find the first partial derivatives of the function. u = 4xy/z ∂u ∂x = ∂u ∂y = ∂u ∂z =

Answer:

18 ÷ 2/3 = 27

-5/6 ÷ 9/10 = -0.925

a) The forecast is approximately miles. b) the Mean Absolute Deviation (MAD) based on the forecast is approximately miles. c) The forecast for year 6 is approximately miles. d) the last forecast is 3,468 miles.

a) To calculate the forecast for year 6 using a 2-year moving average, we take the average of the mileage for years 5 and 4. This provides us with the forecasted value for year 6.

b) The Mean Absolute Deviation (MAD) for the 2-year moving average forecast is calculated by taking the absolute difference between the actual mileage for year 6 and the forecasted value and then finding the average of these differences.

c) When using a weighted 2-year moving average, we assign weights to the most recent and previous periods. The forecast for year 6 is calculated by multiplying the mileage for year 5 by 0.40 and the mileage for year 4 by 0.60, and summing these weighted values.

The MAD for the weighted 2-year moving average forecast is calculated in the same way as in part b, by taking the absolute difference between the actual mileage for year 6 and the weighted forecasted value and finding the average of these differences.

d) Exponential smoothing involves assigning a weight (α) to the most recent forecasted value and adjusting it with the previous actual value. The forecast for year 6 is calculated by adding α times the difference between the actual mileage for year 5 and the previous forecasted value, to the previous forecasted value.

In this case, with α=0.20 and a forecast of 3,100 miles for year 1, we perform this exponential smoothing calculation iteratively for each year until we reach year 6, resulting in the forecasted value of approximately 3,468 miles.

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The use of prime factorization to find the exponents of the given numbers gives  625 = 5⁴, 343 = 7³, 216 = 6³,  169 = 13², 256 = 4⁴; 256 =  2⁸ and 729 = 9³; 729 = 3⁶

When a number is written as a product of its prime factors, we have the prime factorization of the number e.g 8 = 2×2×2

An exponent is defined as a way of expressing large numbers in terms of powers e.g 81 = 3×3×3×3 = 3⁴

Thus, you can use prime factorization to find the exponent of the given numbers as follows:

625 as a power of 5

625 = 5×5×5×5 = 5⁴

343 as a power of 7

343 = 7×7×7 = 7³

216 as a power of 6

216 =  6×6×6 = 6³

169 as a power of 13

169 = 13×13 = 13²

256 as a power of 4; as a power of 2

256 = 4×4×4×4 = 4⁴

256 = 2×2×2×2× 2×2×2×2 = 2⁸

729 as a power of 9; as a power of 3

729 = 9×9×9 = 9³

729 = 3×3×3×3×3×3 = 3⁶

Therefore, 625 as a power of 5, 343 as a power of 7, 216 as a power of 6, 169 as a power of 13, 256 as a power of 4; as a power of 2 and  729 as a power of 9; as a power of 3 are 5⁴, 7³, 6³, 13², 4⁴; 2⁸ and 9³; 3⁶ respectively

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Answer:

1/8

Step-by-step explanation:

So if the entire recipe makes 7 loaves and calls for 7/8 of a cup, you would need to split the 7/8 cups flour into 7. 7/8 ÷ 7=1/8.

Option A: 1/8 of a cup

Rhombus is a type of quadrilateral.

A rhombus is a type of quadrilateral, which means it is a four-sided polygon. What distinguishes a rhombus from other quadrilaterals is that it has four equal sides. Another important property of a rhombus is that its opposite sides are parallel and congruent. This makes the rhombus a type of parallelogram.

A rhombus also has two pairs of opposite angles that are congruent. In other words, if you draw a diagonal line from one vertex of the rhombus to another, you will create two congruent triangles. This property makes the rhombus a type of kite, which is another type of quadrilateral.

The diagonals of a rhombus bisect each other at right angles. This means that the diagonals divide the rhombus into four congruent right triangles. Moreover, the lengths of the diagonals of a rhombus are related by the Pythagorean theorem, which states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of its hypotenuse.

