(100 points so hurry)What is the length of NA?
O2 units
09 units
11 units
14 units

Answer:

3 miles

Step-by-step explanation:

1/8*24=3

Answer:

Step-by-step explanation:

He ran 24 times around the track1

Circumfrence of track=1/8 Mile

Total distance he covered=1/8*24

Distance = 3 miles

The length of the rectangular  playground is 241.86 foot.

Given that area of rectangle is 19,500 sq.ft and length of rectangle is three times its width.The area for rectangle is given by formula: A=LW.

Now according to the given condition, L= 3W. Further we'll solve by putting L= 3W in the formula for rectangle.

A=LW

As given A= 19,500 sq.ft and considering L=3W,

19,500 = 3W*W

19,500 = 3W^2

∴ W^2 = 6500

∴ W = \(\sqrt{6500}\)

∴ W = 80.6225 ft. ≈ 80.62 ft.

Now putting the value W = 80.62 in equation L =3W,

L = 3* 80.62

L = 241.86 ft.

The length of the rectangular playground is 241.86 foot.

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Part 1: Kate should buy 100 coats to maximize profits.Part 2: The probability that the coats sell out is 0.25 (25%), and the probability that they do not sell out is 0.75 (75%).

To maximize profits, Kate should consider the scenario where she sells all the coats without any left over at the end of the season.

Since the sales are uniformly distributed between 100 and 400, buying 100 coats ensures that she meets the minimum expected sales of 100. Purchasing more than 100 coats would increase costs without a guarantee of higher sales, potentially leading to excess inventory and lower profits.

Given that the sales are uniformly distributed between 100 and 400 coats, Kate's purchase of 100 coats covers the minimum expected sales.

The probability of selling out can be calculated by finding the proportion of the range covered by the desired sales (100 out of 300). Therefore, the probability of selling out is 100/300 = 0.25 or 25%. The probability of not selling out is the complement, which is 1 - 0.25 = 0.75 or 75%.

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Answer:

P will remain the same

Step-by-step explanation:

Given

\(V(t) = P(1 + r)^t\) --- Coin value formula [Missing from the question]

Required

What happens to p when r increases

The coin value function is an exponential function which is of the general  form:

\(y = a(1 + b)^x\)

From the given function: \(V(t) = P(1 + r)^t\)

P represents the initial value and r represents the rate

The rate of change (r) and the initial value (P) of a function are both independent, and they do not depend on one another for their values.

An increment or decrement in r will not affect the value of P.

Conclusively, when the rate (r) changes, the initial value (P) will remain the same.

Answer:

A) 15,21

B) -2,-7

C) 25,36

D) These numbers are square roots of 1,2,3,4,....

Hope this will help:)

Answer:

A. 1, 3, 6, 10, 15, 21

B. 8, 7, 5, 2, -2, -7

C. 1, 4, 9, 16, 25, 36

Step-by-step explanation:

A number sequence is a list of numbers governed by a rule. The rule governing the numbers is used to determine other numbers that follow in the sequence.

A. In this sequence, the rule is to increase the difference between the previous two numbers by 1 and then add the result to the last number in the sequence.

(10 - 6) + 1 = 5

5 + 10 = 15

Also (15 - 10) + 1 6

6 + 15 = 21

B. The rule here is to subtract 1 from the negative difference between the previous two numbers in the sequence and then add the result to the last number in the sequence.

(2 - 5) - 1 = -4

2 + (- 4) = -2

Also, (-2 - 2) - 1 = -5

-2 + (-5) = -7

C. The rule here is to square the numbers starting from 1.

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36 and so on.

The other endpoint of the line segment with the given endpoint and midpoint is (19, 15).

To find the other endpoint of the line segment, we can use the midpoint formula. The midpoint of a line segment is the average of the coordinates of the two endpoints. We can use this information to set up the following system of equations:

x_mid = (x₁ + x₂) / 2

y_mid = (y₁ + y₂) / 2

where (x_mid, y_mid) is the midpoint and (x₁, y₁) and (x₂, y₂) are the two endpoints.

