The correct option is option B.
The hypothesis is that the mean energy expenditure has increased from its past level (greater than).
We can interpret the p-value in the following way:
There is a 0.02748 probability of obtaining a sample mean different from $1,618 from a population whose mean is $1,493.
If the null hypothesis is true (the mean expenditure has not changed from the past level), we would expect to obtain sample means that differ from $1,618 by the observed amount or greater about 2.748% of the time (p-value).
Since this is a small value, it suggests that the sample mean is significantly greater than the hypothesized value of $1,493 and the economist has strong evidence that the mean energy expenditure has indeed increased from the past level (he rejects the null hypothesis).
Therefore, the correct answer is B.
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19. Linda mixed 5.15 lb of cashews with 4.32 lb of pistachios. After filling up 6 bags that were the same size with the mixture, he had 0.05 lb of nuts left. What was the weight of each bag? Use a tape diagram and show your calculations. Focus
The weight of each bag of the mixture can be determined by using a tape diagram. Given that Linda mixed 5.15 lb of cashews with 4.32 lb of pistachios, and after filling up 6 bags that were the same size with the mixture, he had 0.05 lb of nuts left.
A tape diagram is a bar model that is used to represent fractions and ratios visually. It is useful when comparing different quantities that are related to each other.Tape DiagramTo solve the problem using a tape diagram, we begin by representing the total weight of the mixture and the weight of each bag using a single length unit. For example, we can choose 1 inch to represent the weight of 1 pound.
In this case, we would represent the total weight of the mixture as 5.15 + 4.32 = 9.47 inches. Next, we divide the total length by the number of bags to find the length of each bag. If the total length of the mixture is 9.47 inches and there are 6 bags, then the length of each bag is:9.47 ÷ 6 = 1.578 inches. Finally, we convert the length of each bag back to pounds by multiplying by the weight of 1 pound, which is 1 inch in our tape diagram. Thus, the weight of each bag is:1.578 × 1 = 1.578 lb. Therefore, the weight of each bag of the mixture is 1.578 lb.
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Employees in 2016 paid 4.15% of their gross wages towards social security (FICA tax), while employers paid another 6.3%. How much will someone earning $47,000 a year pay towards social security out of their gross wages?
Someone earning $47,000 a year will pay a total of $4,911.50 towards social security out of their gross wages.
Understanding FICA TaxEmployee Contribution:
The employee paid 4.15% of their gross wages towards social security. So, to calculate the employee's contribution:
Employee Contribution = (4.15/100) * Gross Wages
For someone earning $47,000 a year:
Employee Contribution = (4.15/100) * $47,000
= (0.0415) * $47,000
= $1,950.50
The employee will pay $1,950.50 towards social security.
Employer Contribution:
The employer paid 6.3% of the employee's gross wages towards social security. So, to calculate the employer's contribution:
Employer Contribution = (6.3/100) * Gross Wages
For someone earning $47,000 a year:
Employer Contribution = (6.3/100) * $47,000
= (0.063) * $47,000
= $2,961.00
The employer will pay $2,961.00 towards social security.
Total Social Security Contribution:
To find the total social security contribution, we add the employee and employer contributions:
Total Contribution = Employee Contribution + Employer Contribution
Total Contribution = $1,950.50 + $2,961.00
= $4,911.50
Therefore, someone earning $47,000 a year will pay a total of $4,911.50 towards social security out of their gross wages.
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You want to fit a least-squares regression line to the following data {(1, 2), (2, 4), (3, 5), (4,7)}. Find the equation of the fitted regression line.
The equation of the fitted regression line for the given data {(1, 2), (2, 4), (3, 5), (4, 7)} is y = 1.5x + 0.5, calculated using least-squares method.
To find the equation of the regression line, we can use the least-squares method. This method aims to minimize the sum of the squared differences between the actual data points and the predicted values on the line. In this case, we want to find a line of the form y = mx + b, where m represents the slope and b represents the y-intercept.
