Answer:
15 Full orbits per day
Step-by-step explanation:
To work out the number of full orbits the ISS does in 1 day, we need to know how long it takes for the ISS to complete one orbit around the Earth.
We can use the information given to us to calculate the time it takes for the ISS to complete one orbit:
Distance traveled in one orbit = 42,600 kilometers
Speed of the ISS = 27,576 kilometers per hour
To calculate the time taken for one orbit:
Time taken = Distance traveled / Speed
Time taken = 42,600 kilometers / 27,576 kilometers per hour
Time taken = 1.54 hours (rounded to 2 decimal places)
So, the ISS takes approximately 1.54 hours to complete one orbit around the Earth.
Now, we can calculate the number of orbits the ISS does in one day:
Number of orbits per day = 24 hours / Time taken for one orbit
Number of orbits per day = 24 hours / 1.54 hours
Number of orbits per day = 15.58 (rounded to 2 decimal places)
Therefore, the ISS completes approximately 15 full orbits around the Earth in one day.
The table below shows a set of points that have been dilated. The rule for the dilation is (x, y).
(x, y)
(0, 1)
(4,-2)
(-6,1)
True
False
Previous
(0,1)
(2,-1)
(-3,2)
O
Therefore, the table showing the original points and their corresponding dilated points is:
Original Point Dilated Point
(0,1) (0,1/2)
(4, -3) (2, -3/2)
(-6,1) (-3,1/2)
What is dilated point?I believe you might have meant "dilated point", which is a term commonly used in geometry. A dilated point is a point that has been enlarged or reduced in size with respect to a fixed center of dilation.
To dilate a point, you need to multiply its coordinates by a scale factor, which is a constant value greater than zero. If the scale factor is greater than one, the point will be enlarged, and if it is less than one, the point will be reduced in size. The fixed center of dilation is the point about which the dilated point is enlarged or reduced.
given by the question.
To apply the dilation rule of (1/2x, 1/2y) to a given point (x,y), we need to multiply the x-coordinate and y-coordinate of the original point by 1/2.
Using this rule, we can find the dilated points for the given set of points as follows:
For the point (0,1), we have:
1/2x = 1/2 * 0 = 0
1/2y = 1/2 * 1 = 1/2
So, the dilated point is (0, 1/2).
For the point (4, -3), we have:
1/2x = 1/2 * 4 = 2
1/2y = 1/2 * (-3) = -3/2
So, the dilated point is (2, -3/2).
For the point (-6,1), we have:
1/2x = 1/2 * (-6) = -3
1/2y = 1/2 * 1 = 1/2
So, the dilated point is (-3,1).
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. in a classroom of 30 students, 3 of the students wear wrist watches. (a) if 14 students are selected with replacement, what is the probability that exactly 2 of them wear wrist watches? (b) if 14 students are selected without replacement,
Probability of
=0.0403.
The probability that exactly two of the 14 students selected with replacement will wear wrist watches is 3/30 * 2/29 * 27/28 * 26/27 = 0.0437.
The probability that exactly two of the 14 students selected without replacement will wear wrist watches is 3/30 * 2/29 * 26/28 * 25/27 = 0.0403.
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find the missing value to the nearest hundredth cos__=7/18
67.11
37.67
22.89
21.25
The missing value is approximately 64.12 degrees, which is closest to option D: 21.25 using inverse cos.
The inverse cosine (or arccosine) of both sides of the equation must be taken in order to locate the missing value in the equation cos = 7/18 to the closest tenth. We will then be able to convert the value of to degrees and round it to the closest hundredth using the value of the radian that is produced.
cos θ = 7/18
= arccos(7, 18, 7)
A 1.1181 radian angle
We can use the conversion factor /180 to convert radians to degrees.
θ = 1.1181 × 180/π
64.12 degrees.
As a result, the figure that is lacking is roughly 64.12 degrees, which is closest to choice D: 21.25.
Due to the periodic nature of the cosine function, there are often two solutions when determining the inverse cosine of a value. But, since the problem states that we should round to the closest hundredth, which suggests a single answer, we can disregard the second option in this instance. By reinserting the value we discovered into the original equation and making sure it equals 7/18, we can further confirm that the result is accurate.
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how to determine if we can apply the existence and uniquness theorem to guarantee that there is exactly one unique soltuion
The Existence and Uniqueness Theorem states that if a system of linear equations has a unique solution, then the solution can be found by solving the associated augmented matrix.
