The number of simple random samples of size 4 that can be obtained from a population of size 48 is 194,580.
To find the number of different simple random samples of size 4 that can be obtained from a population whose size is 48, we can use the combination formula. The combination formula is written as:
C(n, k) = n! / (k!(n-k)!)
where n is the population size (48), k is the sample size (4), and ! denotes a factorial (e.g., 5! = 5 × 4 × 3 × 2 × 1).
So, in this case:
C(48, 4) = 48! / (4!(48-4)!)
C(48, 4) = 48! / (4!44!)
C(48, 4) = (48 × 47 × 46 × 45) / (4 × 3 × 2 × 1)
C(48, 4) = 194580
Therefore, the number of simple random samples of size 4 that can be obtained from a population of size 48 is 194,580.
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Let C be the circle relation defined on the set of real numbers. For every X. YER,CY x2 + y2 = 1. (a) Is Creflexive justify your answer. Cis reflexive for a very real number x, XCx. By definition of this means that for every real number x, x2 + x? -1. This is falsa Find an examplex and x + x that show this is the case. C%. X2 + x2) = X Since this does not equal1, C is not reflexive (b) is symmetric? Justify your answer. C is symmetric -- for all real numbers x and y, if x Cytheny Cx. By definition of C, this means that for all real numbers x and y, if x2 + y2 - 1 y + x2 - 0 This is true because, by the commutative property of addition, x2 + y2 = you + x2 for all symmetric then real numbers x and y. Thus, C is (c) Is Ctransitive? Justify your answer. C is transitive for all real numbers x, y, and 2, if x C y and y C z then x C 2. By definition of this means that for all real numbers x, y, and 2, if x2 + y2 = 1 and 2 + 2 x2 + - 1. This is also. For example, let x, y, and z be the following numbers entered as a comma-separated list. - 1 then (x, y, z) = = Then x2 + y2 = 2+z? E and x2 + 2 1. Thus, cis not transitive
The circle relation C defined on the set of real numbers is not reflexive and transitive but it is symmetric.
(a) C is not reflexive. To be reflexive, for every real number, xCx must hold true, meaning [tex]x^{2} + x^{2}[/tex]= 1. This is false. For example, let x=0. In this case, [tex]x^{2} + x^{2}[/tex] = 0, which does not equal 1. Therefore, C is not reflexive.
(b) C is symmetric. If xCy then yCx, for all real numbers x and y. If we see the definition of C, this means that if [tex]x^{2} + y^{2}[/tex] = 1, then [tex]y^{2} + x^{2}[/tex] = 1. This is true due to the commutative property of addition ([tex]x^{2} + y^{2} = y^{2} + x^{2}[/tex] for all real numbers x and y). Thus, C is symmetric.
(c) C is not transitive. To be transitive, if xCy and yCz, then xCz must hold true for all real numbers x, y, and z. This means that if [tex]x^{2} + y^{2}[/tex] = 1 and [tex]y^{2} + z^{2}[/tex] = 1, then [tex]x^{2} + z^{2}[/tex]must equal 1. This is not always true. Let's take an example (x, y, z) = (1, 0, -1). Then [tex]x^{2} + y^{2}[/tex] = 1, [tex]y^{2} + z^{2}[/tex]= 1, but [tex]x^{2} + z^{2}[/tex] = 2, not 1. Thus, C is not transitive.
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(6, -3) which two
A. Y =-3x + 6
The equations which satisfy (6, -3) are: y = -5x + 27 and y = 2x - 15 (Option C and D)
How do i know which equation will result in (6, -3)?To know which equation will result in (6, -3), we shall determine the value of y in each equation since we know that x = 6. Details below:
For A
y = -3x + 6x = 6y = ?y = -3x + 6
y = -3(6) + 6
y = -18 + 6
y = 12
For B
y = 2x - 9x = 6y = ?y = 2x - 9
y = 2(6) - 9
y = 12 - 9
y = 3
For C
y = -5x + 27x = 6y = ?y = -5x + 27
y = -5(6) + 27
y = -30 + 27
y = -3
For D
y = 2x - 15x = 6y = ?y = 2x - 15
y = 2(6) - 15
y = 12 - 15
y = -3
For E
y = -4x + 27x = 6y = ?y = -4x + 27
y = -4(6) + 27
y = -24 + 27
y = 3
From the above, the equation that satisfy (6, -3) are:
Option C: y = -5x + 27Option D: y = 2x - 15Thus, the correct answer to the question is Option C and D
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QUESTION 14 During oxygen consumption measurement the participants V2 was t.minand coa was. Umin What was the participants at that point in time ove your answer to decimal places QUESTION 15 The follo
Measurement is the process of obtaining the quantity or size of something, usually expressed in numerical values. It is a crucial aspect in various fields, including science, engineering, and mathematics. When it comes to measuring physical activity or exercise, oxygen consumption measurement is a commonly used method. It involves measuring the amount of oxygen that an individual consumes while exercising, which provides insight into their metabolic rate and energy expenditure.
