Exercise 1. A batch of 400 containers for frozen orange juice contains 4 that are defective. Two are selected, at random, without replacement from the batch.
(1) What is the probability that the second one selected is defective given that the first one was defective?
(2) What is the probability that both are defective?
(3) What is the probability that both are non-defective?
Answer:
1. 1/13,300
2. 1/13,300
3. 2607/2660
Step-by-step explanation:
Probability is the ratio of the number of possible outcomes to the number of total outcome. The probability that an event will happen added to the probability of the same even not happening is 1.
Given that there are 400 containers of frozen orange juice with 4 that are defective,
non-defective = 400 - 4 = 396
Probability of selecting
Non-defective = 396/400 = 99/100
Defective = 4/100 = 1/100
the probability that the second one selected is defective given that the first one was defective is the same as the probability that both are defective
= 4/400 *3/399
= 1/13,300
the probability that both are non-defective
= 396/400 * 395/399
= 99/100 * 395/399
= 33*79/20*133
= 2607/2660
I need help plz I’ll appreciated
Answer:
y = x -3
Step-by-step explanation:
Given the definitions of f(x) and g(x) below, find the value of f(g(-1)).
f(x) = x^2+ x + 10
g(x) -5x-3
Answer:
16
Step-by-step explanation:
Given the definitions of f(x) and g(x) below,
f(x) = x^2+ x + 10
g(x) = -5x-3
f(g(x)) = f(-5x-3)
f(-5x-3) = (-5x-3)²+((-5x-3)+10
f(-5x-3) = 25x²+30x+9-5x-3+10
f(-5x-3) = 25x² +25x+16
f(g(x)) = 25x² +25x+16
f(g(-1)) = 25(-1)² +25(-1)+16
f(g(-1)) = 25-25 + 16
f(g(-1)) = 16
Hence f(g(-1)) is 16
4.40 divided by 0.08
Answer:
55
Step-by-step explanation:
Which of the following expressions results in 0 when evaluated at x = 3?
(x + 3)(x + 12)
(x + 20)(x - 3)
-20x(x + 3)
(x + 8)(x - 5)
Fifty boxes labeled with numbers from 1 to 50 are laid on a table. In each box there is a blue ball and a red ball. From each box that you randomly choose, you pick only one ball randomly, without looking into the box. Right after a ball is picked up, its corresponding box is moved away from the table to avoid picking the same box again. You continue this process until 25 boxes are chosen.
a) What is the probability of picking 8 blue balls and 17 red balls from boxes with even numbered labels?
b) If accidentally you see the fifth ball after being picked up to be Red, what would be the probability of picking 8 blue balls mentioned as above.
According to the question Fifty boxes labeled with numbers from 1 to 50 are laid on a table. In each box there is a blue ball and a red ball are as follows :
a) To calculate the probability of picking 8 blue balls and 17 red balls from boxes with even-numbered labels, we need to consider the total number of ways this can occur divided by the total number of possible outcomes.
There are 25 boxes to be chosen, and the boxes with even-numbered labels are numbered 2, 4, 6, ..., 50. There are 25/2 = 12.5 even-numbered boxes.
The probability of picking a blue ball from each even-numbered box is 1/2, and the probability of picking a red ball is also 1/2.
The probability of picking 8 blue balls and 17 red balls from the even-numbered boxes can be calculated using the binomial probability formula:
[tex]\[P(\text{{8 blue balls and 17 red balls from even-numbered boxes}}) = \binom{{12.5}}{{8}} \left(\frac{{1}}{{2}}\right)^8 \left(\frac{{1}}{{2}}\right)^{17}\][/tex]
b) If we accidentally see the fifth ball to be red, it means we have already chosen 4 boxes and picked 4 red balls.
The probability of picking 4 red balls from the first 4 boxes is [tex]\(\left(\frac{{1}}{{2}}\right)^4\).[/tex]
Now we need to calculate the probability of picking 4 blue balls and 13 red balls from the remaining 21 even-numbered boxes.
The probability can be calculated as:
[tex]\[P(\text{{8 blue balls and 17 red balls from remaining even-numbered boxes}}) = \binom{{21}}{{8}} \left(\frac{{1}}{{2}}\right)^8 \left(\frac{{1}}{{2}}\right)^{13}\][/tex]
The overall probability is the product of the two probabilities calculated in part a) and b).