To calculate the slope (m) and y-intercept (b), we can use the following formulas:
m = (nΣ(xy) - ΣxΣy) / (nΣ(x^2) - (Σx)^2)
b = (Σy - mΣx) / n
where n is the number of data points, Σxy is the sum of the products of x and y, Σx is the sum of x values, Σy is the sum of y values, and Σ(x^2) is the sum of squared x values.
Using these formulas and the given data, we can calculate the slope and y-intercept as follows:
Σx = 1 + 2 + 3 + 4 = 10
Σy = 2 + 4 + 5 + 7 = 18
Σxy = (1 * 2) + (2 * 4) + (3 * 5) + (4 * 7) = 2 + 8 + 15 + 28 = 53
Σ(x^2) = (1^2) + (2^2) + (3^2) + (4^2) = 1 + 4 + 9 + 16 = 30
n = 4
Now, let's substitute these values into the slope formula:
m = (4 * 53 - 10 * 18) / (4 * 30 - 10^2)
m = (212 - 180) / (120 - 100)
m = 32 / 20
m = 1.6
Next, we can substitute the calculated slope and the sum values into the y-intercept formula:
b = (18 - 1.6 * 10) / 4
b = (18 - 16) / 4
b = 2 / 4
b = 0.5
Therefore, the equation of the fitted regression line is y = 1.5x + 0.5.
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Plz help!!!! Geometry
The little lines inside the two angles mean they are the same.
The 3 inside angles of a triangle equal 180 degrees.
One angle is 146 , so the other two need to equal 180-146 = 34 total.
34/ 2 = 17
Both angle 1 and angle 2 are 17 degrees each.
17, 17
Step-by-step explanation:
assuming both 1 and 2 are congruent and the total amount of angles should add up to 180* we can subtract 180(total) - 146(given) to get 34(angle 1+2) and and divide by 2 since both 1 and 2 are congruent they are the exact same angle
I need help with this problem
Answer:
3
Step-by-step explanation:
4x-6=x+3
3x=9
x=3
substitute the two equations in for each other because they both equal x.
An angle measures 52° more than the measure of its complementary angle. What is the measure of each angle?
I need to know what mistakes he made (if any)
Will mark brainiiest help please <3
Answer:
0.029g
Step-by-step explanation:
implement an iterator class called scaleiterator that scales elements in an iterable iterable by a number scale.
The ScaleIterator class iterates over an iterable, scaling its elements by a given scale factor.
To implement the ScaleIterator class, we can define a custom iterator that takes an iterable and a scale factor as input. The iterator will then iterate over the elements of the iterable and scale each element by multiplying it with the scale factor.
Here's an example implementation in Python:
class ScaleIterator:
def __init__(self, iterable, scale):
self.iterable = iterable
self.scale = scale
def __iter__(self):
return self
def __next__(self):
element = next(self.iterable)
scaled_element = element * self.scale
return scaled_element
The ScaleIterator class has an __init__ method that initializes the iterator with the given iterable and scale factor. It also implements the __iter__ and __next__ methods to make the class iterable. Each time __next__ is called, it retrieves the next element from the underlying iterable, scales it by multiplying with the scale factor, and returns the scaled element.
Using this ScaleIterator, you can iterate over any iterable and obtain scaled elements by specifying the desired scale factor.
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Is (3,10) a solution to this system of equations?
y=2x+3
y=x+7
Answer: no
Step-by-step explanation:
plug in (3,10) to y=2x+3
10=2(3)+3
10=6+3
10[tex]\neq[/tex]9
A computer selects a number X from 4 to 11 randomly and uniformly. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X-U b. Suppose that the computer randomly picks 35 such numbers. What is the distribution of for this selection of numbers. 2- N c. What is the probability that the average of 35 numbers will be more than 7.77 Hint: Some Helpful Videos: Progress saved Done 0/1 pt 0.1
The probability that the average of 35 randomly selected numbers will be more than 7.77 is approximately 0.2157.