Overall, a rhombus is a unique type of quadrilateral that has several interesting properties, including equal sides, parallel opposite sides, congruent opposite angles, and perpendicular diagonals. Its special properties make it useful in various fields of mathematics and engineering, such as geometry, trigonometry, and architecture.

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The value of sin 2θ is 120/169, for the given value of cosine θ = 5/13, which is obtained using the Pythagorean-identity.

We know that :sin²θ + cos²θ = 1.

Using this identity, we can solve for sin θ as follows:

cos θ = 5/13

sin²θ + cos²θ = 1

We are to calculate trigonometric ratio sine 2θ.

We know that sin 2θ = 2 sin θ cos θ.

To calculate sin θ, we will use the Pythagorean identity,

sin²θ + cos²θ = 1

Since  trigonometric ratio cos θ = 5/13,

sin θ = √(1 - cos²θ)

        = √(1 - 25/169)

        = √(144/169)

         = 12/13

Therefore,sin 2θ = 2 sin θ cos θ

                           = 2 × (12/13) × (5/13)

                            = 120/169

Therefore, the value of sin 2θ is 120/169.

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Comparing the two results, the other bank's offer yields $11,665.62 after 2 years, which is less than what Jim's current bank account generates ($11,762.62). Therefore, Jim's bank with a continuous compounding rate of 7.8% is the better deal.

To determine whether Jim will have enough money to buy a car that costs $51,169.37 after 2 years with his current bank account that pays 7.8% compounded continuously, we can use the formula for continuous compound interest:

A = P * e^(rt)

Where:

A is the final amount

P is the principal amount (initial deposit)

e is the base of the natural logarithm (approximately 2.71828)

r is the interest rate

t is the time in years

For Jim's current bank account:

P = $10,000

r = 7.8% = 0.078 (converted to decimal)

t = 2 years

A = $10,000 * e^(0.078 * 2)

Using a calculator, we find that A ≈ $11,762.62.

Since Jim will have $11,762.62 after 2 years, he will not have enough money to buy the car that costs $51,169.37.

To determine if the other bank's offer of 8% compounded semiannually is a better deal, we can calculate the final amount using the formula for compound interest:

A = P * (1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the interest rate

n is the number of compounding periods per year

t is the time in years

For the other bank's offer:

P = $10,000

r = 8% = 0.08 (converted to decimal)

n = 2 (semiannually, 2 compounding periods per year)

t = 2 years

A = $10,000 * (1 + 0.08/2)^(2*2)

Using a calculator, we find that A ≈ $11,665.62.

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Answer:

-8

Step-by-step explanation:

Hi there! :)

-10+2=-8

Hope this helps!

~Just a determined gal

#CarryOnLearning

Please mark brainliest; I would really appreciate that! :)

\(MysteriousNature :)\)

Answer:

g(x) = 4x - 23

Step-by-step explanation:

We will assume a linear function for g(x)

This will be of the form g(x) = ax + b where a and b are constants

Given the info,

g(3) = a(3) + b = -11

g(7) = a(7) + b = 5

Thus we have two equations in a and b
3a + b = -11  [1]
7a + b = 5    [2]

Subtract [1] from [2]:
7a + b - (3a + b) = 5 - (-11)
7a + b - 3a - b = 5 + 11

4a = 16

a = 4

Substitute for a in equation [2]:

4(7) + b = 5
28 + b = 5

b = 5-28 = -23

So equation of g(x) is
g(x) = 4x - 23

Answer:

90 in²

shoebox:

Another shoebox:

====================

\(\sf (\dfrac{area1}{area2})^3 = (\dfrac{volume1}{volume2} )^2\)

====================

\(\sf \hookrightarrow (\dfrac{x}{160})^3 = (\dfrac{27}{64} )^2\)

\(\sf \hookrightarrow \dfrac{x^3}{160^3} = \dfrac{27^2}{64^2}\)

\(\sf \hookrightarrow \ x^3 = \dfrac{729*4096000}{4096}\)

\(\sf \hookrightarrow \ x^3 = 729000\)

\(\sf \hookrightarrow \ x = \sqrt[3]{729000}\)

\(\sf \hookrightarrow \ x = 90\)

Answer:

V = 56.5 mi^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h where r is the radius and h is the height

V = pi ( 3)^2 (2)

V = 18 pi

Letting p = 3.14

V = 56.52 mi^3

Rounding to the nearest tenth

V = 56.5 mi^3

The probability of getting 3 twice in a row is 1/36

A spinner has 6 equal parts labeled from 1 to 6.

