Therefore, the probability that the first card is a diamond or the second card is a face card is approximately 0.3039.
We can solve this problem by using the addition rule of probability.
The probability of the first card being a diamond is 13/52 (since there are 13 diamonds in a standard deck of 52 cards). The probability of the second card being a face card is 12/51 (since there are 12 face cards left in the deck after the first card is drawn).
To find the probability that either event occurs, we add the probabilities and subtract the probability of both events happening together (since we only want to count that once):
P(diamond or face card) = P(diamond) + P(face card) - P(diamond and face card)
P(diamond or face card) = 13/52 + 12/51 - (3/51) [since there are 3 face cards that are also diamonds]
Simplifying the expression, we get:
P(diamond or face card) = 0.3039
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PLS HELP PEOPLE THIS IS THE LAST QUESTION ON MY FINAL ❗❗❗❗❗
What is the value of x in the diagram?
E(y∣x)=β 0 +β 1 x (a) Now apply the properties of expected value to write the unconditional expectation E(y) as a function of the unconditional expectation E(x). That is, simplify the following expression. [Hint: you should recognize the result as following from the Law of Iterated Expectations.] E(y)=E(β 0 +β 1 x+u)=
The unconditional expectation of y (E(y)) equals β0 + (β1 * E(x)), derived using the Law of Iterated Expectations.
To simplify the expression for the unconditional expectation E(y), we can apply the properties of expected value and the Law of Iterated Expectations. The Law of Iterated Expectations states that the unconditional expectation of a conditional expectation is equal to the unconditional expectation itself.
Starting with the expression for E(y):
E(y) = E(β0 + β1x + u)
We can break down this expression using the linearity of expectation:
E(y) = E(β0) + E(β1x) + E(u)
Since β0 and β1 are constants, their expected values are equal to themselves:
E(y) = β0 + β1E(x) + E(u)
Now, since u is the error term and it is assumed to have a mean of zero (E(u) = 0), the expression simplifies to:
E(y) = β0 + β1E(x)
Therefore, we can conclude that the unconditional expectation of y (E(y)) is equal to the constant term β0 plus the product of the slope coefficient β1 and the unconditional expectation of x (E(x)). This result follows from the Law of Iterated Expectations, which allows us to simplify the expression by considering the expected values of the individual terms separately.
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Find the zeros of functions.Enter the solutions from least to greatest.
F(x)=-(x+6)^2 -49
Lesser x=
Greater x=
The zeros of the function F(x) = -(x+6)^2 - 49 are -6 - 7i and -6 + 7i.
To find the zeros of the function F(x) = -(x+6)^2 - 49, we need to find the values of x when F(x) = 0.
Step 1: Set the function equal to 0.
0 = -(x+6)^2 - 49
Step 2: Isolate the squared term.
49 = -(x+6)^2
Step 3: Divide both sides by -1 to remove the negative sign.
-49 = (x+6)^2
Step 4: Take the square root of both sides.
√(-49) = x+6
Since the square root of a negative number is a complex number (involving an imaginary unit 'i'), there are no real zeros for this function. The zeros are complex and can be written as:
Lesser x = -6 - 7i
Greater x = -6 + 7i
Your answer: The zeros of the function F(x) = -(x+6)^2 - 49 are -6 - 7i and -6 + 7i.
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the heights (in inches) of fifth-grade boy students in a school district in suffolk county, new york are known to be normally distributed. the heights of a random sample of 11 fifth-grade boy students in the school district are shown below. 59.0 57.2 57.1 58.0 57.0 50.1 52.3 55.6 57.8 53.9 57.8 find the value of the test statistic for a test to show that the population mean height of the school district is lower than 59 inches (round off to first decimal place).
To find the test statistic for a test to show that the population mean height of the school district is lower than 59 inches, we can perform a one-sample t-test.
The test statistic is calculated using the sample mean, sample standard deviation, sample size, and the hypothesized population mean.
Given the sample heights of the 11 fifth-grade boy students: 59.0, 57.2, 57.1, 58.0, 57.0, 50.1, 52.3, 55.6, 57.8, 53.9, 57.8, we can calculate the sample mean () and sample standard deviation (s).
