If you're asked how much a 3-week vacation in Canada is worth, on which function of money will you base your answer

The amount received by each person are:

Amount that Wendy will receive is:  $25

Amount that Irene will receive is: $30

The steps to solve this ratio problem are as follows:

Step 1: Add together the parts of the ratio to find the total number of shares.

Step 2: Divide the total amount by the total number of shares.

Step 3: Multiply by the number of shares required.

We are given that:

Age of Wendy = 10

Age of Irene = 12

Total amount to share = 55 cedis

Thus:

Amount that Wendy will receive = (10/22) * 55 = $25

Amount that Irene will receive = (12/22) * 55 = $30

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The area of the circular stained glass window is approximately 28.27 square meters.

To find the area of a circle, we use the formula A = πr², where A is the area and r is the radius of the circle. In this problem, the radius of the circular stained-glass window is given as 3 meters. So, we can plug in this value into the formula to find the area.

A = πr²

A = π(3)²

A = π(9)

A ≈ 28.27 square meters

Therefore, the area of the stained-glass window is approximately 28.27 square meters. This means that if you were to cut the circular window out of a piece of material, the resulting piece would have an area of approximately 28.27 square meters. This calculation is important to understand how much material is needed to make the window, as well as to determine the cost of the materials.

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1. The volume of a cylinder is 351.68 inches³

2. The volume of a sphere is 14.13 unit³.

3. The volume of a cone is 1071 unit³

The formula for the volume of a cylinder is:

V = πr^2h

= 3.14 × 4² × 7

= 351.68 inches³

The formula for the volume of a sphere is:

V = (4/3)πr^3

= 4/3 × 3.14 × 1.5³

= 14.13 unit³

The formula for the volume of a cone is:

= 1/3 × πr²h

= 1/3 × 3.14 × 8² × 16

= 1071 unit³

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In ANOVA (Analysis of Variance), treatments refer to different levels of a factor. A factor is a variable that is controlled or manipulated in an experiment to study its effect on the dependent variable, which is the variable that is being measured. The different levels of a factor correspond to different values or settings of that factor.

For example, in a study comparing the effectiveness of three different drugs for treating a particular condition, the factor would be the drug treatment, and the three different drugs would be the levels of that factor (i.e., the treatments). The dependent variable in this case might be the patient's symptom improvement.

So, in summary, treatments in ANOVA refer to different levels of a factor that are manipulated to study their effect on the dependent variable.

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Answer:

S = 4π(7^2) = 196π square meters

There were 196 children and 110 adults admitted to the amusement park on that day.

Let's use variables to represent the number of children and adults admitted.

Let's say that "c" represents the number of children and "a" represents the number of adults.

We know from the problem that the admission fee for children is $3.00 and the admission fee for adults is $6.00.

So the total admission fee collected can be represented by the equation:

3c + 6a = 1248

We also know that the total number of people admitted is 306, so:

c + a = 306

Now we can use algebra to solve for "c" and "a".

We can rearrange the second equation to solve for "c":

c = 306 - a

Then we can substitute this expression for "c" into the first equation:

3(306 - a) + 6a = 1248

Expand the parentheses:

918 - 3a + 6a = 1248

Combine like terms:

3a = 330

Divide both sides by 3:

a = 110

So there were 110 adults admitted.

We can use the second equation to find the number of children:

c + a = 306

c + 110 = 306

Subtract 110 from both sides:

c = 196

So there were 196 children admitted.

Therefore, there were 196 children and 110 adults admitted to the amusement park on that day.

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Constructing a confidence interval for a proportion requires a random sample, a sample size of at least 30, and a minimum of 10 successes and failures. These conditions can be checked using p-hat, and if they are met, a confidence interval can be calculated using the formula and the appropriate critical value.

Constructing a confidence interval for a proportion requires several conditions to be met. First, the sample used for the proportion must be selected randomly to ensure that it is representative of the population. Second, the sample size must be sufficiently large to meet the requirements of the Central Limit Theorem (CLT), which assumes that the sample size is greater than or equal to 30. Third, the number of successes and failures in the sample must be at least 10 to ensure that the sampling distribution is approximately normal.

