the total of housemates in my house is x. a housemate is not there. Stay some people y If 12-x = (y+3) nuggets in the pan are cooked for housemates y, and distributed equally to all how many nuggets would 'one' y get?​

Answers

Answer 1

Answer:

because of the gravity of the earth


Related Questions

If the exterior angle of a triangle is 150 degrees, what is the adjacent interior angle

If the exterior angle of a triangle is 150 degrees, what is the adjacent interior angle

Answers

Answer:

30

Step-by-step explanation:

Interior angle + exterior angle = 180. 180 - 150 = 30

Answer:

prolly 30 degrees

Step-by-step explanation:

Which expressions are equivalent to z + (z + 6)z+(z+6)z, plus, left parenthesis, z, plus, 6, right parenthesis ?

Answers

Answer:

5 lolsjjhgjh h h gh h h hh f ggugy

Write the algebraic expression (ex. 2x - 5) for this problem: Eight less than a number​

Answers

Answer:

x - 8

Step-by-step explanation:

Answer:

Here you can simply use a single operator:

x - 8

Problems 16 through 21 are based on the following data. Observations of the demand for a certain part stocked at a parts supply depot during the calendar year 1999 were 16. Determine the one-step-ahea

Answers

The one-step-ahead demand forecast for a part can be determined using forecasting methods such as moving averages, exponential smoothing, or regression analysis.

the question mentions "observations of the demand for a certain part stocked at a parts supply depot during the calendar year 1999." From this, we can assume that the demand for this part was recorded over the course of the year.

The question also mentions "one-step-ahead demand forecast" without providing further details. In general, a one-step-ahead demand forecast is a prediction of the demand for a certain period based on historical data.

To determine the one-step-ahead demand forecast, you would typically use forecasting methods such as moving averages, exponential smoothing, or regression analysis. These methods analyze the historical demand data and use it to predict future demand.

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In a transportation problem, the activities correspond to the shipping lanes while the _______ of each activity is the quantity shipped.

Answers

In a transportation problem, the activities correspond to the shipping lanes while the supply of each activity is the quantity shipped.

In the transportation problem, activities are the shipping lanes that are taken to transport goods from sources to destinations.

The quantities to be shipped are known as supplies or availabilities. The transportation problem is a linear programming problem that is used to determine how to allocate resources to obtain a minimum cost or maximum profit.The transportation problem is one of the most widely used problems in linear programming. It is used to solve many real-world problems such as supply chain management, production planning, and logistics.

In the transportation problem, we are given a set of sources and a set of destinations. The supply and demand at each source and destination are also given. The objective is to minimize the total cost of transporting the goods from sources to destinations while satisfying the demand and supply constraints.

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The partial sum 1 + 10 + 19 +.... 199 equals :___________

Answers

The partial sum of the given sequence, 1 + 10 + 19 + ... + 199, can be found by identifying the pattern and using the formula for the sum of an arithmetic series.  Hence, the partial sum of the sequence 1 + 10 + 19 + ... + 199 equals 4497.

To find the partial sum of the given sequence, we can observe the pattern in the terms. Each term is obtained by adding 9 to the previous term. This indicates that the common difference between consecutive terms is 9.

The formula for the sum of an arithmetic series is Sₙ = (n/2)(a + l), where Sₙ is the sum of the first n terms, a is the first term, and l is the last term.

In this case, the first term a is 1, and we need to find the value of l. Since each term is obtained by adding 9 to the previous term, we can determine l by solving the equation 1 + (n-1) * 9 = 199.

By solving this equation, we find that n = 23, and the last term l = 199.

Substituting the values into the formula for the partial sum, we have:

S₂₃ = (23/2)(1 + 199),

= 23 * 200,

= 4600.

However, this sum includes the terms beyond 199. Since we are interested in the partial sum up to 199, we need to subtract the excess terms.

