The origin of the coordinate system is at the carbon atom labeled by "O". It is convenient to choose the basis B defined by the vectors V1 and v2 and the coordinate system it defines. a. Locate the points x for which 1. {x}x= [0] . {x}x= [1] tii {x}x= [?] b. Find the coordinates {x}r for all the carbon atoms in the hexagon whose lower left vertex is labeled "0". C. What are the coordinates {x}g of the center of that hexagon, which is labeled "C"? d. How do the coordinates of the atoms in the hexagon whose lower left corner is labeled "1" compare to the coordinates in the hexagon whose lower left corner is labeled "O"? e. Does the point whose coordinates are s- rdinates are {x}3 = [18] correspond to a carbon atom or the center of a hexagon?

The amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

As per the given problem:

Amount deposited = $60.00

Interest rate per year = 9%

The formula for calculating the interest is given by:

Interest = (Principal × Rate × Time)/100

Where Principal is the initial amount invested or deposited

Rate is the percentage of interest that you earn per annum

Time is the duration for which you want to calculate the interest

Putting the values in the above formula, we get:

Interest = (60 × 9 × 2)/100= (108 × 1)/1= $108

So, the amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

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A one-sample t-test is conducted to determine if recent Miss America winners have a significantly different BMI compared to winners from the 1920s and 1930s. The test results fail to reject the null hypothesis, indicating that recent winners do not appear to be significantly different from those in the 1920s and 1930s.

To determine if recent Miss America winners have a significantly different BMI compared to winners from the 1920s and 1930s, a one-sample t-test can be conducted. Using the given sample, the sample mean BMI is calculated to be 18.5.

The null hypothesis is that the population mean BMI of recent winners is equal to 19.2. The alternative hypothesis is that the population mean BMI of recent winners is different from 19.2.

Assuming a significance level of 0.05 and using a two-tailed test, the calculated t-value is -2.08 and the corresponding p-value is 0.057.

Since the p-value is greater than the significance level, we fail to reject the null hypothesis. This suggests that there is not enough evidence to conclude that recent Miss America winners have significantly different BMI compared to winners from the 1920s and 1930s.

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the fourth-degree Taylor polynomial for the function f(x) = x²(2/1), centered at c = 5, is P4(x) = 25 + 10(x - 5) + (1/2)(x - 5)²2.

To find the nth Taylor polynomial for the function f(x) = x²(2/1), centered at c = 5, we need to compute the derivatives of f(x) and evaluate them at x = c.

First, let's find the derivatives of f(x):

f(x) = x²(2/1)

f'(x) = (2/1)x²(2/1 - 1) = 2x²(1/1) = 2x

f''(x) = 2

f'''(x) = 0 (all higher-order derivatives will also be 0 since the function is a polynomial)

Next, let's evaluate the derivatives at x = c = 5:

f(5) = 5²(2/1) = 25

f'(5) = 2(5) = 10

f''(5) = 2

f'''(5) = 0

Now, we can construct the nth Taylor polynomial Pn(x) using the derivatives evaluated at x = c:

P4(x) = f(c) + f'(c)(x - c) + (f''(c)/2!)(x - c)²2 + (f'''(c)/3!)(x - c)²3

Substituting the values we obtained:

P4(x) = 25 + 10(x - 5) + (2/2!)(x - 5)²2 + (0/3!)(x - 5)²3

      = 25 + 10(x - 5) + (1/2)(x - 5)²2

Therefore, the fourth-degree Taylor polynomial for the function f(x) = x²(2/1), centered at c = 5, is P4(x) = 25 + 10(x - 5) + (1/2)(x - 5)²2.

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The small boxes weigh 30 pounds, and the large boxes weigh 45 pounds.

Let the weight of the small box be x, and the weight of the large box be y. Then we have the following system of equations:x + y = 75 - Equation 1
We can see from the question that the truck is transporting 55 large boxes and 50 small boxes.
Therefore:55y + 50x = 3975 - Equation 2
We can use equation 1 to solve for x in terms of y, by subtracting y from both sides:x = 75 - y - Equation 3
We can substitute equation 3 into equation 2, to obtain:
55y + 50(75 - y) = 3975
This simplifies to:55y + 3750 - 50y = 3975
Simplifying further:5y + 3750 = 3975
Subtracting 3750 from both sides:5y = 225
Dividing both sides by 5:y = 45
Substituting y = 45 into equation 3, we can solve for x:x = 75 - 45x = 30

Therefore, the small boxes weigh 30 pounds, and the large boxes weigh 45 pounds.

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Answer:

52

Step-by-step explanation:

8*16 = 128

8*20 = 180

180-128 =52

The volume of the solid is 9 cubic units, which is determined by the base in the first quadrant bounded by the y-axis, the graph of y = x-1, the horizontal line y = 3, and the vertical line x = 1. As the cross sections perpendicular to the x-axis are squares, the volume can be calculated.

