Two cars leave the same parking lot, with one heading north and the other heading east. After several minutes, the northbound car has traveled 12 kilometers, and the eastbound car has traveled 5 kilometers. Measured in a straight line, how far apart are the two cars?

The bigger engine is larger than the smaller one by 235.4724 cubic centimeters.

We know that 1 inch=2.54 centimeters

Then 1 cubic inches-(2.54)^3 cubic centimeters

We have that:

⇒ 1 cubic inches=(2.54)3 = 16.3870 cubic centimeters

⇒350 cubic inches= 350 x 16.3870 = 5735.4724 cubic centimeters

Since, the other displaces 5,500 cubic centimeters  and 5735.4724< 5500. The difference between them is:

= 5735.4724 - 5500

= 235.4724

Hence, the bigger engine larger than the smaller one by 235.4724 cubic centimeters.

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Answer: 1/2 ( aka 50%) but the answer is 1/2

Answer:

44.12

Step-by-step explanation:

since area of a circle is (pi)(r^2), a semi circle would be that divided by 2. and so plugging in the radius squared, multiplying by pi, then dividing by 2, boom. A=44.12.

The coin makes approximately 16.53 turns when rolled on its edge for 1.34 m.

The circumference of the coin can be calculated as follows to determine the number of turns it makes:

C = πd

where C is the circumference, d is the diameter, and π is the mathematical constant pi (approximately equal to 3.14159).

So, for the given $2 coin with a diameter of 25.75 mm, the circumference is:

C = πd = 3.14159 x 25.75 mm ≈ 80.926 mm

Divide the distance traveled by the coin's circumference to determine the number of turns it makes when rolled on its edge for 1.34 meter:

Number of turns = distance traveled / circumference of the coin

Number of turns = 1.34 m / 0.080926 m

Number of turns ≈ 16.53

Therefore, the coin makes approximately 16.53 turns when rolled on its edge for 1.34 m.

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The length of CD is 6 inches.

We can start by finding the area of triangle EDC

Area of triangle EDC = Area of triangle EDB - Area of triangle EBC

= 60.5 - 27.5

= 33

Using the formula for the area of a triangle, we can write

Area of triangle EDC = (1/2) * CD * ED

Substituting the given values, we get

33 = (1/2) * CD * 11

Multiplying both sides by 2 and then dividing by 11, we get

CD = 6

Therefore, CD is 6 inches.

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Therefore, the solution is equation (x, y) = (52/7, -10/7).

To solve the system of equations by elimination, we need to eliminate one of the variables. We can do this by multiplying one or both equations by a constant to create opposite coefficients for one of the variables. Then, we can add or subtract the equations to eliminate that variable and solve for the other variable. Here's how to solve the given system of equations:

Multiply the first equation by 3 and the second equation by 2 to create opposite coefficients for y:

[tex]3(x - 2y = 12) - > 3x - 6y = 36[/tex]

[tex]2(-5x + 3y = -44) - > -10x + 6y = -88[/tex]

Add the equations to eliminate y:

[tex]3x - 6y + (-10x + 6y) = 36 + (-88)[/tex]

[tex]-7x = -52[/tex]

Solve for x by dividing both sides by -7:

[tex]x = 52/7[/tex]

Substitute x = 52/7 into either equation to solve for y. Using the first equation:

[tex]52/7 - 2y = 12[/tex]

[tex]-2y = 12 - 52/7[/tex]

[tex]-2y = 72/7 - 52/7[/tex]

[tex]-2y = 20/7[/tex]

[tex]y = -(10/7)[/tex]

Check the solution by substituting the values of x and y into both equations:

[tex]x - 2y = 12 - > 52/7 - 2(-10/7) = 12 (true)[/tex]

[tex]-5x + 3y = -44 - > -5(52/7) + 3(-10/7) = -44 (true)[/tex]

Therefore, the solution is (x, y) = (52/7, -10/7).

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Answer: 4545 yards

Step-by-step explanation:

We can use similar triangles to solve this problem. Let's represent the height of the flagpole with the variable "x".