= (59.0 + 57.2 + 57.1 + 58.0 + 57.0 + 50.1 + 52.3 + 55.6 + 57.8 + 53.9 + 57.8) / 11
Next, calculate the sample standard deviation:
s = sqrt(((59.0 - )^2 + (57.2 - )^2 + ... + (57.8 - )^2) / (11 - 1))
Once you have the sample mean and sample standard deviation, you can calculate the test statistic (t):
t = ( - μ) / (s / sqrt(n))
where μ is the hypothesized population mean (in this case, 59 inches), and n is the sample size (11).
By substituting the values into the formula, you can calculate the test statistic rounded off to the first decimal place.
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Sylvia is going to pick out a souvenir hat while she is on vacation. She knows the price of the hat will increase by 5% when she pays sales tax. She writes the expression h+0. 05h to find the total amount she will pay for the hat if it costs h dollars. Jin correctly writes another expression 1. 05h 5hat will also find the total amount Slavia will pay for the hat if it costs h dollars
The expression 1.05h correctly represents the total amount Sylvia will pay for the hat if it costs h dollars.
Sylvia knows that the price of the hat will increase by 5% when she pays sales tax. Let's break down the expressions to understand them better.
Expression 1: h + 0.05h
In this expression, h represents the cost of the hat. Adding 0.05h to h accounts for a 5% increase. However, this expression does not accurately represent the total amount Sylvia will pay because it only considers the increase due to sales tax, not the original cost of the hat.
Expression 2: 1.05h
In this expression, 1.05 represents the total cost multiplier, which includes the original cost of the hat and the 5% increase. Multiplying h by 1.05 accounts for both the original cost and the sales tax increase. This expression correctly calculates the total amount Sylvia will pay for the hat.
Therefore, the expression 1.05h is the correct representation of the total amount Sylvia will pay for the hat if it costs h dollars.
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A researcher is interested in estimating the proportion of voters who favor a tax on e-commerce. Based on a sample of 250 people, she obtains the following 99% confidence interval for the population proportion, p: 0.113 < p <0.171. Which of the statements below is a valid interpretation of this confidence interval? A) If many different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, in the long run 99% of the confidence intervals would contain the true value of p. B) If many different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, 99% of the time the true value of p would lie between 0.113 and C) There is a 99% chance that the true value of p lies between 0.113 and 0.171. D) If 100 different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, exactly 99 of these confidence intervals would contain the true value of p.
Answer:
The correct answer is: A. If many different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, in the long run 99% of the confidence intervals would contain the true value of p.
Step-by-step explanation:
A confidence interval is a range of values that is likely to contain the true value of a population parameter. In this case, the population parameter is the proportion of voters who favor a tax on e-commerce. The confidence interval is constructed from a sample of voters, and it is based on the assumption that the sample is representative of the population.
The 99% confidence interval means that if we were to take many different samples of size 250 and construct a confidence interval for each sample, 99% of the confidence intervals would contain the true value of the population proportion. This does not mean that there is a 99% chance that the true value of the population proportion lies between 0.113 and 0.171. It means that if we were to take many different samples of size 250 and construct a confidence interval for each sample, 99% of the confidence intervals would contain the true value of the population proportion.
The other answer choices are incorrect because they do not correctly interpret the meaning of a confidence interval.
what is $7.00-19 cent?
Answer:
$6.81 or 681 US Cents
Step-by-step explanation:
100 - 19 = 81
7 - 1 = 6
$7.00 - .19 = $6.81
or 681 US Cents.
Find the volume of
the recycling bin
when the length is
doubled.
Recycling
Bin
15 ft
12 ft
10 ft
Volume doubled =
The volume of the recycling bin when the length is doubled is 3,600 cubic feet.
To find the volume of the recycling bin when the length is doubled, we first need to determine the original volume of the bin.
The formula for the volume of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height.
In this case, the length is 15 ft, the width is 12 ft, and the height is 10 ft. So the original volume of the recycling bin is:
V = lwh = 15 ft × 12 ft × 10 ft = 1,800 cubic feet
To find the volume when the length is doubled, we simply need to multiply the original length by 2, and then calculate the new volume using the same formula:
New length = 15 ft × 2 = 30 ft
New volume = lwh = 30 ft × 12 ft × 10 ft = 3,600 cubic feet
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what function computes the value in which one-half of the data is above and one-half is below.
a. Middle
b. Mode c. average
d. Median
A man took a loan of 90000 naira without interest from a cooperative society and he is to be paying back 2500 naira on monthly instalmemt. How many years will it take him to finish paying the debt ?