The excess terms can be calculated by finding the sum of the terms beyond 199, which is (23/2)(9) = 103.5.

Therefore, the partial sum of the given sequence is 4600 - 103.5 = 4496.5, or approximately 4497 when rounded.

Hence, the partial sum of the sequence 1 + 10 + 19 + ... + 199 equals 4497.

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Please help
Find x:


5
31
10
60

Please help Find x:5311060

Answers

Answer:

x=31....................

if sinA=1/2 then find sinA +cos A

Answers

Step-by-step explanation:

Given sinA – cosA = 1/2 squaring on both the sides, we get (sinA – cosA)2 = (1/2)2 ⇒ sin2A + cos2A – 2sinA cosA = 1/4 ⇒ 1 – 2sinA cosA = 1/4 ⇒ 1 – (1/4) = 2sinA cosA ⇒ 2sinA cosA = 3/4 ∴ sinA cosA = 3/8  → (1) (sinA + cosA)2 = (sinA – cosA)2 + 4sinA cosA                         = (1/2)2 + 4(3/8)                         = (1/4) + (3/2) = 7/4 (sinA + cosA) = √(7/4) = (√7)/2 .

Given that,

\(\sin A = \dfrac 12\\\\ \implies \sin^2 A = \dfrac 14\\\\\ \implies 1-\cos^2 A = \dfrac 14\\\\\ \implies \cos^2 A = 1 - \dfrac 14 = \dfrac 34\\\\\ \implies \cos A = \pm \dfrac{\sqrt 3}2\\\\\text{Case 1:}\\\\\sin A + \cos A = \dfrac 12 + \dfrac{\sqrt 3}2 = \dfrac{1 + \sqrt 3}2\\\\\text{Case 2:}\\\\\sin A + \cos A = \dfrac 12 +\left(- \dfrac{\sqrt 3}2\right) = \dfrac 12 - \dfrac{\sqrt 3}2=\dfrac{1 - \sqrt 3}2\)

he people she works with, she would really like to be a literary agent. She would like to go on her own in about 6 years and figures she'll need about $70,000 in capital to do soi ilven that she thinks she can make about 7 percent on her money, use Worksheet 11.1 to answer the following questions. a. How much would Ashley have to invest today, in one fump sum, to end up with $70,000 in 6 years? Round the answer to the nearest cent. 3 b. If she's starting from scratch, how much would she have to put away annually to accumulate the needed capital in 6 years? Round the answer to the nearest cent. 5 6. How about It she already has $20,000 socked away; how much would she have to put away annually to accumulate the required capitat in 6 years? Round the answer to the nearest cent. 3 d. Given that Ashley has an idea of how much she needs to save, briefly explain how she could use an inveatment plan to heip reach her objective.

Answers

a. Ashley would need to invest approximately $49,302.55 in one lump sum today. b. Ashley would need to put away approximately $9,167.42 annually to accumulate the required capital in 6 years. c. Ashley already has $20,000 saved, she would need to put away approximately $6,111.57 annually to accumulate the required capital in 6 years.

a. To determine how much Ashley would need to invest today, in one lump sum, to end up with $70,000 in 6 years, we can use the future value formula:

Future Value (FV) = Present Value (PV) * (1 + interest rate)^time

In this case, FV = $70,000, interest rate = 7% (0.07), and time = 6 years. Plugging in these values into the formula, we can solve for PV:

$70,000 = PV * \((1 + 0.07)^6\)

PV = $70,000 /\((1.07)^6\)

PV ≈ $49,302.55

Therefore, Ashley would need to invest approximately $49,302.55 in one lump sum today.

b. If Ashley is starting from scratch, we need to calculate how much she would have to put away annually to accumulate the needed capital in 6 years. This can be calculated using the present value of an ordinary annuity formula:

PV = Annual Payment * [(1 - (1 + interest rate)^(-time)) / interest rate]