Using the triangle formed by Carla's line of sight, the height of the apartment building, and the top of the flagpole, we can set up the following proportion:

x / (x + 1515) = 15 / 20

Simplifying this proportion, we get:

4x = 3(x + 1515)

4x = 3x + 4545

x = 4545

Therefore, the height of the flagpole is 4545 yards.

True.  

The decision that would result from a Type I error is:

Closing the park when the lead levels are within the allowed limit. C

In this scenario, the null hypothesis is that the lead levels are okay, and the alternative hypothesis (Ha) is that lead levels exceed the limit.

The decisions that would result from the Type I error are:

Closing the park when the lead levels are in excess of the allowed limit.

This decision would be a false positive, as the park would be closed even though the lead levels are actually within the allowed limit.

This is a Type I error.

Closing the park when the lead levels are within the allowed limit.

This decision would be a correct decision as the park should be closed if the lead levels are not within the allowed limit.

This is not a Type I error.

Keeping the park open when the lead levels are in excess of the allowed limit.

This decision would be a false negative, as the park would remain open even though the lead levels are actually above the allowed limit.

This is a Type II error.

Closing the park because of the increased noise level in the neighborhood.

This decision is not related to the hypothesis testing for lead levels in the park, and therefore, it is not a Type I error.

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Answer:

Step-by-step explanation:

The circumference of a circle is found by the formula 2πr. r is defined as the radius, which is the distance from the middle of the circle to any point on its outer curve. In this case, we are given the radius from the line that is drawn halfway through the circle. We can plug in this value (11) and solve it.

C = 2πr

C = 2π(11)

C = 22π cm

Hope this helps!

The only ball that weighs 30g is ball A. So the answer is: Ball A weighs 30g.

To determine which ball weighs 30g, we need to compare the weights of each ball.

We know that there are five balls, and that their weights are 30g, 50g, 50g, 50g, and 80g.

Since we are looking for the ball that weighs 30g, we can eliminate the other weights one by one. We know that ball E weighs 80g, so it cannot be the one we're looking for. We can also eliminate balls B, C, and D since they all weigh 50g.

Therefore, the only ball that weighs 30g is ball A. So the answer is: Ball A weighs 30g.

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The radius of the base of the cone can be found by dividing the circumference by 2π:

radius = (8.5π)/(2π) = 4.25 inches

Using the formula for the volume of a cone, V = (1/3)πr^2h, we can substitute the values we know:

V = (1/3)π(4.25^2)(15) ≈ 270.62 cubic inches

Rounding to the nearest hundredth, the volume of the cone in terms of π is approximately 270.62π cubic inches.

Answer:

The amplitude is 1/2, the period is 2π/4 = π/2, and the phase shift is π/2.

Step-by-step explanation:

The given function is:

f(t) = -1/2(4t - 2π)

We can rewrite this function in the form:

f(t) = A cos(B(t - C)) + D

where A is the amplitude, B is the period, C is the phase shift, and D is the vertical shift.

Comparing this with the given function, we can see that:

A = 1/2

B = 4

C = π/2

D = 0

Therefore, the amplitude is 1/2, the period is 2π/4 = π/2, and the phase shift is π/2.

Note that the negative sign in front of the function does not affect the amplitude, period, or phase shift. It simply reflects the function across the x-axis.

The monthly interest rate is the annual interest rate divided by 12

To calculate the monthly interest rate, we need to divide the annual interest rate by 12 (since there are 12 months in a year).

So if the annual interest rate is 8%, the monthly interest rate can be calculated as:

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 8% / 12

Monthly interest rate = 0.6667%

Therefore, the monthly interest rate would be 0.6667%.

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Answer:

[tex] \frac{ {g}^{4} {h}^{2} }{ g{h}^{6} } = \frac{ {g}^{3} }{ {h}^{4} } [/tex]

because other values are 1, and this one is less, because g<h

These investments do indeed produce a net return of $133.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

Let's call the amount Devon invested in the real estate fund "x". Then, we know that the amount invested in the large cap stock fund is twice that, or "2x". The total amount invested is $9500, so we can write:

x + 2x + y = 9500

where "y" is the amount invested in the bond fund.

