the probability that the weak splices are ugly is 2/3. find the probability that an ugly splice is weak.
The probability that an ugly splice is weak is 2/3.
This can be calculated by multiplying the probability of weak splices (1/1000) with the probability of ugly splices (1/20) and the probability that a weak splice is also ugly (2/3).
In order to calculate the probability that an ugly splice is weak, we need to use the equation: P(A∩B) = P(A) * P(B|A). In this equation, A represents the probability of weak splices (1/1000), and B represents the probability of ugly splices (1/20).
The probability that a weak splice is also ugly (2/3) is then multiplied by A and B, giving us a final answer of 2/3. This means that 2 out of every 3 ugly splices are weak.
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a state lottery involves the random selection of six different numbers between 1 and 20. how many different possible six-number combinations could be generated?
Answer:
64,000,000
Step-by-step explanation:
To find out how many combinations there are, you first must do an equation of multiplying these numbers.
20×20×20×20×20×20
Reason being: There are six different number combinations that all are between 1 and 20, so you must multiply all of these numbers.
If you multiply them all together, you would get 64,000,000 different combinations.
Hope it helped!
PLEASE HELP FAST!
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 98° is added to the data, how does the mean change?
The mean increases by 8.2°.
The mean decreases by 8.2°.
The mean increases by 1.4°.
The mean decreases by 1.4°.
Answer:
The mean increases by 1.4
what is 2 3/11 as an improper fraction?
Answer:
[tex]\frac{25}{11}[/tex]
Step-by-step explanation:
an improper fraction is one where the value on the numerator is larger than the value on the denominator.
2 [tex]\frac{3}{11}[/tex] is a mixed number, that is a whole number and a fraction
this can be converted to an improper fraction by summing the 2 parts , that is the whole number and the proper fraction as
2 + [tex]\frac{3}{11}[/tex]
= [tex]\frac{22}{11}[/tex] + [tex]\frac{3}{11}[/tex]
= [tex]\frac{22+3}{11}[/tex]
= [tex]\frac{25}{11}[/tex]
or
multiplying the whole number by 11 and adding 3 , over 11
[tex]\frac{2(11)+3}{11}[/tex]
= [tex]\frac{22+3}{11}[/tex]
= [tex]\frac{25}{11}[/tex]
Solve for y.
3y - 6x = 24
y = [? ]x +
Answer: y = 2x + 8
Step-by-step explanation:
3y - 6x = 24
3y = 6x + 24
y = (6x + 24) / 3
y = 2x + 8
Describe and correct the error a student made in identifying the growth or decay factor for the
function y = 2.55(0.7)
Step 1 The base of the function
is 0.7, so it represents
exponential decay.
Step 2 The function in the form
y = a(1-r)* is
y = 2.55(1-0,7)*
Step 3 The decay factor is 0.3.
X
The corrected version has a base of 0.7, representing exponential decay, and has the function[tex]y = a(1-r)x[/tex] as [tex]y = 2.55(0.7)x[/tex] with a [tex]0.3[/tex] decay factor.
Explain function?
A function is a link or statement that contains one or more values. Both inputs and outputs are numerous. With each input, there is only one output. The links between the inputs and the results are described by the function.
The error the student made is in Step 2 where they incorrectly wrote the function in the form [tex]y = a(1-r)*.[/tex]The correct form for exponential decay is [tex]y = a(1-r)^x[/tex], where x is the number of time periods. So, the correct equation for the given function is [tex]y = 2.55(0.7)^x.[/tex]
To find the decay factor, the student should have subtracted the base from 1, instead of multiplying it by -1. Therefore, the correct decay factor is [tex]1 - 0.7 = 0.3.[/tex]
So, the corrected version of the solution is:
Step 1: As the function's base is[tex]0.7[/tex], it simulates exponential decay.
Step 2: The function in the form [tex]y = a(1-r)^x is y = 2.55(0.7)^x.[/tex]
Step 3: The decay factor is [tex]0.3.[/tex]
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What is the distance from −12 to −5 on a number line?
A -17
B -7
C 17
D 7
What is 8z + 3;z = 8 but evaluate it.
Answer:
Step-by-step explanation:
the answer is
z=0.625
-1/5+2/15 what is the answer the answer to that
Answer:
-0.06666666666
hope it helps :)
Between which two benchmarks is 3/8 how do you know?
Answer:
Step-by-step explanation:
To find the benchmarks between which 3/8 falls, we need to identify the nearest fractions with denominators that are multiples of 8.