To check if these conditions have been met, we use p-hat, which is the sample proportion. The sample proportion should be calculated and used in the confidence interval formula. Additionally, we should check that the sample size is greater than or equal to 30 and that the number of successes and failures is at least 10.

If the conditions are met, we can construct a confidence interval for a proportion using the formula: p-hat ± z* (standard error), where z* is the critical value of the standard normal distribution at the desired level of confidence and the standard error is calculated as the square root of (p-hat * (1-p-hat) / n).

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The account would be worth approximately $62,420.80, which includes both the initial investment of $36,000 and the accumulated interest.

Assuming that the $200 has been added each month for the past 15 years, the total amount of money invested would be $200 x 12 months x 15 years = $36,000.
To calculate the amount of money earned from the 4% interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal (the initial investment), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
Plugging in the values, we get:
A = $36,000(1 + 0.04/12)^(12*15)
Simplifying, we get:
A = $36,000(1.0033)^180
A = $36,000(1.7328)
A = $62,420.80
Therefore, after 15 years, the account would be worth approximately $62,420.80, which includes both the initial investment of $36,000 and the accumulated interest.

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The balance of the account after 15 years is given as follows:

$49,218.

The balance of an account, considering periodic deposits, is given as follows:

[tex]B = \frac{P\left(\left(1 + \frac{r}{n}\right)^{nt}-1\right)}{\frac{r}{n}}[/tex]

The meaning of each parameter is given as follows:

The parameter values for this problem are given as follows:

P = 200, r = 0.04, n = 12, t = 15.

Hence the balance of the account after 15 years is given as follows:

[tex]B = \frac{P\left(\left(1 + \frac{r}{n}\right)^{nt}-1\right)}{\frac{r}{n}}[/tex]

[tex]B = \frac{200\left(\left(1 + \frac{0.04}{12}\right)^{12 \times 15}-1\right)}{\frac{0.04}{12}}[/tex]

B = 49,218.

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The mean, variance, and standard deviation of the number of federal government employees who use e-mail are 172, 34.4, and 5.87, respectively.

Given that 80% of federal government employees use e-mail, the probability of an individual employee using e-mail is:

p = 0.80.

If a sample of 215 federal government employees is selected, the number of employees who use e-mail, X, follows a binomial distribution with parameters n = 215 and p = 0.80.

The mean of the number of employees who use e-mail is:

μ = np

= (215)(0.80)

= 172

The variance of the number of employees who use e-mail is:

[tex]\sigma ^2 = np(1-p) = (215)(0.80)(0.20) = 34.4[/tex]  

The standard deviation of the number of employees who use e-mail is:

[tex]\sigma = \sqrt{(\sigma ^2) } = \sqrt{(34.4) } = 5.87[/tex]  (rounded to two decimal places).

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Answer:

$4.00

Step-by-step explanation:

To calculate the mean for the four Fridays in March, you add each payment she received and then divide it by the number of times she was paid:

(15.50+26.75+30.00+27.25) / 4 = 24.875

To calculate the mean for the Fridays in April, I did something different. I computed the mean in the same way, but I chose not to include the extra 16 in the division.

(15.50+26.75+30.00+27.25+16.00) / 4 = 28.875.

28.875 - 24.875 = $4.00

Extra explanation:

If you are wondering why I didn't include 16 in the division for the second part of the problem, it's because it would lead to a negative.

If I included 16 in the division, the result would have led to 23.1.

23.1 - 24.875 = -1.775

1. Null hypothesis: The mean age of purchasers and non-purchasers of toothpaste is the same. Alternative hypothesis: The mean age of purchasers and non-purchasers of toothpaste is significantly different.

2. The test statistic T can be calculated using the formula T = (X1 - X2) / (S1^2/n1 + S2^2/n2)^0.5, where X1 and X2 are the mean ages of purchasers and non-purchasers, S1 and S2 are the standard deviations of purchasers and non-purchasers, and n1 and n2 are the sample sizes. In this case, T = (37.21 - 30.7) / (6.612/50 + 8.35^2/50)^0.5 = 4.035.

