120 is 30 percent of 400
find the inverse of the function
F(x) = x² + 2x₁ [-1, 00]
the product of 2 rational numbers is 16/3.If one of the rational number is -26/3,find the other rational number
Answer:
- [tex]\frac{8}{13}[/tex]
Step-by-step explanation:
let n be the other rational number , then
- [tex]\frac{26}{3}[/tex] n = [tex]\frac{16}{3}[/tex]
[a number × its reciprocal = 1 ]
multiply both sides by the reciprocal - [tex]\frac{3}{26}[/tex]
n = [tex]\frac{16}{3}[/tex] × - [tex]\frac{3}{26}[/tex] ( cancel the 3 on numerator/ denominator )
n = - [tex]\frac{16}{26}[/tex] = - [tex]\frac{8}{13}[/tex]
i have a small area that i want to place 2 bench press machines. how much room will i need to reserve for those?
To place two bench press machines in a small area, you will need a space of approximately 10 feet by 10 feet. Let's discuss it in detail below. Here are the dimensions of the bench press machine, which can help determine the amount of space required to fit two bench press machines in a small area:
The length of the bench press machine is between 48 inches and 54 inches.
The width of the bench press machine is between 28 inches and 32 inches.
The height of the bench press machine is between 48 inches and 56 inches.
Based on the above dimensions of the bench press machine, two machines can be placed in a small area of 10 feet by 10 feet. However, for safe use, the following guidelines should be followed:
There should be at least 6 feet of distance between the two bench press machines. There should be at least 3 feet of clearance in the front of the bench press machine to allow for safe movement during exercises. There should be at least 2 feet of clearance behind the bench press machine to allow for a safe exit in case of an emergency.
Thus, to place two bench press machines in a small area, you will need a space of approximately 10 feet by 10 feet.
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which of the following was traditionally an assumption underlying the independent samples t-test question 10 options: a) scores must be drawn from a normally distributed population b) variances should be unequal in both groups c) data should be at the nominal level d)all of the above
The assumption underlying the independent samples t-test is that the scores must be drawn from a normally distributed population. Option A is correct.
What is a t-test?A t-test is a statistical method that determines whether two groups of observations are significantly different from one another. When comparing the means of two populations, the t-test is commonly used. The t-test is used to determine whether two groups' means are significantly different when the samples are drawn from normally distributed populations with equal variances.
The t-test is a powerful tool for determining whether a sample is significantly different from a population or whether two samples are significantly different from one another. The independent samples t-test, as opposed to the dependent samples t-test, is a t-test that compares the means of two independent groups. In this situation, the groups are separate and distinct.
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Jayden evaluated the expression a + (2 + 1. 5) for a = 14. He said that the value of the expression was 8. 5. Select all the statements that are true. Jayden's solution is incorrect. Jayden added inside the parentheses before dividing. Jayden substituted the wrong value for a. Jayden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
It is true that Jayden's solution is incorrect. It is false that Jayden added inside the parentheses before dividing.
It is false that Jayden substituted the wrong value for a. It is true that Jayden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
1) The correct solution is
Given,
a ÷ (2 + 1. 5)
Substituting the value of a which is 14
= 14 ÷ (2 + 1. 5)
= 14 ÷ 3.5
= 4
2) As there is no term which needs to be divided so, the second statement is false.
3) Jayden didn't substitute the wrong value of a he just solved the given expression without considering the bracket and divided the 14 which is the value of a by 2.
4) Jyaden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
i.e. a ÷ (2 + 1. 5)
14 ÷ 2 + 1. 5
7+1.5
8.5
This is the way Jayden solved the equation due to which he arrived at the wrong solution.
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The Correct question is as below
Jayden evaluated the expression a ÷ (2 + 1.5) for a = 14. He said that the answer was 8.5. Choose True or False for each statement.
1. Jayden's solution is incorrect.
2. Jayden added in the parentheses before dividing.
3. Jayden substituted the wrong value for a.
4. Jayden divided 14 by 2 and added 1.5
A car travelling at a constant speed travels 60 km 30 minutes .how far will it travel in 2hrs,if it continues at the same constant speed
Answer: 240 miles in 2 hours
Step-by-step explanation:
we know the car is traveling 60 km per half hour (30 minutes)
so to find km per hour, multiply both by 2.
the rate of speed is 120 miles per 60 minutes (1 hour)
multiply 120 mph by the 2 hours given = 240 miles in 2 hours
Answer:
240 km in 2 hours
Step-by-step explanation:
If the car travels 60 km in 30 minutes, then its speed can be calculated as follows:
Speed = distance ÷ time
Speed = 60 km ÷ (30 minutes ÷ 60) = 120 km/hour
Since the car is traveling at a constant speed, we can use the formula:
Distance = Speed × Time
To find how far the car will travel in 2 hours, we can substitute the values we have found:
Distance = Speed × Time
Distance = 120 km/hour × 2 hours
Distance = 240 km
Therefore, the car will travel 240 km in 2 hours if it continues at the same constant speed.