We also know the returns of each fund, so we can calculate the total return on the investments:

0.047(2x) - 0.122x + 0.054y = 133

Simplifying this equation, we get:

0.998x + 0.054y = 133

We have two equations and two unknowns (x and y), so we can solve for them. Let's start by solving the first equation for y:

y = 9500 - 3x

Now we can substitute this expression for y into the second equation:

0.998x + 0.054(9500 - 3x) = 133

Simplifying and solving for x, we get:

0.888x = 459.8

x = 517.57

So Devon invested $517.57 in the real estate fund. The amount invested in the large cap stock fund is twice that, or $1035.14. The amount invested in the bond fund is:

y = 9500 - 3x = 8464.29

To check that these investments produce a net return of $133, we can calculate the total return on each investment and add them up:

0.047(2x) - 0.122x + 0.054y = 0.047(2517.57) - 0.122517.57 + 0.054*8464.29 = 133.00

So these investments do indeed produce a net return of $133.

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Answer:  the answer is A. 14.

Step-by-step explanation: In each trial of the reenactment, Scott chooses one card from the stack and records its digit. Based on the given data, a digit of or 1 speaks to a objective scored, and a digit of 2 through 9 speaks to a missed endeavor.

Out of the 5 endeavors per amusement, on the off chance that Scott scores precisely 2 objectives, it implies he missed 3 endeavors. Subsequently, the likelihood of this occasion can be calculated as:

P(exactly 2 objectives) = (0.2)²(0.8)³ = 0.008192

This likelihood can be utilized to discover the anticipated number of diversions in which Scott scores precisely 2 objectives, by duplicating it by the overall number of diversions reenacted:

Anticipated number of recreations = P(exactly 2 objectives) × Add up to number of recreations = 0.008192 × 84 ≈ 0.68

Adjusting to the closest entire number, we get that Scott is anticipated to score precisely 2 objectives in 1 diversion out of the 84 recreated diversions.

Sampled 200 delinquent credit card accounts instead of 100, the margin of error would decrease.

Sampled 200 delinquent credit card accounts, the margin of error for the sample mean at a 95% confidence level would be $80.164.

Smaller than the margin of error we found earlier for a sample size of 100.

The margin of error for the sample means at a 95% confidence level, we need to use the formula:
[tex]Margin of error = z\times (standard deviation / square root of sample size)[/tex]
[tex]z\times[/tex] is the z-score for the 95% confidence level, which is 1.96.
So, plugging in the given values, we get:
[tex]Margin of error = 1.96 \times  (578 / \sqrt 100)[/tex]
[tex]Margin of error = 1.96 \times 57.8[/tex]
Margin of error = 113.008
Therefore, the margin of error for the sample mean at a 95% confidence level is $113.008.
Repeated samples of 100 delinquent credit card accounts and computed the sample mean each time, we would expect the true population mean to be within $113.008 of our sample mean about 95% of the time.
The margin of error is inversely proportional to the square root of the sample size. So, as the sample size increases, the margin of error decreases.
To see this, let's plug in the new sample size into the margin of error formula:
[tex]Margin of error = 1.96 \times (578 / \sqrt 200)[/tex]
[tex]Margin of error = 1.96 \times 40.9[/tex]
Margin of error = 80.164

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The probability that the point is in the smaller, shaded square is approximately 14.06%.

Probability is the measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will certainly occur. The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes. Probability is widely used in various fields, including mathematics, statistics, science, finance, and engineering.

The area of the large square is (8 cm)² = 64 cm², and the area of the shaded square is (3 cm)² = 9 cm². The probability of choosing a point at random that is in the shaded square is equal to the ratio of the area of the shaded square to the area of the large square:

Probability = (area of shaded square) / (area of large square)

Probability = 9 cm² / 64 cm²

Probability = 0.140625 or 14.06% (rounded to two decimal places)

Therefore, the probability that the point is in the smaller, shaded square is approximately 14.06%.

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Answer:x= -67 over 24

Step-by-step explanation:

The distance between the two points can be found to be, and the number that goes beneath the radical symbol is 80.

To find the distance between two points in a plane, you can use the distance formula derived from the Pythagorean theorem. The distance formula is:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

In this case, the coordinates of the two points are (-4, 1) and (4, 5). So, x₁ = -4, y₁ = 1, x₂ = 4, and y₂ = 5.

