Five percent of the parts produced by a machine are defective. Fifteen parts are selected at random. Use the binomial probability tables to answer the following questions. (a) What is the probability that exactly 3 parts will be defective? (Round your answer to four decimal places.) (b) What is the probability that the number of defective parts will be more than 2 but fewer than 6? (Round your answer to four decimal places.) (c) What is the probability that fewer than 3 parts will be defective? (Round your answer to four decimal places.) (d) What is the expected number of defective parts? (e) What is the variance for the number of defective parts?
Answers
The variance for the number of defective parts is 0.7125.
(a) What is the probability that exactly 3 parts will be defective? (Round your answer to four decimal places.)In the given question, the probability of a part being defective is 5%, which is represented as p=0.05. The probability of a part being non-defective is (1 - 0.05) = 0.95.The given question represents a binomial experiment, which includes the following conditions:The experiment consists of n identical trials.Each trial has only two possible outcomes, a success, and a failure.Success has probability p and failure has probability 1-p.The trials are independent.To calculate the probability of exactly 3 parts being defective when 15 parts are selected randomly, we use the following formula:P (X = k) = nCk x pk x (1-p) n-kWhere P(X=k) is the probability of getting k defective parts, nCk is the number of ways of getting k defects from n parts, pk is the probability of getting k defective parts, and (1-p) n-k is the probability of getting n-k non-defective parts.p = 0.05q = (1 - 0.05) = 0.95n = 15a. P (X = 3) = 15C3 x 0.05³ x 0.95¹² = 0.2508The probability of getting exactly 3 defective parts is 0.2508. Hence, the required probability is 0.2508.(b) What is the probability that the number of defective parts will be more than 2 but fewer than 6? (Round your answer to four decimal places.)b. We need to calculate the probability of getting defective parts more than 2 but less than 6.P (3 < X < 6) = P (X = 3) + P (X = 4) + P (X = 5)P (X = 3) = 15C3 x 0.05³ x 0.95¹² = 0.2508P (X = 4) = 15C4 x 0.05⁴ x 0.95¹¹ = 0.0925P (X = 5) = 15C5 x 0.05⁵ x 0.95¹⁰ = 0.0204P (3 < X < 6) = 0.2508 + 0.0925 + 0.0204 = 0.3637The probability of getting defective parts between 2 and 6 is 0.3637. Hence, the required probability is 0.3637.(c) What is the probability that fewer than 3 parts will be defective? (Round your answer to four decimal places.)c. We need to calculate the probability of getting fewer than 3 parts defective. The probability of getting zero defective parts or getting one defective part is given by:P (X = 0) = 15C0 x 0.05⁰ x 0.95¹⁵ = 0.4630P (X = 1) = 15C1 x 0.05¹ x 0.95¹⁴ = 0.3456P (X < 3) = P (X = 0) + P (X = 1) = 0.4630 + 0.3456 = 0.8086The probability of getting fewer than 3 defective parts is 0.8086. Hence, the required probability is 0.8086.(d) What is the expected number of defective parts?The expected number of defective parts is given by:μ = npμ = 15 × 0.05μ = 0.75The expected number of defective parts is 0.75.(e) What is the variance for the number of defective parts?The variance for the number of defective parts is given by:σ² = npqσ² = 15 × 0.05 × 0.95σ² = 0.7125The variance for the number of defective parts is 0.7125.
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Related Questions
a bitmap is a grid of square colored dots, called
Answers
Answer:
Step-by-step explanation:
A bitmap is a digital image format that is made up of a grid of square colored dots called pixels.
Each pixel in the bitmap contains information about its color and position, which allows the computer to display the image on a screen or print it on paper. Bitmaps are commonly used for photographs, illustrations, and other complex images that require a high degree of detail and color accuracy.
However, because bitmaps store information for each individual pixel, they can be memory-intensive and may result in large file sizes. Additionally, resizing a bitmap can lead to a loss of quality, as the computer must either interpolate or discard pixels to adjust the image size.
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I am very much lost if anybody understand this can u help me
Please
Answers
Answer:
y= -2/7x-7
Step-by-step explanation:
slope intercept form is just a fancy way of saying y=mx+b
x being your input, y your output, m your slope, and b your y intercept
you can use the slope to determine your equation will look something like: y=-2/7x+b. To find your y-intercept all you do is determine how much the point will increase or decrease so it is equal to (0, y). In this case it will increase by 14 on the x's (so x is equal to 0) and 14*-2/7. When you have determined your y-int and slope you can then plug them into the equation instead of the variables.
