a. Probability defective hard drive from F2 ≈ 0.3226.
b. Probability defective hard drive from F4 ≈ 0.7742.
c. Probability non-defective hard drive ≈ 0.9785.
To solve this problem, we can use Bayes' theorem, which states:
[tex]\[ P(A|B) = \frac{P(B|A) \times P(A)}{P(B)} \][/tex]
Where:
- [tex]\( P(A|B) \)[/tex] is the probability of event A happening given that event B has occurred.
- [tex]\( P(B|A) \)[/tex] is the probability of event B happening given that event A has occurred.
- [tex]\( P(A) \)[/tex] and [tex]\( P(B) \)[/tex] are the probabilities of events A and B, respectively.
Let's solve each part of the problem:
a. If a defective HDC hard drive is picked at random, what is the probability that it was produced at F2?
Let:
- A be the event that the hard drive is defective.
- B be the event that the hard drive was produced at F2.
We need to find [tex]\( P(B|A) \)[/tex], the probability that the hard drive was produced at F2 given that it is defective.
[tex]$\begin{aligned} & P(B \mid A)=\frac{P(A \cap B)}{P(A)} \\ & P(A \cap B)=P(A \mid B) \times P(B)=0.02 \times 0.25=0.005 \\ & P(A)=P(A \cap F 1)+P(A \cap F 2)+P(A \cap F 3)+P(A \cap F 4) \\ & P(A)=0.015 \times 0.20+0.02 \times 0.25+0.01 \times 0.15+0.03 \times 0.40=0.0155 \\ & P(B \mid A)=\frac{0.005}{0.0155} \approx 0.3226\end{aligned}$[/tex]
b. If a defective HDC hard drive is picked at random, what is the probability that it was produced at F4?
We need to find [tex]\( P(F4|A) \)[/tex], the probability that the hard drive was produced at F4 given that it is defective.
[tex]\[ P(F4|A) = \frac{P(A \cap F4)}{P(A)} \][/tex]
[tex]\[ P(A \cap F4) = P(A|F4) \times P(F4) = 0.03 \times 0.40 = 0.012 \][/tex]
[tex]\[ P(F4|A) = \frac{0.012}{0.0155} \approx 0.7742 \][/tex]
c. If an HDC hard drive is picked at random, what is the probability that it is non-defective?
Let P(non-defective) = P(non-defective at F1) + P(non-defective at F2) + P(non-defective at F3) + P(non-defective at F4)
P(non-defective) = [tex](1 - 0.015) \times 0.20 + (1 - 0.02) \times 0.25 + (1 - 0.01) \times 0.15 + (1 - 0.03) \times 0.40[/tex]
P(non-defective) = [tex]0.985 \times 0.20 + 0.98 \times 0.25 + 0.99 \times 0.15 + 0.97 \times 0.40[/tex]
P(non-defective) = 0.197 + 0.245 + 0.1485 + 0.388 = 0.9785
So, the probability that an HDC hard drive picked at random is non-defective is approximately [tex]\( 0.9785 \)[/tex].
At middle ave school 1/3 of the students are on the track team.the track coach offered to buy a pizza or subs for everyone on the team.of the students for whom the coach bought good 3/5 ordered pizza.what fraction of the students at middle ave school atenpizza
Final answer:
To determine how many students at Middle Ave School ate pizza, multiply the fraction on the track team (1/3) by those who ordered pizza (3/5), which equals 3/15 or simplified to 1/5 of the students.
Explanation:
To find out what fraction of the students at Middle Ave School ate pizza, you need to multiply the fractions that represent the students on the track team and those who ordered pizza. Initially, we know that 1/3 of the students are on the track team. Of these students, 3/5 ordered pizza. Multiplying these two fractions gives us the fraction of the entire student body that ordered pizza.
To multiply fractions, you multiply the numerators together and then the denominators together. So, for this problem, you'd multiply 1 by 3 to get the numerator, and then 3 by 5 to get the denominator:
1/3 * 3/5 = 3/15
But 3/15 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
3/15 = 1/5
Therefore, 1/5 of the students at Middle Ave School ate pizza.
A recycling box holds 151,875 cm3 of material and has a square base with sides measuring 45 cm. What is the height of the recycling box? a. 33.8 cm b. 75 cm c. 1687.5 cm d. 3375 cm
Please the question is on the picture
Halves of the following
12
10
13
15
8
5
Find the general solution of the differential equation x^2y′′+xy′−y=2x for x>0 by first showing that the function yp=−12x+x ln(x)is a particular solution for the differential equation.
What is the volume of this triangular pyramid?
You run around the perimeter of a baseball field at a rate of at least 11 feet per second. Which of the following are possible amounts of time that it takes you to run around the baseball field?
The correct answer for your question is 79 seconds.
last year, a married couple had their first child. should they file their federal income tax return using the 1040EZ form instead of the 1040 form?