You can substitute the values and calculate the probabilities using a calculator or computer software.
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WILL MARK BRAINLIEST ON CORRECT ANSWER
Which type of line symmetry does the figure have?
vertical
horizontal
diagonal
none
The volume of a sphere is 36 cubic inches. What is the radius of the sphere?
Answer:
ok we know that volume of a sphere is 4/3 pi r cubed so just replace the letters with the entities given
Answer:
2.7 cm
Step-by-step explanation:
What is move-in costs and what might be included in move-in costs?
Answer:
A move in cost is a non-refundable fee that landlords charge new tenants to cover the cost of touch ups and small changes made to the rental
Find critical value t*n−1 depends on the confidence level, C, and the number of degrees of freedom, n−1.
Find The confidence interval for the population mean, μ is y±t*n−1sn, where y is the sample mean, s is the sample standard deviation, and n is the sample size. The critical value t*n−1
The confidence interval for the population mean, μ is y ± t*n-1sn, where y is the sample mean, s is the sample standard deviation, and n is the sample size.
The critical value t*n-1 depends on the confidence level, C, and the number of degrees of freedom, n-1.Critical value t*n−1:The critical value t*n-1 refers to the value of t that separates the middle 100C% of the t distribution from the extreme (tail) regions, where C is the specified confidence level.
The number of degrees of freedom is n - 1. A t-value can be used to determine the confidence interval for a population mean with unknown standard deviation if the sample size is less than 30 or the population is not normally distributed.
Confidence interval:If y is the sample mean and s is the sample standard deviation, the confidence interval for the population mean μ is y ± t*n-1sn, where n is the sample size. The confidence interval is a range of values around the sample statistic that is likely to contain the true population parameter. The confidence interval is used to estimate the value of an unknown parameter, such as a population mean or proportion, and to quantify the level of uncertainty surrounding that estimate.
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Find the distance between the two points (-4,1) (4,5)
Triangle EFG is dilated by a scale factor of 1/4 to form triangle E'F'G'. Side E'F' measures 12.512.5. What is the measure of side EF?
Answer: 3.125
Step-by-step explanation:
Given
Triangle is dilated by a factor of [tex]\frac{1}{4}[/tex] i.e. each side multiplies to 0.25.
Side E'F' becomes 0.25 times the original length
[tex]\Rightarrow E'F'=\dfrac{1}{4}\times 12.5=3.125[/tex]
I need help with this plssss
Expert plsss help meeeee
Answer: 350
Step-by-step explanation:
Answer:
1,283 m3
Step-by-step explanation:
Ok so the volume formula is:
V = π×r² × h/3π (pi) = 3.14
² = power of two so that number times that number
Example:
3² = 3 × 3 = 9
To find the radius since the diameter is given divide by 2:
14 / 2 = 7
Next we solve the equation:
V = 3.14 × 7² × 25/3 = 1282.817
To round to the neareast whole number 1,283
Part B
What percentage of Americans would you predict wear glasses?
Answer: 64%
75% of adults use some sort of vision correction. About 64% of them wear eyeglasses, and about 11% wear contact lenses, either exclusively, or with glasses. Over half of all women and about 42% of men wear glasses.
63.8% of Americans are predicted to wear glasses
How to determine the percentage?The given parameters are:
Glasses = 638Sample size = 1000The percentage of Americans that wear glasses is calculated as:
Percentage = Glasses/Sample size
This gives
Percentage = 638/1000
Evaluate the quotient
Percentage = 0.638
Express as percentage
Percentage = 63.8%
Hence, 63.8% of Americans would wear glasses
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Find The Circumference Of A Circle With D =22.1
Answer:
138.86
Step-by-step explanation:
Multiply the radius by 2 to get the diameter.
Multiply the result by π, or 3.14 for an estimation.
That's it; you found the circumference of the circle.
PLEASE HELP ME PUT THEM IN ORDER
Answer
picture below of order. Not entirely
Step-by-step explanation:
12. What is the equation of the following parabola?
A y = 2(x + 1)2 - 4
B y = 3(x - 1)2 - 4
C y = 3(x + 1)2 - 4
Dy=2(x - 1)2 - 4
Answer:
c
Step-by-step explanation:
what is the range of the following data set ? 16, 19, 24, 27, 29, 32, , 33, 34
Arthur has a balance of $2330 on his credit card, which he plans to pay off by
making a payment of the same amount each month. Which of these monthly
amounts will allow Arthur to pay off his balance the fastest?