How to calculate probability of average?a. The distribution of X is uniform, meaning each number from 4 to 11 has an equal probability of being selected. The probability of selecting any specific number is 1/8 since there are 8 numbers in the range.
b. If the computer randomly picks 35 numbers, the distribution of the selection can be approximated by a normal distribution. This is known as the Central Limit Theorem. The mean of the distribution will still be the same as in part a, which is (4 + 11) / 2 = 7.5. The standard deviation of the distribution can be calculated using the formula:
Standard deviation = (b - a) / √(12)
where a and b are the lower and upper bounds of the range, respectively. In this case, a = 4 and b = 11.
Standard deviation = (11 - 4) / √(12) ≈ 1.6794
Therefore, the distribution of the selection of 35 numbers can be approximated by a normal distribution with a mean of 7.5 and a standard deviation of 1.6794.
c. To find the probability that the average of 35 numbers will be more than 7.77, we need to calculate the z-score and then use the standard normal distribution table.
z-score = (7.77 - 7.5) / (1.6794 / √35) ≈ 0.7832
Using the standard normal distribution table or a calculator, we can find the probability associated with the z-score of 0.7832. Let's assume it is P(Z > 0.7832).
The probability that the average of 35 numbers will be more than 7.77 can be calculated as:
P(Z > 0.7832) = 1 - P(Z < 0.7832)
Referencing the standard normal distribution table or using a calculator, we find the probability to be approximately 0.2157.
Therefore, the probability that the average of 35 numbers will be more than 7.77 is approximately 0.2157 (rounded to 4 decimal places).
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What are closing costs and how do you calculate closing costs?
Answer:
Closing costs are fees paid at the closing of a real estate transaction. Typically home owners will pay between 2 to 5 percent of the purchase price of their home in closing fees. So, if your home cost $150,000, you might pay between $3,000-$7,000 in closing costs.
12% of what number is 1044?
8,700*
12/100=1044/y Equation
1044 x 100= 104,400 Cross multiply
104,400÷12=8700 Divide quotient by pecentage out of 100 (12)
the decimal $0.76$ is equal to the fraction $\frac{4b 19}{6b 11}$, where $b$ is a positive integer. what is the value of $b$?
The value of b is 3. By equating the decimal and the fraction, we solve for b and find that b = 3.
To find the value of b, we equate the decimal 0.76 to the fraction $\frac{4b + 19}{6b + 11}$. We can set up the equation:
0.76 = $\frac{4b + 19}{6b + 11}$
To eliminate the fraction, we cross-multiply:
0.76(6b + 11) = 4b + 19
Expanding and simplifying the left side of the equation:
4.56b + 8.36 = 4b + 19
Next, we isolate the variable b by moving all terms involving b to one side:
4.56b - 4b = 19 - 8.36
0.56b = 10.64
Finally, we divide both sides by 0.56 to solve for b:
b = $\frac{10.64}{0.56}$ ≈ 19
Since b is a positive integer, the closest value is b = 3.
Therefore, the value of b is 3.
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An earthquake measured 4.5 on richter scale how many times less
powerful is it than a 6.3 earthquake
A 4.5 magnitude earthquake is approximately 316.22776 times less powerful than a 6.3 magnitude earthquake.
The Richter scale is a logarithmic scale that measures the magnitude or strength of earthquakes. Each whole number increase on the Richter scale represents a tenfold increase in the amplitude of seismic waves and approximately 31.6 times more energy released. Therefore, to compare the power or strength of two earthquakes on the Richter scale, we can use the formula:
Ratio =[tex]10^((Magnitude2 - Magnitude1) * 1.5)[/tex]
In this case, we want to compare a 4.5 magnitude earthquake to a 6.3 magnitude earthquake. Plugging the values into the formula, we get:
Ratio = 1[tex]0^((6.3 - 4.5) * 1.5) ≈ 316.22776[/tex]
This means that the 4.5 magnitude earthquake is approximately 316.22776 times less powerful than the 6.3 magnitude earthquake.