In this case, PV = $70,000, interest rate = 7% (0.07), and time = 6 years. Plugging in these values, we can solve for the annual payment:

$70,000 = Annual Payment *\([(1 - (1 + 0.07)^(-6)) / 0.07]\)

Annual Payment ≈ $9,167.42

Therefore, Ashley would need to put away approximately $9,167.42 annually to accumulate the required capital in 6 years.

c. If Ashley already has $20,000 saved, we can subtract this amount from the required capital and calculate the annual payment for the remaining amount:

Remaining Amount = Required Capital - Initial Savings

Remaining Amount = $70,000 - $20,000 = $50,000

Using the same formula as in part b, we can calculate the annual payment:

$50,000 = Annual Payment\(* [(1 - (1 + 0.07)^(-6)) / 0.07]\)

Annual Payment ≈ $6,111.57

Therefore, if Ashley already has $20,000 saved, she would need to put away approximately $6,111.57 annually to accumulate the required capital in 6 years.

d. Ashley can use an investment plan to help reach her objective by following these steps:

- Set a specific financial goal, such as accumulating $70,000 in 6 years.

- Determine the required investment amount, whether it's a lump sum or an annual payment.

- Consider her risk tolerance and investment options. Since she estimates a 7% return, she can explore various investment vehicles like stocks, bonds, mutual funds, or other investment instruments.

- Develop an investment plan that aligns with her financial goals and risk tolerance. This plan may involve diversifying her investments, considering different time horizons, and regularly monitoring her progress.

- Continuously track the performance of her investments and make adjustments if needed.

- Stay disciplined and committed to her investment plan, making regular contributions or adjusting investments as necessary to reach her desired capital.

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A population of 752,000 people decreases at a rate of 1.4% each year. What will be the population after 18 years?

Answers

Answer:

562496

Step-by-step explanation:

i think

Answer:189504

Step-by-step explanation:

To get the 1.4% of population you need to multiply it like this: 752000 × 1.4% = 10528.

10528 is the population decrease every year, to find the population decrease after 18 years you need to multiply it again like this: 10528 × 18 = 189504.

189504 is the population decrease after 18 years.

12

Carson's favorite band is playing 5 concerts. The ticket prices, in dollars, for each of the 5 concerts are listed below.

14, 14, 16,20,21

What is the mean absolute deviation of the ticket prices for the 5 concerts?

Answers

To find the mean absolute deviation of the ticket prices for Carson's favorite band's concerts, we first need to find the mean (average) of the ticket prices. We add up all the ticket prices and divide by the total number of concerts. the mean absolute deviation of the ticket prices for Carson's favorite band's concerts is $2.80.

(14+14+16+20+21) / 5 = 17

So the mean ticket price is $17.

Next, we need to find the absolute deviation for each ticket price by subtracting the mean from each individual ticket price and taking the absolute value.

|14-17| = 3
|14-17| = 3
|16-17| = 1
|20-17| = 3
|21-17| = 4

Now, we add up these absolute deviations and divide by the total number of concerts (5) to get the mean absolute deviation.

(3+3+1+3+4) / 5 = 2.8

So the mean absolute deviation of the ticket prices for Carson's favorite band's concerts is $2.80.


To calculate the mean absolute deviation, follow these steps:

1. Find the mean of the ticket prices: (14 + 14 + 16 + 20 + 21) / 5 = 85 / 5 = 17.
2. Calculate the absolute deviations: |14-17| = 3, |14-17| = 3, |16-17| = 1, |20-17| = 3, |21-17| = 4.
3. Find the mean of the absolute deviations: (3 + 3 + 1 + 3 + 4) / 5 = 14 / 5 = 2.8.

The mean absolute deviation of the ticket prices for the 5 concerts is 2.8 dollars.

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how many feet in acre

Answers

Answer:

43,560ft

Step-by-step explanation:

What are units?

A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.

1 Acre = 43,560 feet

Therefore, for every 1 acre it is equivalent to 43,560 feet.