To calculate the number of years it will take to finish paying the debt, we need to determine the total number of monthly installments required.
Loan amount: ₦90,000
Monthly installment: ₦2,500
Total number of installments: Loan amount / Monthly installment
Total number of installments: ₦90,000 / ₦2,500 = 36
Therefore, it will take the man 36 months to finish paying the debt. To convert this into years, we divide the number of months by 12 since there are 12 months in a year.
Number of years: 36 months / 12 months/year = 3 years
Hence, it will take him approximately 3 years to finish paying the debt.
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What would be the interest for Rs. 1000 in 2 years at the rate of Rs. 2 per month per hundred rupees? discribe
Answer:
Step-by-step explanation:
principle=1000
time= 2 years
rate = 2×12=24/100=0.24%
simple intrest= p×r×t
= 1000 × 0.24 × 2
=480 rupees
total amount will be 1000 + 480= 1480
E
Find the lateral area for the regular pyramid.
O36√91 sq. units
O48 91 sq. units
O18√91 sq. units
8√91 sq. units
The lateral area for the regular pyramid is 18√91 sq. units
The base of the pyramid has a side length of 6 units
Hypotenuse of triangle is the lateral edge
base = 6 and height = 8
Lateral edge = 10
To find the slant height
The height of triangle with base 3 and hypotenuse 10 is Slant height
Slant height = √91
To find the area of single face
Area = bh/2
b = 6 and h = √91
Area = (6×√91)/2 = 3√91
To find the lateral area of pyramid
Lateral area = 6×face area = 6×3√91 = 18√91 square units
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The perimeter of the trapezium, in millimeters (mm) is
The perimeter of trapezium, is 0.92 meters. And 0.92 meters in millimeters is 920 mm. Therefore, option B is the answer.
Let's name the trapezium as ABCD.
AB= 0.41m
BD= 0.21m
CD= 0.18m
AC= 0.12m
∴ AB and CD are parallel sides and AC and BD are oblique sides.
The perimeter of trapezium = Sum of parallel sides + Sum of oblique sides
The perimeter of trapezium = (AB+CD) + (AC+BD)
= (0.41+0.18) + (0.12+0.21)
= 0.59 + 0.33
∴ The perimeter of trapezium ABCD = 0.92 meters.
Converting 0.92 meters into millimeters (mm)
0.92 × 1000 = 920 millimeters (mm)
Therefore, the perimeter of trapezium in millimeters is 920 mm.
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Put the following equation of a line into slope-intercept form, simplifying all fractions. 9 � + 3 � = 9x+3y= − 9 −9
The equation of the line in Slope-intercept form is y = -3x - 3.
The equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, we need to solve for y.
Starting with the given equation:
9x + 3y = -9
We can isolate y by subtracting 9x from both sides:
3y = -9x - 9
Now we can simplify the equation by dividing both sides by 3:
y = (-9/3)x - 3
Simplifying the fraction, we get:
y = -3x - 3
Therefore, the equation of the line in slope-intercept form is y = -3x - 3.
The slope of the line is -3, which means that for every 1 unit increase in x, y decreases by 3 units. The y-intercept is -3, which means that the line crosses the y-axis at the point (0, -3).
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Given: Triangle ABC is a right triangle. Angle C = 90 degrees; The measures of the sides are 5, 12, 13.
What is the measure of both acute angles?
Do not label. Round your final answers to the nearest tenth.
The value of the acute angles are 67.4° and 22.6° respectively
What is trigonometric ratio?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
sin(tetha) = opp/hyp
cos( tetha) = adj/hyp
tan(tetha) = opp/adj
Here the longest side which is the hypotenuse is 13 and the other legs of the right triangle are 12 and 13.
Represent the acute angle by A and B. If 12 is that opposite and 5 is the adjascent
sin A = 12/13
A = sin^-1( 0.923)
A = 67.4°
sinB = 5/13
B = sin^-1( 0.385)
B = 22.6°
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Farm workers harvested 5 kg of
raspberries from 8 different bushes.
