The probability that at least 10% of the boards are defective can be approximated using a normal distribution, while the exact probability of having 10 defectives in the batch can be calculated using the binomial formula. For large samples, normal approximation can be used for convenience.
Explanation:To find the probability that at least 10% of the boards are defective, we can use the binomial distribution since each board's condition is independent of the other boards. The formula for binomial probability is P(X = k) = (n choose k) * pk * (1-p)(n-k), where n is the number of trials, p is the probability of success on each trial, and k is the number of successes. However, for large sample sizes and when the sample proportion is close to the population proportion, we can approximate the binomial distribution with a normal distribution.
To use the normal approximation, we calculate the mean and standard deviation with the formulas μ = n * p and σ = √(n * p * (1-p)). For the batch of 250 boards with 5% defective rate, μ = 250 * 0.05 = 12.5 and σ = √(250 * 0.05 * 0.95) ≈ 3.4641. We then convert the problem into a z-score and use standard normal distribution tables or software to find the probability that Z > (25 - 12.5)/3.4641.
To find the exact probability of having exactly 10 defectives in the batch, we use the binomial formula since the normal approximation is less accurate for exact probabilities. The calculation would be P(X = 10) = (250 choose 10) * 0.0510 * 0.95240.
A microwave is placed on top of two boxes. One box is 2 feet 5 inches tall the other box is 3 feet 11 inches tall and the other microwave is 3 feet 3 inches tall how tall are they combined?
Find all the local maxima, local minima, and saddle points of the function
Final answer:
To find local maxima, minima, and saddle points, find critical points using the first derivative test and then apply the second derivative test.
Explanation:
To find the local maxima, local minima, and saddle points of a function, we first need to find the critical points. These are the points where the derivative of the function is either zero or undefined. To check whether each critical point is a local maxima, local minima, or saddle point, we use the second derivative test.
The second derivative test states that if the second derivative is positive at a critical point, then the point is a local minimum. If the second derivative is negative, then the point is a local maxima. If the second derivative is zero, the test is inconclusive.
By applying the second derivative test to each critical point, we can determine whether it is a local maxima, local minima, or saddle point.
Mrs Rivera baked 112 cookies there are 28 students in her class how many cookies will each student receive
Each student will receive 4 cookies.
Explanation:To find out how many cookies each student will receive, we need to divide the total number of cookies by the number of students. In this case, Mrs. Rivera baked 112 cookies and there are 28 students, so we can divide 112 by 28 to find the answer.
Divide 112 by 28: 112 ÷ 28 = 4Therefore, each student will receive 4 cookies.Learn more about cookies divided among students here:https://brainly.com/question/34263620
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Find the exact value of cos pi/12 using half angle identities
Answer:
[tex]\cos \left(\frac{\pi }{12}\right)=\frac{\sqrt{2+\sqrt{3}}}{2}[/tex]
Step-by-step explanation:
To find the exact value of [tex]\cos \left(\frac{\pi }{12}\right)[/tex] using half angle identities you must:
Write [tex]\cos \left(\frac{\pi }{12}\right)[/tex] as [tex]\cos \left(\frac{\frac{\pi }{6}}{2}\right)[/tex]
Using the half angle identity [tex]\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos \left(x\right)}{2}}[/tex]
[tex]\cos \left(\frac{\frac{\pi }{6}}{2}\right)=\sqrt{\frac{1+\cos \left(\frac{\pi }{6}\right)}{2}}[/tex]
Use the following identity: [tex]\cos \left(\frac{\pi }{6}\right)=\frac{\sqrt{3}}{2}[/tex]
[tex]\sqrt{\frac{1+\cos \left(\frac{\pi }{6}\right)}{2}}=\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}[/tex]