To determine whether a system of linear equations has a unique solution, the number of equations must equal the number of unknowns. Additionally, the equations must not be linearly dependent. If these criteria are met, then the Existence and Uniqueness Theorem guarantees that there is exactly one unique solution.
To illustrate, consider the system of equations:
x1 + x2 - x3 = 2
2x1 - x2 + 2x3 = 8
3x1 + 2x2 - 4x3 = 0
= 4. Therefore, the Existence and Uniqueness Theorem guarantees that there is exactly one unique solution for this system.
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1. Two congruent solids 1 and 2 have the property that 1 ∩ 2 is a right
triangular prism with height√3 and a base that is an equilateral triangle of
side length 2. If the volume of 1 ∪ 2 is 25 units
3
, find the volume of 1.
The volume of solid 1 is 14 cubic units calculated through the formula of volume.
What is volume?Volume is the maximum quantity of space that an object can contain. Volume, which is essentially a measurement of an object's size, is the quantity of space a thing occupies. A three-dimensional object's volume, which is calculated in cubic units, is the quantity of space it takes up. For instance, glass has a cylindrical form and can hold a certain volume of water.
Let V1 and V2 be the volumes of the congruent solids 1 and 2, respectively. The volume of their union is given
V1 U V2 = V1+V2-V1∩V2
We know that V1 ∩ V2 is a right triangular prism with height √3 and a base that is an equilateral triangle of side length 2. So, the volume can be calculated with the following formula:
V1 ∩ V2 = (1/2) * base * height * heightbase
where base is the area of the equilateral triangle, which is √3, height is √3, and height base is 2. Plugging in these values, we get:
V1 ∩ V2 = (1/2) * √3 * √3 * 2 = 3
Now we can use the given information to find the volume of 1:
25 = V1 + V2 - V1 ∩ V2
25 = V1 + V2 - 3
We also know that V1 = V2, since the solids are congruent.
Substituting the following value with the above equation, we get:
25 = 2V1 - 3
28 = 2V1
V1 = 14
Therefore, the volume of solid 1 is 14 cubic units.
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there are 20 rows of seats on a concert hall: 25 seats are in the 1st row, 27 seats on the 2nd row, 29 seats on the 3rd row, and so on. if the price per ticket is $2,300, how much will be the total sales for a one-night concert if all seats are taken?
The total sales for a one-night concert with all seats taken will be $2,024,000.
To solve this problem, we need to find the total number of seats in the concert hall. We know that the first row has 25 seats, the second row has 27 seats, and the third row has 29 seats.
We can represent the number of seats in each row using an arithmetic sequence with a first term of 25 and a common difference of 2. The nth term of this sequence can be found using the formula:
a_n = a_1 + (n - 1)d
where a_1 is the first term (25), d is the common difference (2), and n is the number of the row.
Using this formula, we can find the number of seats in the 20th row
a_20 = 25 + (20 - 1)2
a_20 = 25 + 38
a_20 = 63
Therefore, the total number of seats in the concert hall is the sum of the seats in all 20 rows:
total seats = 25 + 27 + 29 + ... + 63
To find this sum, we can use the formula for the sum of an arithmetic sequence
S_n = (n/2)(a_1 + a_n)
where S_n is the sum of the first n terms of the sequence. In this case, n = 20, a_1 = 25, and a_n = 63.
S_20 = (20/2)(25 + 63)
S_20 = 10(88)
S_20 = 880
Therefore, there are a total of 880 seats in the concert hall. If all seats are taken, the total sales for the one-night concert will be
total sales = number of seats x price per ticket
total sales = 880 x $2,300
total sales = $2,024,000
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in a standard deck of 52 cards (4 suits, 13 numbers per suit), how many hands can we be dealt 5 cards that do not share a number
Answer: 1287
Step-by-step explanation:
What is a global firm? A) A firm that operates in one country and exports its goods and services to foreign countries. B) A firm that operates in more than one country and has a sales and marketing staff in those countries. C) A firm that operates in more than one country and captures R&D, production, logistical, marketing, and financial advantages not available to purely domestic competitors. D) A firm that sells its products and services across the world but restricts manufacturing to the home country. E) A firm that operates in more than one country but restricts the sale of its products to the home country.