Substituting the given values, we get:

6 = (-7 + x₂) / 2

7 = (-1 + y₂) / 2

Solve for x₂ and y₂.

12 = (-7 + x₂)

x₂ = 19

14 = (-1 + y₂)

y₂ = 15

Therefore, the other endpoint is (x₂, y₂) = (19, 15).

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In Luther v. Borden, 1849, it is true that the Supreme Court abdicated its role in clarifying whether the people had the right to abolish their state governments. The great statesman Daniel Webster argued that people do indeed possess the right to overthrow their government.

Luther v. Borden, 1849 was a United States Supreme Court case that decided whether the court should intervene in a political question, specifically the Rhode Island Dorr Rebellion of 1841 to 1842. In this case, the court declined to do so and ruled that the authority to decide whether a rebellion against a state government exists or not, rests solely with the United States government. The Court refused to support either side in the rebellion and thus upheld the lower court's decision.

The decision is well-known for declaring that the federal government must guarantee a "republican form of government" in the states. In this context, Webster argued that people possess the right to overthrow their government as they possess the ultimate sovereignty. True.

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Given that the dimensions of the poster are Length = 24 cm and Width = 36 cm. We have to find the dimensions of the poster at a fraction 1/4 times its current size. the dimensions of the poster at fraction 1/4 times its current size would be L = 6 cm and W = 9 cm.

Let's see how to solve the problem.The area of a rectangle is given by;A = Length x WidthLet the new dimensions of the poster be length = L and width = W. Then, we have;New area of the rectangle = 1/4 x current area of the rectangleSubstituting the values we get;New area = 1/4 x (Length x Width)New area = 1/4 x (24 cm x 36 cm)New area = 1/4 x 864 sq cmNew area = 216 sq cm

As we know that the area of a rectangle is given by the product of its length and width. Hence, L x W = 216 sq cm.We also know that the new dimensions of the poster are 1/4 times the current dimensions of the poster. Thus;L = 1/4 x 24 cmL = 6 cmW = 1/4 x 36 cmW = 9 cmTherefore,

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The domain and range of the function are [-3, 3] and [-2, 4], respectively and The function values for (a) f(-1), (b) f(0), (c) f(1) and (d) f(2) are 0, -2, 4, and 3, respectively. The total number of words used is 163.

Given that the graph of the function is shown below, the domain and range of the function need to be determined along with finding the function values for (a) f(−1), (b) f(0), (c) f(1) and (d) f(2).Graph of the function:Graph of the function for the given graph of the function, we can observe that the domain of the function is from -3 to 3 as the graph is defined within these limits.In order to find the range of the function, we need to look at the range of the y-coordinates.

The minimum value of y is -2 and maximum value of y is 4.Range of the function: [-2, 4]a) f(-1) means the function value for x = -1. As we can observe from the graph, the point where x = -1 is on the graph of the function is (1, 0). Therefore, f(-1) = 0b) f(0) means the function value for x = 0. As we can observe from the graph, the point where x = 0 is on the graph of the function is (0, -2).

Therefore, f(0) = -2c) f(1) means the function value for x = 1. As we can observe from the graph, the point where x = 1 is on the graph of the function is (2, 4). Therefore, f(1) = 4d) f(2) means the function value for x = 2. As we can observe from the graph, the point where x = 2 is on the graph of the function is (3, 3). Therefore, f(2) = 3

Thus, the domain and range of the function are [-3, 3] and [-2, 4], respectively. The function values for (a) f(-1), (b) f(0), (c) f(1) and (d) f(2) are 0, -2, 4, and 3, respectively. The total number of words used is 163.

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By using function, it can be concluded that-

The predictor variables are bed, bath, floor

What is function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

In a function y = f(x), x is the independent variable and y is the dependent variable.

The price of an apartment is dependent on the number of bedrooms, bathrooms and the floor of the apartment

So the required function is p = f(bed, bath, floor) where p is the price of the apartment

The predictor variables are bed, bath, floor

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Mrs. Hough would need 31.5 feet of fencing for the other three sides of the garden.

To calculate the amount of fencing needed for Mrs. Hough's raised garden, we first need to determine the dimensions of the garden.