If they harvested the same amount
from each bush, how many kilograms
of raspberries come from one bush?
PLSSS HELP DUE TODAY
Help please step by step
Answer:
32.5
Step-by-step explanation:
if it completes a pack per second then it’s 32.5 g per second but this question does not have much detail on what you need to do
The cost C (in dollars) of buying three boxes of popcorn and a fountain drink is represented by the equation C = 3x + 1.75. How much is one box of popcorn when the cost is $9.70?
Answer:
$9.25
Step-by-step explanation:
One box of popcorn costs $2.65 while the total cost of three boxes of popcorn and a fountain drink is $9.70.
We have,
We are given that the cost C of buying three boxes of popcorn and a fountain drink is represented by the equation C = 3x + 1.75.
Where x is the number of popcorn.
Now,
We want to find the cost of one box of popcorn when the cost is $9.70.
Let's first substitute C = 9.70 into the equation:
9.70 = 3x + 1.75
Next, we'll isolate x by subtracting 1.75 from both sides:
9.70 - 1.75 = 3x
7.95 = 3x
Finally, we'll solve for x by dividing both sides by 3:
x = 7.95/3 = 2.65
Therefore,
One box of popcorn costs $2.65 while the total cost of three boxes of popcorn and a fountain drink is $9.70.
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an airplane has 29 seats. the price for coach seat is 600, and the price for a first-class seat is $1,050. the airline collected a total of $21,900 for a flight
Answer:
x = 19
Step-by-step explanation:
Let's use the following variables:
Let x be the number of coach seats sold.
Let y be the number of first-class seats sold.
We know that there are 29 seats in total, so:
x + y = 29
We also know that the total amount collected for the flight was $21,900, so:
600x + 1050y = 21,900
We can solve this system of equations by substitution or elimination. Let's use elimination.
Multiplying the first equation by 600, we get:
600x + 600y = 17400
Subtracting this equation from the second equation, we get:
450y = 4500
Dividing both sides by 450, we get:
y = 10
Substituting this value into the first equation, we get:
x + 10 = 29
x = 19
Therefore, the airline sold 19 coach seats and 10 first-class seats.
a professor does not believe that his students spend 2 hours on average studying for the final exam. he thinks they spend more time than that. what are the null and alternative hypotheses, respectively?
The null hypothesis (H0) is that the average time spent studying is 2 hours or less, while the alternative hypothesis (H1 or Ha) is that the average time spent studying is more than 2 hours.
The null hypothesis (H0) is a statement of no effect or no difference, while the alternative hypothesis (H1 or Ha) is a statement of the opposite, suggesting that there is an effect or a difference.
In this case, the professor does not believe that his students spend 2 hours on average studying for the final exam and thinks they spend more time than that.
The null hypothesis (H0) would be that the average time spent studying for the final exam is indeed 2 hours or less:
H0: μ ≤ 2
The alternative hypothesis (H1 or Ha) would be that the average time spent studying for the final exam is more than 2 hours:
Ha: μ > 2
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Use the formula to find the surface area of the figure. Show your work.
Answer:
SURFCE AREA =2pie r squired + 2 pie × r×hI will give 25 points to whoever can help with this surface area and volume question
Answer:
Surface area = 408.2cm²
Volume = 628cm²
Step-by-step explanation:
r = radius
h = height
Surface Area
A = 2xπxrxh+2xπxr²
A = 2 x 3.14 x 5 x 8 + 2 x 3.14 x 25
A = 251.2 + 157
A = 408.2cm²
Volume
V = πr²h
V = 3.14 x 5 x 5 x 8
V = 628cm²
agencia de viajes quiere incrementar el turismo nacional por carretera, para ello genera una estrategia
publicitaria, cuyos resultados exitosos se verían reflejados cuando
A. se mantengan los porcentajes de respuesta a la pregunta 2
B. se aumente el porcentaje de personas que prefieren viajar a lugares cercanos a su residencia, en la
pregunta 3
C. los porcentajes de respuesta a la pregunta 1 quedan intercambiados y se mantengan los porcentajes en
las otras preguntas
D. se disminuyan los porcentajes de los que no prefieren viajar por carretera, en la pregunta
Options B and D are the most relevant to the Objective of increasing national tourism by road. By increasing the percentage of people who prefer to travel to nearby destinations and reducing the percentage of those who do not prefer road travel, the travel agency can effectively promote road tourism within the country.