In the given scenario, the participant's V2 was measured in units of t.min, and their coa was measured in units of Umin. To determine the participant's oxygen consumption rate at that specific point in time, we need to use the formula VO2 = V2/((t2-t1) x (coa-cob)). Here, t1 and t2 represent the start and end time of the measurement, while cob and coa represent the initial and final carbon dioxide levels.
Since we do not have information about the start and end times or the carbon dioxide levels, we cannot accurately determine the participant's oxygen consumption rate. Therefore, we cannot provide a decimal value as requested in the question.
In regards to Question 15, there seems to be incomplete information, and therefore, we cannot provide a response. However, it is essential to note that accurate and precise measurements are crucial in obtaining reliable data and making informed decisions in various fields.
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Type non Find the p-value for the hypothesis test. A random sample of size 53 is taken. The sample has mean of 424 and a standard deviation of 83. 10 points H0: u= 400 Ha: u = 400 The p-value for the hypothesis test is______
Your answer should be rounded to 4 decimal places,
The p-value for the hypothesis test is 0.0314.
To find the p-value for this hypothesis test, we can use a t-test since the population standard deviation is unknown.
The test statistic is calculated as:
t = (x - μ) / (s / √n)
where x is the sample mean, μ is the hypothesized population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size.
In this case, we have:
x = 424
μ = 400
s = 83
n = 53
So the test statistic is:
t = (424 - 400) / (83 / √53) ≈ 2.2071
To find the p-value, we need to compare this test statistic to the t-distribution with n-1 degrees of freedom (df = 52, in this case). Using a t-distribution table or calculator, we find that the probability of getting a t-value as extreme or more extreme than 2.2071 (in either direction) is approximately 0.0157.
Since this is a two-tailed test (Ha: u ≠ 400), we need to double this probability to get the p-value:
p-value = 2 * 0.0157 ≈ 0.0314
Therefore, the p-value for the hypothesis test is approximately 0.0314 (rounded to 4 decimal places).
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Please help
The problem below is solved incorrectly.
Part A: Find the mistake in the work/answer and explain what the mistake is.
Part B: Find the correct answer.
The given figure is a right triangular prism, with 2 parallel and congruent triangular faces and 3 rectangular faces.
The triangular faces have sides 13 ft, 13ft and 24 ft and the height of 5 ft.
Two of the rectangular faces are 13 ft x 30 ft and the remaining face is 24 ft x 30 ft.
Surface area is the sum of areas of all 5 faces.
Area formula for triangle is A = bh/2 and for rectangle is A = ab.
Let's verify the steps of calculation.
Part AStep 1
13 x 30 = 390, right390 x 2 = 780, rightThis is right
Step 2
30 x 24 = 720, right720 x 2 = 1440, wrong as there is only one face of same dimensionsThis is wrong
Step 3
24 x 5 x 0.5 = 60, right60 x 2 = 120, rightThis is right
Step 4
780 + 1440 + 120 = 2340 sq ft, this is wrong because of wrong step 2Part BCorrection in step 2, it should be 720 but not 1440.
Correction in last step, the sum:
780 + 720 + 120 = 1620 sq ftName: Math 203 6. Let A be an m x n matrix, and let B be an n xp matrix such that AB = 0. Show ixn that rank A + rank Bn. (Hint: Which of the subspaces Col A, Nul A, Col B, and Nul B are subsets of each other?)
If A is an m x n matrix, and let B be an n xp matrix such that AB = 0, then rank A + rank B ≤ n
To start, we can use the fact that for any matrix A, rank A + dim Nul A = n, where n is the number of columns in A. This is a result of the rank-nullity theorem.
Now, let's consider the subspaces associated with A and B. The column space of A, Col A, is a subspace of R^m, and the null space of A, Nul A, is a subspace of R^n. Similarly, the column space of B, Col B, is a subspace of R^n, and the null space of B, Nul B, is a subspace of R^p.