The volume of the solid can be calculated by finding the area of the base and then multiplying it by the height of the solid. The base of the solid is in the first quadrant and is bounded by the y-axis, the graph of y = x-1, the horizontal line y = 3, and the vertical line x = 1. This region forms a trapezoid, with an area of 6. As the cross sections perpendicular to the x-axis are squares, the height of the solid is 3 units. Thus, the volume of the solid is 6 multiplied by 3, which gives us a total volume of 9 cubic units. To calculate the volume, it is important to identify the base of the solid and the shape of the cross sections perpendicular to the x-axis. This will allow us to calculate the area of the base, and multiply it by the height of the solid to determine the total volume.

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the equation of the tangent line is y = -46x + 166.

To find the slope of the tangent line to the graph of the function at the given value of x, we need to take the derivative of the function and evaluate it at x = 1.

Differentiate the function f(x) = x^4 - 25x^2 + 144 with respect to x:

f'(x) = 4x^3 - 50x

Evaluate the derivative at x = 1:

f'(1) = 4(1)^3 - 50(1) = 4 - 50 = -46

So, the slope of the tangent line is -46.

To find the equation of the tangent line, we can use the point-slope form of a linear equation. We have the point (1, f(1)) on the tangent line, and we know the slope is -46.

Find the value of f(1):

f(1) = (1)^4 - 25(1)^2 + 144 = 1 - 25 + 144 = 120

Use the point-slope form with the point (1, 120) and slope -46:

y - y1 = m(x - x1)

y - 120 = -46(x - 1)

y - 120 = -46x + 46

y = -46x + 166

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Answer:

D 141

Step-by-step explanation:

since it has to equal 180 just add each answer to the other number on the diagram so you answer us

39 + 141= 180

141

PLZ MARK ME BRAINLIEST

Answer:

i hope that is what you are looking for

Step-by-step explanation:

100/2 is 50 dollars per hour

160/5 is 32 dollars per hour

Answer: The cold length exceeded by only 20% of cold sufferers is approximately 8.76 days.

Step-by-step explanation:

We need to find the value of the cold length (number of days of symptoms) that is exceeded by only 20% of cold sufferers, which corresponds to the 80th percentile of the normal distribution with a mean of 7.5 days and a standard deviation of 1.5 days.

Using a standard normal table or calculator, we can find the z-score that corresponds to the 80th percentile:

z = invNorm(0.8) = 0.8416

We can then use the formula for z-score:

z = (x - μ) / σ

where x is the cold length, μ is the mean, and σ is the standard deviation.

Substituting the given values, we get:

0.8416 = (x - 7.5) / 1.5

Solving for x, we get:

x - 7.5 = 0.8416 * 1.5

x - 7.5 = 1.2624

x = 8.7624

Therefore, the cold length exceeded by only 20% of cold sufferers is approximately 8.76 days.

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The branch of mathematics that analyzes situations in which players must make decisions and then receive payoffs most often used by economists is "game theory". So, option C is the correct answeer.

Game theory is a branch of mathematics that studies how people or organizations interact in situations where there are choices to be made and where the outcome of each choice depends on the choices made by others. It is often used in economics to model the behavior of firms and consumers in markets, and to analyze strategic interactions between competitors in oligopolistic industries.

One of the most famous examples of game theory is the prisoner's dilemma, which is a simple model that illustrates how two individuals might not cooperate, even if it appears that it is in their best interest to do so.

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The required answers are a) 17.1 km b) 7.1 km, c) 18.6 km away from town A on a bearing of 293°.

To solve this problem, we can use vector addition to find the displacement vector from town A to the cyclist's destination.

a) To find how far east the cyclist's destination is from town A, we need to find the east component of the displacement vector. We can break down the displacement vector into its north and east components using trigonometry:

\($$\text{East displacement} = 5\text{ km} + 10\text{ km}\cos(45^\circ) = 5\text{ km} + 10\text{ km}\frac{\sqrt{2}}{2} = 10\text{ km} + 5\sqrt{2}\text{ km} \approx 17.1\text{ km}$$\)

So the cyclist's destination is approximately 17.1 km east of town A.

b) Similarly, to find how far north the cyclist's destination is from town A, we need to find the north component of the displacement vector:

\($$\text{North displacement} = 10\text{ km}\sin(45^\circ) = 10\text{ km}\frac{\sqrt{2}}{2} = 5\sqrt{2}\text{ km} \approx 7.1\text{ km}$$\)

So the cyclist's destination is approximately 7.1 km north of town A.

c) To find the distance and bearing of the cyclist's destination from town A, we can use the Pythagorean theorem and trigonometry. The displacement vector is the hypotenuse of a right triangle with legs of length 17.1 km and 7.1 km, so its length is:

\($$\text{Displacement} = \sqrt{(17.1\text{ km})^2 + (7.1\text{ km})^2} \approx 18.6\text{ km}$$\)

To find the bearing of the displacement vector, we can use the inverse tangent function:

\($$\text{Bearing} = \tan^{-1}\left(\frac{\text{East displacement}}{\text{North displacement}}\right) \approx 67^\circ$$\)

However, this angle is measured clockwise from north, so we need to subtract it from 360° to get the bearing measured counterclockwise from north:

\($$\text{Bearing} = 360^\circ - 67^\circ = 293^\circ$$\)

So the cyclist's destination is approximately 18.6 km away from town A on a bearing of 293°.