The government sees your egg apparatus and decides to use it as a model to create structures to protect food that is dropped over areas for disaster relief. if eggs are typically 2.5 ounces and there are 16 ounces in a pound and a bag of rice is 65 pounds, assuming the size of the rice apparatus is directly proportional to the egg apparatus, how much bigger does the rice apparatus need to be?

Answers

We are given that an egg weighs 2.5 ounces and that there are 16 ounces in a pound. We also know that the rice apparatus is directly proportional to the egg apparatus. The rice apparatus needs to be the same weight and size as the egg apparatus.



To find out how much bigger the rice apparatus needs to be, we need to determine the weight of the rice apparatus. First, we calculate the weight of the bag of rice by multiplying the weight of a pound (16 ounces) by the number of pounds (65 pounds). This gives us 1040 ounces (16 * 65).


Next, we need to determine the ratio between the egg apparatus and the rice apparatus. Since they are directly proportional, we can set up a proportion using their weights:


(egg weight) / (rice weight) = (egg size) / (rice size)


Substituting the values we have, we get:

2.5 / (rice weight) = 2.5 / (1040)


Now, we can solve for the weight of the rice apparatus:

(rice weight) = (2.5 * 1040) / 2.5


Simplifying, we find:

(rice weight) = 1040


Therefore, the weight of the rice apparatus needs to be the same as the weight of the bag of rice, which is 1040 ounces.


In terms of size, since the weight of the rice apparatus is directly proportional to the egg apparatus, we can conclude that the rice apparatus needs to be the same size as the egg apparatus.


In summary, the rice apparatus needs to be the same weight and size as the egg apparatus.

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HELP PLS PLS ILL MARK U BRAINLIEST

HELP PLS PLS ILL MARK U BRAINLIEST

Answers

Answer:

angle XYW = -20x + 155

Step-by-step explanation:

angle XYZ = 150

angle WYZ = 20x - 5

angle XYW = y

angle XYZ = 20x - 5 + y

150 = 20x - 5 + y

150 + 5 = 20x + y

y = -20x + 155

So angle XYW = -20x + 155


150=-20x-5

angle XYW=-20x+155

Decrease 64 g by 123%
please help i need a step by step explanation​

Answers

Answer:

-14.72g

Step-by-step explanation:

64g represents a 100% value

To reduce it by 123% means 100%-123%=-23%

So calculate-23% of 64g

=-23/100×64g

=-14.72g

Which graph models function m?
x- 0 1 2 3 4 5
m(x)- -9 -4 -1 0 -1 -4

Which graph models function m?x- 0 1 2 3 4 5m(x)- -9 -4 -1 0 -1 -4

Answers

The answer is graph c

4. Write each of the following improper fractions as mixed numbers.
51
8
(a)
(b)
169
4
(c)
389
24

4. Write each of the following improper fractions as mixed numbers.518(a)(b)1694(c)38924

Answers

Answer:

Step-by-step explanation:

1. 51/8 = 6 3/8

2. 169/4 = 42 1/4

3. 389/24 = 16 5/24

If each shelf can hold at most 20 books, what is the least number of shelves needed to store the 175 books?

Answers

Answer- 9 shelves

In order to find out how many shelves are need we must divided 175 into 20. 175 divided by 20 is 8.75. But, because you cannot have have .75 of a shelf, you have to round this to a whole. This means that 9 shelves will be the least needed number of shelves need to store 175 books. To check this answer 20 books X 8 shelves is 160 books, which means eight shelves can only store 160 books, we will need and additional shelf to store the last 15 books.

HOPE THIS HELPS & GOOD LUCK!

I need somebodys help quickly please!
(look at the attachment it shows the math equation).​

I need somebodys help quickly please!(look at the attachment it shows the math equation).