We want to show that rank A + rank B ≤ n, so let's consider the dimensions of the subspaces. We know that dim Col A = rank A and dim Col B = rank B. We also know that AB = 0, which means that every column of B is in the null space of A, Nul A. In other words, Col B is a subset of Nul A.
Using the fact that dim Col B + dim Nul B = n, we can write:
rank B + dim Nul B = n - dim Col B
Since Col B is a subset of Nul A, we know that dim Nul A ≥ dim Col B. Therefore:
dim Nul B ≥ dim Nul A
Substituting this inequality into the previous equation, we get:
rank B + dim Nul B ≥ rank B + dim Nul A = n - dim Col A
Finally, we can use the fact that rank A + dim Nul A = n to substitute for dim Nul A:
rank B + dim Nul B ≥ n - rank A
Adding rank A to both sides, we get:
rank A + rank B + dim Nul B ≥ n
But we know that dim Nul B ≥ 0, so:
rank A + rank B ≤ n
Therefore, we have shown that rank A + rank B ≤ n, as desired.
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Find the smallest number n of terms needed to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6. k=1 n=
The smallest value of n that satisfies this inequality is n = 11. Therefore, we need at least 11 terms to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6.
To find the smallest number of terms needed to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6, we need to use the formula for the partial sum of a series. The partial sum of the given series up to n terms is:
S(n) = IM8 + 12e + 0.49(2^2) + 0.49(3^2) + ... + 0.49(n^2)
We want to find the smallest value of n such that the error between S(n) and the true value of the series is less than 10^-6. The error between S(n) and the true value of the series can be approximated by the absolute value of the next term in the series:
|an+1| = 0.49((n+1)^2)
So we need to find the smallest value of n such that:
|an+1| < 10^-6
0.49((n+1)^2) < 10^-6
(n+1)^2 < (10^-6)/0.49
n+1 < sqrt((10^-6)/0.49)
n < sqrt((10^-6)/0.49) - 1
n < 11.75
Since n must be a whole number, the smallest value of n that satisfies this inequality is n = 11. Therefore, we need at least 11 terms to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6.
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Find the derivative of
Rud-cost at F(x)=
Your answer:
() cos(x2)
() -2xcos(x2)
() sin)+c
() 1-cox7(x2)
Answer:
I assume that "Rud" is a typo and you mean "Sin" instead.
To find the derivative of Sin(x^2) - Cos(x), we need to use the chain rule and the derivative of the trigonometric functions.
The derivative of Sin(x^2) is:
d/dx [Sin(x^2)] = Cos(x^2) * d/dx [x^2] = 2x * Cos(x^2)
The derivative of -Cos(x) is:
d/dx [-Cos(x)] = Sin(x)
Therefore, the derivative of the function Sin(x^2) - Cos(x) is:
2x * Cos(x^2) + Sin(x)
So the answer is option (b) -2xcos(x^2) + sin(x).
The answer is option (b): -2xcos(x^2).
Assuming that "Rud-cost" is a typo and the function is meant to be "Rudin-cost", which is a function defined as:
Rudin-cost(x) = cos(x^2)
To find the derivative of Rudin-cost(x), we can use the chain rule and the power rule for differentiation. Specifically, if we let u = x^2, then we have:
Rudin-cost(x) = cos(u)
Using the chain rule, we get:
Rudin-cost'(x) = -sin(u) * u'
where u' is the derivative of u with respect to x, which is:
u' = d/dx(x^2) = 2x
Substituting this back into the expression for Rudin-cost'(x), we get:
Rudin-cost'(x) = -sin(x^2) * 2x
Therefore, the answer is option (b): -2xcos(x^2).
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the number of square feet per house are normally distributed with a population standard deviation of 137 square feet and an unknown population mean. a random sample of 19 houses is taken and results in a sample mean of 1350 square feet. find the margin of error for a 80% confidence interval for the population mean. z0.10z0.10 z0.05z0.05 z0.025 z 0.025 z0.01z0.01 z0.005 z 0.005 1.282 1.645 1.960 2.326 2.576 you may use a calculator or the common z values above. round the final answer to two decimal places.
The margin of error for a 80% confidence interval for the population mean is 57.82 square feet.
The number of square feet per house are normally distributed with a population standard deviation of 137 square feet and an unknown population mean. To find the margin of error for a 80% confidence interval, we need to use the formula:
Margin of error = z*(σ/√n)
where z is the z-score corresponding to the level of confidence (80% corresponds to z=1.282), σ is the population standard deviation (given as 137), and n is the sample size (given as 19).