Now, apply the distance formula:

d = √[(4 - (-4))² + (5 - 1)²]

d = √[(8)² + (4)²]

d = √(64 + 16)

d = √80

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we can reject the null hypothesis at the 5% significance level since the p-value is less than 0.05.

To calculate the p-value, we need to perform a hypothesis test.

Let's assume the null hypothesis is that the proportion of defective systems produced by x-game is equal to or less than the industry standard of 0.02, while the alternative hypothesis is that the proportion is greater than 0.02.

We can use the normal approximation to the binomial distribution since we have a large sample size (n=120) and np and n(1-p) are both greater than or equal to 10.

The test statistic can be calculated as:

[tex]z = (p_hat - p) / \sqrt{(p*(1-p)/n)}[/tex]

where [tex]p_hat[/tex]  is the sample proportion of defective systems, p is the hypothesized proportion under the null hypothesis, and n is the sample size.

Using the values given in the question, we have:

[tex]p_hat = 6/120 = 0.05[/tex]

p = 0.02

n = 120

Plugging these values into the formula, we get:

[tex]z = (0.05 - 0.02) / \sqrt{(0.02*(1-0.02)/120) = 2.041}[/tex]

The p-value can be calculated as the probability of getting a test statistic as extreme or more extreme than 2.041 under the null hypothesis.

Since this is a one-tailed test (the alternative hypothesis is one-sided), we look up the area in the right tail of the standard normal distribution table.

Using a standard normal distribution table, we find that the area to the right of 2.041 is 0.0207.

Therefore, the p-value is 0.0207.

Therefore, we can reject the null hypothesis at the 5% significance level since the p-value is less than 0.05.

This means that there is strong evidence that the proportion of defective systems produced by x-game exceeds the industry standard of 0.02.

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The probability that more than 7 of the invoices will be paid within ten working days is 0.8281

This is a binomial distribution problem where:

n = 10 (sample size)

p = 0.5 (probability of success, i.e., an invoice being paid within ten working days)

We need to find the probability of getting more than 7 invoices paid within ten working days, i.e., P(X > 7), where X is the number of invoices paid within ten working days.

Using the binomial probability formula, we get:

[tex]P(X > 7) = 1 - P(X ≤ 7)[/tex]

=[tex]1 - ∑(i=0 to 7) [nCi * p^i * (1-p)^{(n-i)][/tex]

where nCi is the number of ways to choose i items from n items, given by [tex]nCi = n! / (i! * (n-i)!).[/tex]

Calculating the above expression, we get:

[tex]P(X > 7) = 1 - [10C0 * 0.5^0 * 0.5^10 + 10C1 * 0.5^1 * 0.5^9 + ... + 10C7 * 0.5^7 * 0.5^3][/tex]

[tex]= 1 - 0.1719[/tex]

[tex]= 0.8281[/tex]

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When the width of the rectangle is 4 in, the length is 6 in.

Let's call the length of the rectangle "L" and the width "W". The problem states that the area of the rectangle is constant, so we can write:

LW = A

where A is some constant. We are also told that the length varies inversely with the width, which means that if the width increases, the length must decrease proportionally to keep the area constant. Mathematically, this means

L ∝ 1/W

or

L = k/W

where k is some constant of proportionality. We can find k by using the information given in the problem. We are told that when the width is 3 in, the length is 8 in

8 = k/3

Multiplying both sides by 3 gives:

24 = k

Now we can use this value of k to find the length when the width is 4 in:

L = k/W = 24/4 = 6 inches

When the width of the rectangle is 4 in, the length is 6 in, where the length and width of the rectangle are related by the inverse proportion L = k/W, with k = 24.

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As likely as not (assuming the bag contains an equal number of magnets for each letter in the alphabet).

Probability is a measure of the likelihood or chance that a particular event will occur. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.

In probability theory, the probability of an event is calculated by dividing the number of ways that the event can occur by the total number of possible outcomes. This is known as the probability formula:

probability = Number of favorable outcomes / Total number of possible outcomes

Probability is used in a wide range of fields, including statistics, finance, physics, and engineering, to model and analyze uncertain situations and make predictions.