The statement "A global firm is a firm that operates in more than one country and captures R&D, production, logistical, marketing, and financial advantages not available to purely domestic competitors." is the correct .
Therefore option C is correct.
What is a global firm?
A global firm is a company that operates in more than one country and has access to research and development, production, logistical, marketing, and financial advantages that are not available to purely domestic rivals.
Global companies have expanded beyond their home country's boundaries to capitalize on the advantages of global sourcing and production.
Global companies have a variety of advantages that pure domestic companies do not have.
The following are some of the benefits of global businesses:
They are able to take advantage of cost savings in various areas, such as lower labour costs or more efficient production processes.They have access to a broader market, which means they can sell more products and services.They have access to a wider pool of resources, which can help them develop and innovate faster.They can leverage their size and reach to negotiate more favourable contracts with suppliers, customers, and other stakeholders.In conclusion, a global firm is a firm that operates in more than one country and captures R&D, production, logistical, marketing, and financial advantages not available to purely domestic competitors.
Therefore option C is correct.
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Rewrite the expression 2(10+12) using the distributive property of multiplication over addition
The expression 2(10+12) can be rewritten as 44 using the distributive property of multiplication over addition.
The distributive property is a fundamental property of arithmetic that relates multiplication to addition and subtraction. The distributive property of multiplication over addition states that for any numbers a, b, and c
a( b + c ) = ab + ac
Using this property, we can rewrite the expression 2(10+12) as
2( 10 + 12 ) = 2(10) + 2(12)
Here, we have distributed the factor of 2 over the terms inside the parentheses, using the distributive property. This gives us:
2(10+12) = 20 + 24
Simplifying further, we get
2(10+12) = 44
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_______ is/are formed immediately after the union of sperm and ovum in the fallopian tube.
A Zygote is/are formed immediately after the union of sperm and ovum in the fallopian tube.
What is a zygote?A zygote is a cell formed when two gamete cells are fused by means of sexual reproduction. These cells contain a single set of chromosomes from both the father and the mother of the offspring. As a result, the zygote contains all of the genetic information required to create a completely new person. After the fertilization of the ovum by the sperm, the zygote is formed. The zygote will continue to divide into a multicellular embryo and eventually a fetus after fertilization has taken place.
The fusion of a sperm cell with an ovum in the fallopian tube leads to the formation of a zygote, which involves the combination of genetic material from both parents resulting in the creation of a single-celled zygote. This zygote then initiates the process of cell division and progresses into an embryo.
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Each voter from a random sample of 334 registered voters was asked their impression of two candidates running for the same national office. The
table summarizes the responses.
Which of the following is the me
Candidate A?
Favorable
Unfavorable
No opinion
Have not heard of
Candidate A. Candidate B
Favorable 138 200
Unfavorable 44 47 No Opinion 88 47 Haven’t heard of 64 40
Which of the following is the most appropriate method to use to estimate the proportion of all registered voters who have a favorable impression of Candidate A?
A. A one-sample z-interval for estimating a sample proportion
B. A one-sample z-interval for estimating a population proportion
C. A matched-pairs t-interval for estimating a mean difference
D. A two-sample z-interval for estimating a difference between sample proportions
E. A two-sample z-interval for estimating a difference between population proportions
The answer choice that is the most appropriate is B. A one-sample z-interval for estimating a population proportion
Why is this the most appropriate?
This is the most appropriate method because you are trying to estimate the proportion of all registered voters who have a favorable impression of Candidate A based on the sample data.
A one-sample z-interval is used when you want to estimate a population proportion using a sample proportion.
To calculate the one-sample z-interval for estimating a population proportion, you can use the following formula:
Confidence Interval = p ± Z * sqrt((p * (1 - p)) / n)
where:
p is the sample proportion (favorable opinions of Candidate A / total voters in the sample)Z is the critical value corresponding to the desired level of confidence (e.g., 1.96 for a 95% confidence interval)n is the sample size (334 in this case)sqrt represents the square root functionUsing this method, you will calculate a confidence interval that estimates the true proportion of registered voters who have a favorable impression of Candidate A, based on the sample data.
This is the most appropriate method because it focuses on estimating a single population proportion and incorporates the sample data and sample size into the calculation.
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original sample: 84, 71, 79, 96, 87. do the values given constitute a possible bootstrap sample from the original sample?
