The sample space refers to option (c) the set of all possible experimental outcomes. In probability theory and statistics, a sample space represents all possible outcomes of an experiment or a random event.
The correct answer is c. The sample space refers to the set of all possible experimental outcomes. This includes every possible outcome that could occur in an experiment, whether or not it actually occurs. For example, if you flip a coin, the sample space would be {heads, tails}. This encompasses every possible outcome of the experiment. It provides a foundation for calculating probabilities and understanding the range of results that may occur in a given situation. Sample spaces can vary in size and complexity, depending on the nature of the experiment or event being studied. Understanding the sample space is crucial for making accurate predictions and informed decisions based on data.
Option a is also correct to some extent, as any particular experimental outcome can be considered a part of the sample space. However, it is not a complete definition of the sample space as it only focuses on one outcome and not all possible outcomes.
Option b is incorrect, as the sample space is not limited to just one particular experimental outcome. It is the set of all possible outcomes.
Option d is also incorrect as the sample space has nothing to do with the sample size or the number of participants in the experiment. It is solely based on the set of all possible outcomes of the experiment.
In conclusion, the sample space is the set of all possible experimental outcomes, including both successful and unsuccessful outcomes. It is an important concept in probability theory and is used to calculate the probability of specific events occurring in an experiment.
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If it is known that the cardinality of the set A X A is 16. Then the cardinality of A is: Select one: a. None of them b. 512 c. 81 d. 4 e. 18
If it is known that the cardinality of the set A X A is 16. Then the cardinality of A is: option d. 4
Cardinality refers to the number of elements or values in a set. It represents the size or count of a set. In other words, cardinality is a measure of the "how many" aspect of a set. We know that the cardinality of A X A is 16, which means that there are 16 ordered pairs in the set A X A. Each ordered pair in A X A consists of two elements, one from A and one from A. So, the total number of possible pairs of elements in A is the square root of 16, which is 4. Therefore, the cardinality of A is 4. So, the answer is d. 4.
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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
The diameter of the earth is 13,000,000 meters. Rewrite this number in scientific notation.
A researcher designs a study where she goes to high schools throughout Oregon and measures the pulse rates of a group of female seniors, and then compares the averages of her sample at each school to the averages at other schools in Oregon.
a) What distribution would you expect the average pulse rates to follow?
From a previous study, it is known that the mean pulse rates of female high school seniors is 77.5 beats per minute (bpm), with a standard deviation of 11.6 bpm.
b) Find the percentiles P1 and P99 of the high school female pulse rates.
c) Estimate the mean and standard deviation of a sample of n = 36 female high school seniors.
d) Find the probability that a school's average female pulse rate is between 70 and 85, i.e. find the probability P(70 < x < 85) when the sample size is n = 25 female high school seniors. Shade in the area of interest on a normal probability curve.
P1 is 51.9 bpm and P99 is 103.1 bpm.
The probability that a school's average female pulse rate is between 70 and 85 bpm is approximately 1.
a) The distribution of the average pulse rates is expected to follow a normal distribution.
b) To find the percentiles P1 and P99, we can use the z-score formula:
z = (x - μ) / σ
where x is the pulse rate, μ is the population mean (77.5 bpm), and σ is the population standard deviation (11.6 bpm).
For P1, we want to find the pulse rate such that only 1% of the population has a lower pulse rate. Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 1st percentile is -2.33. Thus,
-2.33 = (x - 77.5) / 11.6
Solving for x, we get:
x = 51.9 bpm
For P99, we want to find the pulse rate such that only 1% of the population has a higher pulse rate. Using the same method as above, we find that the z-score corresponding to the 99th percentile is 2.33. Thus,
2.33 = (x - 77.5) / 11.6
Solving for x, we get:
x = 103.1 bpm
Therefore, P1 is 51.9 bpm and P99 is 103.1 bpm.