Since the garden is next to a 13.5 ft fence, we know that one side of the garden is 13.5 ft.

Let's assume the other two sides of the garden have lengths x and y.

The area of the garden is given as 121.5 sq ft, so we have the equation:

x × y = 121.5

To find the dimensions of the garden, we can solve this equation. One possible solution is x = 9 ft and y = 13.5 ft.

Therefore, the dimensions of the garden are 9 ft by 13.5 ft.

Now, to calculate the amount of fencing needed, we add up the lengths of the three sides (excluding the side next to the fence):

Fencing needed = x + y + x = 9 ft + 13.5 ft + 9 ft = 31.5 ft

Mrs. Hough would need 31.5 feet of fencing for the other three sides of the garden.

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1.) The z-score is -1.29. An NBA player whose height is 74 inches is shorter than the average.

2.) The z-score is 1.55. An NBA player whose height is 85 inches is taller than the average.

3.) A z-score of 3.6 equates to a height of approximately 93.40 inches. There are likely no NBA players this tall, so it is highly improbable that the player's z-score is 3.6.

To calculate the z-score, we use the formula: z = (x - μ) / σ, where x is the observed value, μ is the mean, and σ is the standard deviation.

1.) For a height of 74 inches:

The z-score is calculated as follows:

z = (74 - 79) / 3.89 ≈ -1.29

Interpretation: An NBA player whose height is 74 inches has a z-score of -1.29. This means that their height is approximately 1.29 standard deviations below the mean. They are shorter than the average NBA player.

2.)For a height of 85 inches:

The z-score is calculated as follows:

z = (85 - 79) / 3.89 ≈ 1.55

Interpretation: An NBA player whose height is 85 inches has a z-score of 1.55. This means that their height is approximately 1.55 standard deviations above the mean. They are taller than the average NBA player.

3.) For a reported z-score of 3.6:

To find the corresponding height, we rearrange the formula: x = z * σ + μ

x = 3.6 * 3.89 + 79 ≈ 93.40 inches

Interpretation: A reported z-score of 3.6 corresponds to a height of approximately 93.40 inches. We can determine the number of NBA players at this height by calculating the proportion of players with a z-score greater than or equal to 3.6.

Since the z-score is quite high, it is highly unlikely that there are any NBA players of this height. Therefore, it is improbable that the player's claim of having a z-score of 3.6 is accurate.

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Answer:

I don't know if this is right but 27

Step-by-step explanation:

Because 3 x 4 = 12 so that's A, and 5 x 3 = 15 so that's B. Add them together and get 27 for BA

Answer:

D

Step-by-step explanation:

A. Sin 42=0.669

Cos=52=0.617

B. Sin 90=1

cos 90=0

C. cos30=0.866

sin 70=0.940

D. sin80=0.985

cos 10=0.985

The statement " Rate of college enrollment immediately after completing high school was 67% by 1997" is an example of (a) Descriptive Statistics.

The Descriptive statistics involves the use of measures, such as averages, proportions, and frequencies, to summarize and describe the main features of a set of data.

In this statement, the rate of 67% is a summary statistic that describes the proportion of high school graduates who enrolled in college immediately after completing high school in 1997.

Whereas; the inferential statistics involves making inferences or predictions about a population based on a sample of data.

The statement provides a summary statistic for the rate of college enrollment for a specific year, 1997, but it does not provide any inferences or predictions about the rate of college enrollment for other years or other populations , so it denoted a Descriptive Statistics .

The given question is incomplete , the complete question is

What type of Statistics does the statement "the rate of college enrollment immediately after high school completion was 67" represents ?

(a) Descriptive

(b) Inferential

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The mean score for the first four matches is 44. The team will need to score 44 points in the next match to maintain the same mean score.

The given scores of the first four matches of a basketball team are 43, 55, 41 and 37 points.

We are supposed to find the mean of these scores in order to calculate the score that the team needs to maintain the same mean score.

Step 1: We can find the mean of the four scores by adding the four scores and then dividing by the number of scores.

Here we have four scores.

So we add them and then divide by 4:

Mean score = (43 + 55 + 41 + 37) / 4

= 176 / 4

= 44.