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Answer:

1.6

So one whole orange and a sixth of another orange

Step-by-step explanation:

The group you wish to generalize your results to is called the population (option b).

In statistical terms, the population refers to the entire set of individuals, items, or elements that possess certain characteristics of interest and from which a sample is drawn.

When conducting research or experiments, it is often not feasible or practical to collect data from the entire population due to factors such as time, cost, and accessibility.

Instead, a smaller subset known as a sample is selected to represent the larger population.

The purpose of sampling is to obtain information about the population by studying a more manageable and representative subset.

The goal is to make inferences and draw conclusions about the population based on the characteristics observed in the sample.

Generalizing the results from a sample to the population involves assuming that the sample is representative and accurately reflects the larger population.

Statistical techniques and methods are used to estimate population parameters, such as means, proportions, or relationships between variables, based on the data collected from the sample.

It is important to recognize that the accuracy of generalizations depends on the quality of the sample and the sampling methods employed. Additionally, sampling error (option c) refers to the variability or discrepancy between sample statistics and population parameters, which is inherent in the process of sampling.

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The statement that shows equivalent measurements is "52 meters = 520 decimeters." Option C.

To determine the equivalent measurements, we need to understand the relationship between different metric units.

In the metric system, each unit is related to others by factors of 10, where prefixes indicate the magnitude. For example, "deci-" represents one-tenth (1/10), "centi-" represents one-hundredth (1/100), and "kilo-" represents one thousand (1,000).

Let's analyze each statement:

5.2 meters = 0.52 centimeters: This statement is incorrect. One meter is equal to 100 centimeters, so 5.2 meters would be equal to 520 centimeters, not 0.52 centimeters.

5.2 meters = 52 decameters: This statement is incorrect. "Deca-" represents ten, so 52 decameters would be equal to 520 meters, not 5.2 meters.

52 meters = 520 decimeters: This statement is correct. "Deci-" represents one-tenth, so 520 decimeters is equal to 52 meters.

5.2 meters = 5,200 kilometers: This statement is incorrect. "Kilo-" represents one thousand, so 5.2 kilometers would be equal to 5,200 meters, not 5.2 meters.

Based on the analysis, the statement "52 meters = 520 decimeters" shows equivalent measurements. So Option C is correct.

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Note the correct and the complete question is

Select the statement that shows equivalent measurements.

A.) 5.2 meters = 0.52 centimeters

B.) 5.2 meters = 52 decameters

C.) 52 meters = 520 decimeters

D.) 5.2 meters = 5,200 kilometers

Answer:

The OUT for -3 is 6, and the OUT for 1 is 2.

Step-by-step explanation:

The rule is for any x, OUT(x) = IN(x) * (x+1)

Below is showing the rule:

IN=2: 2*3=6

IN=4: 4*5=20

IN=10: 10*11=110

etc.

If I helped, a brainliest would be greatly appreciated!

Answer:

2a²+a-6

Step-by-step explanation:

you have to simplify it using the foil method

Answer:

2x + 2

Step-by-step explanation:

LOLOL☝️answer is up there☝️LOLOL

Answer:

$9257.5

Step-by-step explanation:

plug into the equation  known variables

Answer:

2257.50

Step-by-step explanation:

B=p(1+r)^t

p= principal amount= $7000 in the saving account

r= interest rate= 15%= .15

t- number of years = 2

B= 7000(1+.15)^2

B= 7000(1.15)^2

B= 7000(1.15)(1.15)

B= 9257.50

She has a total of 927.50 dollars in the account after two years. To find out how much of that is interest we take the Balance and subtract what she invested.

B-p= 9257.50-7000= 2257.50 earned in interest.

Answer:

4 1/4

Step-by-step explanation:

Hey there!☺

Look at image attached below!

Please flip the image if you want to see it properly.

Hope this helps!

The molarity of sodium sulfate in the resulting solution is 0.259 M. To determine the molarity (M) of the sodium sulfate solution, we need to calculate the number of moles of Na2SO4 present in the 4.05 g sample and then divide it by the volume of the solution in liters.