Answers

Answer: 1 & 6

Step-by-step explanation:

It x³ is positive, then x also has to be positive

Save works for negatives

x³ = 1

x = ∛1 = 1

x³ = 216

x = ∛216 = 6

tyrone drew a logo and a dilation of the same logo on the coordinate plane. describe the dilation. then write a coordinate rule to represent it.

Answers

Dilation in coordinate geometry refers to the process of increasing or stretching the size of the originally drawn geometrical figure to a new figure by multiplying the co-ordinates of the original figure with a scale factor and obtain new co-ordinates to plot and form on the graph.

In the given figure, we observe that the original co-ordinates of the logo drew by Tyrone are:

A (-2,0) ; B (-2,3) ; C(2,2) ; D(2,-1)

From the graph, we see that the co-ordinates are multiplied by a scale factor of 5/2 and hence turn to new co-ordinates:

A'(-5,0) ; B'(-5, 15/2); C'(5,5) ; D'(5, -5/2)

Thus, we see that the rule followed to form the dilation of the logo on the coordinate plane was (5/2x, 5/2y).

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tyrone drew a logo and a dilation of the same logo on the coordinate plane. describe the dilation. then

In which number is the value of the red digit ten times as great as the value of the green digit envision math

Answers

Let's consider a two-digit number where the value of the red digit is ten times greater than the value of the green digit. We can represent this number as "10r + g," where r represents the value of the red digit and g represents the value of the green digit.

To find the specific number that satisfies this condition, we need to find a pair of digits that meets the given criteria. Since the value of the red digit is ten times greater than the green digit, we have the equation r = 10g By substituting this equation into our representation of the number, we get the number as 10(10g) + g, which simplifies to 100g + g. Therefore, the number can be written as 101g. From this, we can conclude that any two-digit number where the red digit is ten times greater than the green digit can be represented as 101g, where g can be any digit from 0 to 9.

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Please Help!!
I really need to pass

Please Help!! I really need to pass

Answers

Answer:

None of these

Step-by-step explanation:

The lines aren't parallels so none of these property's can be applied

Ur answer is none of these

how to find the maximum height of a quadratic equation

Answers

the maximum height of a quadratic equation can be find Use the formula: x = -b / (2a) then Substitute the value of x back into the quadratic equation to find the corresponding maximum height.

To find the maximum height of a quadratic equation, you need to determine the vertex of the parabolic curve. The vertex represents the highest or lowest point of the quadratic function, depending on whether it opens upward or downward.

A quadratic equation is generally written in the form of y = ax² + bx + c, where "a," "b," and "c" are coefficients.

The x-coordinate of the vertex can be found using the formula: x = -b / (2a). This formula gives you the line of symmetry of the parabola.

Once you have the x-coordinate of the vertex, substitute it back into the original equation to find the corresponding y-coordinate.

The resulting y-coordinate represents the maximum height (if the parabola opens downward) or the minimum height (if the parabola opens upward) of the quadratic equation.

Here's an example:

Consider the quadratic equation y = 2x² - 4x + 3.

1. Identify the coefficients:

a = 2

b = -4

c = 3

2. Find the x-coordinate of the vertex:

x = -(-4) / (2 * 2) = 4 / 4 = 1

3. Substitute x = 1 back into the equation to find the y-coordinate:

y = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1

Therefore, the maximum height of the quadratic equation y = 2x² - 4x + 3 is 1.

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The maximum height of a quadratic equation can be found by determining the vertex of the parabolic shape represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), and the corresponding y-coordinate represents the maximum height.

To find the maximum height of a quadratic equation, we need to determine the vertex of the parabolic shape represented by the equation. The vertex is the point where the parabola reaches its highest or lowest point.

The general form of a quadratic equation is ax^2 + bx + c, where a, b, and c are constants. To find the x-coordinate of the vertex, we can use the formula x = -b / (2a).

Once we have the x-coordinate, we can substitute it back into the equation to find the corresponding y-coordinate, which represents the maximum or minimum height of the quadratic equation.