c) The mean of a sample of n = 36 female high school seniors is estimated to be the same as the population mean of 77.5 bpm. The standard deviation of the sample is estimated to be:
s = σ / sqrt(n) = 11.6 / sqrt(36) = 1.933 bpm
d) To find the probability that a school's average female pulse rate is between 70 and 85 bpm when the sample size is n = 25, we first need to calculate the standard error of the mean:
SE = s / sqrt(n) = 1.933 / sqrt(25) = 0.387 bpm
Next, we find the z-scores for 70 and 85 bpm:
z1 = (70 - 77.5) / 0.387 = -19.34
z2 = (85 - 77.5) / 0.387 = 19.34
Using a standard normal distribution table or calculator, we find that the area to the left of z1 is essentially 0 and the area to the left of z2 is essentially 1. Therefore, the probability that a school's average female pulse rate is between 70 and 85 bpm is approximately 1.
Shading the area of interest on a normal probability curve would show the entire curve as it represents the entire population of high school female seniors, but the area of interest would be shaded in the middle of the curve.
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In circle I I J = 9 and the area of shaded sector = 36π. Find m ∠JIK.
The measure of the central angle m ∠JIK is 160°.
Given that the circle I, in which IJ is the radius of 9 units, the area of shaded sector = 36π, we need to find the m ∠JIK, the central angle.
Area of the sector = central angle / 360° × π × radius²
∴ 36π = m ∠JIK / 360° × π × 9²
m ∠JIK = 360° × 4 / 9
m ∠JIK = 160°
Hence, the measure of the central angle m ∠JIK is 160°.
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The mean per capita consumption of milk per year is 138 liters with a standard deviation of 28 liters. If a sample of 60 people is randomly selected, what is the probability that the sample mean would be less than 132. 25 liters? round your answer to four decimal places
The probability that the sample mean would be less than 132.25 liters is 0.0564 (or 5.64% when expressed as a percentage), rounded to four decimal places.
We can use the central limit theorem to approximate the distribution of the sample mean as normal with a mean of 138 liters and a standard deviation of 28/sqrt(60) liters.
z = (132.25 - 138) / (28 / sqrt(60)) = -1.5811
Using a standard normal distribution table or a calculator, we can find the probability of getting a z-score less than -1.5811. The probability is approximately 0.0564.
Therefore, the probability that the sample mean would be less than 132.25 liters is 0.0564 (or 5.64% when expressed as a percentage), rounded to four decimal places.
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Can I get the answer soon please??!!!!!<3
The given statement translated to an inequality is 5 + 6w > 24
Writing an inequality from a statementFrom the question, we are to translate the given sentence into an inequality
From the given information,
The given statement is:
Five increased by the product of a number and 6 is greater than 24.
Also,
From the given information,
We are to use the variable w for the unknown number
Thus,
The inequality can be written as follows
"the product of a number and 6" can b written as w × 6
w × 6 = 6w
Then,
"Five increased by the product of a number and 6" is:
5 + 6w
Finally,
"Five increased by the product of a number and 6 is greater than 24" becomes
5 + 6w > 24
Hence,
The inequality is 5 + 6w > 24
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Question 3 (10 marks):
The ABC television network is deciding whether to launch a new show. It will earn $400K if the show is a hit and loses $100K on a flop. Of all the shows launched by the network, 25% turn out to be hit. For $40K, a market research firm will have an audience view pilot prospective of the show and give its view about whether the show will be a hit or flop. If the show is actually going to be a hit, there is 90% chance that the firm will predict the show a hit. If the show is actually going to be a flop, there is an 80% chance that the firm will predict flop.
Use decision tree to determine what ABC should do to max expected profits. What is the expected profit?
Hint: You need to obtain the following probabilities:
P(Hit Prediction), P(flop prediction)
P(Hit | Hit prediction), P(flop | hit prediction), P(Hit | flop prediction), P(flop | flop prediction)
The expected profit is $67.5K
To determine what ABC should do to maximize expected profits, we can use a decision tree to analyze the different possible outcomes and their probabilities.