Hence, the mean of the first four scores is 44.

Step 2: To find out what score the team needs to maintain the same mean score, we will add the score in the next match and then divide by 5 (the new number of scores).

The mean score should remain at 44, so:

(43 + 55 + 41 + 37 + x) / 5

= 44

Here, we will find the value of x, which will be the score needed in the next match:

43 + 55 + 41 + 37 + x = 220 (multiplying both sides by 5)

⇒ 176 + x = 220 (adding both sides by -176)

⇒ x = 44

Therefore, the team will need to score 44 points in the next match to maintain the same mean score of 44.

So, the answer is:

The mean score for the first four matches is 44.

The team will need to score 44 points in the next match to maintain the same mean score.

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It is true that when you design an algorithm, it should be general enough to provide a solution to many problem instances, not just one or a few of them.

In mathematics, an algorithm is a process, a description of a series of steps that may be used to solve a problem; however, they are now far more prevalent than that.

Although many areas of research (and daily life) employ algorithms, long division's step-by-step process is probably the most prevalent example.

Thus, It is true that when you design an algorithm, it should be general enough to provide a solution to many problem instances, not just one or a few of them.

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If random sample of 1000 applicants, 392 applicants were accepted, then (c) interval is from 36.2% to 42.2%. Since value of 42% lies in interval, Bridgeton's claimed acceptance rate is accurate.

The "Confidence-Interval" is defined as "range-of-values" which contain the "true-value" of a population parameter with a certain probability.

To calculate the 95% confidence interval, we use the formula:

⇒ CI = p ± z × √((p(1-p))/n),

where : p = sample proportion (accepted applicants / total applicants)

⇒ z is = z-score associated with desired "level-of-confidence" (95% corresponds to z = 1.96)

⇒ n is = sample size = (1,000),

First, we calculate the "sample-proportion" (p) :

⇒ p = 392 / 1000 = 0.392,

Substituting the values,

We get,

⇒ CI = 0.392 ± 1.96 × √((0.392(1-0.392))/1000),

⇒ 0.392 ± 0.030,

So, the 95% confidence interval for the proportion of accepted applicants at Bridgeton University is (0.362, 0.422) = 36.2% to 42.2%.

Next, To evaluate whether Bridgeton's claim of accepting 42% of applicants seems accurate, we can check if the claim falls within the confidence interval.

The claim of 42% falls within the 95% confidence interval of (0.362, 0.422). So, acceptance rate claimed by Bridgeton is accurate.

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

Bridgeton University claims to accept 42% of applicants. In a random sample of 1,000 Bridgeton University applicants, 392 were accepted. Calculate the 95% confidence interval and evaluate whether Bridgeton's claim seems accurate.

(a) The interval is from 36.7% to 41.7%. Since the value of 42% does not lie in the interval, Bridgeton's claimed acceptance rate does not seem accurate.

(b) The interval is from 36.2% to 42.2%. Since almost 40% of the sample was accepted, Bridgeton's claimed acceptance rate seems accurate.

(c) The interval is from 36.2% to 42.2%. Since the value of 42% lies in the interval, Bridgeton's claimed acceptance rate seems accurate.

(d) The interval is from 36.7% to 41.7%. Since only 40% of the sample was accepted, Bridgeton's claimed acceptance rate does not seem accurate.

The question is that the number of particles of contamination per pound of material is modeled variable  by a Poisson random variable with a mean of 0.01 particle per pound.

This means that on average, there are 0.01 particles of contamination per pound of material.To study the raw materials for contamination, the number of particles per pound is observed and analyzed. This information helps determine the level of contamination in the raw materials and allows for appropriate actions to be taken if necessary.

By using a poisson random variable, it is possible to calculate the probability of a certain number of particles per pound occurring. This can help in assessing the likelihood of contamination and making informed decisions based on the observed data.In summary, raw materials are studied for contamination using a poisson random variable with a mean of 0.01 particle per pound. This allows for the analysis of the number of particles of contamination per pound and helps in assessing the level of contamination in the raw materials.