Plugging in the values, we get:
Margin of error = 1.282*(137/√19) = 57.82
Therefore, the margin of error for a 80% confidence interval is 57.82 square feet.
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The middle of {1, 2, 3, 4, 5} is 3. The middle of {1, 2, 3, 4} is 2 and 3. Select the true statements (Select ALL that are true)
A. An even number of data values will always have one middle number.
B. An odd number of data values will always have one middle value
C. An odd number of data values will always have two middle numbers.
D. An even number of data values will always have two middle numbers.
B. An odd number of data values will always have one middle value is true.
D. An even number of data values will always have two middle numbers is also true.
What happens in odd and even set of data?In an odd set of data, there will always be one exact middle number. But in an even set of data, there will be two middle numbers, and they will be the two numbers closest to the center.
So if the middle of {1, 2, 3, 4, 5} is 3 and the middle of {1, 2, 3, 4} is 2 and 3, the correct statements will be;
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Help bc this is due soon
The measures of angle B is derived as 75° to the nearest degree using the cosine rules.
What is the cosine rulesThe cosines rule relates the lengths of the sides of a triangle to the cosine of one of its angles.
Using the cosine rule:
2² = 5² + (√45)² - 2(5)(√45)cosB
4 = 25 + 45 - 250cosB
4 = 70 - 250cosB
250cosB = 70 - 4 {collect like terms}
250cosB = 66
B = cos⁻¹(66/250) {cross multiplication}
B = 74. 6925°
Therefore, the measures of angle B is derived as 75° to the nearest degree using the cosine rules.
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A 35-year-old person who wants to retire at age 65 starts a yearly retirement contribution in the amount of $5,000. The retirement account is forecasted to average a 6.5% annual rate of return, yielding a total balance of $431,874.32 at retirement age.
If this person had started with the same yearly contribution at age 40, what would be the difference in the account balances?
A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used.
$378,325.90
$359,978.25
$173,435.93
$137,435.93
The difference in the account balances is $138,435.93.
We have,
We can solve this problem by using the formula for the future value of an annuity:
[tex]FV = PMT \times [(1 + r)^n - 1] / r[/tex]
where FV is the future value of the annuity, PMT is the yearly contribution, r is the annual interest rate, and n is the number of years.
Using the given information, we can find the future value of the annuity if the person starts at age 35:
FV1
= $5,000 x [(1 + 0.065)^30 - 1] / 0.065
= $431,874.32
Now we can find the future value of the annuity if the person starts at age 40:
FV2 = $5,000 x [(1 + 0.065)^25 - 1] / 0.065
= $293,438.39
The difference in the account balances is:
FV1 - FV2
= $431,874.32 - $293,438.39
= $138,435.93
Therefore,
The difference in the account balances is $138,435.93.
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10) How many distinguishable permutations are there for the word “choice”
Answer: 720
Step-by-step explanation:
there are 6 letters in "choice"
and they must be permuted into 6 word letters:
6P6 = 720 distinct possibilities
Evaluate each problem:
Tan 5pi/4
Sin 3pi/2
Cos 7pi/4
The values of each of the given trigonometric ratios are:
Tan 5pi/4 = 1
Sin 3pi/2 = -1
Cos 7pi/4 = 1/√2
How to solve trigonometric problems in radians?There are three main trigonometric ratios and they are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
1) tan 5pi/4 when converted to degrees is tan 225 and using a calculator equals 1
2) Sin 3pi/2 when converted to degrees is sin 270 and using a calculator equals -1
3) Cos 7pi/4 when converted to degrees is cos 315 and using a calculator equals 1/√2
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which is better? A 12.5 oz bag of doritos for 3.79 or a bag oz bag for 1.00
Answer: might be the 2nd one
Step-by-step explanation:
which equation is true when n = 5? A) 2n = 7 B) n + 3 =8 C) 9 -n = 14 D) n/15 = 3
The answer is B.
In order to get the answer, you replace the letter n to 5 and workout the problems to see which one is true.
B is the answer because n + 3 = 8
5 + 3 = 8
Answer:
B
Step-by-step explanation:
n+3 =
5+3=
A finite population correction factor is needed in computing the standard deviation of the sampling distribution of sample means Select one: a. whenever the population is infinite. b, whenever the sample size is more than 5% of the population size. c, whenever the sample size is less than 5% of the population size. d. irrespective of the size of the sample.