First, let's define the events and their probabilities:
H: the show is a hit (P(H) = 0.25)
F: the show is a flop (P(F) = 0.75)
PH: the market research firm predicts a hit (P(PH|H) = 0.9, P(PH|F) = 0.2)
PF: the market research firm predicts a flop (P(PF|H) = 0.1, P(PF|F) = 0.8)
Using these probabilities, we can construct the following decision tree:
/ PH: P = 0.225 (0.25 * 0.9)
/
/
/
H: P = 0.25
\
\
\ PF: P = 0.025 (0.25 * 0.1)
\
\
\
\
\
\ PH: P = 0.15 (0.75 * 0.2)
\
\
F: P = 0.75
/
/
PF: P = 0.6 (0.75 * 0.8)
starting from the top of the tree, we can calculate the expected profits for each decision:
If ABC launches the show without doing the market research, the expected profit is:
E1 = P(H) * $400K + P(F) * (-$100K) = $75K
If ABC does the market research and it predicts a hit, the expected profit is:
E2 = P(H and PH) * $400K - $40K + P(F and PH) * (-$40K) = $89K
If ABC does the market research and it predicts a flop, the expected profit is:
E3 = P(H and PF) * $400K - $40K + P(F and PF) * (-$100K - $40K) = -$52K
Therefore, the decision that maximizes expected profits is to do the market research and launch the show only if the market research predicts a hit.
The expected profit in this case is:
E = P(H and PH) * $400K - $40K + P(F and PH) * (-$40K) = 0.225 * $400K - $40K + 0.15 * (-$40K) = $67.5K
Therefore, the expected profit is $67.5K.
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2
Σ(-52 + n)
n=0
please help with this
The summation notation [tex]\sum\limits^{2}_{n = 0} (-52 + n)[/tex] when evaluated has a value of -153
Evaluating the summation notationFrom the question, we have the following notation that can be used in our computation:
[tex]\sum\limits^{2}_{n = 0} (-52 + n)[/tex]
This means that we substitute 0 to 2 for n in the expression and add up the values
So, we have
[tex]\sum\limits^{2}_{n = 0} (-52 + n) = (-52 + 0) + (-52 + 1) + (-52 + 2)[/tex]
Evaluate the sum of the expressions
So, we have
[tex]\sum\limits^{2}_{n = 0} (-52 + n) = -153[/tex]
Hence, the solution is -153
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If our alternative hypothesis is mu < 1.2, and alpha is .05, where would our critical region be? a) In the lower and upper 2.5% of the null distribution
b) In the upper 5% of the null distribution c) In the lower and upper 2.5% of the alternative distribution d) In the lower 5% of the alternative distribution
e) In the lower 5% of the null distribution In the upper 5% of the alternative distribution
The critical region lies In the lower 5% of the null distribution.
Option E is the correct answer.
We have,
When our alternative hypothesis is mu < 1.2, it means we are testing if the population mean is less than 1.2.
The critical region is the area in the null distribution where we reject the null hypothesis.
Since our alternative hypothesis is a one-tailed test (less than), the critical region will be in the tail of the null distribution on the left side.
If alpha is .05, it means we want to reject the null hypothesis if the probability of observing our sample mean is less than 5% under the null distribution.
This corresponds to the lower 5% of the null distribution, which is our critical region.
Therefore, any sample mean that falls in the lower 5% of the null distribution will lead to rejection of the null hypothesis and acceptance of the alternative hypothesis that mu < 1.2.
Thus,
The critical region lies In the lower 5% of the null distribution.
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Other than one what are the perfect square factors of 792
So the perfect square factors of 792 are 4, 9, 36, 144, 484, and 1089.
The prime factorization of 792 by dividing it by its smallest prime factor repeatedly:
792 ÷ 2 = 396
396 ÷ 2 = 198
198 ÷ 2 = 99
99 ÷ 3 = 33
33 ÷ 3 = 11
So the prime factorization of 792 is [tex]2^3 * 3^2 * 11.[/tex]
To find the perfect square factors, we can look for pairs of factors where both factors have even exponents.