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Shimano Pty Ltd needs to sell a minimum of 300 fishing rods in 2021.

In 2021, Shimano Pty Ltd, a custom fishing rod manufacturer, sells each rod for $900. The variable costs associated with producing each rod amount to 60% of the selling price, which is $540 per rod. Additionally, the business incurs fixed costs of $108,000 for the year.

To calculate the total cost per rod, we need to consider both the variable and fixed costs. The variable cost per rod is $540, and the fixed costs for the year are $108,000. Since the fixed costs are independent of the number of rods produced, they can be spread across the total number of rods manufactured.

To determine the breakeven point, we need to find the number of rods that need to be sold to cover the total costs. The breakeven point can be calculated by dividing the total fixed costs by the contribution margin, which is the selling price minus the variable cost per unit. In this case, the contribution margin is $360 ($900 - $540).

Breakeven Point = Total Fixed Costs / Contribution Margin

Breakeven Point = $108,000 / $360

Breakeven Point = 300 rods

To cover the fixed costs and start generating a profit, Shimano Pty Ltd needs to sell a minimum of 300 fishing rods in 2021.

It's important for the company to keep track of its costs, particularly the variable costs, and carefully consider its pricing strategy to ensure profitability and sustainability in the market.

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The property was not explicitly used in this example, but it is worth noting that adding 0 to any number leaves it unchanged (i.e., a + 0 = a).

The properties that were used to simplify the expression 4 + 3(9 + 2) into 37 are:

Distributive property: The expression was rewritten as 4 + (3 × 9) + (3 × 2) by distributing the 3 over the parentheses.

Associative property: The order of the terms (3 × 9) and (3 × 2) was rearranged without changing the result because of the associative property of multiplication.

Commutative property: The order of the terms 4, 27, and 6 was rearranged without changing the result because of the commutative property of addition.

Identity property: The property was not explicitly used in this example, but it is worth noting that adding 0 to any number leaves it unchanged (i.e., a + 0 = a).

The properties used to simplify the expression are Associative property of addition, Commutative property of addition, and Distributive property and Identity property of addition. Therefore, the correct option is A, C, E and F.

The properties used to simplify the expression are as follows.

1. Distributive property (E): 4 + 3(9 + 2) = 4 + (3 × 9) + (3 × 2)

This property is applied when a number is multiplied with the sum of two or more numbers. In this case, the number 3 is distributed over the numbers 9 and 2.

2. Identity property of addition (F): 4 + 27 + 6 = 4 + 6 + 27

This property states that adding zero to any number does not change its value. Although this property isn't explicitly shown in the given steps, it is implied by the fact that we can rearrange the terms in the addition without changing their value.

3. Commutative property of addition (C): 4 + 6 + 27 = 10 + 27

This property states that changing the order of numbers in an addition does not change the sum. Here, the numbers 4 and 6 were rearranged to make it easier to add them together.

4. Associative property of addition (A): (10 + 27) = 37

This property states that the grouping of numbers in an addition does not affect the sum. In this case, the parentheses are unnecessary since the numbers were already grouped correctly.

In summary, the properties used to simplify the expression are: A) Associative property of addition, C) Commutative property of addition, and E) Distributive property and F) identity property of addition.

Note: The question is incomplete. The complete question probably is: The real number properties can be used to simplify numerical expressions. in this section, you will identify which properties were used to simplify several expressions. Which properties were used to simplify the following expression? select all that apply.

4 + 3(9 + 2)

4 + (3 × 9) + (3 × 2)

4 + 27 + 6

4 + 6 + 27

10 + 27

37

A) associative property of addition B) associative property of multiplication C) commutative property of addition D) commutative property of multiplication E) distributive property F) identity property of addition G) identity property of multiplication

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Answer:

Step-by-step explanation:

To show that `(n + 3)7 ∈ Θ(n7)`, we need to prove that `(n + 3)7 = Θ(n7)`.This can be done by showing that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)` .Now, let's prove the two parts separately:

Proof for `(n + 3)7 = O(n7)`.