Yes, the given values constitute a possible bootstrap sample from the original sample.
Bootstrap samples are taken with replacement from the original data set. In other words, it means that each sample consists of a random sample of the same size as the original data set taken from the original data set.
Hence, a given set of values can be a bootstrap sample from the original sample as long as the values are randomly selected from the original sample and with replacement.
The sample is said to be a bootstrap sample from the original data set if it satisfies the following properties:
1. The bootstrap sample must be of the same size as the original data set.
2. Each observation from the original data set must have an equal chance of being selected in each bootstrap sample.3. The bootstrap samples must be independent of each other.
In the given problem, the sample consists of 5 values, namely 84, 71, 79, 96, and 87.
These values can be a bootstrap sample from the original sample as long as the values were randomly selected with replacement from the original sample.
Since the problem does not provide any information on how the sample was obtained, it cannot be determined whether or not it is a bootstrap sample.
Therefore, the answer is that the given values constitute a possible bootstrap sample from the original sample.
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graph
y = -6
4x + y = 2
if a college instructor alters the distribution of his or her students' midterm exam grades because the class did not do as well as last year's class, with what type of standards is the instructor most concerned?
The college instructor is most concerned with equity standards.
Equity standards are when an instructor adjusts grades to ensure fairness to all students regardless of their individual performances.
This means that if a class as a whole does not do as well as last year, the instructor will alter the distribution of grades so that the overall grades reflect the effort put in by the class.
For example, if the class average is a C, the instructor may raise some grades to a B or even A in order to ensure that the grades are fair to all students in the class.
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5. Janice is creating a design that is part of a logo consisting of a small and a large circle.
The diameter of the small circle is of the diameter of the large circle. The diameter of
the large circle is 27 centimeters. To the nearest tenth of a centimeter, what is the area
of the smaller circle?
27 cm
Answer: The area of the smaller circle is [tex]65.6cm^{2}[/tex].
Step-by-step explanation:
A = [tex]\pi r^{2}[/tex], r is the radius.
1. Find out the diameter of the small circle.
[tex]\frac{1}{3}(27)= 9[/tex]
2) Find out the radius, r.
[tex]radius = \frac{diameter}{2} =\frac{9}{2} =4.5[/tex]
3) We plugin r = 4.5 into the formula to solve the area of the smaller circle.
[tex]A=\pi r^{2}=\pi (4.5)^{2} =65.6cm^{2}[/tex]
a study was conducted to evaluate the stress level of senior business students at a particular college. forty students were selected at random from the senior business class, and their stress level was monitored by attaching an electrode to the frontalis muscle (forehead). for the forty students, the mean emg (electromyogram) activity was found to be 35.8 microvolts. in addition, the standard deviation of the emg readings was found to be 2.5 microvolts. what would be the 99% confidence interval on the true mean emg activity for all seniors in the class? (you should be using statistical software such as statcrunch.) group of answer choices [34.7296, 36.8704] [34.7296, 36.7804] [34.7456, 36.0566] [34.9672, 36.7840]
The 99% confidence interval on the true mean EMG activity for all seniors in the class is option (a) [34.7296, 36.8704]
To calculate the 99% confidence interval for the true mean EMG activity for all seniors in the class, we can use the formula
CI = X ± Zα/2 (σ/√n)
where
X = sample mean = 35.8
Zα/2 = the critical value for the 99% confidence interval, which can be found using a standard normal distribution table or calculator. For a two-tailed test, α/2 = 0.005, so Zα/2 = 2.576.
σ = sample standard deviation = 2.5
n = sample size = 40
Substituting these values into the formula, we get
CI = 35.8 ± 2.576 (2.5/√40) = [34.7296, 36.8704].
Therefore, the correct option is (a) [34.7296, 36.8704]
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which postulate or property can be used to prove that kimball is not between scottsbluff and sidney?
The postulate or property that can be used to prove that Kimball is not between Scottsbluff and Sidney is the Segment Addition Postulate.
The Segment Addition Postulate states that for three points A, B, and C, where B is between A and C,
we have AB + BC = AC.
Given that Kimball is not between Scottsbluff and Sidney, this means that Kimball is either to the west of Scottsbluff or to the east of Sidney.
Let's assume that Kimball is to the west of Scottsbluff.