The factors of 792 are: 1, 2, 3, 4, 6, 8, 11, 12, 18, 22, 24, 33, 36, 44, 66, 72, 88, 132, 198, 264, 396, and 792.
The perfect square factors of 792 are:
[tex]2^2 = 4\\2^2 * 3^2 = 36\\2^2 * 11^2 = 484\\3^2 = 93^2 * 4^2 = 144\\3^2 * 11^2 = 1089[/tex]
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Solve for x to make A||B. A 4x + 41 B 6x + 19 x = [ ? ]
Using the Alternate angles theorem, the value of x in the given diagram is 11
Alternate interior angles theorem: Calculating the value of xFrom the question, we are to calculate the value of x that will make A || B
From the Alternate angles theorem which states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.
In the given diagram,
The angle measures (4x + 41) and (6x + 19) are alternate interior angle measures
Thus.
For A to be parallel to B (A || B)
4x + 41 = 6x + 19
Solve for x
4x + 41 = 6x + 19
41 - 19 = 6x - 4x
22 = 2x
Divide both sides by 2
22 / 2 = x
11 = x
x = 11
Hence,
The value of x is 11
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What is the value of S?
The value of S° in the given adjacent angles would be = 26.7°
What are adjacent angles?Adjacent angles are those angles that are found on the same side of the plane and they share a common vertex.
The adjacent angles are different from the supplementary angles which are angles found in the same side but when measured together sums up to 180°.
The angles 41.6° and S° are two angles that share the same vertex with the sum of 68.3°
Therefore, S° which is the second part of the adjacent angles would be = 68.3+41.6 = 26.7°
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These figures are congruent, what series of transformations move pentagon FGHIJ onto pentagon F’G’H’I’J’
The transformations that move the pentagon FGHIJ onto the pentagon F'G'H'I'J' includes a rotation and a reflection. The correct option therefore is the option C.
C. Rotation, reflection
What is a rotation transformation?A rotation transformation is one in which a geometric figure is rotated about a fixed point or location, known as the center of rotation.
The coordinates of the image are; I(-5, 4), H(-2, 4), G(-1. 3), F(-2, 0), and J(-4, 1)
The coordinates of a point, (x, y), following a 90 degrees clockwise rotation are; (y, -x)
Therefore, the coordinates of the image of the after a 90 degrees rotation are; I'(4, 5), H'(4, 2), G'(3, 1), F'(0, 2), J'(1, 4)
The coordinates of the point on the preimage, (x, y), following a reflection over the y-axis is the point (x, -y), therefore;
The coordinates of the image of the figure F'G'H'I'J' after a reflection over the x-axis are;
I''(4, -5), H''(4, -2), G''(3, -1), F''(0, -2), and J''(1, -4)
The above points corresponds to the coordinates of the figure, F'G'H'I'J' in the diagram, therefore;
The series of transformations that maps the pentagon FGHIJ onto the pentagon F'G'H'I'J' is a 90 degrees clockwise rotation and a reflection over the y-axis. Option C is the correct option
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how do i solve this
Answer: Y-intercept:
Axis of symmetry: X = - 1
Vertex: Y = 2(X + 1)^2-5
Maximum: -1
Minimum: - 5
Domain:
(−∞,∞),{x|x∈R}
Range:
[−5,∞),{y|y≥−5}
Step-by-step explanation:
To add or subtract vectors in component form, you simply add or subtract the corresponding components. For example, to add two vectors u and v, you can use the formula u v
To include two vectors u and v in component shape, you include the comparing components. The equation is: u + v = (u₁ + v₁, u₂ + v₂, u₃ + v₃)
where u = (u₁, u₂, u₃) and v = (v₁, v₂, v₃) are the component vectors of u and v, separately.
So also, to subtract two vectors u and v in the component frame, you subtract the comparing components. The equation is:
u - v = (u₁ - v₁, u₂ - v₂, u₃ - v₃)
where u = (u₁, u₂, u₃) and v = (v₁, v₂, v₃) are the component vectors of u and v, separately.