Let's take an example to illustrate this process:

Suppose we have the quadratic equation y = 2x^2 + 3x + 1. To find the maximum height, we first need to find the x-coordinate of the vertex.

Using the formula x = -b / (2a), we can substitute the values from our equation: x = -(3) / (2 * 2) = -3/4.

Now, we substitute this x-coordinate back into the equation to find the y-coordinate: y = 2(-3/4)^2 + 3(-3/4) + 1 = 2(9/16) - 9/4 + 1 = 9/8 - 9/4 + 1 = 9/8 - 18/8 + 8/8 = -1/8.

Therefore, the maximum height of the quadratic equation y = 2x^2 + 3x + 1 is -1/8.

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In anova, by dividing the mean square between groups by the mean square within groups, a(n) _____ statistic is computed.group of answer choices

Answers

In anova, by dividing the mean square between groups by the mean square within groups, a(n) Analysis of variance  statistic is computed.

What is Analysis of variance ?

With the help of the statistical analysis approach known as ANOVA, apparent aggregate variability within a data set is explained by separating systematic components from random factors. Systematic influences, but not random ones, statistically affect the data set that is being presented.

What are some instances where ANOVA has been applied?

An ANOVA demonstrates the link between the dependent variable and the level of the independent variable. For illustration: In order to determine whether there is a difference in the number of hours of sleep each night as your independent variable, you divide the groups into low, medium, and high social media use categories.

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Which expression represents a rational number?

Which expression represents a rational number?

Answers

Answer:

C

Step-by-step explanation:

2/7+sqrt121 is just 2/7+11.

This is rational.

Answer:

2/7 + sqrt 121

Step-by-step explanation:

the square root of 121 is a whole number - 11, which is rational and makes the equation rational

(a) If you choose a single nucleotide at random from each of the two regions, what is the probability that they are the same nucleotide?
(b)You random sample a three-nucleotide sequence from each of the 2 regions. What is the chance that the triple chosen from the first region will be identical to the triple chosen from the second region? (assume that nucleotides occur independently within each region)

Answers

(a) The probability that a randomly chosen nucleotide from the first region is the same as a randomly chosen nucleotide from the second region is 1/4.

(B) The chance that the triple chosen from the first region will be identical to the triple chosen from the second region is 1/4096.

Nucleotide Probabilities: Single and Triple

(a) If we assume that there are four possible nucleotides (A, C, G, T) and that each nucleotide is equally likely to occur in each region, then the probability that a randomly chosen nucleotide from the first region is the same as a randomly chosen nucleotide from the second region is 1/4, since there is a 1 in 4 chance that the nucleotide chosen from the first region will be the same as the nucleotide chosen from the second region.

(b) If we again assume that there are four possible nucleotides (A, C, G, T) and that each nucleotide is equally likely to occur in each region, then the probability of choosing a particular three-nucleotide sequence is (1/4)³ = 1/64.

The probability of choosing the same three-nucleotide sequence from both regions is the product of the probabilities of choosing that sequence from each region, or (1/64) x (1/64) = 1/4096. Therefore, the chance that the triple chosen from the first region will be identical to the triple chosen from the second region is 1/4096.

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Given tan u=15/8, with u in quadrant III and cos v=-5/13 with v in quadrant II. find sin(u+v)

Answers

The value of sin(u+v) given tan u = 15/8 is -9/221

What are trigonometric ratios?

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the their angles.

A right-angled triangle has 3 sides, hypotenuse, opposite and adjacent. The following should be noted:

Sin = Opposite / Hypothenuse

Tan = Opposite / Adjacent

Cos = Adjacent / Hypothenuse

When tan u = 15/8

Opposite = 15

Adjacent = 8

Hypothenuse will be:

= ✓(15² + 8²)

= ✓(225 + 64)

= ✓289

= 17

Therefore sin u = 15/17

When cos v = -5/13, it should be noted that sin v will be -12/13.