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Athletes were doing a timed 100-metre dash. Athletes times were organized into a Normal Curve distribution of frequencies. If the mean was 10 seconds (µ), with a standard deviation of 2(σ), create the 1-2-3 curve. Place the actual research data values in the 1-2-3 curve sketch.
If an athlete got a time of 9 seconds (x), calculate their Z-score and place it on the curve.
Use the Z-tables to determine what percentage of the team was below the athlete and above the athlete
The Z-score for an athlete with a time of 9 seconds is -0.5. Approximately 30.85% of the team was below the athlete, and approximately 69.15% of the team was above the athlete based on the Z-score.
To create the 1-2-3 curve, we can use the mean (µ) and standard deviation (σ) to mark the values on the curve. The 1-2-3 curve represents the standard deviations away from the mean.
1-2-3 Curve:
1st Standard Deviation: Mean ± σ
2nd Standard Deviation: Mean ± 2σ
3rd Standard Deviation: Mean ± 3σ
We have that the mean (µ) is 10 seconds and the standard deviation (σ) is 2 seconds, we can mark the 1-2-3 curve as follows:
1st Standard Deviation: 8 to 12 seconds
2nd Standard Deviation: 6 to 14 seconds
3rd Standard Deviation: 4 to 16 seconds
If an athlete has a time of 9 seconds (x), we can calculate their Z-score using the formula: Z = (x - µ) / σ.
Z-score: (9 - 10) / 2 = -0.5
Placing the Z-score of -0.5 on the curve, we find that it falls between the mean and the first standard deviation (8 to 12 seconds).
To determine the percentage of the team below the athlete and above the athlete, we can use the Z-table. Looking up the Z-score of -0.5 in the table, we find that the area below the Z-score is 0.3085. This means that approximately 30.85% of the team's times were below the athlete's time of 9 seconds.
To compute the area above the Z-score, we subtract the area below from 1: 1 - 0.3085 = 0.6915. This indicates that approximately 69.15% of the team's times were above the athlete's time of 9 seconds.
Therefore, approximately 30.85% of the team was below the athlete, and approximately 69.15% of the team was above the athlete based on the Z-score of -0.5.
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For the linear function(straight line) y = 7x - 3,ar function(straight line) y = 7x - 3,
a) What is the slope of the given function?
b) Is the function increasing or decreasing?
c) What is the y-intercept(0, b) of the given function?
Answer:
a) slope is 7
b) slope is positive, so Increasing
c) y-intercept is -3
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Which is true about the solution to the system of inequalities shown?
y > 3x + 1
y < 3x – 3
On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.
Only values that satisfy y > 3x + 1 are solutions.
Only values that satisfy y < 3x – 3 are solutions.
Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.
There are no solutions. Edge 2022
6. give the figure at the right,what is the measure of dbc
A. 54°
b. 36°
C. 126°
D. 116°
Answer:
c.126
Step-by-step explanation:
180-54=126
What’s the answer plzzzzzzzz?
Step-by-step explanation:
please forgive me if I have done something wrong there I am in a hurry I have to go ccooking. if there's something wrong there you can tell me I check it out when I come back good luck.