For illustration, on the off chance that u = (1, 2, -3) and v = (4, -2, 5), at that point u + v = (1 + 4, 2 - 2, -3 + 5) = (5, 0, 2) and u - v = (1 - 4, 2 + 2, -3 - 5) = (-3, 4, -8).
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Complete Question: To add or subtract vectors in component form, you simply add or subtract the corresponding components, For example to add two vectors u and v, you can use the formula u v. Describe the component vectors of u and v.
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Find the LCM for each polynomial.
1)5x^2-20 , 3x+6
2)9c-15 , 21c-35
Please step by step!
>T.5 Find a missing coordinate using slope 5C7
10
A line with a slope of passes through the points (j, 5) and (-10,-5). What is the value of j?
The value of j is equal to -9.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
10 = (-5 - 5)/(-10 - j)
10(-10 - j) = -10
(-10 - j) = -1
j = -10 + 1
j = -9
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Complete Question:
A line with a slope of 10 passes through the points (j, 5) and (-10,-5). What is the value of j?
3. Use slope and/or the distance formula to
determine the most precise name for the
figures A(-6, -7), B(-4,-2), C(2,-1), D(0,
[A] rectangle
[C] square
[B] quadrilateral
[D] rhombus
6. Use slope and/or the distance formula to
determine the most precise name for the
figure: A(-3,-5), B(4, -2), C(7, -9), D(0,-12).
[A] square
[C] trapezoid
[B] rhombus
[D] kite
3. Using slope and/or the distance formula .The most precise name for the
figures A(-6, -7), B(-4,-2), C(2,-1), D(0) is: [A] rectangle.
4. Using slope and/or the distance formula. The most precise name for the
figure: A(-3,-5), B(4, -2), C(7, -9), D(0,-12) is: [D] kite.
What is the most precise name ?3. We must look at the sides and angles characteristics to identify the figure's name. We can plot the four points on a graph to see how the figure appears since we have four points.
When we plot the points on a graph we can see that BC and AD and AB and CD have the same length. In addition every angle is 90 degrees. The figure is a rectangle.
Therefore the correct option is A.
4. Once more we can graph the points and analyze the sides and angles characteristics.
Since AB, BC, and CD have different lengths when the points are plotted on a graph the figure is neither a rhombus nor a square. The figure is a kite since the diagonals AC and BD both connect at a straight angle.
Therefore the correct option is D.
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PROBABILITY AND STATISTICS:
The random size distribution table is:
X
-4
-2
0
1
3
5
p
0,2
0,1
0,25
0,2
0,2
0,05
a) Write down the function of distribution of this random size by regions. A drawing, formula and detailed calculation are required for each area.
b) Express the result obtained as F (x) =***
c) Calculate the value of F(3) -F(0).
d) In which area is the probability of entering F (3) -F (0)? (Answer as region X ≤ 9 or -9 ≤ X ≤ 9
etc., think carefully about which endpoint of the area is included and which is not.)
The value of F(3) -F(0). d) In which area is the probability of entering F (3) -F (0) is "0 ≤ X < 3".
a) The function of distribution by regions is:
For x < -4: F(x) = 0
For -4 ≤ x < -2: F(x) = 0.2
For -2 ≤ x < 0: F(x) = 0.2 + 0.1 = 0.3
For 0 ≤ x < 1: F(x) = 0.3 + 0.25 = 0.55
For 1 ≤ x < 3: F(x) = 0.55 + 0.2 = 0.75
For 3 ≤ x < 5: F(x) = 0.75 + 0.2 = 0.95
For x ≥ 5: F(x) = 1
b) Expressing the result obtained as F(x) =:
F(x) = {0, x < -4
0.2, -4 ≤ x < -2
0.3, -2 ≤ x < 0
0.55, 0 ≤ x < 1
0.75, 1 ≤ x < 3
0.95, 3 ≤ x < 5
1, x ≥ 5
c) F(3) - F(0) = 0.95 - 0.55 = 0.4
d) The probability of entering F(3) - F(0) is the probability of the random variable falling between 0 and 3. This can be expressed as:
P(0 ≤ X < 3) = F(3) - F(0) = 0.4
Therefore, the answer is "0 ≤ X < 3".