A pool has a length of x - 5 and a width of x + 3. What is the area of the pool?
Answers
Answer:
Area or Volume?
Step-by-step explanation:
Approximately students attend Jones Middle School. Below is the data collected from two random samples of students regarding school lunch preference. Which of the following inferences can be made based on the data collected? Select all that apply.
Answers
Answer:
there is nothing to select. u need to provide more info
−2(5 − 4c) + 0.6(5c − 2) Please help me
Answers
Answer:
11c−11.2
Step-by-step explanation:
Answer:
-11.2 + 11c
Step-by-step explanation:
PEMDAS
-2(5 - 4c) + 0.6(5c - 2)
-10 + 8c + 3c - 1.2 (Combine like terms)
-11.2 + 11c
Sorry if I'm wrong in advance!
Subtract: 22²+8242²+122-16
O22²+122-12
4(x+4)(x-1)
O -x²+12x-12
4x(x+4)(x-1)
-2²+6x-6
о 22(x+4)(x-1)
H
-2x²+12-12
2(x+4)(x-1)
=
6-2(x-1)
6
2x(x+4)= 4(x+4)(x-1) = 2z(x+4)-2(x-1)
x.x
4(x+4)(x-1)-
Answers
Answer:
the correct answer is the second one
Step-by-step explanation:
I will add a photo of my solution, because there's a lot to type here
Rewrite 8 + 12 using the GCF and factoring.
2(2 + 6)
4(8 + 12)
4(2 + 3)
8(1 + 12)
Answers
Answer:
4(2+3) is the answer
Step-by-step explanation:
Those are both factors of 8 and 12 and it is re written.
4(2+3)
4*2 + 4*3
8+12
find hte volume of revolution when the area enclosed by y= root x, y=0, and x=9 is revolved about the line x=9
Answers
The volume of revolution is 81π/2 cubic units.
To find the volume of revolution, we can use the method of cylindrical shells.
The axis of rotation is x=9, so we need to express the function in terms of x-9. We have y=sqrt(x), so x=y^2. Therefore, x-9 = y^2 - 9.
The limits of integration are 0 and 3 (since y=sqrt(9-x) when x=6, and y=0 when x=9).
The height of each cylindrical shell is the difference between the right and left boundaries, which is 9 - (y^2 - 9) = 18 - y^2.
The radius of each cylindrical shell is simply y.
The volume of each shell is given by:
dV = 2πy(18 - y^2) dy
Integrating from 0 to 3:
V = ∫[0,3] 2πy(18 - y^2) dy
= 2π ∫[0,3] (18y - y^3) dy
= 2π [(9y^2 - (1/4)y^4)]_[0,3]
= 2π (81/4)
= 81π/2
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A cube has a volume of (0.75xy)3 cubic centimeters.
What is the volume of the cube expressed as a fraction?
Answers
The volume of the cube expressed as a fraction will be 27x³y³ / 64.
Given that:
Volume, V = (0.75xy)³
It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.
The volume of the cube expressed as a fraction is calculated as,
V = (0.75xy)³
V = (3xy/4)³
V = 27x³y³ / 64
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A nutrition researcher wants to determine the mean fat content of hen's eggs. She collects a sample of 40 eggs. She calculates a mean fat content of 23 grams with a sample standard deviation of 8 grams. From these statistics, she calculates a 90% confidence interval of 20.9 grams to 25.1 grams. What can the researcher do to decrease the width of the confidence interval?
a. increase the confidence level
b. decrease the confidence level
c. decrease the sample size
d. none of the above
Answers
To decrease the width of the confidence interval, the researcher can take the following steps:
1. Decrease the confidence level: The confidence interval width is inversely proportional to the confidence level. By decreasing the confidence level, the researcher can have a narrower interval. However, it is important to note that decreasing the confidence level also increases the chance of the interval not capturing the true population mean.
2. Increase the sample size: The sample size affects the precision of the estimate. Increasing the sample size reduces the standard error, which leads to a narrower confidence interval. This is because a larger sample provides more information about the population.