Answer:
1. 4310.3
2.1809.6
3. 2414.7
4. 230.9
5. 767.8
6. 70.3
7.1143.4
8.125.7
9. 1382.0
10. 158.5
Step-by-step explanation:
Solve the following exponential equations
Answer:
x = 2, y = - 25
Step-by-step explanation:
(1)
note that 36 = 6² , then
[tex]6^{x}[/tex] = 6²
Since bases on both sides are equal then equate the exponents
x = 2
------------------------------------------
(2)
Using the rule of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
note that 25 = 5² , then
[tex]25^{11+3y}[/tex] = [tex](5^2)^{11+3y}[/tex] = [tex]5^{22+6y}[/tex]
Then
[tex]5^{5y-3}[/tex] = [tex]5^{22+6y}[/tex]
Since bases on both sides are equal then equate the exponents
22 + 6y = 5y - 3 ( subtract 5y from both sides )
22 + y = - 3 ( subtract 22 from both sides )
y = - 25
Let S denote the vector space of solutions to the differential equation my" - 8«y' + 18y = 0. Circle each set below, if any, that is a basis for S. Show work or explanation to justify your answer: Si = {x} S2 = {x",) S3 = {3.8 +67"} Su = {z + 4x0,728 - } Ss = {x....) b). • Prove that if S-AS = B for some invertible matrix S and v is an eigenvector of A corresponding to then S-lv is an eigenvector of B corresponding to . c) • Let {vi. Va be a linearly independent set of vectors in a vector space V. Prove that if va span{ V1.va). then {V1, V2, V3} is a linearly independent set. d). TRUE or FALSE: If A is a 13 x 4 matrix will nullity(A) 0, then colspace(A) = R'.
The sets given are not bases for the vector space of solutions to the differential equation. A property of invertible matrices is explained. If a set of vectors is linearly independent and spans a subspace, then adding another vector to the set maintains linear independence. The statement about nullity and column space is false.
a) None of the sets Si, S2, S3, Su, or Ss is a basis for the vector space S of solutions to the given differential equation.
b) Let A be the matrix associated with the linear transformation defined by the differential equation. If S is an invertible matrix such that SAS⁻¹ = B, where B is another matrix, and v is an eigenvector of A corresponding to the eigenvalue λ, then S⁻¹v is an eigenvector of B corresponding to the eigenvalue λ.
c) Suppose {v₁, v₂, v₃} is a linearly independent set of vectors in a vector space V. If va spans the subspace span{v₁, v₂}, then {v₁, v₂, v₃} is also a linearly independent set.
d) FALSE. If A is a 13 x 4 matrix with nullity(A) = 0, it means that the matrix has no nontrivial solutions to the homogeneous system Ax = 0. This implies that the columns of A are linearly independent, but it does not guarantee that colspace(A) = ℝⁿ. The column space of A could still be a proper subspace of ℝⁿ.
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Help please with number 1. Writw the orderd pair that coresponds to Point H.
Answer: yeah you got it
Step-by-step explanation:
Which is a better deal: 30 fluid ounces of shampoo for $3.55 or 50 fluid ounces of shampoo for $6?
30 fl oz for $3.55
if we make them each 10 fl oz then here are the costs:
$1.18 (originally 30 fl oz)
$1.20 (originally 50 fl oz)
Label the following statements as being true or false. For the following, V and W are vector spaces with ordered (finite) bases a and B, respectively, and T:V + W is linear. A and B are matrices. (a) ([T]2)-1 = [T-] (b) T is invertible if and only if T is one-to-one and onto. (c) T= LA, where A = [T].. (d) M2x3(F) is isomorphic to FS. (e) P.(F) is isomorphic to Pm(F) if and only if n = m. (f) AB = I implies that A and B are invertible. (g) (A-1)-1 = A. (h) A is invertible if and only if L, is invertible. (i) A must be square in order to possess an inverse.
The following are the correct answers for the statement V and W are vector spaces with ordered (finite) bases a and B, respectively, and T:V + W is linear. A and B are matrices:
(a) False. ([T]2)-1 refers to the inverse of the square of the matrix representing the linear transformation T, while [T-] refers to the inverse of the matrix representing the linear transformation T itself. These two are not necessarily equal.
(b) True. T is invertible if and only if it is both one-to-one (injective) and onto (surjective). This property ensures that there exists a unique inverse transformation that undoes the effects of T.
(c) False. T is a linear transformation, and A is the matrix representation of T. So, T = [T], where A = [T] is the matrix representation.