3. The p-value can be calculated using a t-distribution with 98 degrees of freedom (since we have two samples of size 50 and therefore 98 degrees of freedom). Using Excel, the p-value is 0.0001.
4. The critical value can be found using a t-distribution with 98 degrees of freedom and a significance level of 0.01. Using Excel, the critical value is 2.364.

5. Since the calculated test statistic (T = 4.035) is greater than the critical value (2.364), we reject the null hypothesis and conclude that the mean age of purchasers and non-purchasers of toothpaste is significantly different at the 1% significance level.

6. Therefore, we can conclude that age is a significant factor in determining whether someone purchases toothpaste or not. Further research may be necessary to investigate other factors that may influence purchasing decisions. The attached Excel file includes all calculations and output.

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The expected value and the variance of the number of inspected bottles with serious defects of 0.18.

To find the expected value and variance of the number of inspected bottles with serious defects, we first need to define the probability distribution for this situation. Since the probability of each bottle having a serious defect is independent of the others, we can use the binomial distribution.

Let's define the following variables:

- X: the number of inspected bottles with serious defects
- p: the probability of a single bottle having a serious defect (0.1)
- n: the sample size (2)

Using the formula for the binomial distribution, we can find the expected value and variance of X:

- Expected value (E[X]) = n * p = 2 * 0.1 = 0.2
- Variance (Var[X]) = n * p * (1 - p) = 2 * 0.1 * (1 - 0.1) = 0.18

This means that we expect to find 0.2 bottles with serious defects on average out of the two inspected bottles. However, there is some variability in this number due to chance, which is represented by the variance of 0.18.

It's important to note that these calculations assume that the sampling is done randomly and independently and that the production line does not change its defect rate during the inspection period. If these assumptions are violated, the expected value and variance may not be accurate.

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A philosophy professor assigns letter grades on a test according to the following scheme is A score that falls within the top 12% of all scores on the test would receive an A grade. A.

The grading scheme for the philosophy professor is:

A: Top 12% of scores

B: Scores below the top 12% and above the bottom 58%

C: Scores below the top 42% and above the bottom 25%

D: Scores below the top 75% and above the bottom 8%

F: Bottom 8% of scores

To clarify, the percentages given in the scheme are used to determine the cutoffs for each letter grade.

A score that falls within the top 12% of all scores on the test would receive an A grade.

It is important to note that the percentages given in the grading scheme are not fixed values, but rather are dependent on the distribution of scores on the test.

For instance, if the scores on the test were very tightly clustered together, it is possible that the cutoff for an A grade might be higher than the top 12%.

This grading scheme rewards students who perform well on the test while still allowing for some degree of variation in scores.

Students perform poorly relative to their peers may receive a lower letter grade but are still given the opportunity to learn and improve in future assignments.

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When analyzing categorical data, it is often useful to examine the relationship between two variables. Crosstabs, or contingency tables, are commonly used to display the counts of observations in each combination of the two variables. However, these raw counts can be difficult to interpret, especially if the totals for each variable are different.
By transforming the counts into percentages of row or column totals, we can better understand the patterns and relationships in the data. Percentages allow us to compare the proportions of one variable within each category of the other variable, regardless of the total number of observations. This can help us identify any trends or patterns in the data that may not be immediately apparent from the raw counts.

For example, suppose we have a crosstab of gender and favorite color. The raw counts may show that more females than males prefer blue, but it's difficult to know if this difference is meaningful without knowing the total number of males and females in the sample. By transforming the counts to percentages of row totals, we can see that 40% of females prefer blue, while only 30% of males do. This suggests that there may be a relationship between gender and favorite color.

Overall, transforming raw counts into percentages of row or column totals can help us better understand the relationship between two categorical variables, especially when the totals are different.

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Equating the two expressions representing the total charges for each plan, it will take 475 minutes for the cost of the two plans to be equal.

Mathematical expressions combine variables with constants, values, and numbers without using the equal symbol (=).

On the other hand, equations are two or more mathematical expressions that are shown to be equal or equivalent.