The correct answer is c. Whenever the sample size is less than 5% of the population size, a finite population correction factor is needed in computing the standard deviation of the sampling distribution of sample means.
This correction factor takes into account the fact that when the sample size is small relative to the population, the variability of the sample means is affected. Without the correction factor, the standard deviation of the sampling distribution would be overestimated. However, if the sample size is large enough (more than 5% of the population size), the effect of finite population correction is negligible and can be ignored. If the population is infinite, the correction factor is not necessary as the sample size can be considered as a small proportion of the infinite population.
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What is the value of this expression when a = 3 and b = negative 2?
(StartFraction 3 a Superscript negative 2 Baseline b Superscript 6 Baseline Over 2 a Superscript negative 1 Baseline b Superscript 5 Baseline EndFraction) squared
The calculated value of the expression when a = 3 and b = -2 is 1
Evaluating the value of this expression when a = 3 and b = -2?The expression is given as
(StartFraction 3 a Superscript negative 2 Baseline b Superscript 6 Baseline Over 2 a Superscript negative 1 Baseline b Superscript 5 Baseline EndFraction) squared
Mathematically, this can be expressed as
(3a^-2b^6/2a^-1b^5)^2
The values of a and b are given as
a =3 and b = -2
substitute the known values in the above equation, so, we have the following representation
(3(3)^-2(-2)^6/2(3)^-1(-2)^5)^2
Evaluate
So, we have
1
Hence, the solution is 1
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which is the better deal 18 oz for 6.60 or 12 oz for 4.75
Answer:
The 18 oz jar is the better buy.
Step-by-step explanation:
When a bush was first planted in a garden, it was 12 inches tall. After 2 weeks, it was 120% as tall as when it was first planted. How tall was the bush after 2 weeks?
The bush is 26.4 inches tall after 2 weeks. This means it has grown by 14.4 inches since it was first planted and the percentage increase is 120%
To calculate the height of the bush after 2 weeks, we can use the following formula:
New height = initial height + (percent increase/100) * initial height
In this case, the initial height of the bush is 12 inches, and the percent increase is 120%. Plugging in these values, we get:
New height = 12 + (120/100) * 12
New height = 12 + 14.4
New height = 26.4 inches
Therefore, the bush is 26.4 inches tall after 2 weeks. This means it has grown by 14.4 inches since it was first planted.
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Find all real solutions of this equation to answer the question.
(6 – 2x)(3 – 2x)x = 40
Yes. Because 3/2 is a root, you can cut squares with sides of 3/2 in. to make the box
No. This equation has no real solutions.
No. The only real solution is x = 4. It is not possible to cut squares of this size.
Answer:
Please mark me the brainliest
Step-by-step explanation:
To solve the equation (6 – 2x)(3 – 2x)x = 40, we can start by simplifying the left-hand side:
(6 – 2x)(3 – 2x)x = 40
(18x – 12x^2 – 6x + 4x^2)x = 40
(2x^3 – 8x^2 + 18x)x = 40
2x^4 – 8x^3 + 18x^2 = 40
2x^4 – 8x^3 + 18x^2 – 40 = 0
We can try to factor this equation by grouping terms:
2x^4 – 8x^3 + 18x^2 – 40 = 0
2(x^4 – 4x^3 + 9x^2 – 20) = 0
2((x^2 – 2x + 1)(x^2 – 2x – 20)) = 0
2(x – 1)^2(x – 5)(x + 4) = 0
Therefore, the real solutions of the equation are x = 1 (with multiplicity 2), x = 5, and x = -4.
Now, to answer the question, we need to determine whether it is possible to cut squares with sides of 3/2 in. to make a box. We can use the value of x = 3/2 to find the dimensions of the box:
length = 6 – 2x = 6 – 2(3/2) = 3 in.
width = 3 – 2x = 3 – 2(3/2) = 0 in.
height = x = 3/2 in.
Since the width is 0, it is not possible to cut squares with sides of 3/2 in. to make a box. Therefore, the correct answer is:
No. It is not possible to cut squares of this size.
making a profit rotter partners is planning a major investment. from experience, the amount of profit x (in millions of dollars) on a randomly selected invest- ment of this type is uncertain, but an estimate gives the following probability distribution: profit: 1 1.5 2 4 10 probability: 0.1 0.2 0.4 0.2 0.1 based on this estimate, mx
Rotter Partners is planning a major investment, and to ensure that the investment is profitable, it is essential to understand the expected profit from the investment. The probability distribution of profits from similar investments indicates that the expected profit (mx) can be calculated as the weighted average of profits, where the weights are the probabilities associated with each profit level.