Find the 8th term of the arithmetic sequence x + 1 x+1, 8 x − 3 8x−3, 15 x − 7 ,
Answer: 50x - 27
Step-by-step explanation:
To find the 8th term of the arithmetic sequence, we need to first find the common difference between consecutive terms:
Common difference (d) = second term - first term
d = (8x - 3) - (x + 1)
d = 7x - 4
Now, we can use the formula to find the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where a1 is the first term, d is the common difference, and n is the term number we want to find.
Plugging in the values, we get:
a8 = (x + 1) + (8 - 1)(7x - 4)
a8 = x + 1 + 7(7x - 4)
a8 = x + 1 + 49x - 28
a8 = 50x - 27
Therefore, the 8th term of the arithmetic sequence x + 1, 8x - 3, 15x - 7 is 50x - 27.
If point is slid(translated) 4 units to the right, what would the new coordinates be (3,-4)
a certain congressional committee consists of 13 senators and 9 representatives. how many ways can a subcommittee of 5 be formed if at least 2 of the members must be representatives?
Answer:
Step-by-step explanation:
BRAINLY AND 20 POINTS IF ANSWERED!!!!!! roberto is walking. The distance, D, in meters, he walks can be found using the equation D=1. 4t, where t is time in seconds
[ ] meters per second
1.4m/s is the rate that Roberto is walking. We know the formula for calculating the time i.e. t= d/r.
The term "distance" refers to how far we move. The rate is a measurement of our trip speed. Time is measured by how far we travel. The distance an object will travel over time and at a specific average rate is the subject of rate problems.
Given,
Distance = D
D= 1.4t
Rate= ?
Substituting the given values in the formula t= d/r
where,
t= time in seconds
d= distance
r= rate
We get,
t= 1.4t/r
t/1.4t= 1/r
t gets cancelled
so we have,
1/1.4= 1/r
r= 1.4m/s
Therefore, 1.4m/s is the rate at which Roberto is walking.
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The complete question is as follows:
Roberto is walking. The distance, D, in meters, he walks can be found using the equation D=1. 4t, where t is time in seconds.
What is the rate that Roberto's walking in meters per second?
Find the area of the cicumfrance of a circle with diameter of 5ft use 3.14 for pi
Step-by-step explanation:
The formula to solve for the area of a circle is given by,
A
=
1
4
π
d
2
where
d
is the diameter.
Substituting the given, we have
A
=
1
4
×
3.14
×
(
3
ft
)
2
=
1
4
×
3.14
×
9
ft
2
A
=
7.065
ft
2
Next, solve for the circumference.
The formula for the circumference of a circle is written as,
C
=
π
d
where
d
is the diameter.
Substituting the given, we have
C
=
3.14
×
3
ft
C
=
9.42
ft
Hence, the
Area
=
7.065
ft
2
and the
Circumference
=
9.42
ft
.
Answer:
A = 19.625 ft²
C = 15.7 ft
Step-by-step explanation:
The equation for the area of a circle is πr², where r is the radius.
The radius is half of the diameter, so the radius here is 2.5.
Plug the radius into the equation and substitute 3.14 for π:
A = 3.14 x 2.5²
2.5² = 2.5 x 2.5 = 6.25
A = 3.14 x 6.25 = 19.625
Area = 19.625 ft²
The equation for the circumference of a circle is 2πr.
Plug the radius into the equation and substitute 3.14 for π:
C = 2 x 3.14 x 2.5
C = 15.7
Circumference = 15.7 feet.
A simplified carbon cycle with aerobic and anaerobic processes is depicted here. Although much of the emphasis on global climate change has been on increasing carbon dioxide levels, methane is also a greenhouse gas whose levels are increasing due to human and other activity. Which of these actions would increase methane levels in the atmosphere and potentially affect global climate change? Select ALL that apply.
--------------------------------------------------------------------------------------------------------------------------------
A Agricultural practices in rice cultivation releases methane.Agricultural practices in rice cultivation releases methane.