                            First Plan    Second Plan

Monthly fee              $19               $0

Unit fee per minute $0.10           $0.14

Let the minutes under each Plan = x

19 + 0.10x ...Expression for Plan 1

0.14x ...Expression for Plan 2

For the cost of the two plans to be equal,

19 + 0.10x = 0.14x

19 = 0.04x

x = 475

Check for Total Costs:

Plan 1: 19 + 0.10x = 19 + 0.10(475) = $66.50

Plan 2: 0.14x = 0.14(475) = $66.50

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Grace's skillset includes the ability to tie a square knot and operate an automobile with a standard transmission. These abilities demonstrate her proficiency in manual tasks and mechanical knowledge.

It is important to note that these skills may not be relevant in all situations, but they can be useful in specific circumstances. For example, the square knot may be used in camping or boating, while the standard transmission automobile may be preferred by some drivers for its greater control and fuel efficiency.

Overall, Grace's skills highlight her versatility and adaptability in various settings. A square knot is a secure, binding knot used in various applications, while a standard transmission refers to a manual gearbox in an automobile, requiring the driver to change gears manually. Both of these skills showcase her adaptability and competence in diverse area.

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Both methods give similar intervals that do not overlap with 0.5, the expected proportion under the null hypothesis of no difference between green and white flowers, indicating a significant deviation from the null hypothesis.

To calculate a confidence interval for the proportion of pea plants with green flowers in Mendel's experiment, we can use the following methods:

Normal approximation method:

This method assumes that the distribution of the sample proportion is approximately normal when the sample size is large enough (n ≥ 30) and the proportion is not too close to 0 or 1.

The formula for the confidence interval is: [tex]\bar p+ za/2 \times \sqrt{(\bar p(1-\bar p/n)}[/tex], where  is the sample proportion, zα/2 is the critical value from the standard normal distribution corresponding to the desired level of confidence (e.g., 1.96 for 95% confidence), and n is the sample size.

Substituting the values from Mendel's experiment, we get: 0.249 ± 1.96 × √(0.249×0.751/8000) = (0.227, 0.271) at 95% confidence level.

Clopper-Pearson method:

This method provides a conservative confidence interval that guarantees the true proportion is within the interval with at least the desired level of confidence.

The formula for the confidence interval is: , where B is the inverse cumulative distribution function of the beta distribution with parameters [tex]n(1-\bar p)+1 and n\bar p+1[/tex], and α is the significance level (e.g., 0.05 for 95% confidence).

Substituting the values from Mendel's experiment, we get: [0.232, 0.267] at 95% confidence level.

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The word problem described by this division expression would be: "A grocery store sold 144 pieces of fruit, with 12 more apples sold than oranges. How many oranges were sold?"

One afternoon, a local grocery store sold 144 pieces of fruit, which included both apples and oranges. If there were 12 more apples sold than oranges, how many oranges were sold?

To solve this problem, we can use division by dividing the total number of fruits sold by the difference in the number of apples and oranges sold. The division expression would be:

Number of oranges sold = (total number of fruits sold) ÷ (difference in the number of apples and oranges sold)

So, the word problem described by this division expression would be: "A grocery store sold 144 pieces of fruit, with 12 more apples sold than oranges. How many oranges were sold?"

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A prediction interval is an interval estimate of an individual y value, given values of the independent variables.

A prediction interval is an interval estimate that quantifies the uncertainty associated with a single future observation of the dependent variable (y), given a set of values for the independent variables.

The prediction interval takes into account both the error inherent in the model and the variability of the individual observations.

So, a prediction interval provides a range of plausible values for an individual observation, based on the model's prediction and the uncertainty associated with it.

It is wider than a confidence interval because it includes the variability of the individual observations in addition to the uncertainty in the model.

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To find the distance between the foot of the ladder and the wall, we'll use trigonometry.