We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≤ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≤ n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + n7
≤ 2n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6
≤ 2n7 + 84n6 + 441n5 + 2205n4 + 10395n3 + 45045n2 + 153609n + 729
```Thus, we can take `c = 153610` and `k = 1` to satisfy the definition of big-Oh notation. Hence, `(n + 3)7 = O(n7)`.Proof for `(n + 3)7 = Ω(n7)`We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≥ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≥ n7
```Thus, we can take `c = 1` and `k = 1` to satisfy the definition of big-Omega notation. Hence, `(n + 3)7 = Ω(n7)`.

As we have proved that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)`, therefore `(n + 3)7 = Θ(n7)`.Thus, we have shown that `(n + 3)7 ∈ Θ(n7)`.From the proof, we can see that we used the Binomial theorem to expand `(n + 3)7` and used algebraic manipulation to bound it from above and below with suitable constants. This technique can be used to prove the time complexity of various algorithms, where we have to find the tightest possible upper and lower bounds on the number of operations performed by the algorithm.

Hence, we have shown that `(n + 3)7 ∈ Θ(n7)` for non-negative integer n.

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The value of first limit is 0.

To evaluate the limit lim x→3 [(sin(4x) + x³) / (x + 3)], we substitute x = 3 into the expression:

[(sin(4(3)) + 3³) / (3 + 3)] = [(sin(12) + 27) / 6].

Since sin(12) is a bounded value and 27/6 is a constant, the numerator remains bounded while the denominator approaches a nonzero value as x approaches 3. Therefore, the limit is 0.

For the second limit, lim x→3 [(x - 5)(x² - 9) / (x - 3)], we substitute x = 3 into the expression:

[(3 - 5)(3² - 9) / (3 - 3)] = [(-2)(0) / 0].

The denominator is 0, and the numerator is nonzero. This results in an undefined expression, indicating that the limit does not exist.

Therefore, the main answer for the second limit is "The limit does not exist."

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This distance of 8.66 centimeters is the maximum separation of the tips of the hour and minute hands of an analog clock over a 24 hour period.

The distance between the two tips of the hands of an analog clock can be calculated with the Pythagorean Theorem. The difference in time between the two hands is 1 hour, or 15 degrees

1. Calculate the angle between the two hands:

1 hour = 15 degrees

2. Calculate the hypotenuse of the triangle formed by the two hands:

3 cm and 4 cm = 5 cm

3. Calculate the distance between the two tips using the cosine of the angle:

5 cm x 1.73= 8.66 cm

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To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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The correct answer is [B] You are increasing your liability.

When you buy a pair of shoes for $85, your cash balance decreases by $85, which means that your wealth also decreases by $85. This is represented by [A] and [C].

[D] You are incurring an expense is also true, because you are spending money on the shoes.

[E] You are acquiring (non-cash) asset is also true, because you are obtaining an asset (the shoes) that you can use or sell in the future.

[B] You are increasing your liability is not true, because a liability is a debt or an obligation that you owe to someone else. In this case, you are not taking on any debt or obligation by buying the shoes, so your liability does not increase.

Using function concepts, we have that:

A function has the following format: y = f(x).

In which each value of y is a function of one value of x, and thus, x is the independent variable and y is the dependent variable.

That is, the input of the function is the independent variable and the output is the dependent variable.

For this problem, the volume is a function of time, hence Volume = f(Time) and:

The decay rate is constant, meaning that we have a decreasing linear function, and graph H fits this problem.

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The fourth term of the geometric sequence is 6.4.

We have to given that,

The first term of a geometric sequence is 20 and the second term is 8.

Let's denote the common ratio of the geometric sequence by r.

We know that the first term is 20,

so a₁ = 20,

And the second term is 8,

so a₂ = 20r = 8.

Solving for r, we get:

r = a₂/a₁ = = 8/20 = 2/5

Now, we want to find the fourth term of the sequence, which is a₄.

We can use the formula for the nth term of a geometric sequence, which is:

a (n) = a₁ rⁿ⁻¹

Plugging in n=4, a₁=20, and r=2/5, we get:

a₄ = 20 (2/5)³

a₄ = 6.4

Therefore, the fourth term of the geometric sequence is 6.4.

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