A travel agency's goal is to increase national tourism by road, and they have developed an advertising strategy to achieve this. The success of this strategy will be reflected in certain criteria. Let's examine the options:
A. Maintaining the response rates to question 2.
This option does not directly indicate how it relates to the objective of increasing national tourism by road. It does not specify how the response rates to question 2 contribute to achieving the goal.
B. Increasing the percentage of people who prefer to travel to places close to their residence, as mentioned in question 3.
This option aligns with the objective of promoting national tourism by road. By encouraging people to choose destinations that are closer to their residences, the travel agency aims to promote road travel within the country. Therefore, this option is relevant to the goal of increasing national tourism by road.
C. Exchanging the percentages of answers to question 1 and maintaining the percentages in the other questions.
This option does not provide clear information on how it relates to the objective of increasing national tourism by road. Swapping the percentages of answers to question 1 alone may not directly contribute to the goal unless the specific content of the question is known.
D. Reducing the percentages of those who do not prefer to travel by road, as mentioned in the question.
This option is directly aligned with the objective of increasing national tourism by road. By reducing the percentage of people who do not prefer road travel, the travel agency aims to attract more travelers to choose road transportation for their trips.
In conclusion, options B and D are the most relevant to the objective of increasing national tourism by road. By increasing the percentage of people who prefer to travel to nearby destinations and reducing the percentage of those who do not prefer road travel, the travel agency can effectively promote road tourism within the country.
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The spinner shown is spun once. find each probability p(6), p(prime number), p(odd or unshaded)
use the spinner below to help u solve this
The probabilities for this problem are given as follows:
p(6) = 1/12.p(prime number) = 1/2.p(odd or unshaded) = 3/4.How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The total number of regions is given as follows:
12.
One of these 12 regions is a six, hence:
p(6) = 1/12.
Six of these numbers are prime numbers, hence:
p(prime number) = 6/12 = 1/2.
Six of the numbers are odd, while 4, 6 and 9 are unshaded even numbers, hence:
p(odd or unshaded) = 9/12 = 3/4.
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The table shows the number of laps Candice and her two friends ran each day for five days. Drag the names to order them from the least consistent number of laps each day (at the bottom) to the most consistent number of laps each day (at the top).
The order of Candice and her friends in terms of who was more consistent would be :
Zoe Malaya Candice How to order the consistency ?Candice is judged to be the least consistent of the friends because of her range which is:
= Largest laps - least laps
= 8 - 5
= 3 laps
Malaya and Zoe the same range so this cannot be used to show which of them was more consistent. Instead, we will use the mode. The person that has the mode which appears more times is more consistent.
Zoe has a mode of 8 laps which appears 3 times as opposed to the mode of 3 laps for Malaya which only appears twice. Zoe is therefore most consistent.
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segment jk has coordinates j(3 -6) and k(-3 2). Find the coordinates of the midpoint M. Find the distance between the endpoints of JK.
The coordinates of the midpoint M of segment JK are (-0. 3). The distance between the endpoints of JK is sqrt(104) or approximately 10.198.
To find the coordinates of the midpoint M of segment JK, we can use the midpoint formula, which states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints. So, for segment JK with endpoints J(3, -6) and K(-3, 2), the x-coordinate of the midpoint is (-3+3)/2 = 0 and the y-coordinate of the midpoint is (-6+2)/2 = -2. Therefore, the coordinates of the midpoint M are (0, -2).
To find the distance between the endpoints of JK, we can use the distance formula, which states that the distance between two points with coordinates (x1, y1) and (x2, y2) is given by the square root of [(x2-x1)^2 + (y2-y1)^2]. So for segment JK with endpoints J(3, -6) and K(-3, 2), the distance is sqrt[(-3-3)^2 + (2-(-6))^2] = sqrt[36 + 64] = sqrt(100) = 10. Therefore, the distance between the endpoints of JK is approximately 10.198.