Based on the given probability distribution, the expected profit (mx) can be calculated as follows:
mx = (1 x 0.1) + (1.5 x 0.2) + (2 x 0.4) + (4 x 0.2) + (10 x 0.1)
mx = 0.1 + 0.3 + 0.8 + 0.8 + 1
mx = 2.7
Therefore, the expected profit from the investment is $2.7 million. This estimate is valuable to Rotter Partners as it can help them make informed decisions about the investment. If the expected profit is lower than the cost of the investment, then the investment may not be worthwhile. On the other hand, if the expected profit is higher than the cost of the investment, then the investment is likely to be profitable. In any case, the expected profit is a useful metric for assessing the potential success of the investment.
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Let f:(-1,1) →R be continuous at 2 = 0. Suppose that f(x) = f(x³) Vx∈(-1,1). Show that f(x) = f(0) for all x ∈ (-1,1).
We have shown that f(x) = f(0) for all x ∈ (-1,1).
Since f is continuous at 0, we have:
lim x → 0 f(x) = f(0)
Since f(x) = f(x³) for all x ∈ (-1,1), we can substitute x = x³ and get:
f(x) = f(x³) = f(x⁹) = f(x²⁷) = ...
Since |x| < 1, we have x² < |x| < 1, and thus:
lim x² → 0 f(x²) = f(0)
Therefore, we can apply the limit of the sequence of nested intervals to obtain:
f(x) = f(x³) = f(x⁹) = f(x²⁷) = ... = lim n → ∞ f(x^(3ⁿ)) = lim y → 0 f(y) = f(0)
where we have made the substitution y = x^(3ⁿ), which implies that x = y^(1/(3ⁿ)) → 0 as n → ∞.
Thus, we have shown that f(x) = f(0) for all x ∈ (-1,1).
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A shirt order consists of 10 small, 5 medium, and 8 large
shirts. The prices of the shirts are small $5.00; medium
$7.50; large $12.00. There is a mail order charge of $.50
per shirt for shipping and handling. Write an equation
for the total cost of ordering the shirts by mail.
The equation for total cost is The Total cost = (10s + 5m + 8l + 0.5n)
Equation of total cost calculation.
First, we can calculate the total cost plus the both the shipping and the handling charge:
The Small shirts is 10 x $5.00 = $50.00
Medium shirts is 5 x $7.50 = $37.50
Large shirts is 8 x $12.00 = $96.
Lets add three amounts plus also the shipping and the handling charge to the over all total cost:
The Total cost is (10 x $5.00) + (5 x $7.50) + (8 x $12.00) + (23 x $0.50)
Total cost = 195.00
Therefore, the equation of total cost is
The Total cost = (10s + 5m + 8l + 0.5n) s, m, and l refer to the prices of small, medium, and large shirts, respectively, n is the total number of shirts.
let now substitute the values of s, m, l, and n.
The Total cost = 10 x 5.00 + 5 x 7.50 + 8 x 12.00 + 23 x 0.50) in dollars
Therefore, the Total cost = $195.00
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philosophy question. introduction of logic. please answer correctlyand fully.Use the first thirteen rules of inference to derive the conclusions of the following symbolized arguments: A. 1. X-M 2. M |-(v-M) B. 1. L» (B v 0) 2.-(-0.-B) S Los C. 1. Ko (Y.Z) 2. (K.C) v ( MK) Z
Using the first thirteen rules of inference to derive the conclusions of the given symbolized arguments.
A. Conclusion: v-X
X-M (Premise)M (Assumption for Conditional Proof)|-(v-M) (Premise)v (Disjunctive Syllogism: 3, M)v-X (Conditional Proof: 2-4)B. Conclusion: L
L» (B v 0) (Premise)-(-0.-B) (Premise)-0 v -(-B) (Material Implication: 2)-0 v B (Double Negation: 3)B v 0 (Commutation: 1)-B»0 (Material Implication: 5)-B (Disjunctive Syllogism: 4,6)0 (Modus Ponens: 6,7)L (Disjunctive Syllogism: 1,8)C. Conclusion: Z
Ko (Y.Z) (Premise)(K.C) v ( MK) (Premise)-Z (Assumption for Conditional Proof)-(Y.Z) (Material Implication: 1)-Y v -Z (De Morgan's Law: 4)Y (Disjunctive Syllogism: 2, MK)-Z v -Z (Addition: 3)Z (Negation Elimination: 7)In the first argument, the disjunctive syllogism and conditional proof rules were used to derive the conclusion. In the second argument, the material implication, double negation, commutation, modus ponens, and disjunctive syllogism rules were used to derive the conclusion. In the third argument, the material implication, De Morgan's Law, disjunctive syllogism, addition, and negation elimination rules were used to derive the conclusion.