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(a) What proportion of the time does Mrs. Starnes finish
an easy Sudoku puzzle in less than 3 minutes?
In a study of cell phone usage and brain hemispheric dominance, an Inte survey was e-mailed to 6585 subjects andomly sidected from an online group involved with ears. These were 1344 aury. Use a 0.01 significance level to test the claim that the retum rate is less than 20%. Use the Palue method and use the normal distribution as an approximation to the binomial distribution
Identify the null hypothesis and alternative hypothes
OA. He p>02
OB. Hg: p-02
OC. H₂ p<02
OD. H₂ p=0.2
OF H: 02
The null hypothesis is H₀: p ≥ 0.2 (the return rate is greater than or equal to 20%). The alternative hypothesis is H₁: p < 0.2 (the return rate is less than 20%).
We will first identify the null hypothesis (H₀) and alternative hypothesis (H₁). The null hypothesis represents the assumption that there is no significant difference or effect. In this case, the return rate is assumed to be equal to 20%. The alternative hypothesis represents the claim we want to test, which is that the return rate is less than 20%. So, the null hypothesis and alternative hypothesis are: H₀: p = 0.2 H₁: p < 0.2 Based on the provided options,
The correct answer is: OB. H₀: p = 0.2 OC. H₁: p < 0.2
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Let y(x) be the solution of the initial value problem
dy/dx = 3x²y, y(2) = 3.
(a) Use Taylor series method of order three to estimate y(2.01) in one step.
(b) Estimate the local truncation error that incurred in the approximation of y(2.01) using the next term in the corresponding Taylor series.
The local truncation error incurred in the approximation of y(2.01) using the next term in the corresponding Taylor series is O(0.0001)
We can use the Taylor series method of order three to estimate y(2.01) in one step. Let's first write the Taylor series expansion of y(x) about x=2 up to the third derivative:
[tex]y(x) = y(2) + (x-2)y'(2) + \frac{(x-2)^{2} }{2!} y''(2) + \frac{(x-2)^{3} }{2!} y'''(2) + O((x-2)^{4} )[/tex]
where [tex]y'(x) = 3x^{2} y(x), y''(x) = 6xy(x) + 3x^{2} y'(x), y'''(x) = 9x^{2} y'(x) + 18xy'(x) + 6x^{2} y''(x).[/tex]
(a) To estimate y(2.01) in one step, we need to evaluate the above expression at x=2.01. Using y(2) = 3 and [tex]y'(2) = 3(2)^{2} (3) = 36[/tex], we get:
[tex]y(2.01) = y(2) + (2.01-2)y'(2) + \frac{(2.01-2)^{2} }{2!} y''(2)[/tex]
[tex]= 3 + 0.01(36) + \frac{(0.01)^{2} }{2!} (6(2)(3) + 3(2)^{2} (3)(3))[/tex]
=3.1089
Therefore, y(2.01) =3.1089.
(b) The local truncation error is given by the next term in the Taylor series expansion, which is O((x-2)⁴) in this case. Evaluating this term at x=2.01, we get:
O((2.01-2)⁴) = O(0.0001)
Therefore, the local truncation error incurred in the approximation of y(2.01) using the next term in the corresponding Taylor series is O(0.0001).
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From the attachment, what is the missing side?
The value of x in the triangle is 21, option B is correct.
The given triangle is right triangle
We know that the sine function is the ratio of opposite side and hypotenuse
Opposite side =19
Hypotenuse =x
We have to find the value of x
Sin 65 = 19/x
0.91 =19/x
x=19/0.91
x=20.8
x=21
Hence, the value of x in the triangle is 21, option B is correct.
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60 by 90 dilated by scale factor of 3
The new dimensions of the shape that is being dilated by the scale factor of 3 would be = 180 by 270.