B Anaerobic digestion of cellulose by cows produces methane.Anaerobic digestion of cellulose by cows produces methane.
C Photosynthesis by phytoplankton converts carbon dioxide into the atmosphere.Photosynthesis by phytoplankton converts carbon dioxide into the atmosphere.
D Industrial combustion of fossil fuels releases methane into the atmosphere.Industrial combustion of fossil fuels releases methane into the atmosphere.
E Anaerobic decomposition of landfill material releases methane into the atmosphere.
In attempts to reduce greenhouse gas emissions and the effects of climate change, these sources must be taken into account.
what is equation ?A mathematical equation is a claim that two expressions are equal, typically represented with an equal sign (=) between them. The terms "left hand side" (LHS) and "right hand side" (RHS) of the equation, respectively, refer to the expressions on either side of the equal sign. Equations are a common tool for problem solving because they may be used to depict relationships between variables or quantities and to determine the value(s) of the unknown variable(s) that satisfies the equation. For instance, the link between the variables x and the integers 2, 5, and 11 is represented by the equation 2x + 5 = 11. Finding the value of x that makes the left and right sides of the equation equal is necessary to solve this equation.
given
A) Rice farming operations release methane into the atmosphere.
B) Methane is created when cows break down cellulose anaerobically.
E) Methane is released into the atmosphere when landfill material decomposes anaerobically.
Any of the aforementioned behaviours would raise the atmospheric methane concentrations and may have an impact on climate change globally.
Methane is a greenhouse gas that causes the atmosphere of the Earth to warm.
It is produced by both natural and artificial processes. Examples of human activities that contribute to methane emissions into the atmosphere include the production of rice, cattle digestion, and landfill decomposition.
In attempts to reduce greenhouse gas emissions and the effects of climate change, these sources must be taken into account.
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Your teacher prepares a large container full of colored
beads. She claims that 1/8 of the beads are red, 1/4 are
blue, and the remainder are yellow. Your class will take a
simple random sample of beads from the container to test the teacher's claim. The smallest number of beads you
can take so that the conditions for performing inference
are met is.
15
16
30
40
90
The smallest number of beads we can take so that the conditions for performing inference are met is 40.
Probability:
The probability of an event is a number that indicates the probability of the event occurring. Expressed as a number between 0 and 1 or as a percent sign between 0% and 100%. The more likely an event is to occur, the greater its probability. The probability of an impossible event is 0; the probability of a certain event occurring is 1. The probability of two complementary events A and B - A occurring or B occurring - adds up to 1.
According to the Question:
Given in the question,
Teacher prepares a large container filled with colored beads. She claims that 1/8 beads are red, 1/4are blue, and the rest are yellow. Your class will test the teacher's claim by randomly drawing a simple sample of beads from the container.
Quadrant Frequency
1 18
2 22
3 39
4 21
The proportions are 1/8 , 1/4 and 5/8
Here, the smallest probability is 1/8 , thus it would be used to compute the frequency.
Now,
The expected frequencies are calculated as:
E = np₁ = 15 (1/8) = 1.875
E = np₂ = 16(1/8) = 2
E = np₃ = 30(1/8) = 3.75
E = np₄ = 40(1/8) = 5
E = np₅ = 80(1/8) = 10
Here, conditions are fulfilling for 40 and 90 but the smallest sample size is contained by 40. Thus, the correct option is 40.
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Work out the fraction and ratio that
complete the equations below.
Give each answer in its simplest form.
a) h:k=5:6
h =
k
b) 2x=9y
x:y
=
:
The fraction and ratio that complete the equations in its simplest term is 5/6k and 2 : 9 respectively.
What is the fraction and ratio that complete the equations?h : k = 5 : 6
h/k = 5/6
cross product
h × 6 = k × 5
6h = 5k
divide both sides by 6
h = 5/6k
Then,
2x = 9y
2/9 = x/y
2 : 9 = x : y
Ultimately, the simplest form of fraction and ratio which completes the equation is 5/6k and 2:9.
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what percentage of the area under the normal curve falls between ±2 standard deviations?
Approximately 95.44% of the data falls within ±2 standard deviations of the mean in a normal distribution.
How the 95.44% of the area under the normal curve falls between ±2 standard deviations?To find the percentage of the area under the normal curve that falls between ±2 standard deviations, we need to follow the following steps:
We need to know the mean (μ) and standard deviation (σ) of the normal distribution in question. If we assume a standard normal distribution (i.e., a normal distribution with mean of 0 and standard deviation of 1), then we can use a z-score table to find the percentage of area under the curve.
