Given the following forecast and demand information, what is the ME? And what is the MAD?
Demand Forecast Error Absolute Value Squared Error Absolute Percent Error
1258 1295 -37 37 1369 .0294
1267 1275 -8.33 8.33 69.44 0.0066
1256 1262 -6 6 36 .0048
1268 1260 7.67 7.67 58.78 .0060
1277 1264 13.33 13.33 177.78 .0104
1277 1267 10 10 100 .0078
1297 1274 23 23 529 .0177

The point on the graph where the tangent plane is parallel is (52, 52, -5382).

What is the tangent plane?

The surface that contains all tangent lines of the curve at a point, $P$, that lies on the surface and passes through the point is represented by the tangent plane. We discovered earlier in our talks of derivatives and tangent lines that we can use tangent lines to mimic the behavior of a graph. We may employ tangent planes for a similar reason now that we're working with multivariable functions and three-dimensional coordinate systems.

Here, we have

Given: Let P be the tangent plane to the graph of g(x, y) = 26 – 13x² – 26y² at the point (4, 2, –286). Let f(x, y) = 26 – x² - y².

We have to find the point on the graph where the tangent plane is parallel.

Let P be the tangent plane to the graph z = g(x, y) = 26 – 13x² – 26y² at the point (4, 2, –286).

φ(x,y,z) = 13x² + 26y² + z - 26

Δφ = 26xi + 52yj + k

Δφ(4, 2, –286) = 104i + 104j + k

Then,

P: 104(x-4) + 104(y-2)+1(z+286) = 0

104x + 104y + z = 338...(1)

Now, Let

ψ(x,y,z) =  x² + y² + z - 26

Δψ = 2xi + 2yj + k

Let (x₀,y₀,z₀) be the point of the graph z = f(x,y) = 26 – x² - y² where the tangent plane in the plane is parallel to equation (1).

Δψ (x₀,y₀,z₀)  =  (2x₀,2y₀,1)

= 2x₀/104 = 2y₀/104 = 1/1

x₀ = 52 = y₀

Now, z₀ = 26 – x₀² - y₀² = 26 – 52² - 52²= -5382

Hence,  the point on the graph where the tangent plane is parallel is (52, 52, -5382).

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5)

we need first to calculate the radius of the circumference, this is the distance between the center to any point of the circumference, then the radius will be:

then the circumference equation is:

After 6 months of birth the weight will become 6.95 kg.

A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set.

from given condition, a baby weigh 3. 35 kilogram at birth and  the baby weight constantly increase every two month by 1. 2 kilogram.

so, the weight after 2 months of birth is 3.35 kg + 1.2 kg = 4.55 kg

and the weight after 4 months of birth is 4.55 kg + 1.2 kg = 5.75 kg

and the weight after 6 months of birth is 5.75 kg + 1.2 kg = 6.95 kg

Therefore, after 6 months of birth the weight will become 6.95 kg.

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Answer:

1

Step-by-step explanation:

GCF of 343 and 477 is 1, because no number can multiply and get both of them.

The greatest common factor of 343 and 477 is 1, indicating that the two numbers have no common factors other than 1.

To find the greatest common factor (GCF) of 343 and 477, we can determine the common factors of both numbers and identify the largest one.

First, let's list the factors of each number:

The factors of 343 are: 1, 7, 49, 343.

The factors of 477 are: 1, 3, 9, 53, 159, 477.

Now, we identify the common factors from both lists: 1.

Therefore, the greatest common factor of 343 and 477 is 1.

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The points on a graph should be equally distributed above and below the line if that line correctly describe the data set. As we can see in the pictures, the majority of the points on the graph on the left are above the line, while on the right we can see data points above and below the line.

Therefore, the trend line on the right fits the data better.

Answer:

x<11

Step-by-step explanation:

4x>54-10

4x>44

x<11 [sign change]

Answer:

x > 11

Step-by-step explanation:

4x + 10 > 54

Step 1: Subtract 10 from both sides.

4x + 10 - 10 > 54 - 10

4x > 44

Step 2: Divide both sides by 4.

4x/4 > 44/4

x > 11

Ariel takes 0.52 pages of notes for an hour of class.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

From the information given,

The number of note pages per hour Ariel makes can be obtained by dividing the total number of pages by the total hours which is,

= (45/86) pages.

= 0.52 papes.

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Answer: 190 cm = 2.07787 yards, rounded to the nearest hundredth, 2.08 yards.

Step-by-step explanation:

divide 190 cm by 91.44 to get your answer.