Therefore, the researcher can decrease the width of the confidence interval by either decreasing the confidence level or increasing the sample size. Both approaches will result in a narrower interval, providing a more precise estimate of the mean fat content of hen's eggs.
The researcher can decrease the width of the confidence interval by either decreasing the confidence level or increasing the sample size. Both approaches will result in a more precise estimate of the mean fat content of hen's eggs.
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Sum or difference (-4p^2-p+9)+(p^2+3p-1)
Answers
The sum or difference of the given expressions is -3p^2 + 2p + 8.
To find the sum or difference of the two expressions (-4p^2 - p + 9) and (p^2 + 3p - 1). To do this, we'll follow these steps:
Step 1: Write down the given expressions side by side.
(-4p^2 - p + 9) + (p^2 + 3p - 1)
Step 2: Remove the parentheses.
-4p^2 - p + 9 + p^2 + 3p - 1
Step 3: Combine like terms. In this case, we have three groups of like terms: p^2 terms, p terms, and constant terms. We'll combine each group separately.
a) Combine the p^2 terms: -4p^2 and p^2
-4p^2 + p^2 = -3p^2
b) Combine the p terms: -p and 3p
-1p + 3p = 2p
c) Combine the constant terms: 9 and -1
9 - 1 = 8
Step 4: Write the simplified expression by combining the results from Step 3.
-3p^2 + 2p + 8
So, the sum or difference of the given expressions is -3p^2 + 2p + 8.
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(a)
A farmer bought a tractor for Rs 400000 and sold it after using at 10% depreciation rate per year.what is the cost of the tractor after 2years?
Answers
Answer:
320,000
Step-by-step explanation:
Step-by-step explanation:
Hope my answer helps mark me brainliest
Find the values of the variables and the measures of the indicated angles. (help)
Answers
Answer:
x = 30
Step-by-step explanation:
You want the measure of the acute angle where a tangent meets a chord that intercepts an arc of 300°.
Inscribed angleAn angle inscribed in a circle has half the measure of the arc it intercepts.
If one leg of that inscribed angle degenerates in length to zero, then the "inscribed" angle becomes the angle between the remaining chord and the tangent to one end of that chord.
In other words, the measure of the angle marked x° is half the measure of the arc it intercepts.
x° = 1/2(360° -300°) = 1/2(60°)
x° = 30°
The value of the variable x is 30.
for what values of x does the graph of f (x) = ex −2x have a horizontal tangent line?
Answers
The graph of the function f(x) = ex - 2x has a horizontal tangent line at x = 0.693.
To find the values of x for which the graph of the function f(x) = ex - 2x has a horizontal tangent line, we need to determine when the derivative of the function is equal to zero. A horizontal tangent line occurs when the slope of the function is zero, which corresponds to the critical points of the function.
To find the critical points, we differentiate f(x) with respect to x. The derivative of ex is ex, and the derivative of -2x is -2. Setting the derivative equal to zero, we have ex - 2 = 0.
Adding 2 to both sides, we get ex = 2. Taking the natural logarithm of both sides, we have ln(ex) = ln(2), which simplifies to x = ln(2).
Therefore, the graph of f(x) = ex - 2x has a horizontal tangent line at x = ln(2) or approximately x = 0.693. At this point, the slope of the function is zero, indicating a horizontal tangent line.
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What is the value of h(-2) if h(x)=4x^2-x+9?
Answers
= 4(4x^2)+2x+9 = 16x^2 + 2x + 9
Answer:
16x² + 2x + 9
Step-by-step explanation:
To evaluate h(- 2x) , substitute x = - 2x into h(x), that is
h(- 2x)
= 4(- 2x)² - (- 2x) + 9
= 4(4x²) + 2x + 9
= 16x² + 2x + 9
suppose a is invertible. (a) show or explain why at a is also invertible for any matrix a.
Answers
If A is an invertible matrix, then ATA is also invertible. This is because the determinant of ATA is the product of the determinants of AT and A, and since A is invertible, its determinant is not equal to zero. Therefore, the determinant of ATA is also not equal to zero, which means that ATA is invertible.