Calculate the z-scores for ±2 standard deviationsThe z-score formula is:
z = (x - μ) / σ
For ±2 standard deviations, the values of x are μ ± 2σ. Therefore, the z-scores are:
z = (μ + 2σ - μ) / σ = 2
z = (μ - 2σ - μ) / σ = -2
Use a z-score table to find the percentage of area under the curveA z-score table gives the percentage of area under the standard normal curve that falls to the left of a given z-score. Since the normal distribution is symmetric, the percentage of area to the right of a negative z-score is the same as the percentage of area to the left of the corresponding positive z-score.
Using a z-score table, we find that the percentage of area under the standard normal curve that falls to the left of z = 2 is 0.9772, or 97.72%. Therefore, the percentage of area under the curve that falls between ±2 standard deviations is:
97.72% - (100% - 97.72%) = 95.44%
This means that approximately 95.44% of the data falls within ±2 standard deviations of the mean in a normal distribution.
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In order to make the same amount of money, they would have to each sell ______ bicycles. They would both make $______.
In order to make the same amount of money, they would have to each sell 5 bicycles. They would both make $500
How many bicycle would they sell to make the same amount of money?To find the number of bicycles they would need to sell to make the same amount of money,
We can set Jim's and Tom's weekly earnings equal to each other and solve for the number of bicycles:
250 + 50x = 400 + 20x
30x = 150
x = 5
So they would need to sell 5 bicycles to make the same amount of money.
How much would they make for selling that amountTo find out how much money they would make for selling 5 bicycles, we can substitute x = 5 into either equation.
Let's use Jim's equation:
250 + 50(5) = 500
So they would make $500 for selling 5 bicycles.
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tomas has $1,000 to spend on a vacation. his plane ticket costs $348.25. if he stays 5.5 days at his destination, how much can he spend each day? write an inequality and then solve.
Tomas can spend at most $118.50 each day. The inequality equation is 5.5x ≤ 651.75.
Tomas has $1,000 to spend on a vacation. His plane ticket costs $348.25. If he stays 5.5 days at his destination, how much can he spend each day? Write an inequality and then solve.
Let x be the amount that Tomas can spend each day. Since Tomas has to pay for the plane ticket, he will have $1,000 − $348.25 = $651.75 left to spend on the rest of the vacation.
Then, since he is staying for 5.5 days, the total amount he can spend would be 5.5x dollars. The inequality that represents the problem is as follows:
5.5x ≤ 651.75
To solve for x, divide both sides by 5.5
5.5x/5.5 ≤ 651.75/5.5x ≤ 118.5
Therefore, Tomas can spend at most $118.50 each day.
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Answer:
The answer to this solution is 118.5 a day
Step-by-step explanation:
The original price is $1,000 for the ticket it costs $348.25 and Tomas is staying for 5.5 days so dividing 651.75 by 5.5 is the ANSWER 118.5
auditors compared opinions about treatment (very good/acceptable/poor) at four va hospitals (labeled a,b,c,d) among veterans aged 50 and above. what are the hypotheses for a chi-square test of independence on the data? select one:
The hypotheses for a chi-square test of independence on the data that auditors compared opinions about treatment (very good/acceptable/poor) at four VA hospitals (labeled a,b,c,d) among veterans aged 50 and above are:
Null hypothesis, H0: There is no association between the opinions about treatment of the VA hospitals and veterans aged 50 and above.
Alternative hypothesis, Ha: There is an association between the opinions about treatment of the VA hospitals and veterans aged 50 and above.
Hypothesis Testing is a type of statistical analysis in which you put your assumptions about a population parameter to the test. It is used to estimate the relationship between 2 statistical variables.
An analyst performs hypothesis testing on a statistical sample to present evidence of the plausibility of the null hypothesis. Measurements and analyses are conducted on a random sample of the population to test a theory. Analysts use a random population sample to test two hypotheses: the null and alternative hypotheses.
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She begins at sea level, which is an elevation of 0 feet.
She descends for 50 seconds at a speed of 5 feet per second.
She then ascends for 54 seconds at a speed of 4.4 feet per second.
Answer:
The diver descends:
50 seconds x 5 feet/second = 250 feet
The diver ascends:
54 seconds x 4.4 feet/second = 237.6 feet
Therefore, the total change in elevation is:
250 feet (descent) - 237.6 feet (ascent) = 12.4 feet
So, the diver's final elevation is:
0 feet (starting elevation) - 12.4 feet (change in elevation) = -12.4 feet
Therefore, the diver ends up 12.4 feet below sea level.