A. No, partly because they will be able to claim a dependent.
B. No, partly because they will not be able to claim a dependent
C. Yes, partly because they will not be able to claim a dependent.
D. Yes, partly because they will be able to claim a dependent.
Answer:
A
Step-by-step explanation:
Apex just did the quiz:))
Option A is correct, No, partly because they will be able to claim a dependent.
What is Income tax?An income tax is a tax imposed on individuals or entities in respect of the income or profits earned by them. Income tax generally is computed as the product of a tax rate times the taxable income.
Having a dependent usually makes the 1040EZ form insufficient for most taxpayers, as the 1040EZ form is only recommended for those with simple tax situations.
In this case, the couple can claim their dependent as a tax credit, which is not possible on the 1040EZ form.
They should file a 1040 or 1040-SR form instead.
Hence, Option A is correct, No, partly because they will be able to claim a dependent.
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subtract 1/4 from 7/8
7/8 - 1/4
rewrite 1/4 with the same denominator as 7/8
1/4 = 2/8
now you have 7/8 - 2/8 = 5/8
answer is 5/8
solve for y: when 3x + 2x+3y =180
Tony is building a dog house, and the front view of the roof is shown below
Answer:
The height is 21 inches.
Step-by-step explanation:
We can find the height by using Pythagoras theorem.
As we know it is an isosceles triangle. So, the base can be divided equally in 2 parts for both triangles.
So, we can take the hypotenuse as 29 inches and base as 20 inches.
Now applying Pythagoras theorem, we get;
[tex]29^{2} =20^{2} +x^{2}[/tex]
[tex]841=400+x^{2}[/tex]
=>[tex]841-400=x^{2}[/tex]
=>[tex]x^{2} =441[/tex]
[tex]x=\sqrt{441}[/tex]
x=[tex]\sqrt{3*7*3*7}[/tex]
=> [tex]x=21[/tex]
Hence, the height is 21 inches.
Ms.jones has a decorative pyramid that sits on her fireplace mantle .the base is an equilateral triangle with an area of 6 square inches. The height of the pyramid is 15 inches. What is the volume?
Final answer:
To find the volume of Ms. Jones's pyramid with an equilateral triangle base area of 6 square inches and a height of 15 inches, we use the volume formula for a pyramid, V = [tex]\frac{1}{3}[/tex] × base area × height, resulting in a volume of 30 cubic inches.
Explanation:
To calculate the volume of the pyramid, we use the formula for the volume of a pyramid which is V = [tex]\frac{1}{3}[/tex] × base area × height. The base of Ms. Jones's decorative pyramid is an equilateral triangle with an area of 6 square inches, and the pyramid's height is 15 inches. First, we need to find the volume using the given base area and height.
Substituting the values into the formula, we get:
V = [tex]\frac{1}{3}[/tex] × 6 in² × 15 in
V = 2 in² × 15 in
V = 30 in³
Therefore, the volume of Ms. Jones's pyramid is 30 cubic inches.
find the surface area of the composite solid round your answer to the nearest tenth and explain your answer
Write the following statement as an equation and solve. Jake Drewrey, owner of Jake's Landscape Service, knows that one of his fertilizer tanks holds four times as many gallons of liquid fertilizer as a second tank. The two tanks together hold 286 gal. If both tanks are filled to capacity, how many gallons of fertilizer does each tank hold?
Final answer:
The equation is : x + 4x = 286, where x represents the smaller tank's capacity.
Explanation:
To write the statement as an equation and solve it, let's denote the smaller tank's capacity as x gallons. Therefore, the larger tank would be 4x gallons because it holds four times as much. The problem states that together they hold 286 gallons, which gives us the equation:
x + 4x = 286
Combining like terms, we get 5x = 286. Dividing both sides of the equation by 5 to solve for x, we find:
x = 286 / 5
x = 57.2
Therefore, the smaller tank holds 57.2 gallons, and the larger tank holds 4 times that amount, which is 57.2 * 4 = 228.8 gallons.
Your friend asks you to help him with his snow shoveling business and will pay you 3 3 pennies for the first job. You agree to help if he triples your payment for each job completed. After 2 2 shoveling jobs, you will receive 9 9 pennies, and after 3 3 shoveling jobs, you will receive 27 27 pennies. What is the exponent?
Give a big-o estimate for the number of operations (where an operation is an addition or a multiplication) used in this segment of an algorithm. t := 0 for i := 1to3 for j := 1to4 t := t + ij
A pack of six cans of coffee cost 12$ . How much would 15 cans of coffee cost
The cost for 15 cans of coffee is found by first determining the cost per single can, which is $2, and then multiplying this cost by the number of cans, resulting in a total of $30 for 15 cans.
To calculate the cost of 15 cans of coffee when a pack of six cans costs $12, we first need to find the cost of a single can. To do this, we divide the cost of the pack by the number of cans in the pack:
Cost per can = Total cost of the pack / Number of cans in the pack
Cost per can = $12 / 6 = $2
Now that we know the cost of one can, we can calculate the cost for 15 cans:
Total cost for 15 cans = Cost per can * Number of cans
Total cost for 15 cans = $2 * 15 = $30
Giving brainiest with legit answer is my answers correct?