1. If A is invertible, then det(A) ≠ 0.
2. The determinant of ATA is equal to the product of the determinants of AT and A, i.e. det(ATA) = det(AT) * det(A).
3. Since A is invertible, det(A) ≠ 0, and det(AT) = det(A), we have det(ATA) = det(A) * det(A) ≠ 0.
4. Therefore, ATA is also invertible.
In conclusion, if A is an invertible matrix, then ATA is also invertible.
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Definition of a derivative (limit of the difference quotient)
Answers
The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:
f'(a) = lim (h → 0) [f(a + h) - f(a)] / h
What is derivative?
The derivative of a function in calculus measures the function's sensitivity to changes in its input variable. Specifically, at a particular point, it represents the function's rate of change with respect to its input variable at that moment.
The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:
f'(a) = lim (h → 0) [f(a + h) - f(a)] / h
This limit represents the instantaneous rate of change or slope of the function at the point x = a. The difference quotient is the change in the function value divided by the change in the input variable (or the distance between two points on the graph of the function).
The derivative is a fundamental concept in calculus, and it has many applications in various fields of science, engineering, and economics. It allows us to calculate important quantities such as velocity, acceleration, and marginal cost, and it is used to optimize functions and solve many real-world problems.
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Last year 500 people attended a concert this year 900 people attended what was the percent increase in attendance from last year to this year
Answers
Answer:
80
Step-by-step explanation:
500 to 900? = 80.
In a certain town, 25% of people commute to work by bicycle. If a person is selected randomly from the town, what are the odds against selecting someone who commutes by bicycle?
Answers
Answer:
So if 25% of the people go to work by bicycle then that means that 75% of people go to work by other means of transportation.
Therefore the odds against selecting someone who commutes by bicycle are 75% or 75/100 or 0.75.
Step-by-step explanation:
The odds against selecting someone who commutes by bicycle are 75%
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of sample
Given that In a certain town, 25% of people commute to work by bicycle. If a person is selected randomly from the town.
25% of the people go to work by bicycle then which means that 75% of people go to work by other means of transportation.
Therefore the odds against selecting someone who commutes by bicycle are 75% or 75/100 or 0.75.
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Expand: (m + 4) 0 m2 + 8m + 16 0 m2 + 4m + 16 O mp + m +- 8
Answers
we have the next squared binomial
\((m+4)^2\)we have the next formula in order to expand a squared binomial
\((a+b)^2=a^2+2ab+b^2\)So we can expand
\((m+4)^2=m^2+2(4)(m)+4^2=m^2+8m+16\)so the correct answer is the first one
Show that if A and B are sets with A ⊆ B, then a. A ∪ B = B b. A ∩ B = A
Answers
If A and B are sets with A⊆B the a) A ∪B = B, b) A∩B = A.
a) Let A⊆B
Let x ∈ A∪B
Then x ∈ A or x ∈ B .....(i)
By definition of union we have
x ∈ A ⇒ x ∈ B .....(ii)
Using (i) and (ii), if x ∈ A, then x ∈ b. If x ∈ B, then clearly x ∈ B.
Thus given A⊆ B, then A∪B = B.
b) First assume A∩B which implies that x ∈ A and x ∈ B.
Hence we can implies the
A∩ B ⊆ A (we started with the element in A∩B and concluded that it is in A) ------(i)
Now, let x ∈ A which implies x ∈ B ( as A⊆ B)
Hence, x ∈ A∩B, which in turn imply
A ⊆ A∩B -----(ii)
From (i) and (ii) we get
A∩B = A
Therefore if A and B are sets with A⊆B, then A ∩B = B and A∩B = A.
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PLZ HELPPP its due in 10 minutes ;-;
Solve this system of equations using either the elimination method or substitution method, explain what method u used and how u solved it
2x + y = 25
x + y = 20
Answers
Answer:
we have tow equation here
2x+y=25
and
x+y=20
so if we multiply the second equation with- and add it to the first equation we will find the x
x=5
and the we will fin the why by writing the value of the x in the equation you want
y=15
Answer:
x=5 y=15
Step-by-step explanation:
Solving by Elimination:
Multiply the bottom equation (x+y=20) by -1 to solve for x
Subtract -x-y=-20 from 2x+y=25 to get x=5
Now that you have solved for x, plug 5 back into the equation 2x+y=25 and solve for y
(2)(5)+y=25
10+y=25
-10 -10
y=15
A man purchased a $21,000, 1-year term-life insurance policy for $450. Assuming that the probability that he will live for another year is 0.98, find the company's expected net gain
Answers
The company's expected net gain from this 1-year term-life insurance policy is $30.