Step-by-step explanation:

By trigonometry :

cos A = 6/12

cos A = 1/2

A = 60°

and, values of B :

cos B = 6√3/12

cos B = √3/2

B = 30°

Values of A and B are 60° and 30°

Subject : Mathematics

Level : JHS

Chapter : Geometry

Answer:

5

Step-by-step explanation:

The probability that a car buyer bought an alarm system or bucket seats is 0.50.

Probability of ,

Alarm system p(A) = 40/100 = 0.40

Bucket seat p(B) = 30/100 = 0.30

Alarm system and bucket seat p(A and B) = 20/100 = 0.20

Probability of alarm system or bucket seat is :

= p(A)+p(B)-p(A and B)

= 0.40+0.30-0.20

= 0.50

In mathematics, probability is the likelihood of an event occurring. It is quantified as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is to occur. A simple example is the tossing of a coin, where the probability of either head or tail is 1/2.

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The inverse function of the function f(x) will be f⁻¹(x) = 4x + 48. Then the correct option is D.

The complete question is attached below.

Suppose that the given function is

f: X → Y

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

 f⁻¹: Y → X

It simply means, inverse of 'f' is an undo operator, that takes back the effect of 'f'

The function is given below.

f(x) = (1/4)x – 12

Then the inverse function of the function f(x) will be

(1/4)f⁻¹(x) - 12 = x

            f⁻¹(x) = 4x + 48

Then the correct option is D.

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Part A) The value of the car as a function of time after it was purchased is best modeled with an exponential decay function.

Part B) The value of If the value of the car 2 years after it was purchased is $17,918, its value when it was purchased was $24,800.

Exponential functions are classified into two: exponential growth and exponential decay functions.

Exponential decay functions are modeled as y = a(1 - r)ˣ, where y is the decreased or decay value, a is the initial value, r is the decay rate, while x is the exponent, representing the number of periods.

Annual decreasing rate in value = 15% = 0.15

Decay factor = 0.85 (1 - 0.15)

f(x) = a(1 - 0.15)^t

Where x = the value of the car after t years

a = the initial or purchase value of the car

t = the years expired after the purchase date

B) If t = 2 years

x = $17,918

f(x) = a(1 - 0.15)^t

17,918 = a(0.85)^2

a = $24,800

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Answer: 140°

Step-by-step explanation:

- all straight lines are 180°

- since ACD and DCB help to create the straight line they must equal 180° when combined

- so 180 - 40 = 140

- therefore, ACD is 40° and DCB is 140°

hope this helps :)

Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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Answer:

B. \(75 + 0.55m\)

Step-by-step explanation:

We know that the constant is $75. You only pay this once.

Whereas $0.55 you pay per mile. Which means that you will multiply 0.55 by how many miles you drive.

This means that the equation will look like:

\(75 + 0.55m\)

Hope this helps! :)

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \: f = 2\)

____________________________________

\( \large \tt Solution \: : \)

Let's consider two points (1 , 3) and (7 , f), now we can write the slope (m) of line in form of these points as :

\( \qquad \tt \rightarrow \: m = \cfrac{y2 - y1}{x2 - x1} \)

\(\qquad \tt \rightarrow \: - \dfrac{1}{6} = \dfrac{f - 3}{7 - 1} \)

\(\qquad \tt \rightarrow \: - (7 - 1) = 6(f - 3)\)

\(\qquad \tt \rightarrow \: - 6 = 6(f - 3)\)

\(\qquad \tt \rightarrow \: f - 3 = - \dfrac{6}{6} \)

\(\qquad \tt \rightarrow \: f - 3 = - 1\)

\(\qquad \tt \rightarrow \: f = - 1 + 3\)

\(\qquad \tt \rightarrow \: f = 2\)

Value of f is 2, so the point is : (7 , 2)

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Answer:

thirty thousand, six hundred and eighty-two!

Step-by-step explanation:

Answer:

thirty thousand six hundred eighty two

Answer:

Jasper has 24 quarters and 26 dimes in his coin collection.

Step-by-step explanation:

Let's assume Jasper has "q" quarters and "d" dimes in his collection.

According to the problem, he has a total of 50 coins, so we can write the equation:

q + d = 50

The value of a quarter is $0.25, and the value of a dime is $0.10. We are told that the total value of the coins is $8.60, so we can write another equation:

0.25q + 0.10d = 8.60

Now we have a system of two equations:

q + d = 50

0.25q + 0.10d = 8.60

To solve this system, we can use substitution or elimination. Let's use substitution.

We rearrange the first equation to solve for q:

q = 50 - d

We substitute this expression for q in the second equation:

0.25(50 - d) + 0.10d = 8.60

Simplifying the equation:

12.50 - 0.25d + 0.10d = 8.60

Combining like terms:

-0.15d = 8.60 - 12.50

-0.15d = -3.90

Dividing both sides of the equation by -0.15 to solve for d:

d = (-3.90) / (-0.15)

d = 26

We found that Jasper has 26 dimes.