Find the length of the chord of a circle of radius 100 feet subtended by an angle of 75◦ ?
A company sells boxes that are 2 3/8 feet high, 3 5/8 feet long, and 1 7/8 feet wide. John has a storage room that is 8 feet wide, 10 feet deep, and 12 feet high. You may rotate the boxes so that the width and length are interchanged, but the boxes may not be laid on their sides. a. What is the maximum number of boxes that he may stack on top of one another? b. How much room will there be left between the top of the stack of boxes and the ceiling?
What is the period of the function y = 3 csc x?
The period of the function is 2π.
What is period of the function?The time interval between two waves is known as a Period whereas a function that repeats its values at regular intervals or periods is known as a Periodic Function.
Given:
y = 3 csc x
As, csc(x) carry the reciprocal identity of sin(x).
So, they both have the same period
The period of sin(x) is 2π.
Hence, the period of csc(x) is 2π.
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The equation of straight lines L1 And L2 are .....
see the photo
Certain kinds of goods tend to have inelastic demand; a good usually has inelastic demand if what?
1. You are visiting Baltimore, MD and a taxi company charges a flat fee of $3.00 for using the taxi and $0.75 per mile.
A. Write an equation that you could use to find the cost of the taxi ride in Baltimore, MD. Let x represent the number of. miles and y represent the total cost.
B. How much would a taxi ride for 8 miles cost?
C. If a taxi ride cost $15, how many miles did the taxi travel?
Answers to all parts are as follows -
The equation to find the cost will be y(x) = 0.75x + 3 For 8 miles of travel, the total cost would be $9.For a total fare of $15, we can ride for 16 miles.What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is taxi company charges a flat fee of $3.00 for using the taxi and $0.75 per mile.
PART - A
Assume that [x] represent the number of miles and [y] represent the total cost. Therefore, the equation that you could use to find the cost of the taxi ride in Baltimore can be written as-
y(x) = 0.75x + 3
or
y(x) = 3x/4 + 3
PART - B
For [x] = 8 miles, the total cost will be -
y(8) = (3 x 8)/4 + 3
y(8) = 6 + 3
y(8) = 9
For 8 miles of travel, the total cost would be $9.
PART - C
For a total fare of $15 -
15 = 3x/4 + 3
12 = 3x/4
x = (12 x 4)/3
x = 16
For a total fare of $15, we can ride for 16 miles.
Therefore -
The equation to find the cost will be y(x) = 0.75x + 3 For 8 miles of travel, the total cost would be $9.For a total fare of $15, we can ride for 16 miles.To solve more questions on equation modelling, visit the link below-
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The following stem-and-leaf plot represents the scores earned by Mr. Roberts's class on their most recent science test.
What is the median of the scores?
78
80
81
86
Answer:
81
Step-by-step explanation:
The data in the table illustrate a linear function x -3, 0, 3, 6 y -6, -2, 2, 6 what is the slope of the linear function?
Answer:
[tex]slope=\dfrac{4}{3}[/tex]
Step-by-step explanation:
Given: The table of linear function.
x : -3 , 0 , 3, 6
y : -6 , -2 , 2, 6
Slope=change in y over change in x
[tex]slope=\dfrac{-2+6}{0+3}=\dfrac{4}{3}[/tex]
Passing point: (0,-2)
Point slope form:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y+2=\dfrac{4}{3}(x-0)[/tex]
[tex]y=\dfrac{4}{3}x-2[/tex]
Slope of the linear function [tex]=\dfrac{4}{3}[/tex]
Linear function is [tex]y=\dfrac{4}{3}x-2[/tex]
Hence, The slope of linear function is [tex]\dfrac{4}{3}[/tex]
If mc019-1.jpg and n(x) = x – 3, which function has the same domain as mc019-2.jpg?
Answer:
It's C to save you time.
Step-by-step explanation:
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Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.
B = 46°, a = 12, b = 11
A) A = 38.3°, C = 95.7°, c = 8; A = 141.7°, C = 84.3°, c = 8
B) A = 51.7°, C = 82.3°, c = 8; A = 128.3°, C = 5.7°, c = 8
C) A = 38.3°, C = 95.7°, c = 15.2; A = 141.7°, C = 84.3°, c = 15.2
D) A = 51.7°, C = 82.3°, c = 15.2; A = 128.3°, C = 5.7°, c = 1.5
For Anya's birthday her father gave out colorful birthday hats that were cone shaped. The opening of the bottom of the hat was 3 cm and the height of the cone was 7 cm. Anya fills her hat with candy. What is the exact volume of candy?
J. 65.97 cubic centimeters
K. 20.36 cubic centimeters
L. 16.49 cubic centimeters
M. 56.48 cubic centimeters
Answer:
Step-by-step explanation:
For the florist problem you would do 6 assistance
Reduce the following fraction -32abc/64a^2bc^3
IMPORTANT
[how do you]Find sin theta if tan theta = 3/4