First, we calculate the number of moles of Na2SO4 using its molar mass. The molar mass of Na2SO4 is calculated as follows: 2(Na) + 1(S) + 4(O) = 2(22.99 g/mol) + 32.07 g/mol + 4(16.00 g/mol) = 142.04 g/mol.

Next, we convert the mass of the sample to moles by dividing it by the molar mass:

moles of Na2SO4 = 4.05 g / 142.04 g/mol = 0.0285 mol.

The volume of the solution is given as 125 mL, which is equivalent to 0.125 L.

Finally, we divide the number of moles of Na2SO4 by the volume in liters to obtain the molarity:

Molarity (M) = moles of Na2SO4 / volume of solution (in liters) = 0.0285 mol / 0.125 L = 0.228 M.

Therefore, the molarity of sodium sulfate in the resulting solution is 0.259 M.

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Answer:

a. 16

b. 26

c. (11,13) and (17,19)

d. 3,8,12

Step-by-step explanation:

1. 2x8 = 16, sum of 1 +6 ( 2 digits)= 7

2. 2+3+5+7+11= 28

3. 10 to 20 ( 11,13,17,19) so we can make a pair that has difference of 2 like (11,13)

4. I will attach

The statement is true. Information system planning is aimed at determining how a company will utilize and control its information system resources in order to achieve its strategic goals.

Information system planning involves the process of outlining the strategies and actions required to effectively leverage information system resources within an organization. It encompasses various aspects such as identifying the information needs of the business, assessing available resources, defining goals and objectives, and formulating a roadmap for implementing and managing the information systems. The primary purpose of this planning is to align the use of information system resources with the overall strategic objectives of the firm. By doing so, organizations can ensure that their information systems are utilized efficiently, enabling them to make informed decisions, improve operational efficiency, enhance competitiveness, and support the achievement of strategic goals. Therefore, the statement stating that the main objective of information system planning is to clarify how a firm intends to use and manage information system resources to fulfill its strategic objectives is indeed true.

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The dimensions of the rectangle are 6 miles by 12 miles

From the question, we have the following parameters

Width = 6 miles less than the length

Area = 72 square miles

The above parameters can be represented as

A = 72

w = l - 6

The area of a rectangle is calculated using

Area = Length * Width

Substitute w = l - 6 in Area = Length * Width

A = l * (l - 6)

So, we have

l^2 - 6l = A

This gives

l^2 - 6l = 72

Rewrite as

l^2 - 6l - 72 = 0

Expand

l^2 + 6l - 12l - 72 = 0

Factorize

l(l - 6) - 12(l - 6) = 0

This gives

(l - 12)(l - 6) = 0

Solve for l

l = 12 and l = 6

When l = 6, w = l - 6 will be 0

So, we have

l = 12

Substitute l = 12 in w = l - 6

w = 12 - 6

Evaluate

w = 6

Hence, the rectangle's dimensions are 6 miles by 12 miles

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Chance is 1/10

Given that the die has 20 different numbers, ranging from 1-20, we are to determine the chance that the top side will be either a 9 or a 10.When throwing a die with a different number of faces or sides, each face has an equal chance of showing up as the top side. Thus, to determine the chance that the top side will be either a 9 or a 10, we need to find the probability of rolling a 9 or 10.To calculate the probability of a single event occurring, we divide the number of favorable outcomes by the total number of possible outcomes. Thus, in this case, the probability of rolling a 9 or a 10 would be:Probability of rolling a 9 or a 10= number of favorable outcomes/ total number of possible outcomesNumber of favorable outcomes: 2 (since there are only 2 sides of the die that have a 9 or a 10)Total number of possible outcomes: 20 (since there are 20 different numbers on the die)Probability of rolling a 9 or a 10 = 2/20 = 1/10Therefore, the chance that the top side will be either a 9 or a 10 is 1/10.

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Answer:

HOPE THIS HELPS!

Step-by-step explanation:

The Empirical Rule or 68-95-99.7% Rule gives the approximate percentage of data that fall within one standard deviation (68%), two standard deviations (95%), and three standard deviations (99.7%) of the mean. This rule should be applied only when the data are approximately normal.

The 68% of the data will fall between 20 and 100.

According to statistics, the empirical rule indicates that 99.7% of data in a normal distribution falls within three standard deviations of the mean. In order to do this, 68% of the observed data will fall within the first standard deviation, 95% within the second deviation, and 97.5% within the third standard deviation.

According to 68-95-99.7% Rule, often known as the empirical rule, indicates about what proportion of data are within one standard deviation (68%), two standard deviations (95%), and three standard deviations (99.7%) of the mean.

Only when the data are substantially normal should this rule be used.

Then, the values 20 and 100 will approximately 68% of the data.

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Answer:

4.35 pounds each gets

Step-by-step explanation:

if you divide 17.4 by 4 you get 4.35 pound per each of the 4 people get