Answer:
it is 1
Step-by-step explanation:
its is 1 2 3 hsvs jafsnsjhd jsusgsmsi jshsbjdg
Determine if the ordered pair (-2, -4) is a solution for equation 2y - 3x = -2.
Answer:
Step-by-step explanation:
2(-4) - 3(-2) = -2
-8 + 6 = -2
-2 = -2
Find the measure of the last angle of the triangle below.
28⁰
35°
Measure of last angle of triangle is 117°
Triangle PropertiesThe triangle's characteristics include:
All triangles have a total of 180 degrees in their angles.The length of the longest two sides of a triangle is greater than the length of the third side.The length of the third side of a triangle is shorter than the difference between its two sides.Angle Sum PropertyThe angle sum property states that the sum of a triangle's three interior angles is always 180 degrees.
Angle of Triangle are
28° and 35°
Let the third angle be x
According to angle sum property
28°+35°+x=180°
x=117°
Measure of last angle of triangle is 117°
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The complete question is;
Find the measure of the last angle of the triangle below.
28⁰
35°
Image is attached below.
please help fast I am baffled
The expression for the number of non-adult sizes is s - 19.
What are expressions?A value or amount is represented by an expression, which is a collection of numbers, variables, and mathematical operations like addition, subtraction, multiplication, and division. Calculations, complicated mathematical equations, and issues in a variety of disciplines, including science, engineering, economics, and statistics, may all be solved using expressions. Functions that depict a connection between variables, such as sin(x) and log(x), can also be included in expressions. Expressions are frequently employed to simulate real-world circumstances and provide predictions based on mathematical analysis.
Given that the total number od sweatshirts = s.
The number of non-adult sweatshirts can be calculated by:
Number of non-adult sizes = Total number of sweatshirts sold - Number of adult sizes
= s - 19
Hence, the expression for the number of non-adult sizes is s - 19.
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how many liters of a 25 % 25%, percent saline solution must be added to 3 33 liters of a 10 % 10, percent saline solution to obtain a 15 % 15, percent saline solution?'
Answer:
Here, x represents the amount (in liters) of the 25% saline solution to be added.
We can see that the 25% saline solution needs to be mixed with the 10% saline solution to obtain a mixture that is 15% saline. The ratio of the volumes of the 25% and 10% solutions can be found by subtracting the concentrations of the two solutions and dividing by the difference between the desired concentration and the concentration of the 10% solution:
x / (3.33 - x) = (15 - 10) / (25 - 10) = 5/15 = 1/3
Multiplying both sides by 3.33 - x, we get:
x = (1/3) (3.33 - x)
Multiplying both sides by 3, we get:
3x = 3.33 - x
Solving for x, we get:
x = 0.833 liters
Therefore, 0.833 liters of the 25% saline solution must be added to 3.33 liters of the 10% saline solution to obtain 4.163 liters of a 15% saline solution.
Step-by-step explanation:
Aamena buys a business costing $23000
She pays part of this cost with $12000 of her own money
Calculate what percentage of the $23000 this is
Show your calculations
Answer:
52.17%
Step-by-step explanation
[tex]\frac{12000}{23000}[/tex] ×100%
[tex]\frac{1200}{23}[/tex]
52.17
Find a basis for the space of 2x2 lower triangular matrices:
A basis for the space of 2x2 lower triangular matrices is [tex]\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)[/tex].
Lower triangular matrices resemble the following:
[tex]\left[\begin{array}{ccc}a&0\\b&c\end{array}\right][/tex]
We can write it like this:
[tex]a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right][/tex]
This demonstrates the set's
[tex]\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)[/tex]
covers the set of lower triangular matrices with dimensions 2x2. Moreover, these are linearly independent, so attempting to
[tex]a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]=\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]
leads to
[tex]\left[\begin{array}{ccc}a&0\\b&c\end{array}\right] =\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]
which results in a = b = c = 0 right away. As there is no other way to
[tex]a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]=\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]
, these matrices are linearly independent if a = b = c = 0.
Since
[tex]\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)[/tex]
they serve as a foundation by spanning the collection of 2x2 lower triangular matrices and being linearly independent.