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helpp pls Triangle abc has side lengths b=13.5 and c=8.9 angel a has a measure of 29°. What is the length of side a
a.14.9
b.6.0
c.7.2
d.10.1
The length of side a is approximately 6.0 in the triangle. The correct option is (b) 6.0.
To find the length of side a in triangle ABC, we can use the Law of Sines.
The Law of Sines states that the ratio of a side length to the sine of its opposite angle is constant for all sides of a triangle.
In this case, we have:
a/sin(A) = b/sin(B) = c/sin(C)
Given that angle A has a measure of 29°, we can substitute the known values:
a/sin(29°) = 13.5/sin(B) = 8.9/sin(C)
Solving for side a, we have:
a = sin(29°) × 13.5 / sin(B)
To find sin(B), we can use the fact that the sum of the angles in a triangle is 180°:
B = 180° - A - C = 180° - 29° - 90° (since angle C is 90° in a right triangle)
B = 61°
Now we can calculate side a:
a = sin(29°) × 13.5 / sin(61°)
a ≈ 6.0
Therefore, the length of side a is approximately 6.0. The correct option is (b) 6.0.
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I need some help with this asap!
The inverse of f(x) = 11x - 8 include the following: C. [tex]f^{-1}(x) = \frac{x+8}{11}[/tex]
What is an inverse function?In Mathematics and Geometry, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In this exercise, you are required to determine the inverse of the function f(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;
f(x) = y = 11x - 8
x = 11y - 8
11y = x + 8
By dividing both sides of the equation by 11, we have:
y = x/11 + 8/11
f⁻¹(x) = (x + 8)/11
[tex]f^{-1}(x) = \frac{x+8}{11}[/tex]
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The school day is 6 hours, 15 minutes long. Jenna says that it’s 61
4 hours. Henry says it’s
6. 25 hours. Can they both be correct? Explain. What part of the length of the school day is the same in all three ways
the time is given
No, Jenna and Henry cannot both be correct. Jenna’s answer of 614 hours is incorrect, as it is much too long for a school day. Henry’s answer of 6.25 hours is also incorrect, as it is much too short for a school day.
The part of the length of the school day that is the same in all three ways the time is given is the hours. In the first way, the school day is given as 6 hours and 15 minutes.
In the second way, the school day is given as 6.25 hours. In the third way, the school day is given as 375 minutes. In each case, the number of hours in the school day is the same: 6 hours. However, the way that the minutes are expressed differs, leading to different numerical values.
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a factory has two machines A and B producing 300 and 720 bulbs per day respectively. machine A produces 1% defective bulbs and machine B produces 1.5% defective bulbs. One bulb is chosen at random at the end of a day and found. what is the probability that machine B produce defective bulb ?
The Probability that the defective bulb was produced by machine B is approximately 0.664 or 66.4%.
To find the probability that the defective bulb was produced by machine B, we can use Bayes' theorem.
Let event A be the defective bulb being chosen, and event B be the bulb being produced by machine B. We want to find P(B|A), the probability that the bulb was produced by machine B given that it is defective.
From the information given, we know that machine A produces 300 bulbs per day, of which 1% (3 bulbs) are defective, while machine B produces 720 bulbs per day, of which 1.5% (10.8 bulbs) are defective.
Thus, the total number of defective bulbs produced per day is 3 + 10.8 = 13.8.
The probability of choosing a defective bulb is equal to the total number of defective bulbs divided by the total number of bulbs produced per day:
P(A) = 13.8 / (300 + 720) = 0.016
The probability of machine B producing a bulb is equal to the number of bulbs produced by machine B divided by the total number of bulbs produced per day:
P(B) = 720 / (300 + 720) = 0.706
The probability of a bulb being defective given that it was produced by machine B is equal to the number of defective bulbs produced by machine B divided by the total number of bulbs produced by machine B:
P(A|B) = 10.8 / 720 = 0.015
Now, we can use Bayes' theorem to find P(B|A):
P(B|A) = P(A|B) * P(B) / P(A)
Substituting in the values we have calculated, we get:
P(B|A) = 0.015 * 0.706 / 0.016
Simplifying the equation, we get:
P(B|A) = 0.664
Therefore, the probability that the defective bulb was produced by machine B is approximately 0.664 or 66.4%.
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