The fraction 3/8 is halfway between 1/4 and 1/2, which can be written as 2/8 and 4/8 respectively. So, we know that 3/8 is greater than 2/8 and less than 4/8.
Therefore, the benchmarks between which 3/8 falls are 2/8 and 4/8. Alternatively, we can express these fractions as decimals and say that 3/8 falls between 0.25 and 0.5.
What is an equation of the line that passes through the point (-5, 7) and is parallel
to the line x - 5y = 15?
Answer:
Step-by-step explanation:
What is an equation of the line that passes through the point (-5, 7) and is parallel
to the line x - 5y = 15?
We have two values, x and y, from our ordered pair.
Plugging those in we have -5 - 35y = 15
Add 5 to both sides: -35y = 20
Divide both sides by 35 : approx. 0.57
Our slope is 0.57
THIS IS URGENT AM I CORRECT PLEASE HALP!!!!!!
Answer: The answer is 32.
Step-by-step explanation: Yes since you did 9.5+13.6+5.7+3.2 is 32.00 or 32.
julie the jeweler has two gold necklaces worth $105, seven silver necklaces valued at $100, twenty-seven plated necklaces valued at $55, and twenty-two beaded necklaces worth $25. what is the average value of a necklace at julie's shop? express your answer rounded to the nearest cent.
The average value of a necklace at Julie's shop is $4.90. For further explanation;-
Julie the jeweler has two gold necklaces worth $105, seven silver necklaces valued at $100, twenty-seven plated necklaces valued at $55, and twenty-two beaded necklaces worth $25. The average value of a necklace at Julie's shop can be calculated by finding the sum of the values of all the necklaces and dividing it by the total number of necklaces.
The total value of all the necklaces is $105 + $100 + $55 + $25 = $285. The total number of necklaces is 2 + 7 + 27 + 22 = 58.
Therefore, the average value of a necklace is $285 / 58 = $4.90. This answer should be rounded to the nearest cent, giving an average value of $4.90 per necklace at Julie's shop.
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we have a group of 53 people, including 22 us citizens, 15 mexican citizens, and 27 canadian citizens. among them, 4 people have a dual us-mexican citizenship, 5 have us-canadian citizenship, and 6 have canadian-mexican citizenship. how many people have a triple citizenship?
As per the combination method, there are 12 people with a triple citizenship.
To find out how many people have a triple citizenship, we need to first find out how many people have two citizenships. We can do this by adding up the number of people with each combination of citizenship:
US-Mexican: 4
US-Canadian: 5
Canadian-Mexican: 6
Total number of people with two citizenships = 4 + 5 + 6 = 15
Next, we need to find out how many people have only one citizenship. We can do this by subtracting the number of people with two citizenships from the total number of people:
Total number of people = 53
Number of people with two citizenships = 15
Number of people with only one citizenship = 53 - 15 = 38
Now, we can use combinations again to find out how many people have a triple citizenship.
However, we need to subtract out the people who have only two citizenships, since we don't want to count them twice:
n(US-Mexican-Canadian) = n(US-Mexican) + n(US-Canadian) + n(Canadian-Mexican) - n(with 2 citizenships)
= 4 + 5 + 6 - 3 (since 3 people have 2 citizenships)
= 12
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What is measure of angle r?
help this needs to be done, please
The measure of angle R in ΔSRT which is drawn inside the circle is 77.5°.
What is circles?Circle is a two-dimensional shape that is defined as the set of all points that are equidistant from a central point. It is often represented as a round shape with a curved boundary.
Since SR is a diameter of the circle, it follows that angle STR is a right angle (90°). Therefore, we can find the measure of angle SRT using the following equation:
∠SRT + ∠STR = 180°
(2x-23°) + 90° = 180°
2x + 67° = 180°
2x = 180° - 67°
2x = 113°
x = 56.5°
∠TRS = 5x-97°
∠TRS = 5(56.5°)-97°
∠TRS = 192.5°
Finally, we can find the measure of angle SRT:
∠SRT = 180° - ∠STR - ∠TRS
∠SRT = 180° - 90° - 192.5°
∠SRT = -102.5°
Therefore, to find the measure of angle R, we need to add 180° to angle SRT:
∠R = ∠SRT + 180°
∠R = -102.5° + 180°
∠R = 77.5°
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1/2x - 1/3y = 5
x= 2/3y + 10
solve for x (Please leave an explanation)
The value of x for the angle 100 + x under the top parallel line is equal to -10.