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a manager recorded the number of gallons of ice cream sold for the past six periods. he asked you to choose a forecasting model to predict the demand for gallons of ice cream in period 7. you consider applying a two-period moving average model and a two-period weighted moving average model with weights of 0.6 and 0.4. a) which model is better for this data set (hint: show all your work including forecasts for each period and calculations using measures of forecast accuracy)? (9 points)
The two-period moving average model and the two-period weighted moving average model are both common forecasting methods used to predict future demand. and we understand that the model with the lower MAD and MSE values will have the most accurate forecast.
To determine which model is better for this particular data set, we need to compare the accuracy of each model. To do this, we will calculate the Mean Absolute Deviation (MAD) and the Mean Squared Error (MSE) for each model.
For the two-period moving average model, we can calculate the forecast for period 7 by taking the average of p5 and 6:
Period 7 forecast = (Gallons in Period 5 + Gallons in Period 6)/2
For the two-period weighted moving average model, we can calculate the forecast for period 7 by using the weights of 0.6 and 0.4:
Period 7 forecast = (0.6 x Gallons in Period 5) + (0.4 x Gallons in Period 6)
We can then compare the accuracy of each model by calculating the MAD and MSE. To calculate MAD, we need to subtract the actual demand in each period from the forecasted demand and take the absolute value:
MAD = |Actual demand – Forecasted demand|
To calculate MSE, we need to square the differences between the actual demand and the forecasted demand:
MSE = (Actual demand – Forecasted demand)^2
After calculating the MAD and MSE for each model, we can compare the results to determine which model is better for this data set. The model with the lower MAD and MSE values will have the most accurate forecast.
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y is inversely proportional to the square of x. It is given that y = 8 for a particular value of x. k= When x increases by 300%, find the new value of y,
Answer:
1/2 or .5
Step-by-step explanation:
If y is inversely proportional to the square of x, we can express this relationship using the formula:
y = k/x^2
where k is a constant of proportionality. We are told that y = 8 for a particular value of x, so we can substitute these values into the equation:
8 = k/x^2
To find the value of k, we can solve for it:
k = 8x^2
Now we are asked to find the new value of y when x increases by 300%. This means that the new value of x will be 4 times the original value (since an increase of 300% means an increase by a factor of 3, and we need to add the original value to get the new value). So we can substitute 4x for x in our equation:
y = k/(4x)^2 = k/16x^2
We already know the value of k, so we can substitute it in and simplify:
y = (8x^2)/(16x^2) = 1/2
Therefore, the new value of y is 1/2 when x increases by 300%.
Write the first four terms of the sequence defined by a n = 5
{5, if n=1
a n -1 -5, if n>1
Answer:
The sequence is defined as follows:
a1 = 5
an = an-1 - 5, for n > 1
Using this definition, we can find the first four terms of the sequence as follows:
a1 = 5
a2 = a1 - 5 = 5 - 5 = 0
a3 = a2 - 5 = 0 - 5 = -5
a4 = a3 - 5 = -5 - 5 = -10
Therefore, the first four terms of the sequence are: 5, 0, -5, -10.
If p and q vary invarsely and p is 11 when q is 28, determine q when p is equal to 4
77 is the value of Q in linear equation.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
P ∝ 1/Q
PQ = K
AT P= 11
Q = 28
11 * 28 = K
K = 308
AT P = 4
4Q = 308
Q = 77
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You are playing a game with a friend. It costs you $2 to play. If you roll a 1 on a 6-sided die you win $4. If you roll a 2, 3, 4, 5, or 6 you win nothing and lose $2 the cost to play. How much should the player be willing to pay to play this game and not lose money in the long run?
The player should be willing to pay up to $1.33 to play this game and not lose money in the long run.
The expected value is the sum of the products of each possible outcome and its probability. Let's calculate the expected value of the game:
E(X) = (1/6) * $4 + (5/6) * (-$2)
E(X) = $0.67
This means that on average, the player can expect to win $0.67 per game. Since it costs $2 to play, the player should not be willing to pay more than $2 - $0.67 = $1.33 to play the game and not lose money in the long run.
Probability theory is based on axioms, which are basic assumptions about the nature of probability. It is used to quantify uncertainty and to make predictions based on the available information. Probability is expressed as a number between 0 and 1, with 0 meaning an event is impossible, and 1 meaning an event is certain.
The concept of probability is used in a variety of fields, including statistics, economics, engineering, and physics. In statistics, probability is used to model random variables, estimate parameters, and test hypotheses. In economics, probability is used to model financial risks and decision-making under uncertainty. In engineering and physics, probability is used to model complex systems and predict the behavior of particles.
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