(d) False. M2x3(F) represents the set of 2x3 matrices over the field F, while FS represents the set of column vectors of finite length over the field F. These two vector spaces are not isomorphic since they have different dimensions.
(e) True. P.(F) represents the set of polynomials over the field F, and Pm(F) represents the set of polynomials of degree at most m over the field F. These two vector spaces are isomorphic if and only if the degree of the polynomials is equal (n = m).
(f) False. AB = I implies that A and B are left and right inverses of each other, respectively, but it does not necessarily imply that they are invertible. Invertibility is determined by the existence of an inverse matrix, which is not guaranteed by AB = I alone.
(g) True. The inverse of the inverse of a matrix is the matrix itself.
(h) True. If A is invertible, then its matrix representation [A] is invertible as well. Similarly, if [A] is invertible, then A is invertible.
(i) True. In order to possess an inverse, a matrix must be square (i.e., have the same number of rows and columns). Non-square matrices do not have inverses.
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janice exercises everyday. she spends 35% of her exercise time swimming. she spends the rest of her exercise time jogging.which percent bar represents the percent of exercise time janice spends swimming
Answer:
35%
Step-by-step explanation:
100% - 35% = 65%
Janice spends 35% swimming
And spends 65% jogging
Brian has deposited $2,200 in a savings account that earns 7%
simple interest every year. His friend, Carlos, deposited $2,100 in a
saving account that earns 8% simple interest. Both Brian and Carlos
opened their accounts on the same day and have not made any more
deposits in either account. What will be the difference in their savings
accounts after 5 years?
Answer:
The difference after 5 years is 772.57
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!
Answer:
All integers are rational numbers
Step-by-step explanation:
Since any integer can be written as the ratio of two integers, all integers are rational numbers. Remember that all the counting numbers and all the whole numbers are also integers, and so they, too, are rational.
Answer:
True
Step-by-step explanation:
An integer is a number including positive and negatives with 0 that are whole numbers and are not fractions or decimals
lora has 9 fish and dylan has 2 fish. lora wants to know how many more fish does she has then dylan lora has 9 fish and dylan has 2 fish. lora wants to know how many more fish does she has then dylan lora has 9 fish and dylan has 2 fish. lora wants to know how many more fish does she has then dylan lora has 9 fish and dylan has 2 fish. lora wants to know how many more fish does she has then dylan
Answer:
7
Step-by-step explanation:
Answer: 7
Because 9-2=7
In January of 2022, an outbreak of the PROBAB-1550 Virus occurred at the Johnaras Hospital in wards A, B and C. It is known that:
• Ward A has 35 patients, 10 percent of whom have the virus,
• Ward B has 70 patients, 15 percent of whom have the virus,
• Ward C has 50 patients, 20 percent of whom have the virus. (1 point)
(a) What is the probability that a randomly selected student from these three wards has the virus? (1 point)
(b) If a randomly selected student from the hospital has the virus, what is the proba- bility that they are in Ward C?
(a) The probability that a randomly selected student from the three wards has the virus is 24%.
(b) The probability that a randomly selected student from the hospital who has the virus is in Ward C is approximately 24.5%
a) The probability that a randomly selected student from the three wards has the virus is: (10% of 35) + (15% of 70) + (20% of 50) = 3.5 + 10.5 + 10 = 24%.Thus, the probability that a randomly selected student from the three wards has the virus is 24%.
b) If a randomly selected student from the hospital has the virus, the probability that they are in Ward C is given by Bayes' theorem. The formula for Bayes' theorem is:P(A|B) = P(B|A) x P(A) / P(B)where:P(A|B) is the probability of event A occurring given that event B has occurred. In this case, A is the event that the student is in Ward C and B is the event that the student has the virus.P(B|A) is the probability of event B occurring given that event A has occurred. In this case, it is the proportion of patients in Ward C who have the virus, which is 20%.P(A) is the probability of event A occurring. In this case, it is the proportion of all patients in the hospital who are in Ward C, which is 50 / (35 + 70 + 50) = 0.2941.P(B) is the probability of event B occurring. In this case, it is the probability of a randomly selected student having the virus, which is 24%.Thus, the probability that a randomly selected student from the hospital who has the virus is in Ward C is:P(A|B) = 0.2 x 0.2941 / 0.24 ≈ 0.245 or 24.5%.Hence, the probability that a randomly selected student from the hospital who has the virus is in Ward C is approximately 24.5%.