Substituting the value of d back into the first equation to solve for q:

q + 26 = 50

q = 50 - 26

q = 24

We found that Jasper has 24 quarters.

Therefore, the solution is that Jasper has 24 quarters and 26 dimes in his coin collection.

their distance from home as a function of time

\(f(x)=50x+20\)

The reasonable domain for this situation is

\(0\leq x\leq 2\)

Given :

Aubrey and Charlie are driving to a city that is 120 miles from their house. They have already traveled 20 miles, and they are driving at a constant rate of 50 mi/h.

Given driving speed is 50 miles per hour

They already travelled 20 miles. We need to frame linear equation because we are given with constant rate.

Linear equation is \(f(x)=mx+b\)

where m is the constant rate and b is the initial miles travelled

m=50 and b=20

the function f(x) is the distance from home

\(f(x)= 50x+20\)

Now we find out the domain x. Given that they travelled 120 miles

so f(x) is 120

\(120=50x+20\\120-20=50x\\100=5x\\x=2\)

Domain is the number of hours travelled

hours cannot be negative . So the domain x for this situation is

\(0\leq x\leq 2\)

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 The sample we collect plays a cruciThe sample we collect can significantly affect our understanding of a population,

especially when it comes to making generalizations or drawing conclusions about the entire population based on the sample data. The key aspect in this regard is whether the sample is representative of the population.

A representative sample is one that accurately reflects the characteristics, diversity, and distribution of the population from which it is drawn. When our sample is representative, we can have greater confidence in generalizing the findings from the sample to the larger population. However, if our sample is not representative, our understanding of the population may be biased or limited.

In the provided example, the given data represents different age groups and their reported time spent with friends per day. If we were to collect a sample from this population, it would be crucial to ensure that the sample includes individuals from each age group in proportion to their representation in the population. This would help ensure that our sample accurately reflects the age distribution of the population.

If our sample is not representative, it may lead to inaccurate conclusions. For instance, if we only surveyed individuals from the age group 55-64 and ignored the other age groups, our understanding of the population's time spent with friends would be limited to that specific age group. We wouldn't be able to generalize our findings to the entire population because we would have missed important variations in behavior across other age groups.

To improve the representativeness of our sample, we could use random sampling techniques, such as simple random sampling or stratified sampling, to ensure that individuals from all age groups are included in the sample. By doing so, we can enhance our understanding of the population as a whole and make more accurate inferences.

In conclusion, the sample we collect plays a crucial role in shaping our understanding of a population. A representative sample enables us to make valid generalizations and draw reliable conclusions about the entire population. It ensures that the characteristics and diversity of the population are properly reflected in the sample, allowing for more accurate insights and informed decision-making.al role in shaping our understanding of a population

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Answer: y=13/11x+12/11

Step-by-step explanation:

13x-11y=12

-13x     -13x

-11y=-13x-12

divide by -11 on each side

y=13/11x+12/11

The median is the best measure of center, and it equals 19.

The median is a measure of central tendency that represents the middle value of a dataset when it is arranged in order. Specifically, it is the value that separates the dataset into two halves, with half of the data falling below the median and half of the data falling above the median.

The appropriate measure of center for the given data is the median, which is the middle value when the data is arranged in numerical order.

From the given box plot, we can see that the box extends from 17 to 21 on the number line, with a line in the box at 19. This means that 50% of the data falls between 17 and 21, with the middle value (median) being 19.

Therefore, the correct answer is:

The median is the best measure of center, and it equals 19.

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The numerical or verbal descriptions that usually result from measurements are called data or observations.

When measurements are conducted, whether in scientific experiments, surveys, or other data collection processes, the outcome is typically a set of data or observations.

These measurements can be represented numerically, such as numerical values or quantities, or verbally, using descriptive terms or categories.

Numerical descriptions provide precise quantitative information, such as measurements of length, weight, temperature, time, or any other measurable attribute. These measurements are often expressed using numbers or units of measurement.

Verbal descriptions, on the other hand, use words or qualitative descriptions to convey information about the observations.

For example, when conducting a survey, respondents might provide verbal responses that describe their opinions, preferences, or experiences.

Both numerical and verbal descriptions play important roles in data analysis and interpretation.

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Answer:

h = 18 units

Step-by-step explanation:

(9 sqrt 2)^2 + (9 sqrt 2)^2 = h^2

162 + 162 = h^2

Sqrt 324 = h

h = 18 units

Answer:

r = 4 - ax

Step-by-step explanation:

Step 1: Write equation

ax + r = 4

Step 2: Solve for r