What are angles formed by a pair of parallel lines cut by a transversal line?When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, and alternate angles.
The angle 100 + x formed by the top parallel line and the transversal line perpendicular to to it is equal to 90° so we can solve for the value of x as follows:
100 + x = 90
subtract 100 from both sides
x = 90 - 100
x = -10.
Therefore, the value of x for the angle 100 + x under the top parallel line is equal to -10.
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you flip a coin 4 times and get 4 heads in a row what is the probability that the 5th coin flipped is a head
The probability of flipping a coin 4 times and getting 4 heads in a row is 0.0625, and the probability of getting a head on the 5th coin flip is 0.5.
The probability of getting a head on the 5th flip is still 50%. This is because each coin flip is an independent event, and each coin flip is not affected by the outcome of the previous coin flips. Thus, the probability of getting a head on the 5th coin flip is 0.5, regardless of the previous 4 coin flips.
To summarize, the probability of flipping a coin 4 times and getting 4 heads in a row is 0.0625, and the probability of getting a head on the 5th coin flip is 0.5.
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That the question so yh I don't get it
Answer:
25 euros
Step-by-step explanation:
The ratio is 5:2. Sean received 10 euros. This means that Cheryl received 25 euros. You can multiply both sides of the ratio by 5 to get this answer.
this is the answer for the questions
Lydia uses 6. 2 pints of blue paint and white paint to paint her bedroom walls. 3
5
of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls?
Lydia used a total of approximately 16.33 pints of paint to paint her bedroom walls, with 6.2 pints being blue and 10.33 pints being white.
We know that 3/5 of the total paint used is blue, and the remaining 2/5 must be white.
Let x be the total amount of paint used in pints. Then, we can write:
3/5 x = 6.2 (pints of blue paint used)
2/5 x = ? (pints of white paint used)
To solve for the pints of white paint used, we need to isolate the variable x in the second equation:
2/5 x = (2/3) * 3/5 x (multiply both sides by 2/3 to simplify)
2/5 x = 6.2 * 2/3
2/5 x = 4.1333...
Now we can solve for x by multiplying both sides by 5/2:
x = (5/2) * (2/5) x = (5/2) * 4.1333... = 10.3333...
Therefore, Lydia used approximately 10.33 pints of white paint and 6.2 pints of blue to paint her bedroom walls.
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if atharv has 10 nickels and dimes in his pocket, and they have a combined value of 70 cents, how many of each coin does he have?
If Atharv has 10 nickels and dimes in his pocket, and they have a combined value of 70 cents, then he has 1 nickels and 4 dimes.
Let x be the number of nickels and y be the number of dimes. A nickel is worth 5 cents, and a dime is worth 10 cents. Therefore, we can write two equations:
x + y = 10 (since he has 10 coins in total)
5x + 10y = 70 (since the combined value of the coins is 70 cents)
We can simplify the second equation by dividing both sides by 5:
x + 2y = 14
Now we can use the first equation to solve for one of the variables in terms of the other. Let's solve for x:
x + y = 10x = 10 - y
Now we can substitute this expression for x into the second equation:
x + 2y = 14(10 - y) + 2y = 14
Simplifying, we get:
10 + y = 14
y = 4
Therefore, Atharv has 5 - 4 = 1 nickel and 5 - 1 = 4 dimes.
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I don't know how to do this −1(−3 1/2)
Answer:
3.5
Step-by-step explanation:
The parenthesis means you multiply the inside number by the outside number.
the negatives cancel each other out so the answer would be positive 3.5.
Ω = {whole numbers from 2 to 9} A = {even numbers} B = {prime numbers} List the elements in:
a. A’
b. A∩B
c. A∪B
A' is complement of A, A∩B is intersection of A and B, A∪B is union of A and B.
What is complement?In set theory, the complement of a set is the set of all elements in the universal set that are not in the given set. In other words, it is the set of all elements in the universal set that are outside of the given set.
According to question:Ω = {2, 3, 4, 5, 6, 7, 8, 9} (whole numbers from 2 to 9)
A = {4, 6, 8} (even numbers from Ω)
B = {2, 3, 5, 7} (prime numbers from Ω)
a. A' (complement of A, i.e. elements in Ω that are not in A)
A' = {2, 3, 5, 7, 9} (odd numbers and 9 are not in A)
b. A∩B (intersection of A and B, i.e. components found in both A and B)
A∩B = {2} (the only even prime number is 2)
c. A∪B (union of A and B, i.e. elements that can be found in A, B, or both)
A∪B = {2, 3, 4, 5, 6, 7, 8} (all the even numbers and prime numbers from Ω).