Join [tex]1+\frac{\sqrt{3}}{2}[/tex]
[tex]1+\frac{\sqrt{3}}{2}=\frac{1\cdot \:2}{2}+\frac{\sqrt{3}}{2}=\frac{2+\sqrt{3}}{2}[/tex]
[tex]\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}=\sqrt{\frac{\frac{2+\sqrt{3}}{2}}{2} } =\sqrt{\frac{2+\sqrt{3}}{4}} =\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}=\frac{\sqrt{2+\sqrt{3}}}{2}[/tex]
Therefore,
[tex]\cos \left(\frac{\pi }{12}\right)=\frac{\sqrt{2+\sqrt{3}}}{2}[/tex]
simplify the complex fraction. 9/y/6/y-7
Solve the system of linear equations. separate the x- and y- values with a coma. 20x=-58-2y
17x=-49-2y
Find the probability that the mean annual preciptiation will be between 32 and 34 inches. variable is normally distributed
Anjali went to Citizens Bank and borrowed $7,000 at a rate of 8%. The date of the loan was September 20. Anjali hoped to repay the loan on January 20. Assuming the loan is based on ordinary interest, Anjali will pay back how much interest on January 20? A. $187.18 B. $187.17 C. $189.78 D. $188.22
Answer:
$189.78
Step-by-step explanation:
"The computation of the interest on January 20 is shown below:
= Principal × interest rate × number of days ÷ total number of days in a year
= $7,000 × 8% × 122 days ÷ 360 days
= $7,000 × 8% × 0.338
= $189.78
The 122 days are calculated below:
September - 10 days
October - 31 days
November - 30 days
December - 31 days
January - 20 days
Total - 122 days
And we assume the 360 days in a year"
what is x in _-18x−45=-12_
Sam is a waiter at a local restaurant where he earns wages of $7 per hour. Sam figures that he also earns about $5 in tips for each person he serves. Sam works 6 hours on a particular day.
Answer:
y=5x+42
Where y is the money he earns and x is the number of person he serves.
Step-by-step explanation:
Let the number of person he serves =x
It is given that he earns $5 as tip for each person he serves.
Hence total tip earned for serving x person=5x
His fixed wages are $7 per hour and he works for 6 hours a day. Hence his wages per day are $7*6 =$42
Hence total money earned for a day , say y can be represented as
y=5x+42
Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels 20 miles per hour faster than the westbound train. If the two trains are 750 miles apart after 5 hours, what is the rate of the eastbound train?
east bound train = x
westbound train = x-20 ( 20 miles slower than east bound)
5x + 5(x-20) = 750
5x +5x -100=750
10x -100 = 750
10x =850
x = 850/10 = 85
east bound train is 85 mph
west bound train is 85-20 = 65 mph
check: 85*5 = 425
65*5 = 325
325+425 = 750
Fractions EXPLAIN your answer.
You earn $20 per hour doing landscaping work your total earnings depend on the amount of hours you spend landscaping what is the independent variable
given the rectangle below, which of the following transformations will map the figure onto itself?
one quart or one gram is greater
rob cuts a 15-foot wire into 8 equal pieces.about how long is each piece ?
A food truck sells salads for $6.50 each and drinks for $2.00 each. The food truck’s revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day? A) 77 B) 93 C) 99 D) 105
Find the limit, if it exists. (if an answer does not exist, enter dne.) lim (x, y) → (0, 0) x4 − 20y2 x2 + 10y2
The limit of the expression as (x, y) approaches (0, 0) does not exist.
Explanation:To find the limit as (x, y) approaches (0, 0) of the expression \(\frac{x^4 - 20y^2}{x^2 + 10y^2}\), we can try approaching the limit along different paths. Let's consider approaching along the x-axis (y=0) and along the y-axis (x=0) separately.
Approaching along the x-axis: \(\lim_{{(x, 0) \to (0, 0)}} \frac{{x^4 - 20(0)^2}}{{x^2 + 10(0)^2}} = \lim_{{(x, 0) \to (0, 0)}} \frac{{x^4}}{{x^2}} = \lim_{{(x, 0) \to (0, 0)}} x^2 = 0.
Approaching along the y-axis: \(\lim_{{(0, y) \to (0, 0)}} \frac{{(0)^4 - 20y^2}}{{(0)^2 + 10y^2}} = \lim_{{(0, y) \to (0, 0)}} \frac{{-20y^2}}{{10y^2}} = \lim_{{(0, y) \to (0, 0)}} -2 = -2.
Since the limit approaches different values along different paths, the limit does not exist.