The spinner is spun twice.
First time what is the conditions {1,2,3,4,5,6}

Second time choices are

{1,1} {1,2} {1,3} {1,4} {1,5} {1,6}

{2,1} {2,2} {2,3} {2,4} {2,5} {2,6}

{3,1} {3,2} {3,3} {3,4} {3,5} {3,6}

{4,1} {4,2} {4,3} {4,4} {4,5} {4,6}

{5,1} {5,2} {5,3} {5,4} {5,5} {5,6}

{6,1} {6,2} {6,3} {6,4} {6,5} {6,6}

So we have total 6*6 = 36 choices

{3,3} comes only 1 times.

We know the formula for probability:

Probability(Event) = Favorable Outcomes/Total Outcomes.

Favorable Outcomes = 1.

Total Outcomes=36.

So the probability of getting a 3 twice in a row is 1/36.

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Answer:

the volume of the cylinder is 41x^3

Step-by-step explanation:

The computation of the volume of the cylinder is shown below:

As we know that

The Volume of the cylinder is

= base × height

= (4x)^2 + (5x)^2

=16x^2 + 25x^2

= 41x^3

Hence, the volume of the cylinder is 41x^3

The probability that the mean yield of the 80 one acre plots chosen will be within 2 bushels of the population mean is 0.9332. The assumptions made to answer part (a) are that the population standard deviation is known, the sample is randomly selected, and the sample size is large (n>=30)

a) We can use the central limit theorem to approximate the distribution of the sample mean. The distribution of the sample mean can be approximated as a normal distribution with a mean of 107 bushels and a standard deviation of 12/√80=1.34 bushels. Therefore, we can find the probability that the sample mean falls within 2 bushels of the population mean using the standard normal distribution.

P(105 ≤ X ≤ 109) = P(Z ≤ (109-107)/1.34) - P(Z ≤ (105-107)/1.34)

= P(Z ≤ 1.49) - P(Z ≤ -1.49)

= 0.9319 - 0.0681

= 0.8638

Therefore, there is an 86.38% probability that the mean yield of the 80 one acre plots will be within 2 bushels of the population mean.

b) Assumptions made:

The sample of 80 one acre plots is selected at random.

The one acre plots are independent of each other.

The population standard deviation is known and remains constant.

The distribution of the yield of corn per acre is approximately normal.

The sample size is large enough (n≥30) to apply the central limit theorem.

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Answer:

This is done by stating descriptions of these terms.

Step-by-step explanation:

Undefinable terms are terms with no formal definitions. Formal definitions are obtained when specific words are used to define a term. In mathematics, specifically, Geometry words like line, point, and plane have no definite definition, So descriptions are used to identify them.

For example, in describing a point, we note that a point has no dimensions, it is usually denoted with a capital letter, and it indicates a position. Also in a coordinate plane, it is denoted with descriptions such as  (u,v). Corresponding descriptions are given of other undefinable terms.

The time interval when the speed is decreasing 0< t<3

Instatenous speed is the speed of a object in motion at any given moment of time.

When the speed starts deceasing the instatenous acceleration dv/dt<0

differentiating the distance with time with second order

dv/dt= d^2x/dt^2

dv/dt= 18t- 54

dv/dt<0

18t-54<0

18t<54

t<3

Therefore the time interval when the speed start deceasing is 0 to 2

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The cost of 7 bags of bananas will be $52.78.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition,substraction, multiplication, and division.

Given that at the produce store, you can buy 4 bags of bananas for $30.16. The cost of 7 bags will be calculated as:-

4 bags = $30.16

1 bag = $30.16 / 4

7 bags = ( 7 x $30.16) / 4

7 bags = $52.78

Therefore, the cost of 7 bags of bananas will be $52.78.