Answer:
C. $80
Step-by-step explanation:
A. $70
B. $65
C. $80
D. $75
When he pays $70 monthly
Number of months = $2330 / $70
= 33.3 months
When he pays $65 monthly
Number of months = $2330 / $65
= 35.9 months
When he pays $80 monthly
Number of months = $2330 / $80
= 29.1 months
When he pays $75 monthly
Number of months = $2330 / $75
= 31.1 months
The monthly amounts that will allow Arthur to pay off his balance the fastest is $80 per month
Assuming that P ? 0, a population is modeled by the differential equation
dP/dt = 1.1P(1-P/4100)
1. For what values of P is the population increasing? Answer (in interval notation):
2. For what values of P is the population decreasing? Answer (in interval notation):
3. What are the equilibrium solutions? Answer (separate by commas): P =
1. The population is increasing for 0 < P < 4100. The answer in interval notation is (0, 4100).
2. The population is decreasing for P > 4100. The answer in interval notation is (4100, ∞).
3. The equilibrium solutions are P = 0 and P = 4100.
To determine when the population is increasing or decreasing, we need to examine the sign of the derivative dP/dt.
1. For what values of P is the population increasing?
The population is increasing when dP/dt > 0.
In this case, we have dP/dt = 1.1P(1 - P/4100).
To find the values of P for which the population is increasing, we need to solve the inequality 1.1P(1 - P/4100) > 0.
To do this, we can consider the sign of each factor:
1.1 is positive.
P is the variable.
(1 - P/4100) is positive when P < 4100 and negative when P > 4100.
From this, we can determine the intervals where the population is increasing:
When P < 0 (since P cannot be negative in a population context), the term 1.1P is negative, so the entire expression is negative. The population is not increasing in this interval.
When 0 < P < 4100, both 1.1P and (1 - P/4100) are positive, so the entire expression is positive. The population is increasing in this interval.
When P > 4100, 1.1P is positive, but (1 - P/4100) is negative. The entire expression is negative. The population is not increasing in this interval.
Therefore, the population is increasing for 0 < P < 4100. The answer in interval notation is (0, 4100).
2. For what values of P is the population decreasing?
The population is decreasing when dP/dt < 0.
In this case, we have dP/dt = 1.1P(1 - P/4100).
To find the values of P for which the population is decreasing, we need to solve the inequality 1.1P(1 - P/4100) < 0.
Using the same analysis as in the previous part, we can determine the intervals where the population is decreasing:
When P < 0, the population is not decreasing.
When 0 < P < 4100, the population is not decreasing.
When P > 4100, the population is decreasing.
Therefore, the population is decreasing for P > 4100. The answer in interval notation is (4100, ∞).
3. What are the equilibrium solutions?
Equilibrium solutions occur when the population remains constant, meaning dP/dt = 0.
In this case, we have dP/dt = 1.1P(1 - P/4100)
= 0.
To find the equilibrium solutions, we solve the equation 1.1P(1 - P/4100) = 0.
This equation is satisfied when either 1.1P = 0 or (1 - P/4100) = 0.
From 1.1P = 0, we have P = 0.
From (1 - P/4100) = 0, we have P = 4100.
Therefore, the equilibrium solutions are P = 0 and P = 4100.
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answer this for 15 and branlyist
Answer:
Financial Literacy = 25
Model with mathematics:
a) cranes = 40 panthers = 40
b) yes, finding the mean is a good way of determining which team has the better record, because "finding the mean" is just finding the average.
Step-by-step explanation:
Financial Literacy:
24 = [tex]\frac{x+15+20+10+12+20+16+80+18}{9}[/tex] → [tex]24 = \frac{191}{9}[/tex]
24×9=x · 191
→ 216 = x · 191
→ 216-191=x
x = 25
Model with Mathematics:
Add all six wins and divide by how many seasons there are. (do it for both sides. Also, I'm too lazy to type it out.)
How many unit cubes are on each layer of this cube
There are 16 cubes in each layer.
What are cube?A cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross.
