C(x) = 0.000002x3 − 0.03x2 + 400x + 80,000 where C(x) denotes the total cost incurred in producing x sets. Find the level of production that will yield a maximum profit for the manufacturer. Hint: Use the quadratic formula
Answers
Answer:
The producer will have maximum profit when x is 5000.
Step-by-step explanation:
Given C(x) = 0.000002x³ - 0.03x² + 400x + 80000
To find the level of production that will yield the maximum profit for the manufacturer, firstly, we differentiate C(x) to obtain C'(x), we then set the resulting quadratic expression to zero and solve. Whichever of the two values obtained from the quadratic equation will be tested to see what we want to find.
Differentiate C(x)
C'(x) = 3(0.000002)x² - 2(0.03)x + 400
= 0.000006x² - 0.06x + 400
Set C'(x) = 0
0.000006x² - 0.06x + 400 = 0
Solve using quadratic formula.
x = [-b ± √(b² - 4ac)]/2a
a = 0.000006
b = -0.06
c = 400
x = [-(-0.06) ± √((-0.06)² - 4(0.000006 × 400)]/2(0.000006)
= [0.06 ± √(0.0036 - 0.0096]/0.000012
= (0.06/0.000012) ± i√(0.006)/0.000012
= 5000 ± 6454.97i
x = 5000 + 6454.97i
Or
x = 5000 - 6454.97i
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Can you help with the question
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(write down the given to be clear)
PQ=21 cm
QR=5 cm
But one very important thing:
As Aman said, the length of PR would definitely not be greater than the sum of the other two sides/legs....
Why? Because then it gives a STRAIGHT LINE!
which means: PR will be less than that sum
PR<sum of PQ and QR
PR<21+5
PR<26
Time for Pythagoras Theorem!
We can now split it into Two ways, since we dont know if PR is just a leg or the hypotenuse of the triangle:
And therefore:
Assuming PR is a leg:
(PQ seems to be the larger number)
PQ²=PR²+QR²
21² =PR²+5²
21²-5²=PR²
√21²-5²=PR
20.396 cm=PR
≈20.4 cm
20.4≤PR<26 (which means it can be 20.4 as well, but not any lower as it is very obvious)
Assuming that PR is the hypotenuse:
PR²=PQ²+QR²
PR²=21²+5²
PR=√21²+5²
PR=21.587 cm≈ 21.6 cm
21.6≤PR<26
So basically, the length can be 21.6 itself or higher.
Answers
Cause it can't be calculate.
Answers
1. Mean (μ) of x' = 66, Standard Deviation (σx') = 2.
2. Shape tends towards normal with increasing sample size.
3. Z-scores: -1.2 for x' = 63.6, 1.6 for x' = 69.2.
4. Probabilities: P(x' ≥ 63.6) ≈ 0.8849, P(x' < 69.2) ≈ 0.9452, P(63.6 ≤ x' ≤ 69.2) ≈ 0.0603, P(x' > 69.2) ≈ 0.0548.
Let's break down each part of your question step by step:
1. Mean and Standard Deviation of the Sampling Distribution of x':
The mean of the sampling distribution of the sample mean (x') is equal to the population mean (μ), which is 66 in this case.
The standard deviation of the sampling distribution of the sample mean (x') is equal to the population standard deviation (σ) divided by the square root of the sample size (n). So:
Standard Deviation of x' = σ / √n = 12 / √36 = 12 / 6 = 2
2. Shape of the Sampling Distribution of x':
The shape of the sampling distribution of the sample mean (x') tends to follow a normal distribution, especially as the sample size increases. This is known as the Central Limit Theorem. The larger the sample size, the closer the sampling distribution resembles a normal distribution.
3. Z-Scores for x' = 63.6 and x' = 69.2:
To calculate the z-scores, you can use the formula:
Z = (X - μ) / (σ/√n)
- For x' = 63.6:
Z = (63.6 - 66) / (12/√36) = (-2.4) / (2) = -1.2
- For x' = 69.2:
Z = (69.2 - 66) / (12/√36) = (3.2) / (2) = 1.6
4. Probability Calculations:
- P(x' ≥ 63.6): To find this probability, you can use a standard normal distribution table or calculator. P(Z ≥ -1.2) ≈ 0.8849 (rounded to 4 decimals).
- P(x' < 69.2): Similarly, P(Z < 1.6) ≈ 0.9452 (rounded to 4 decimals).
- P(63.6 ≤ x' ≤ 69.2): This is the difference between the two probabilities above: P(63.6 ≤ x' ≤ 69.2) ≈ 0.9452 - 0.8849 ≈ 0.0603 (rounded to 4 decimals).
5. There is a 60% chance that the value of x' is above (to 4 decimals):
To find the probability that x' is above a certain value, you need to calculate P(x' > 69.2). You can use the complement rule:
P(x' > 69.2) = 1 - P(x' < 69.2) ≈ 1 - 0.9452 ≈ 0.0548 (rounded to 4 decimals).
So, there is a 5.48% chance (rounded to 4 decimals) that the value of x' is above 69.2.
To know more about Mean, refer here:
#SPJ3
Answer:
μ = 66, σ = 2; The distribution is bell-shaped; Yes, this depends on the sample size; z = -1.2; z = 1.6; P(X ≥ 63.6) = 0.8849; P(X < 69.2) = 0.9452; P(63.6 ≤ X ≤ 69.2) = 0.8301; 65.5
Step-by-step explanation:
The central limit theorem states that if the sample size is greater than 30, the sample mean is roughly the same as the population mean. This means it is 66.
The standard deviation of a sampling distribution of means is given by
σ/√n
For our data, this is
12/(√36) = 12/6 = 2
The central limit theorem states that the sampling distribution is approximately normal, so it will be bell-shaped.
The formula for the z score of a sampling distribution of means is
For the value of x = 63.6,
z = (63.6-66)/(12/(√36)) = -2.4/2 = -1.2
For the value of x = 69.2,
z = (69.2-66)/(12/(√36)) = 3.2/2 = 1.6
Using a z table, we see that the area under the curve to the left of z = -1.2 (for x = 63.6) is 0.1151. However, we want P(x̄ ≥ 63.6); this means we want the area to the right. We subtract our value from 1:
1-0.1151 = 0.8849
Using a z table, we see that the area under the curve to the left of z = 1.6 (for x = 69.2) is 0.9452. This is P(x̄ < 69.2).
Since we have the area under the curve to the left of each endpoint, to find P(63.6 ≤ x̄ ≤ 69.2) we subtract these values:
0.9452-0.1151 = 0.8301
To find the value that would correspond in 60% of values being larger than, we first consider the fact that the z table gives us areas to the left of values, which is probabilities less than the value. Our question is what number has a probability of 60% being larger than; this means we need to subtract from 1:
1-0.6 = 0.4
In a z table, we find the value as close to 0.4 as we can get. This is 0.4013, which corresponds with a z score of -0.25.
Substituting this into our z formula, we have
Multiply both sides by 2:
2(-0.25) = ((X-66)/2)(2)
-0.5 = X-66
Add 66 to each side:
-0.5+66 = X-66+66
65.5 = X
Answers
Answers
Since q and s are non zero, the sum is a rational number.
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes
Answers
Answer:No A
Step-by-step explanation:
2hours 24 minutes