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The complete question is:
ASAP
Ω = {whole numbers from 2 to 9} A = {even numbers} B = {prime numbers} List the elements in:
a. A’
b. A∩B
c. A∪B
Rename 1 foot with an equivelint fraction in yards
Renaming 1 foot to equivalent fraction in yards as 1/3 yards
We multiply the number of feet by 1/3 to convert this to yards, and then we need to identify the two elements of this equation that have a functional relationship.
As we are aware,
1 foot equals 3 yards.
As a result, we must multiply the unknown numbers, denoted by the letter x, by 1/3 in order to get the feet.
Let's say that the variables in this situation are x and y, where x stands for feet and y for yards.
To get the unit in yards, multiply the unit in feet by a factor of three-quarters. x = 1/3y
Hence, the renaming of 1 feet as 1/3 yards, where the fraction is 1/3.
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Darren kept track of the number of e-mails he received from one of his customers each day for 14 days on the dot plot.
A number line goes from 1 to 12. 1 dot is above 2. 2 dots are above 7. 3 dots are above 8. 1 dot is above 9. 3 dots are above 11. 4 dots are above 12.
Which statement must be true according to the dot plot?
The data is skewed left and shows that on half of the days, Darren received 11 or 12 e-mails from the customer.
The data is skewed left and shows that on half of the days, Darren received 7 to 9 e-mails from the customer.
The data is skewed right and shows that on half of the days, Darren received 11 or 12 e-mails from the customer.
The data is skewed right and shows that on half of the days, Darren received 7 to 9 e-mails from the customer.
A statement that must be true according to the dot plot include the following: A. the data is skewed left and shows that on half of the days, Darren received 11 or 12 e-mails from the customer.
What is a dot plot?In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.
By critically observing the given dot plots which is used to illustrate the number of e-mails that Darren received from one of his customers each day for 14 days, we can reasonably infer and logically deduce that the data set is skewed left, which ultimately implies that that on half of the days (7 days), Darren received a total of 11 or 12 e-mails from this customer.
In conclusion, the dot plot is skewed left because it has a long tail on its left side and 7 days is the half of 14 days.
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Help, need to finish this class asap
A medical equipment industry manufacturers x-ray machines. The unit cost C (the cost in dollars to make each x-ray machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function C(x)=0.6x^2-372x+63,308. How many machines must be made to minimize the unit cost? Do not round
To find the number of machines that minimize the unit cost, we need to find the value of x that minimizes the function C(x). We can do this by finding the critical points of C(x) and determining which one corresponds to a minimum.
First, we take the derivative of C(x) with respect to x:
C'(x) = 1.2x - 372
Then, we set C'(x) equal to zero and solve for x:
1.2x - 372 = 0
1.2x = 372
x = 310
So the critical point is x = 310.
To determine whether this critical point corresponds to a minimum or a maximum, we need to examine the second derivative of C(x):
C''(x) = 1.2
Since C''(x) is positive for all values of x, we know that the critical point x = 310 corresponds to a minimum.
Therefore, the number of machines that must be made to minimize the unit cost is 310.
If f(x) = x + 5, then f(x - 5) =
a. 0
b. x
c. x-25
d. 2x-25
e. -5x
Answer:f(x-5)=x
Step-by-step explanation:To evaluate f(x-5) we need to subtitute x - 5 for x in the expression for f(x):
f(x-5) = (x-5) + 5
The +5 and -5 cancel out, so we are left with f(x-5)=x
excel a university found that 5% of its students who enroll in an introductory statistics class withdraw. assume 90 students have registered for an introductory statistics course this semester. (a) what is the probability that no student will withdraw from the course?
The probability that no student will withdraw from the course is approximately 0.008 or 0.8%, assuming a binomial distribution with n=90 and p=0.05.
Since each student's decision to withdraw or not is independent of others, we can model the number of students who withdraw as a binomial random variable with n=90 and p=0.05.
To find the probability that no student will withdraw from the course, we want to find P(X=0), where X is the number of students who withdraw. This is given by the binomial probability mass function:
P(X=0) = (n choose 0) * p^0 * (1-p)^(n-0) = (90 choose 0) * 0.05^0 * 0.95^90
Using a calculator or software, we find:
P(X=0) ≈ 0.008
Therefore, the probability that no student will withdraw from the course is approximately 0.008 or 0.8%.
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