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Answer:

yes and no yes if there was no tax and no if their is tax

Step-by-step explanation:

im going to clear the yes up normally the tax would be 3 dollars so no the tax is already their i hope i hepd

Answer:

36.66

Step-by-step explanation:

Basically you just find the tip 4.782 and add it to 31.88 the total. 36.662 and then round to to get 36.66.

Answer:

36.66

Step-by-step explanation:

Basically you just find the tip 4.782 and add it to 31.88 the total. 36.662 and then round to to get 36.66.

Answer:

x= 56

Step-by-step explanation:

since angle DF is half a circle it has to = 180 so you subtract 64 from 180 then you subtract 60 from that

If the depth of the pond is 1. 5 meter and total height of the pillar is 51. 5 meter, the value of theta is 74.38 degrees.

Given that the diameter of a circular pond is 100 meters and a pillar is fixed at the center of the pond. A person finds the angle of elevation of the top of the pillar is 0° from the bank of the pond. The depth of the pond is 1.5 meters and the total height of the pillar is 51.5 meters.

Therefore, the value of θ is 74.38 degrees (approx) if the diameter of a circular pond is 100 meters, a pillar is fixed at the center of the pond, a person finds the angle of elevation of the top of the pillar is 0° from the bank of the pond, the depth of the pond is 1.5 meters, and the total height of the pillar is 51.5 meters.

θ = angle of elevation of the top of the pillar from the point of observation

So, we will calculate the value of θ using the following steps:

Let the point of observation be O and the base of the pillar be A. On the diagram, draw OA which will be a tangent to the circle of the pond at point A. On the diagram, draw AB perpendicular to OA, so that it intersects OA at B.

Hence, AB will be the height of the pillar AB will be equal to 51.5 meters. Draw BC perpendicular to OA, so that it intersects the surface of the pond at C.

Hence, BC will be the depth of the pond. BC will be equal to 1.5 meters. Also, since O is on the bank, OA is 50 meters. We now have a right-angled triangle OAB. The angle of elevation of the top of the pillar is zero. Therefore, angle ABO is 90°.Therefore, angle OAB is equal to 90° - θ

Therefore, using the tangent ratio, we can say that tan (90° - θ) = AB/OA

Since AB = 51.5 meters, and OA = 50 meters, we get;

tan (90° - θ) = 51.5/50tan (90° - θ)

= 1.03

Therefore, (90° - θ) = tan-1 (1.03)θ

= 90° - tan-1 (1.03)θ

= 74.38 degrees (approx)

Therefore, the value of θ is 74.38 degrees (approx) if the diameter of a circular pond is 100 meters, a pillar is fixed at the center of the pond, a person finds the angle of elevation of the top of the pillar is 0° from the bank of the pond, the depth of the pond is 1.5 meters, and the total height of the pillar is 51.5 meters.

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Answer:

The last option:  \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Step-by-step explanation:

Main concepts:

Concept 1. Parts of a Radical

Concept 2. Radicals as exponents

Concept 3. Exponent properties

Concept 4. How to simplify a radical

Concept 1. Parts of a Radical

Radicals have a few parts:

If the index isn't shown, it is the default index of "2".  This default index for a radical represents a square root, which is why people sometimes erroneously call the radical symbol a square root even when the index is not 2.

In this situation, the radical's index is 4, and the radicand is 81 x^18 y^6.

Concept 2. Radicals as exponents

For any radical, the entire radical expression can be rewritten equivalently as the radicand raised to the power of the reciprocal of the index of the radical.  In equation form:

\(\sqrt[n]{x} =x^{^{\frac{1}{n}}}\)

So, the original expression can be rewritten as follows:

\(\sqrt[4]{81x^{18}y^{6}}\)

\((81x^{18}y^{6})^{^{\frac{1}{4}}}\)

Concept 3. Exponent properties

There are a number of properties of exponents:

Continuing with our expression, \((81x^{18}y^{6})^{^{\frac{1}{4}}}\), we can apply the "distributive" property since all of the parts are multiplied to each other...