Given that, a cube,
Since, we know that, all sides of a cube are equal and the cross-section of the cube is a square,
Therefore, counting the cubes of the front face,
4 cubes vertical and 4 cubes horizontal,
Therefore, total cube in front face = 4×4 = 16
Therefore, cubes in each layer is 16.
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what do you think???
Answer:
To entertain
Step-by-step explanation:
Because the dad made a joke to entertain, and the story is entertaining the readers.
Answer: entertain
Step-by-step explanation:
Joanne has a health insurance plan with a $1000 calendar-year deductible, 80% coinsurance, and a $5,000 out-of-pocket cap. Joanne incurs $1,000 in covered medical expenses in March, $3,000 in covered expenses in July, and $30,000 in covered expenses in December. How much does Joanne's plan pay for her July losses? (Do not use comma, decimal, or $ sign in answer)
Joanne's plan pays $2400 for her July losses, as she is responsible for 20% of the covered expenses during that month.
Joanne's health insurance plan with a $1000 deductible, 80% coinsurance, and a $5000 out-of-pocket cap requires her to pay for her medical expenses until she reaches the deductible.
After reaching the deductible, she is responsible for 20% of the covered expenses, up to the out-of-pocket cap. The plan pays the remaining percentage of covered expenses.
To calculate how much the plan pays for Joanne's July losses, we need to consider her deductible, coinsurance, and out-of-pocket cap.
In March, Joanne incurs $1000 in covered medical expenses.
Since this amount is equal to her deductible, she is responsible for paying the full amount out of pocket.
In July, Joanne incurs $3000 in covered expenses. Since she has already met her deductible, the coinsurance comes into play.
According to the plan's coinsurance rate of 80%,
Joanne is responsible for 20% of the covered expenses.
Therefore, Joanne is responsible for paying 20% of $3000, which is $600.
The plan will pay the remaining 80% of the covered expenses, which is $2400.
In December, Joanne incurs $30,000 in covered expenses. Since she has already met her deductible and reached her out-of-pocket cap, the plan pays 100% of the covered expenses.
Therefore, the plan will pay the full $30,000 for her December losses.
To summarize, Joanne's plan pays $2400 for her July losses, as she is responsible for 20% of the covered expenses during that month.
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Find the inverse of the function and state its domain and range. {(-3, 4), (-1,5), (0, 2), (2, 6), (5, 7)} a. {(4, -3), (5, -1), (2.0), (6,2), (7,5)} D = {2, 4, 5, 6, 7); R = {-3, 1,0, 2, 5) b. {(3, 4), (1,5), (0, 2), (-2, 6), (-5, 7)); D = (3, 1,0.-2. -5); R = {2, 4, 5, 6, 7} O (3.-4), (1,-5), (0, -2), (-2, -6). (-5, -7)}; D = (3, 1, 0, -2. -5); R = (-7 -6, -5, -4.-2} c. [(-3.-4), (-1, 5), (0.2). (2. -6), (5,-2)}; D = (-3, 1.0, 2.5); R = (-7 -6, 5, 4-2)
The inverse function is obtained by interchanging the x and y values of each point. The correct option is b: {(3, 4), (1, 5), (0, 2), (-2, 6), (-5, 7)}; D = {3, 1, 0, -2, -5}; R = {4, 5, 2, 6, 7}.
The domain of the inverse function consists of the x-values from the original function, and the range consists of the y-values from the original function
To compute the inverse of the function, we interchange the x and y values of each point. The inverse function is {(4, 3), (5, 1), (2, 0), (6, -2), (7, -5)}.
The domain of the inverse function is D = {3, 1, 0, -2, -5} which consists of the x-values from the original function. The range of the inverse function is R = {4, 5, 2, 6, 7} which corresponds to the y-values from the original function.
It's important to note that in the inverse function, the roles of the domain and range are swapped. The x-values of the original function become the y-values of the inverse function, and vice versa.
Therefore, the correct answer is option b: {(3, 4), (1, 5), (0, 2), (-2, 6), (-5, 7)}; D = {3, 1, 0, -2, -5}; R = {4, 5, 2, 6, 7}.
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Please Help!
Factor the following trinomial
[tex]9x^2-24x+16[/tex]
Please show work
=> 9x² - 24x + 16
Split the middle term(term with x) in such a manner so that the product of those parts is equal to the product of term with x² and constant. Here, those parts are 12 & 12 as 12*12 = 9*16.