B. Likely (assuming the bag contains an equal number of magnets for each letter in the alphabet, and that there are more consonants than vowels in the alphabet).

C. Unlikely (assuming the deck contains an equal number of red and black cards).

D. Impossible (assuming the deck contains only standard playing cards with 52 cards, including 13 cards for each of the four suits).

E. Unlikely (assuming the deck contains only standard playing cards with 52 cards, including 4 cards for each number or face value).

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The sorted order of the impairs [3 7], [4 6], [3 4] using impair. compare to would be:
[C] [3 2], [4 6], [3 7]

When comparing in pairs using impair. compare to, the first element taking priority over the second element. So, in the list [3 7], [4 6], [3 4], the impair [3 2] would come first because 3 is smaller than both 4 and 3, and the second element (2) is also smaller than the second element of the other in pairs. Then, the impair [4 6] would come next as it has the second smallest first element, and finally, the impair [3 7] would come last as it has the largest first element. Therefore, the sorted order is [3 2], [4 6], [3 7], denoted as option C.

To sort the given list of in pairs ([3 7], [4 6], [3 4]) using impair. compared, follow these steps:

1. Compare the first elements of the in pairs (3, 4, and 3). If there is a tie, move to step 2.
2. Compare the second elements in pairs with the same first elements (7 and 4).
3. Arrange the impairs in ascending order based on the comparison results.

The sorted order is [3 4], [3 7], [4 6]. However, this order is not present in the given options. Please check the question for any discrepancies or provide the correct in pairs to sort.

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The sorted order of the impairs [3 7], [4 6], [3 4] using impair. compare to would be:

[C] [3 2], [4 6], [3 7]

When comparing in pairs using impair. compare to, the first element taking priority over the second element. So, in the list [3 7], [4 6], [3 4], the impair [3 2] would come first because 3 is smaller than both 4 and 3, and the second element (2) is also smaller than the second element of the other in pairs. Then, the impair [4 6] would come next as it has the second smallest first element, and finally, the impair [3 7] would come last as it has the largest first element. Therefore, the sorted order is [3 2], [4 6], [3 7], denoted as option C.

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Froph can purchase 2 naxvips and 1 dubble with a maximum budget of $6.

How to solve the question?

Part 1:

Let's assume Froph purchased "x" naxvips and "y" dubbles. The cost of each naxvip and dubble is $2. Therefore, the total cost of purchasing "x" naxvips and "y" dubbles can be calculated as:

2x + 2y <= 6

This inequality can be simplified by dividing both sides by 2:

x + y <= 3

This is the standard form of the inequality that models the relationship between the number of naxvips and dubbles Froph can purchase with a maximum budget of $6.

Part 2:

One possible pair of numbers that satisfies the inequality is (2, 1). If Froph purchases 2 naxvips and 1 dubble, the total cost would be:

2 x $2 + 1 x $2 = $6

This pair of numbers satisfies the inequality since:

2 + 1 = 3 <= 3

Therefore, Froph can purchase 2 naxvips and 1 dubble with a maximum budget of $6.

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The total number of non-empty subsets s of[tex]{1, 2, 3, . . . , 8}[/tex] such that the product of the elements of s is at most 200 is:
[tex]255 - (127 + 63 + 31) + 2 = 36.[/tex]
So, there are 36 such subsets.

Number of non-empty subsets s of[tex]{1, 2, 3, . . . , 8}[/tex] such that the product of the elements of s is at most 200, we can use a method called inclusion-exclusion principle.
First, we need to count the total number of non-empty subsets of the given set.

Since each element can either be included or excluded, there are [tex]2^8 - 1 = 255[/tex] non-empty subsets.
Next, we need to count the number of subsets whose product is greater than 200.

We can start by considering the subsets that contain 8, since 8 is the largest element in the set.

There are only two such subsets: {8} and {1, 8}.

Both of these subsets have a product greater than 200. Similarly, we can consider subsets that contain 7, and so on. We find that there are[tex]2^7 - 1 = 127[/tex] subsets that contain 7, and each of these subsets has a product greater than 200. Similarly, there are [tex]2^6 - 1 = 63[/tex] subsets that contain 6, and each of these subsets has a product greater than 200.
Double-counted the subsets that contain both 6 and 7, as well as those that contain both 6 and 8, and those that contain both 7 and 8.