Then, we can draw the line segment as follows:
Scottsbluff ——————— Kimball ——————— Sidney
Let AB represent the distance between Scottsbluff and Kimball, and let BC represent the distance between Kimball and Sidney. According to the Segment Addition Postulate, AB + BC = AC, where AC is the distance between Scottsbluff and Sidney.
However, if we draw the line segment from Scottsbluff to Sidney without Kimball, we can see that the distance between the two points will always be shorter than the sum of the distances from Scottsbluff to Kimball and from Kimball to Sidney.
This implies that if Kimball is not between Scottsbluff and Sidney, then it is not possible for the segment addition postulate to hold true for the three points.
Therefore, we can use the segment addition postulate to prove that Kimball is not between Scottsbluff and Sidney.
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given the arithmetic sequence what is the domain for N?
The domain for n in the arithmetic sequence is the one in the first option:
all integers where n ≥1
What is the domain of N?We have a arithmetic sequence defined by the general formula:
aₙ = 4 - 3*(n - 1)
And we want to find the domain for the possible values of n that we can use in that formula.
Remember that the terms of a sequence are defined as:
a₁, a₂, a₃,...
So the values of n are positive whole numbers, in this case the first one is n = 1.
a₁ = 4 + 3*(1 - 1)
a₁ = 4
And then we can keep using any positive integer, then the correct option is:
all integers where n ≥1
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What is the MAD of 12, 10, 12, 6, 8, 4, 2, 12,
The mean absolute deviation (MAD) of the given set of data is 3.875.
To calculate the mean absolute deviation, we first need to find the mean of the data set by adding up all the numbers and dividing by the total number of values:
Mean = (12 + 10 + 12 + 6 + 8 + 4 + 2 + 12) / 8
Mean = 8
Next, we find the absolute deviation of each number from the mean. To do this, we subtract the mean from each number and take the absolute value:
|12 - 8| = 4
|10 - 8| = 2
|12 - 8| = 4
|6 - 8| = 2
|8 - 8| = 0
|4 - 8| = 4
|2 - 8| = 6
|12 - 8| = 4
Then, we find the mean of the absolute deviations:
Mean absolute deviation = (4 + 2 + 4 + 2 + 0 + 4 + 6 + 4) / 8
Mean absolute deviation = 26 / 8
Mean absolute deviation = 3.875
Therefore, the mean absolute deviation of the given set of data is 3.875.
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Complete Question:
what is the mean absolute deviation of the following set of data 12 10 12 6 8 4 2 12.
Maggie is 15 years older than Bobby. How old is Bobby? 1) In 3 years, Maggie's age will be 50% greater than Bobby's age.
2) Years ago, when Maggie was 25 years old, Bobby was 10 years old.
Maggie is 30 years old, and Bobby is 15 years old if in 3 years, Maggie's age will be 50% greater than Bobby's age and years ago when Maggie was 25 years old, Bobby was 10 years old.
Maggie is 15 years older than Bobby. We have to determine Bobby's age.
Let's suppose that Bobby's age is x, so Maggie's age would be x + 15 years.
1) In 3 years, Maggie's age will be 50% greater than Bobby's age.
The age of Maggie in 3 years would be (x + 15) + 3, and the age of Bobby would be x + 3.
According to the problem, Maggie's age in 3 years would be 50% greater than Bobby's age in 3 years.
So, (x + 15) + 3 = (1.5)(x + 3)
Simplifying the above equation, we get
x + 18 = 1.5x + 4
Now, we will solve for
x.x - 1.5x = -14-0.5x = -14x = 28
Therefore, Bobby is 28 years old now.
2) Years ago, when Maggie was 25 years old, Bobby was 10 years old.
Let's assume that x years ago Maggie was 25 years old. Thus, Bobby was 10 years old at that time.
So, x + 25 = (x + 10) + 15x = 15
Therefore, Maggie is 30 years old now. And Bobby is 15 years old now.
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what is $510,451 rounded to the nearest 1,000 dolllars?
Answer:
$510,000
Step-by-step explanation:
Since we are rounding to the nearest thousand, we can use the hundreds place to determine the if we need to round down or up.
Remember, 4 or less, round down. 5 or more, round up.
Since the hundreds digit is 4, we do not need to round.
We only need to change the rest of the digits to 0.
So, our answer would be $510,000.