=> 9x² - 24x + 16
=> 9x² - (12 + 12)x + 16
=> 9x² - 12x - 12x + 16
=> 3x(3x - 4) - 4(3x - 4)
=> (3x - 4)(3x - 4)
Method 2
=> 9x² - 24x + 16
=> (3x)² - 2(3x*4) + 4²
=> (3x - 4)²
=> (3x - 4)(3x - 4)
Method 3
In case if you can't find the factors of the middle term.
Say f(x) = 0, find the zeroes using quadratic formula. Zeroes of this eqⁿ are [-(-24) ± √24²-4(9)(16)] / 2(9) = 4/3 & 4/3
Therefore, f(x) = (x - 4/3)(x - 4/3) = (3x - 4)(3x - 4)/9
Ignore the numeric constant.
f(x) = (3x - 4)(3x - 4)
Find the perimeter of a regular hexagon with side length 4 meters.
Answer:
i think it is 24 meters
Answer:
24 meters
Step-by-step explanation:
perimeter of regular hexagon is
perimeter = 6 × a
where a is the side length
so in the problem a = 4 meters
by apply the formula you will have
perimeter = 6 x 4 meters
perimeter =24 meters
Consider the following pair of equations:
y = −2x + 8
y = x − 1
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.
Answer:
y = -2x + 8
x = 3
y = x - 1
y = 2
Step-by-step explanation:
if 2x + y = 8 and x - y = 1
you can solve using substitution, elimination, matrix etc.
You will find that x = 3 and y = 2
Hope this helped.
if the rate of change of f at x = c is twice its rate of change at x =1
The function f(x) is more steeply increasing at all points x than it is at x=1.
If the rate of change of f at x=c is twice its rate of change at x=1, then f(x) is said to be more steeply increasing at x=c than at x=1.
The rate of change of a function f(x) at any point x can be calculated by differentiating the function f(x).
That is, the derivative of the function f(x) gives the rate of change of the function at any point x.
If the rate of change of f(x) at x=1 is f'(1), and its rate of change at x=c is f'(c), then we have f'(c) = 2f'(1)
We can see that f(x) is more steeply increasing at x=c than at x=1 if and only if f'(c) > f'(1).
Since f(x) is twice as steep at x=c than at x=1, we can conclude that f'(c) > f'(1) for all c.
That is, the rate of change of f(x) is greater at any point x=c than at x=1.
Therefore, the function f(x) is more steeply increasing at all points x than it is at x=1.
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for the variable A type the word lambda, fory type the word gamma, otherwise treat these as you would any other variable We will solve the heat equation -6, 0
The required heat equation is u(x, t) = (A×cos(λx) + B×sin(λx)) × exp(-λ²t)
To solve the heat equation in the given interval [-6, 0], we can use the separation of variables method. Let's denote the dependent variable as u(x, t), where x represents the spatial variable and t represents the temporal variable.
The heat equation in one dimension is given by:
∂u/∂t = α ∂²u/∂x²,
where α is the thermal diffusivity constant.
To solve this equation, we assume that the solution can be represented as a product of two functions, each depending on a single variable:
u(x, t) = X(x)T(t).
Substituting this into the heat equation, we have:
X(x)T'(t) = αX''(x)T(t),
where prime (') denotes differentiation with respect to the variable.
Dividing both sides by αX(x)T(t), we get:
T'(t)/T(t) = αX''(x)/X(x).
Since the left side depends only on t and the right side depends only on x, both sides must be equal to a constant, which we'll denote as -λ²:
T'(t)/T(t) = -λ² = αX''(x)/X(x).
Now, let's solve the temporal part of the equation:
T'(t)/T(t) = -λ²
This is a separable ordinary differential equation (ODE), and its general solution is given by:
T(t) = exp(-λ²t).
Next, let's solve the spatial part of the equation:
αX''(x)/X(x) = -λ².
This is also a separable ODE, and its general solution is given by:
X(x) = A×cos(λx) + B×sin(λx),
where A and B are arbitrary constants.
Therefore, the general solution to the heat equation is:
u(x, t) = (A×cos(λx) + B×sin(λx)) × exp(-λ²t).
Since we have the given interval [-6, 0], we can apply appropriate boundary conditions to determine the values of A, B, and λ that satisfy the problem.
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