We have the height of the wall (10 m), the angle between the ladder and the ground (58 degrees), and we want to find the distance from the foot of the wall. We can use the sine function:

sin(angle) = opposite / hypotenuse

In this case, the angle is 58 degrees, the opposite side is the height of the wall (10 m), and the hypotenuse is the length of the ladder. We want to find the adjacent side, which is the distance between the foot of the ladder and the wall. We'll use the cosine function:

cos(angle) = adjacent / hypotenuse

First, find the length of the ladder (hypotenuse) using the sine function:

sin(58) = 10 / hypotenuse
hypotenuse = 10 / sin(58) ≈ 11.71 m

Now, use the cosine function to find the adjacent side:

cos(58) = adjacent / 11.71
adjacent = cos(58) × 11.71 ≈ 6.5 m

So, the ladder is approximately 6.5 meters away from the foot of the wall to the nearest tenth.

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Thus, add approximately 709.76 milliliters of water to a pint of a 5% w/v solution to make a 2% w/v solution.

To prepare a 2% w/v solution from a 5% w/v solution, you will need to perform a dilution using the appropriate amount of water.

Here's are steps to determine the amount of water to add:

1. First, let's set up the dilution formula: C1V1 = C2V2, where C1 is the initial concentration (5%), V1 is the initial volume (1 pint), C2 is the final concentration (2%), and V2 is the final volume.

2. Convert the volume from pints to milliliters: 1 pint = 473.176 milliliters (approximately).

3. Plug in the values into the formula: (5%)(473.176 mL) = (2%)(V2).

4. Solve for V2: V2 = (5%)(473.176 mL) / (2%) = 1182.94 mL (approximately).

5. Calculate the amount of water to add: V2 - V1 = 1182.94 mL - 473.176 mL = 709.764 mL (approximately).

Therefore, you should add approximately 709.76 milliliters of water to a pint of a 5% w/v solution to make a 2% w/v solution.

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This information can be useful for comparing and analyzing test scores, especially when comparing scores from different tests or different populations.

To find the standardized values for students scoring 540, 600, 650, and 700 on the test, we need to use the formula for z-score:
z = (x - mean) / standard deviation
Assuming that the test scores follow a normal distribution with a mean of 500 and a standard deviation of 100 (which are common values for standardized tests), we can calculate the z-scores as follows:
For a score of 540:
z = (540 - 500) / 100 = 0.4
For a score of 600:
z = (600 - 500) / 100 = 1
For a score of 650:
z = (650 - 500) / 100 = 1.5
For a score of 700:
z = (700 - 500) / 100 = 2
These standardized values represent the number of standard deviations that each score is away from the mean. A z-score of 0 means that the score is exactly at the mean, while a z-score of 1 means that the score is one standard deviation above the mean, and so on.
Therefore, we can interpret these standardized values as follows:
- A score of 540 is 0.4 standard deviations above the mean.
- A score of 600 is 1 standard deviation above the mean.
- A score of 650 is 1.5 standard deviations above the mean.
- A score of 700 is 2 standard deviations above the mean.

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1. The length of x and y are 5 and 8.66 respectively

2. The area of the equilateral triangle is 9√3 cm²

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

sin30 = x/10

0.5 = x/10

x = 0.5×10

x = 5

sin60 = y/10

0.866 = y/10

y = 0.866 × 10

y = 8.66

2. The height of the triangle = √6²-3²

= √36-9

= √27

= 3√3

area = 1/2bh

= 1/2 × 6 × 3√3

= 9√3 cm²

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The  sum of the series is -800.

The given series [infinity]∑k=1 9k(k+2) diverges.

To see why, we can use the divergence test. The divergence test states that if the limit of the terms of a series does not approach zero, then the series diverges.

In this case, let's look at the limit of the terms of the series:

lim k → ∞ 9k(k+2)

We can see that this limit approaches infinity as k approaches infinity, since the growth rate of k(k+2) is greater than that of 9k. Therefore, the series diverges.

As for the second series, [infinity]∑n=0(−1)n4n−3(2n+1)!, it converges.

To see why, we can use the ratio test. The ratio test states that if the limit of the ratio of consecutive terms is less than 1, then the series converges absolutely.