6x6x6x6x6x6x6 devided by 6x6x6x6x6x6 in indext form
The result of 6x6x6x6x6x6x6 divided by 6x6x6x6x6x6 in index form is 6.
In index form, 6x6x6x6x6x6x6 divided by 6x6x6x6x6x6 can be written as:
(6⁷) / (6⁶).To divide two exponential expressions with the same base (in this case, 6), we can subtract the exponents:
6⁽⁷⁻⁶⁾ = 6¹ = 6.
Index form, also known as exponential form, is a way of writing numbers or expressions using exponents. In index form, a number is expressed as a base raised to a power or exponent.
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Need help it’s due tomorrow for test corrections!!
We know that the temperature was 56°F at midnight, so we can plot the point (24, 56)
What is graph ?
Graph can be defined as visual representation of given data using the ordered pairs.
To graph Elroy's data, we can use the x-axis to represent the time of day in hours and the y-axis to represent the temperature in degrees Fahrenheit.
First, we can plot the point (6, 50) to represent the temperature at 6am.
Next, we can use the information that the temperature rose 3° per hour for the next 4 hours. This means that at 10am, the temperature would be 50 + 3(4) = 62°F. We can plot this point at (10, 62). Similarly, we can find the temperature at 7am, 8am, and 9am using the same formula and plot those points as well.
Then, we can use the information that the temperature rose 2° per hour for the next 6 hours. This means that at 4pm, the temperature would be 62 + 2(6) = 74°F. We can plot this point at (16, 74). Similarly, we can find the temperature at 11am, 12pm, 1pm, 2pm, and 3pm using the same formula and plot those points as well.
The temperature then stayed steady until 6pm, so we can draw a horizontal line at y = 74 from 4pm to 6pm.
For the next 2 hours, the temperature dropped 1° per hour. This means that at 8pm, the temperature would be 74 - 2 = 72°F. We can plot this point at (20, 72). Similarly, we can find the temperature at 7pm using the same formula and plot that point as well.
Therefore, we know that the temperature was 56°F at midnight, so we can plot the point (24, 56).
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a group of observations measured at successive time intervals is known as a(n) . a. additive time series model b. forecast c. time series
A group of observations measured at successive time intervals is known as a(n) time series. So, correct option is C.
A time series is a collection of observations or measurements that are taken at regular intervals over time. These observations can be of any variable that changes over time, such as stock prices, weather patterns, or population growth. Time series analysis is a statistical technique used to understand and interpret the patterns and trends in such data.
The data in a time series can be analyzed to identify trends, seasonal variations, and other patterns that may exist over time. These patterns can be used to develop forecasts and make predictions about future values of the variable being measured.
On the other hand, an additive time series model is a specific type of model used to analyze time series data. It involves decomposing a time series into its underlying components, such as trend, seasonality, and random fluctuations, and modeling each component separately.
This approach can help to improve the accuracy of forecasts and predictions based on the time series data.
In summary, a time series is a collection of observations measured at successive time intervals, while an additive time series model is a specific type of statistical model used to analyze and forecast time series data.
Therefore, Option C is correct answer.
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A local store charges $1.97 per pound for bananas and $4.49 for a gallon of apple juice what is the cost of 1.5 lb of bananas and 1 gallon of apple juice
The expense of 1.5 lbs of bananas and 1 gallon of apple juice, according to the provided statement, is $7.45.
What does arithmetic multiple mean?Multiplication is one of the four basic operations in mathematics, along with adding, subtracting, and division. Multiply in mathematics refers to the continual adding of sets of identical size.
The cost of 1.5 lb of bananas can be found by multiplying the price per pound by the number of pounds:
Cost of 1.5 lb of bananas = 1.5 x $1.97 = $2.96 (rounded to the nearest cent)
The cost of 1 gallon of apple juice is $4.49.
So, the total cost of 1.5 lb of bananas and 1 gallon of apple juice is:
Total cost = Cost of bananas + Cost of apple juice
Total cost = $2.96 + $4.49
Total cost = $7.45
Therefore, the cost of 1.5 lb of bananas and 1 gallon of apple juice is $7.45.
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PLX SIMPLIFY -2.6+3.9b
Answer: 3.9b−2.6
Step-by-step explanation: Hope this helps
Answer:
1.3b
Step-by-step explanation:
The equation is -2.6+3.9b. A negative number acts like subtraction, so we would subtract 2.6 from 3.9 to get 1.3. The b is still there, and we don't know what it is, so we simplify the equation to 1.3b.