Therefore, sin(u + v) will be:

= 15/17 + (-12/13)

= 15/17 - 12/13

= 195/221 - 204/221

= -9/221

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6. Inverse distance weighting: What is it for? Why is it better than just an average? (5)

Answers

Inverse distance weighting is a useful tool for estimating values at unsampled locations in geostatistics. Another advantage of inverse distance weighting is that it allows for the incorporation of multiple variables into the estimation process.

Inverse distance weighting is a method used in geostatistics to estimate values at unsampled locations based on values at surrounding sample locations. It works by assigning weights to the sample points based on their proximity to the unsampled point. The closer a sample point is to the unsampled point, the higher its weight. The weights are then used to calculate a weighted average of the sample values, which is used as the estimate for the unsampled location.
The benefit of inverse distance weighting over a simple average is that it takes into account the spatial variability of the data. A simple average treats all sample points equally, regardless of their distance from the unsampled point. This can lead to inaccurate estimates if there is a high degree of spatial variability in the data. In contrast, inverse distance weighting gives more weight to sample points that are closer to the unsampled point, which is likely to provide a more accurate estimate.
Another advantage of inverse distance weighting is that it allows for the incorporation of multiple variables into the estimation process. For example, if there are two variables of interest (e.g., temperature and precipitation), inverse distance weighting can be used to estimate values for both variables simultaneously. This is not possible with a simple average.
Overall, inverse distance weighting is a useful tool for estimating values at unsampled locations in geostatistics. Its ability to account for spatial variability and incorporate multiple variables makes it a powerful technique for analyzing spatial data.

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1 At Mr. Garza's florist shop, 1 ž dozen
roses cost $38.70. In dollars and cents,
what is the cost of a single rose?

Answers

Using proportions, it is found that the cost of a single rose is of 3.225 dollars = 322.5 cents.

What is a proportion?

A proportion is a fraction of a total amount.

In this problem, 12 roses cost $38.70, hence the price of a single rose is given by:

p = $38.70/12 = $3.225.

Considering one dollar has 100 cents, the price in cents is given by:

C = 3.225 x 100 = 322.5.

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In ΔABC, m∠A=a, m∠B=β, m∠C=y. AB = c, AC = b, BC = a. Find the remaining parts of each triangle if the following parts are given.
a=6.00, b=7.56, y = 54°

Answers

Answer:

c=6.31, a=50.28 degrees, B=75.72 degrees

Step-by-step explanation:

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. The remaining parts of the triangle can be found as shown.

What is Sine rule?

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,

\(\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ B}{\beta} =\dfrac{Sin\ C}{\gamma}\)

where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,

Sin B is the angle and β is the length of the side of the triangle opposite to angle B,

Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.

Given that the length of side a and b is 6 and 7.56, also, the measure of the angle γ is 54°.

Now, Using the law of cosine, we can write,

\(c =\sqrt{a^2 + b^2 -2ab\cdot \cos\gamma}\)

\(c =\sqrt{(6)^2 + (7.56)^2 -2(6)(7.56)\cdot \cos(54^o)}\)

c = √39.8297

c = 6.311

Now, using the sine law the ratio of the sides and angles can be written as,

\(\dfrac{\sin\alpha}{a} =\dfrac{\sin\beta}{b} =\dfrac{\sin\gamma}{c}\)

\(\dfrac{\sin\alpha}{6} =\dfrac{\sin\beta}{7.56} =\dfrac{\sin (54^o)}{6.311}\)

\(\dfrac{\sin\alpha}{6}=\dfrac{\sin (54^o)}{6.311}\)

α = 50.2775°

\(\dfrac{\sin\beta}{7.56} =\dfrac{\sin (54^o)}{6.311}\)

β = 75.726°

Hence, the remaining parts of the triangle can be found as shown.

Learn more about Sine Rule here:

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