Subtract the number of subsets that contain both 6 and 7, both 6 and 8, and both 7 and 8.

There are [tex]2^5 - 1 = 31[/tex] subsets that contain both 6 and 7, and each of these subsets has a product greater than 200.

Similarly, there are[tex]2^5 - 1 = 31[/tex] subsets that contain both 6 and 8, and each of these subsets has a product greater than 200.

Finally, there are [tex]2^5 - 1 = 31[/tex] subsets that contain both 7 and 8, and each of these subsets has a product greater than 200.
However, we have subtracted too much, since we have now excluded subsets that contain all three of 6, 7, and 8. There are only two such subsets: {6, 7, 8} and {1, 6, 7, 8}. Both of these subsets have a product greater than 200.

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To find the number of non-empty subsets s of {1, 2, 3, . . . , 8} such that the product of the elements of s is at most 200, we can use the concept of power set and combinatorics. By analyzing the pattern, we can determine that there are a total of 120 subsets whose product is at most 200.

To find the number of non-empty subsets s of the set {1, 2, 3, . . . , 8} such that the product of the elements of s is at most 200, we can use the concept of power set and combinatorics. The power set of a set is the set of all its subsets. We know that the number of elements in the power set of a set with n elements is 2n. In this case, we have 8 elements in the set, so the power set will have 28 = 256 subsets. However, we need to find the number of subsets with a product at most 200.

We can analyze the products of all subsets to determine the count.

By analyzing the pattern, we can determine that there are a total of 120 subsets whose product is at most 200. This can be calculated by summing the total number of subsets for each number of elements (1-element subsets + 2-element subsets + 3-element subsets + ... + 8-element subsets).

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The length created by a central angle is 0.04 feet.

What is radius of circle?

The radius of a circle is the distance from the center of the circle to any point on the circle's edge. It is typically denoted by the letter "r" and is one of the fundamental measurements used to describe the geometry of a circle.

First, we need to convert the central angle from degrees to radians. Since there are 60 minutes in a degree, we can divide 18 by 60 to get the angle in degrees as a decimal,

18/60 = 0.3 degrees

Next, we convert this to radians by multiplying by π/180,

0.3 × π/180 ≈ 0.00524 radians

To find the length of the arc created by this central angle, we use the formula,

arc length = radius × central angle

So, for a circle of radius 8 feet and a central angle of 0.00524 radians, the arc length is arc length = 8 × 0.00524 ≈ 0.04192 feet

Rounded to the nearest hundredth, the length of the arc is approximately 0.04 feet.

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a) Any value outside of Q1 - 1.5(IQR) and Q3 + 1.5(IQR) can be considered a potential outlier.

b) This will give us a visual representation of the distribution of income among the full-time students.

c) It is important to analyze outliers carefully to ensure that they are not artificially skewing the results of our analysis.

(a) To check for outliers in the data set, we can use the box-and-whisker plot or the z-score method. However, since we do not have the exact data, we cannot use these methods. One way to identify potential outliers is to calculate the quartiles (Q1, Q2, and Q3) and the interquartile range (IQR).

(b) To draw a histogram of the data, we can use the frequency distribution table given in the question. The x-axis should represent the income ranges (e.g. $0-$100, $100-$200, etc.) and the y-axis should represent the frequency (i.e. the number of students who earned income within each range).

(c) If there are any outliers in the data set, we need to investigate them further to determine the reason for their unusual values. Possible reasons for outliers could be data entry errors, extreme values due to high- or low-income jobs, or unique situations such as unexpected windfalls or emergencies.

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#SPJ11

Step-by-step explanation:

rotate the triangle in your mind (or as actual picture on your phone or computer), so that the right angle is the bottom right or bottom left, and C being the opposite bottom angle.

then we see

28 = cos(C) × 35

21 = sin(C) × 35

and so,

sin(C) = 21/35 = 3/5

cos(C) = 28/35 = 4/5

tan(C) = sin(C)/cos(C) = 3/5 / 4/5 = 3/4