Sorry, this explanation isn't the best. Hope it helped! :)
the population of toledo, ohio, in the year 2000 was approximately 540,000. assume the population is increasing at a rate of 4.7 % per year. a. write the exponential function that relates the total population, , as a function of , the number of years since 2000.
The exponential function that relates the total population, is [tex]P(t)=540,000\left [ 1+(5.1/100) \right ]^t[/tex] and the rate at which the population is increasing in the year 2019 is 69114.53.
The exponential function in mathematics is represented by the symbol eˣ (where the argument x is written as an exponent). The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, however it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.
we know that ,
the population of any city can be modeled in the form of exponential function as follows:
[tex]P(t)=P(0)(1+R)^t[/tex]
where, P(t)=population of the town at any given time t
P(0)=population of the town initially (in the year 2000 for this problem)=540,000
R=rate of increase (=5.1% in the given problem)
substituting the values in eqn(1), we get
[tex]P(t)=540,000\left [ 1+(5.1/100) \right ]^t[/tex]
as we know that
[tex]\because \frac{d}{dx}(a^x )=a^xln(a)[/tex]
so differentiating w.r.t. we get,
[tex]P'(t)=540,000\left [ 1+(5.1/100) \right ]^t*ln(1+(5.1/100) )\\\\P'(t)=540,000\left [ (105.1/100) \right ]^t*ln(105.1/100)\\\\P'(t)=540,000\left [ (1.051) \right ]^t*ln(1.051)[/tex]
so, the rate at which population is increasing in the year 2019 =
[tex]P'(19)=540,000(1.051)^{19}*ln(1.051)[/tex]
P'(19)= 69114.53.
Learn more about Exponential function:
https://brainly.com/question/29235027
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Complete question:
The population of Toledo, Ohio, in the year 2000 was approximately 540,000. Assume the population is increasing at a rate of 5.1 % per year.
a. Write the exponential function that relates the total population, P(t), as a function of t, the number of years since 2000. P(t) = =
b. Use part a. to determine the rate at which the population is increasing in t years. Use exact expressions. P'(t) people per year
c. Use part b. to determine the rate at which the population is increasing in the year 2019. Round to the nearest person per year. P'(19) = people per year
Can yall help me out?
the answer is A: 63 square units
Answer:
A (Im not entirely sure if this is correct)
Step-by-step explanation:
how I got this answer is: I found the area of the two triangles which was 12.5 (because the area of a triangle is 1/2(b*h) and the base is 3 and the height is 7 then you divide that by two) and I added them up to get 21. Then you would multiply 3 by two because a triangle is half of a rectangle and you would do b*h for a rectangle area and then multiply that by 7 ot get 42 and you would add taht to 21 to get 63
Find the missing dimension of the triangle.
Area = 14 ft²
6 ft
b
b = ? ft
help pls I'll mark brainlisest
A sports scout for a team is looking for the more consistent player. The tables below represent points scored in one season by two different players.
Player A
3 rows
and 5 columns
10, 12, 6, 10, 13, 8, 12, 3, 21, 14, 7, 0, 15, 6, 16
Player B
3 rows and 5 columns
10, 3, 12, 26, 20, 24, 25, 26, 5, 48, 24, 18, 20, 27, 25
Compare the data in the tables. Which player should the scout choose? Explain your answer.
Based on the given information, the scout should choose Player A if they are looking for consistency.
What are range and standard deviation?
Range is the difference between the highest and lowest scores in the set.
Standard deviation measures how spread out the scores are from the mean.
To determine which player is more consistent, we need to look at the variability in their scores. One way to measure variability is to calculate the range and the standard deviation of each player's scores.
The smaller the range, the more consistent the player's scores are.
A smaller standard deviation indicates that the scores are closer together, which means the player is more consistent.
Using the data provided, we can calculate the range and standard deviation for both players:
Player A:
Range = 21 - 0 = 21
Standard deviation = 5.70
Player B:
Range = 48 - 3 = 45
Standard deviation = 10.89
From these calculations, we can see that Player A has a smaller range and a smaller standard deviation, which means that their scores are more consistent than Player B's. Therefore, the scout should choose Player A if they are looking for consistency.
To know more about the range and standard deviations visit:
brainly.com/question/14801621
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