Let's apply the ratio test to our series:

|(-1)^(n+1) 4^(n+1) (2n+3)! / (4^n (2n+1)!)| = |(-1)^(n+1) (2n+3)(2n+2)/(4(2n+1)(2n+2))|

= |(-1)^(n+1) (2n+3)/(4(2n+1))|

As n approaches infinity, the absolute value of this ratio approaches 1/2, which is less than 1. Therefore, the series converges absolutely.

To find the sum of the series, we can use the formula for the sum of an alternating series:

S = a1 - a2 + a3 - a4 + ...

where a1 = 4!/1!, a2 = 4^3(3!) / (2!) and so on.

Plugging in the values, we get:

S = 4! - (4^3)(3!) / (2!) + (4^5)(5!) / (4!) - (4^7)(7!) / (6!) + ...

Simplifying each term, we get:

S = 24 - 96 + 384 - 1792 + ...

S = -800

Therefore, the sum of the series is -800.

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When the variables in an equation cancel out and the final sentence is false, the equation has no solutions.

For example, consider the equation:
[tex]2x - 4 = x - 2[/tex]

If we subtract x from both sides, we get:
[tex]x - 4 = -2[/tex]

Now, add 4 to both sides:
[tex]x = 2[/tex]

In this case, the variables did not cancel out, and we have a valid solution, x = 2. However, let's look at a different example:
[tex]x - 3 = x - 5[/tex]

If we subtract x from both sides, the variables cancel out, and we are left with:
[tex]-3 = -5[/tex]

Since this final sentence is false (-3 is not equal to -5), we can conclude that the original equation has no solutions.

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The area of the trapezoid in this problem is given as follows:

A = 102.98 ft².

The area of a trapezoid is given by half the multiplication of the height by the sum of the bases, hence:

A = 0.5 x h x (b1 + b2).

The dimensions for this problem are given as follows:

h = 7.6 ft, b1 = 9.6 ft, b2 = 17.5 ft.

Hence the area of the trapezoid is given as follows:

A = 0.5 x 7.6 x (9.6 + 17.5)

A = 102.98 ft².

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Some of the most common symbols used in formulas include (addition), - (subtraction), * (multiplication), and / (division). These are called "operators". The correct option is c) operators.

Operators are symbols that represent a specific operation to be performed on one or more values or variables. In mathematics and programming, operators are used to build expressions that represent calculations. The most common operators include addition (+), subtraction (-), multiplication (*), and division (/), which are used to perform basic arithmetic operations.

Other operators include exponents (^), modulus (%), and comparison operators (>, <, =, etc.), which are used for more complex operations. Understanding operators is an essential part of learning mathematics and programming, as they form the building blocks for more complex calculations and algorithms. The correct option is c) operators.

The complete question is:

Fill in the blank: Some of the most common symbols used in formulas include + (addition), - (subtraction), * (multiplication), and / (division). These are called _____.

a) references

b) domains

c) operators

d) counts

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Answer:

The sum of the interior angles of a polygon with n sides is given by:

Sum = (n - 2) * 180

We are given that the sum of the interior angles is 1800 degrees. Setting these two expressions equal to each other, we get:

(n - 2) * 180 = 1800

Dividing both sides by 180, we get:

n - 2 = 10

Adding 2 to both sides, we get:

n = 12

Therefore, the polygon has 12 sides.

The minimum sample size required to be 75% confident that the sample mean is within 20 units of the population mean is 24.

To determine the minimum sample size required for 75% confidence that the sample mean is within 20 units of the population mean, you will need to use the formula for sample size calculation in a normally distributed population:
n = (Z * σ / E)^2
where:
n = sample size
Z = Z-score corresponding to the desired confidence level (75%)
σ = population standard deviation (327.8)
E = margin of error (20 units)
First, find the Z-score for a 75% confidence level. This value is 1.15 (you can find it in a Z-table or using statistical software).
Next, plug in the values into the formula:
n = (1.15 * 327.8 / 20)^2
n ≈ 23.27
Since the sample size should be a whole number, round up to the nearest whole number:
n = 24

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Answer: Angle C

Step-by-step explanation:

In any triangle, the side opposite the largest angle is always the longest side.

Here, angle C has the largest measurement of 70 degrees. Therefore, the longest side of triangle ABC will be opposite angle C.