Determine the total cost of the insurance policy:
In this case, the cost of the policy is $450.
Calculate the payout if the man dies:
If the man dies, the insurance company will have to pay out the policy value, which is $21,000.
Determine the probability of each outcome:
The probability that the man will live for another year is given as 0.98.
Since there are only two possible outcomes (the man either lives or dies), the probability that he will die within the year is 1 - 0.98 = 0.02.
Calculate the company's expected gain/loss for each outcome:
- If the man lives, the company's gain will be the cost of the policy ($450) since no payout is made.
- If the man dies, the company's loss will be the policy value ($21,000) minus the cost of the policy ($450), which equals $20,550.
Find the company's expected net gain by multiplying each outcome's gain/loss by its respective probability and adding the results:
- Expected gain if the man lives = 0.98 * $450 = $441
- Expected loss if the man dies = 0.02 * (-$20,550) = -$411
Add the expected gain and expected loss to find the company's expected net gain: $441 + (-$411) = $30.
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pls answer asap the sooner the better :)
Answers
Answer:
a+4=9.1Step-by-step explanation:
first we have two sides which are equalso according to the questionthe equation is4+a=9.1In a recent election, 63% of all registered voters participated in voting. In a survey of 275 retired voters, 162 participated in voting. Which is higher, the population proportion who participated or the sample proportion from this survey?
Answers
The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).
To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.
The population proportion who participated in voting is given as 63% of all registered voters.
This means that out of every 100 registered voters, 63 participated in voting.
In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.
Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .
Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).
Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.
It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.
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Exit
Which tool would you use to measure the amount of oil required for a food recipe?
A. measuring spoon
B. ruler
C. hanging scale
D. platform scale
Answers
Answer:
Measuring Spoon
Step-by-step explanation:
The tool you would use is a measuring spoon.
Answer:
Measuring spoon
Step-by-step explanation:
A triangle has two side lengths: 18 in and 12 in. Which of the following could be the length of the third side?
Answers
Answer:
6<L<30
Step-by-step explanation:
because we know that the third side needs to be in between the sum of the other two it has to be less than 30 and then because it needs to apply to the other sides it is greater then 18-12 or 6.
which triangle is congruent to an isosceles triangle that has the two long sides and the bottom line is short
Answers
An isosceles triangle with two long sides and a short bottom side can have infinitely many possible congruent triangles. However, assuming that the two long sides have a fixed length of 1 unit and the length of the short bottom side is less than 1 unit, there are only two possible congruent triangles.
One of the congruent triangles would have angles of approximately 22.62°, 22.62°, and 135.76°, while the other congruent triangle would have angles of approximately 157.38°, 11.25°, and 11.25°. Therefore, the answer to this question depends on the specific length of the short bottom side and the context of the problem.
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a) down payment, b) amount of the loan, c) monthly payment, and d) finance charge.
Shelly Lemony obtains a small business equipment loan for $120,000. Her down payment is 20% and the APR is 8% for 12 months.
Answers
a) Shelly Lemony's down payment is $24,000.
b) The loan amount is $96,000.
c) The monthly payment is $8,350.89.
d) The finance charge is $4,210.68.
What is the down payment?The down payment represents the initial up-front partial payment for the purchase of the equipment on loan.
The down payment reduces the cost of the equipment to the loan amount. Finance companies demand a down payment to ascertain the buyer's willingness and ability to proceed with the loan arrangement.
It is a sign of commitment to meet the loan contract obligations.
Data and Calculations:Monthly Pay: $8,350.89
Total Loan Amount = $96,000.00
Upfront Payment $24,000.00
Equipment loan = $120,000
Number of periods = 12 months
APR = 8%
Total of 12 Loan Payments = $100,210.68
Total Loan Interest = $4,210.68
Total Cost (price, interest, tax, fees) = $124,210.68
Thus, Shelly will make a down payment of $24,000 or 20% of the equipment loan.
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Verify the property a x (b+c) =(a x b)+(a x c) by taking: a = -7, b = (2/5), c = (-3/7)
Answers
= -14/5 + 3
=1/5