\((81)^{^{\frac{1}{4}}}(x^{18})^{^{\frac{1}{4}}}(y^{6})^{^{\frac{1}{4}}}\)

Applying the "Bases raised to powers, raised again to another power, multiplies powers" rule for the parts with x and y...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{18}{4}}})(y^{^{\frac{6}{4}}})\)

Reducing those fractions, (both the numerators and denominators have a factor of 2)...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{9}{2}}})(y^{^{\frac{3}{2}}})\)

Rewriting the exponent of the "81" back as a radical...

\(\sqrt[4]{81} x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Concept 4. How to simplify a radical

For any radical with index "n", the result is the number (or expression) that when multiplied together "n" times gives the radicand.

In our case, the index is 4.  So, we're looking for a number that when multiplied together four times, gives a result of 81.

One method of simplifying radicals is to completely factor the radicand into prime factors, and forms groups (each containing an "n" number of matching items).

Note that 81 factors into 9*9, which further factors into 3*3*3*3

This is a group of 4 matching items, and since the index of the radical is 4, we have found a group that can be factored out of the radical completely:

\(\sqrt[4]{81} =\sqrt[4]{(3*3*3*3)}=3\)

So, our original expression, simplifies finally to \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

This is the last option for the multiple choice.

Answer:

4 buses and 3 vans

Step-by-step explanation:

45 students in 4 buses = 180

12 students in 3 vans = 36

180 + 36 = 216.

Answer: the opposite of 12 should be -12

Step-by-step explanation:

Answer:

To solve for m, you need to multiply density with volume.

Answer:

c

Step-by-step explanation:

The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

The critical value(s) and rejection region(s) for the type of z-test with a level of significance a = 0.03 and a right-tailed test are as follows :Step 1: Determine the critical value of  zThe critical value is calculated by using the normal distribution table and the level of significance. A right-tailed test will have a critical value of zα. For a level of significance of 0.03, we will look for the z-value that corresponds to 0.03 in the normal distribution table.Critical value for a = 0.03 is z = 1.88 (approx).Step 2: Determine the Rejection Region The rejection region for a right-tailed test is defined as any z-value that is greater than the critical value. That is, if the test statistic is greater than 1.88, we reject the null hypothesis at the 0.03 level of significance, and if it is less than or equal to 1.88, we fail to reject the null hypothesis.Therefore, the rejection region for a right-tailed test with a level of significance of 0.03 is as follows:Rejection Region: Z > 1.88  OR  Z ≤ -1.88Graph: The graph for the given values will be as follows:The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

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Answer:

David needs 7-8 short term rentals monthly to match revenue from a lease. College students need long term housing so he should lease his home.

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

assuming the equation is

T = 2π\(\sqrt{\frac{a}{b} }\)  ( divide both sides by 2π )

\(\frac{T}{2\pi }\) = \(\sqrt{\frac{a}{b} }\) ( square both sides to clear the radical )

( \(\frac{T}{2\pi }\) )² = \(\frac{a}{b}\) , that is

\(\frac{T^2}{4\pi ^2}\) = \(\frac{a}{b}\) ( cross- multiply )

b T² = 4aπ² ( divide both sides by T² )

b = \(\frac{4a\pi ^2}{T^2}\)

Answer:If the letters are 2 inches high in the sketch, and you want them to be 2 feet high in reality, that means you need to scale up the letters by a factor of 12 (since 1 foot = 12 inches).

So the new height of each letter will be:

2 inches/letter × 12 = 24 inches/letter

And the new length of the banner will be:

20 inches/banner × 12 = 240 inches/banner

To find out how much paper to buy, you need to know the width of the paper you'll be using. Let's say the paper is 36 inches wide (3 feet). In that case, you'll need to buy:

240 inches/banner ÷ 36 inches/roll = 6.67 rolls of paper

Since you can't buy a fraction of a roll of paper, you should round up to 7 rolls of paper to ensure you have enough.

Step-by-step explanation:

Answer:

N= 5/112

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