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Using the rules of inference to derive the conclusions of the given symbolized arguments.
A. Conclusion: v-X
X-M (Premise)
M (Assumption for Conditional Proof)
|-(v-M) (Premise)
v (Disjunctive Syllogism: 3, M)
v-X (Conditional Proof: 2-4)
B. Conclusion: L
L» (B v 0) (Premise)
-(-0.-B) (Premise)
-0 v -(-B) (Material Implication: 2)
-0 v B (Double Negation: 3)
B v 0 (Commutation: 1)
-B»0 (Material Implication: 5)
-B (Disjunctive Syllogism: 4,6)
0 (Modus Ponens: 6,7)
L (Disjunctive Syllogism: 1,8)
C. Conclusion: Z
Ko (Y.Z) (Premise)
(K.C) v ( MK) (Premise)
-Z (Assumption for Conditional Proof)
-(Y.Z) (Material Implication: 1)
-Y v -Z (De Morgan's Law: 4)
Y (Disjunctive Syllogism: 2, MK)
-Z v -Z (Addition: 3)
Z (Negation Elimination: 7)
How to explain the informationThe disjunctive syllogism and conditional proof procedures were employed to reach the conclusion in the first argument.
The material implication, double negation, commutation, modus ponens, and disjunctive syllogism rules were employed to reach the conclusion in the second argument. The material implication, De Morgan's Law, disjunctive syllogism, addition, and negation elimination rules were utilized to obtain the conclusion in the third argument.
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Find the equation of the plane tangent to the surfacer=3u2i+(5u−v2)j+3v2kr=3u2i+(5u−v2)j+3v2kat the point P that is (approximately) P(12,9,3).z(x,y)=z(x,y)=
The equation of the plane tangent to the surfacer=3u2i+(5u−v2)j+3v2kr=3u2i+(5u−v2)j+3v2kat the point P that is P(12,9,3).z(x,y)=z(x,y)= 90x + 1296y + 810z = 14218.
To find the equation of the plane tangent to the surface at point P(12, 9, 3), we first need to find the partial derivatives of the surface with respect to u and v:
∂r/∂u = 6ui + 5j
∂r/∂v = -2vj + 6vk
Next, we can evaluate these partial derivatives at the point P(12, 9, 3) to get:
∂r/∂u = 6(12)i + 5j = 72i + 5j
∂r/∂v = -2(9)j + 6(3)k = -18j + 18k
Using these partial derivatives, we can find the normal vector to the tangent plane at point P by taking their cross product:
n = (∂r/∂u) x (∂r/∂v) = (72i + 5j) x (-18j + 18k)
= -90i - 1296j - 90k
Since the tangent plane passes through point P, its equation can be written in the form:
-90(x - 12) - 1296(y - 9) - 90(z - 3) = 0
Simplifying this equation gives:
-90x + 12960 - 1296y - 810z + 1458 = 0
or
90x + 1296y + 810z = 14218
Therefore, the equation of the plane tangent to the surface at point P is 90x + 1296y + 810z = 14218.
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What is the median of the data set?
I will give Brainliest to the best answer only if it is Brainly Expert
A. 10
B. 8.5
C. 8
D. 9
Answer:
The answer to your problem is, A. 10
Step-by-step explanation:
So first add up all the total number of ‘ X ‘
Which is:
4 + 3 + 2 + 1 = 10
Technically 10 is our answer.
Thus the answer to your problem is, A. 10
Not a 100% sure
Answer:
5, 8, 8, 8, 8, 9, 9, 9, 10, 10
The median of this data set is 8.5, so the correct answer is B.
Step-by-step explanation:
Since there are 10 observations, we are looking for the number halfway between the two middle observations (observations #5 and #6) when the data are arranged in order. Here, observation #5 is 8, and observation #6 is 9, so the median of this data set is (8 + 9)/2 = 8.5. B is the correct answer.
let a be a real number for which there exists a unique value of b such that the quadratic equation x^2 + 2bx + (a-b) = 0 has one real solution. find a.