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which of the following represents the factorization of the trinomal below
What is the common ratio for the geometric sequence? 54,36,24,16... Enter your answer in the box.
The common ratio of the geometric sequence is: 2/3.
Common Ratio of a Geometric Sequence
Common ratio, r = a term divided by the consecutive term in the series.
Given the geometric sequence, 54,36,24,16...
common ratio (r) = 16/24 = 2/3.
24/36 = 2/3.
36/54 = 2/3.
Therefore, the common ratio of the geometric sequence is: 2/3.
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Don James wants to invest $55,000 to earn $6260 per year. he can invest in B-rates bonds paying 14% per year or in a certificate of Deposit (CD) paying 8% per year. How much money should be invested in each to realize exactly $6260 in interest per year?
If p(a) = 0.25 and p(b) = 0.65, assuming independence of events, then p(a and
b.is:
The Independent events is 0.1625.Events A and B are considered independent if the likelihood of each event's occurrence is unaffected by the occurrence of the other.
Find the independent events?P(A/B) is equal to P(A.B)/P(B) by definition (A). P(A) = P(B) / P(B) (as A, B are Independent events).
Events A and B are considered independent if the likelihood of each event's occurrence is unaffected by the occurrence of the other. P(A) = P(AB) = 1/2, which suggests that the likelihood of event A occurring has not changed as a result of the occurrence of event B.
P(0.25) = P(0.25 * 0.65) = 1/2
P(0.25) = 0.1625.
The Independent events is 0.1625 .
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justin sold 300 liter of soda at a baseball game.how much is this in milliliters?
Answer:
300,000 mililiters
Step-by-step explanation:
Remember that in international system the convertions are really easy because they are done 10 by 10, so from liters to mili, there are 3 spots, 1000, so there are 1000 mili-liters in a liter, so you just need to multiply the 300 liters of soda by 1000, which is 300,000 mililiters and that is what Justin sold at the baseball game in mililiters.
Suppose f−1 is the inverse of a differentiable function f and f(4) = 0, f′(4) = 1. find (f−1)′(0).
Elspeth knows that PI r=9.42cm. What would she need to do to find the circumference?
The answer would be A! :)
A random variable x takes four possible values, 0, 2, a, and b, where a and b are unknown numbers. if pr[x = 0] = 0.2, pr[x=2] = 0.4, pr[x = a] = 0.3, e[x] = 2.8 and it is the case that a + b = 6, what is the missing value of a ?
a.-1.0
b.5.0
c.7.0
d.cannot be determined without more information
e.none of the above
Final answer:
The missing value of the random variable X can be determined by solving the equation e[x] = 2.8 and substituting the known values. By solving the equation, we find that the missing value is c. 7.
Explanation:
a. In words, X = A random variable that takes four possible values: 0, 2, a, and b.
b. X~ A missing value that represent an unknown number for the random variable X.
c. In words, X = The missing value of the random variable X, denoted by a.
d. X A missing value that we need to determine.
In this case, the missing value of a can be found by substituting the known values into the equation a + b = 6. Since b = 6 - a, we can substitute this expression into the equation e[x] = 2.8 and solve for a. From the equation, we get 0.2(0) + 0.4(2) + 0.3(a) + 0.3(6 - a) = 2.8.
Solving this equation gives us a = 7. Therefore, the missing value of a is 7, so the correct answer is c.
What is the next letter a,z,e,b,I,y,o
Three boys share 28 toy cars equally. How many cars did each boy get and how many were left over
A professor has recorded exam grades for 20 students in his class, but one of the grades is no longer readable. If the mean score on the exam was 81 and the mean of the 19 readable scores is 85, what is the value of the unreadable score?
The value of the unreadable score is [tex]5[/tex]
It should be noted that the mean of numbers simply means the average of the numbers.
Since the mean score of the 20 students was 81, then the total score will be: [tex]= 20 * 81= 1620[/tex]
Then, since the mean score of the 19 students was 85, their total scores will be: = [tex]19 * 85 = 1615[/tex]
The value of the unreadable score will be:
[tex]= 1620 - 1615 = 5[/tex].
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A random sample of is selected from this population. find the probability that the sample mean is greater than 2.1 but less than 2.5.