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A randomly selected student from the hospital has the virus, the probability that they are in Ward C is 0.2.
The solution to the given problem is explained as follows:
(a) What is the probability that a randomly selected student from these three wards has the virus.
The total number of students in the three wards is:
35 + 70 + 50 = 155 students.
Thus, the probability that a randomly selected student from these three wards has the virus is given by:
P(Probab-1550) = P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(B ∩ C) - P(C ∩ A) + P(A ∩ B ∩ C)
WhereP(A) = probability of selecting a student from ward A and
having the virus = 0.1,
P(B) = probability of selecting a student from ward B and
having the virus = 0.15,
P(C) = probability of selecting a student from ward C and
having the virus = 0.2,
P(A ∩ B) = probability of selecting a student from both wards A and B and having the virus.
P(B ∩ C) = probability of selecting a student from both wards B and C and having the virus.
P(C ∩ A) = probability of selecting a student from both wards C and A and having the virus.
P(A ∩ B ∩ C) = probability of selecting a student from all three wards and having the virus = 0.
From the given information:•
Ward A has 35 patients, 10 percent of whom have the virus,•
Ward B has 70 patients, 15 percent of whom have the virus,•
Ward C has 50 patients, 20 percent of whom have the virus
,Thus,P(A) = 35 × 0.1 / 100 = 0.035,
P(B) = 70 × 0.15 / 100 = 0.105,
P(C) = 50 × 0.2 / 100 = 0.10,
And,P(A ∩ B) = 0.035 × 0.105
= 0.00367,P(B ∩ C)
= 0.105 × 0.1 = 0.0105,
P(C ∩ A) = 0.1 × 0.035 = 0.0035,
P(Probab-1550) = 0.035 + 0.105 + 0.1 - 0.00367 - 0.0105 - 0.0035 + 0
= 0.22333
So, the probability that a randomly selected student from these three wards has the virus is 0.22333.
(b) If a randomly selected student from the hospital has the virus, what is the probability that they are in Ward C?
The probability that a randomly selected student from the hospital has the virus is
P(Probab-1550) = 0.22333.
From Bayes’ theorem,
P(C | Probab-1550) = P(Probab-1550 | C) × P(C) / P(Probab-1550)
where,P(C | Probab-1550) is the probability that a randomly selected student from Ward C has the virus,
P(Probab-1550 | C) is the probability that a student from Ward C has the virus,
P(C) is the probability of selecting a student from Ward C.P(Probab-1550 | C) = 0.2
= probability of selecting a student from Ward C and having the virus,
P(C) = 50 / 155 = probability of selecting a student from Ward C,
Therefore,P(C | Probab-1550) = 0.2 × 0.22333 / 0.22333
= 0.2
Thus, if a randomly selected student from the hospital has the virus, the probability that they are in Ward C is 0.2.
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A movie theater gave away coupons for smallmediumand large drinks. Customers could randomly pull a coupon from a box that held 75 small drink coupons , 125 drink coupons , and 150 large drink coupons . What is the probability that the first customer to pull a coupon from the box got a medium drink coupon ?
Answer: 35.7%
Step-by-step explanation:
First find out the total number of all coupons in the box.
= 75 + 125 + 150
= 350 drink coupons
There are 125 medium coupons so the probability that the first customer will pick a medium one is:
= Number of medium coupons / Number of total coupons
= 125 / 350
= 35.7%