We then use the condition that b is unique to obtain a restriction on the values of a. Solving this restriction, we find that a can take any value except a = 2/3.
Let the given quadratic equation be denoted by f(x) = x^2 + 2bx + (a-b) = 0. Since f(x) has only one real solution, its discriminant must be zero: b^2 = a-b. Rearranging this equation, we get a = b^2 + b.
Substituting this expression for a into the equation for f(x), we obtain:
f(x) = x^2 + 2bx + (b^2 + b - b) = x^2 + 2bx + b^2.
This is a quadratic equation in b with discriminant 4x^2 - 4b^2 = 4(x+b)(x-b). For f(x) to have a unique real solution, this discriminant must be zero, which implies that x = -b. Substituting this value into f(x), we get:
f(-b) = (-b)^2 + 2b(-b) + b^2 = b^2 - 2b^2 + b^2 = 0.
Therefore, -b is a root of f(x), and since f(x) is a quadratic, this means that f(x) is divisible by (x+b). Thus we have:
f(x) = (x+b)(x+(a-b)/b) = (x+b)(x+b+1).
Since b is unique, this implies that (a-b)/b = b+1, or equivalently, a = b^2 + 2b.
Finally, we need to find the values of a for which b is unique. Suppose there are two distinct values of b that satisfy the condition above. Then, their difference satisfies:
(b_1)^2 + 2b_1 - (b_2)^2 - 2b_2 = 0,
which factors as (b_1 - b_2)(b_1 + b_2 + 2) = 0. Since b_1 and b_2 are distinct, the only possibility is that b_1 = -b_2 - 2.
Substituting this into the expression for a, we get:
a = (b_1)^2 + 2b_1 = (-b_2 - 2)^2 - 2(b_2 + 2) = b_2^2 + 2b_2 - 4.
Therefore, a - b_2^2 - 2b_2 + 4 = 0, or equivalently, (a-2)/3 = (b_2+1)^2, which implies that a-2 is a perfect square multiple of 3. Since b_2 can be any real number, this restriction on a is necessary and sufficient.
In summary, the value of a for which the given quadratic equation has a unique real solution is a = b^2 + 2b, where b is any real number except b = -1/2. Equivalently, a can take any value except a = 2/3.
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Proof that as the number of Bernoulli trials (N) in the binomial random variable approaches the infinity and the probability of success (P) of each of those trials goes to zero, such that N*P = constant, the distribution tends to be a Poisson distribution.
The relationship between Bernoulli, binomial, and Poisson distributions is fundamental in probability theory. The binomial distribution is the probability distribution of a series of independent Bernoulli trials, where each trial has a binary outcome of success or failure with probability P. The Poisson distribution, on the other hand, describes the probability of a given number of events occurring in a fixed interval of time or space, given the expected number of events per interval.
To show that the binomial distribution approaches a Poisson distribution as the number of trials approaches infinity and the probability of success approaches zero, we can use the following argument:
Suppose we have N independent Bernoulli trials, each with probability P of success. The number of successes X in these N trials follows a binomial distribution with parameters N and P, denoted by X ~ B(N,P).
The mean and variance of a binomial distribution are given by:
E[X] = NP
Var[X] = NP(1-P)
Now, suppose we let N → ∞ and P → 0, such that NP = λ, a constant. This means that as N gets larger, the probability of success gets smaller, but the expected number of successes λ remains constant.
Using this limit, we can rewrite the binomial distribution as:
P(X=k) = (N choose k) P^k (1-P)^(N-k)
= (N(N-1)...(N-k+1)/k!) P^k (1-P)^(N-k)
= λ^k / k! * (N(N-1)...(N-k+1) / N^k) * (1-P)^(N) * (1-P)^(-k)
Now, we can take the limit as N → ∞ and P → 0 while keeping λ = NP constant. The last term goes to 1, and the middle term can be shown to approach 1 using the fact that (1+x/N)^N → e^x as N → ∞. This leaves us with:
lim(N→∞,P→0) P(X=k) = e^(-λ) * λ^k / k!
which is the probability mass function of a Poisson distribution with parameter λ. Therefore, as N → ∞ and P → 0, such that NP = λ, the binomial distribution approaches a Poisson distribution with parameter λ.
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There is a jar with 10 nickels and 5 dimes. If two coins are chosen at random. what is the probability of choosing first a nickel and then a dime?
Answer: you would have a 75% chance