How to calculate new dimensions of a shape using a given scale factor?To calculate the new dimensions of a shape, the formula for a scale factor can be used.
Scale factor = Bigger dimensions/smaller dimensions
Scale factor = 3
Length of bigger dimension = 60
width = 90
Dilated length = 60×3 = 180
width of dilated shape = 90×3= 270
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PLSSSS HELP IF YOU TRULY KNOW THISSS
Answer:
No solution
Step-by-step explanation:
Simplifies to
15-12x=18-12x
15=18
No solution
(5) Determine all values ofpfor which the following series converges using the Integral Test. Make sure you justify why the integral test is applicable.n=3â[infinity]ân(ln(n))p+21â
The series converges for all values of p < -1, and diverges for all values of p ≥ -1.
To apply the Integral Test, we need to verify that the terms of the series are positive and decreasing for all n greater than some fixed integer. For this series, note that the terms are positive since both the base and the natural logarithm are positive. To show that the terms are decreasing, we take the ratio of successive terms:
[tex]a(n+1)/a(n) = [(n+1)ln(n+1)]^p / [nln(n)]^p[/tex]
[tex]= [(n+1)/n]^p * [(1+1/n)ln(1+1/n)]^p[/tex]
Since (n+1)/n > 1 and ln(1+1/n) > 0 for all n, it follows that the ratio is greater than 1 and therefore the terms are decreasing.
To use the Integral Test, we need to find a function f(x) such that f(n) = a(n) for all n and f(x) is positive and decreasing for x ≥ 3. A natural choice is [tex]f(x) = x(ln(x))^p[/tex]. Note that f(n) = a(n) for all n and f(x) is positive and decreasing for x ≥ 3. Then we have:
integral from 3 to infinity of f(x) dx = integral from 3 to infinity of x(ln(x))^p dx
To evaluate this integral, we use integration by substitution with u = ln(x):
[tex]du/dx = 1/x, dx = x du[/tex]
So the integral becomes:
integral from ln(3) to infinity of [tex]u^p e^u du[/tex]
This integral converges for p < -1, by the Integral Test for Improper Integrals.
Therefore, the series converges for all values of p < -1, and diverges for all values of p ≥ -1.
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A savings account balance is compounded weekly. If the interest rate is 2% per year and the current balance is $1,527.00, what will the balance be 8 years from now?
The balance be 8 years from now will be :
A = $1,789.124
What Is Compound Interest?Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.
In this problem we are going to apply the compound interest formula
[tex]A= P(1+r)^t[/tex]
A = final amount
P = initial principal balance
r = interest rate
t = number of time periods elapsed
P= $1,527.00
R= 2%= 2/100= 0.02
T= 8 years
[tex]A = 1,527.00(1+0.02)^8[/tex]
A = $1,789.124
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What is the area of a regular polygon with perimeter
58 and apothem 10 ?
Common resources are not individually owned, which creates the incentive for their overuse and overconsumption. A) True B) False
Common resources are those that are available to everyone and not owned by any individual or group. Examples include air, water, fish in the ocean, and even public parks. Since no one owns them, there is no direct incentive for any individual to conserve or protect these resources.
In fact, the opposite is often true - individuals may feel that they have a right to use these resources as much as they want, leading to overuse and overconsumption. This is known as the tragedy of the commons, where individuals act in their own self-interest, leading to the depletion of a shared resource. To avoid this, it is important to have regulations and policies in place to encourage responsible use of common resources and prevent overuse and overconsumption.
The answer is A) True
Common resources refer to natural or man-made resources that are not individually owned but are available to everyone in a community. Since these resources are not owned by any specific person or organization, there is a lack of control and regulation over their use. This lack of ownership creates an incentive for people to overuse and overconsume these resources, as individuals may want to take advantage of the resources before others do.
This overuse and overconsumption can lead to depletion or degradation of the common resources, making them less available or useful for future generations. In order to prevent this outcome, it is essential to implement proper management and conservation strategies that help maintain the sustainability and accessibility of these shared resources for all users.
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