a 10-segment trapezoidal rule is exact to find integrals of polynomials of order ________ or less

The number equal to 3 thousands + 7 tens + 5 ones is 3,075.

In the Hindu-Arabic numeral system, numbers are represented using place value, where the position of a digit in a number determines its value. The three digits given in the problem can be written as 3 thousands, 7 tens, and 5 ones.

The place value of the first digit on the left is thousands, which means that it is 1,000 times the value of the digit in the ones place. Similarly, the place value of the second digit from the right is tens, which means that it is 10 times the value of the digit in the ones place.

To combine the three digits and obtain the number they represent, we simply add up their values:

3 thousands = 3 x 1000 = 3000

7 tens = 7 x 10 = 70

5 ones = 5 x 1 = 5

Adding these values together, we get:

3000 + 70 + 5 = 3075

Therefore, the number equal to 3 thousands + 7 tens + 5 ones is 3075.

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The null hypothesis and conclude that the mean mercury content of Albacore tuna is greater than 0.126 ppm.

(a) The appropriate method to compute a p-value for a test of whether the mean mercury content of Albacore tuna is greater than 0.126 ppm is a t-test because the sample size is less than 30 and the standard deviation of the population is unknown.

(b) The null hypothesis for this study is that the mean mercury content of Albacore tuna is equal to 0.126 ppm, and the alternative hypothesis is that the mean mercury content is greater than 0.126 ppm.

To find the theory-based p-value, we can use the t-distribution with 42 degrees of freedom (43-1). The test statistic is:

t = (x - μ) / (s / sqrt(n))

where x is the sample mean (0.358 ppm), μ is the hypothesized population mean (0.126 ppm), s is the sample standard deviation (0.138 ppm), and n is the sample size (43).

Substituting the values, we get:

t = (0.358 - 0.126) / (0.138 / sqrt(43)) = 10.29

Using a t-table or calculator, the p-value for a one-tailed test with 42 degrees of freedom and a test statistic of 10.29 is less than 0.001. Therefore, we can conclude that there is strong evidence to reject the null hypothesis and conclude that the mean mercury content of Albacore tuna is greater than 0.126 ppm.

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To find CE, we first need to find the length of AE and EB. We know that AE = 2/3 AB and EB = 1/3 AB, so AE = 4 and EB = 2.

Now we can use the Law of Cosines to find the length of AC:

AC^2 = AB^2 + BC^2 - 2AB*BC*cos(A)

Plugging in the given values, we get:

AC^2 = 6^2 + 5^2 - 2(6)(5)cos(A)

Simplifying:

AC^2 = 61 - 60cos(A)

We also know that AC = 4, so we can set these two equations equal to each other and solve for cos(A):

4^2 = 61 - 60cos(A)

16 = 60cos(A) - 61

77 = 60cos(A)

cos(A) = 77/60

Now we can use the Law of Cosines again to find CE:

CE^2 = AC^2 + AE^2 - 2AC*AE*cos(A)

Plugging in the values we know:

CE^2 = 4^2 + 4^2 - 2(4)(4)(77/60)

Simplifying:

CE^2 = 32/3

Taking the square root:

CE = sqrt(32/3)

Simplifying:

CE = 4sqrt(2/3)

Therefore, CE is approximately equal to 2.309.

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Answer: 401.92

Step-by-step explanation:

V=πr^2h

=π(4^2)(8)

=π(16)(8)

=π128

=401.92

Hope this helps! :)

Arrange the data in an ascending order and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.

median: 34

The mode is the element that occurs most in the data set. In this case, 13, 34 occurs 2 times.

mode: 13, 14

The mean of a set of numbers is the sum divided by the number of terms.

mean: 38.2

Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is

69−13=56.

Range: 56

The equation of the line in slope-intercept form is y = -3x + 1.

To work out the values of m and c for the line, we need to rearrange the equation into the slope-intercept form, which is y = mx + c, where m is the slope of the line and c is the y-intercept.

In slope-intercept form, the equation of a line is y = mx + c, where m is the slope of the line and c is the y-intercept.

To obtain this form from the given equation y + 3x = 1, we need to isolate y on one side by subtracting 3x from both sides, giving us:

y = -3x + 1

Starting with the given equation y + 3x = 1, we can subtract 3x from both sides to get:

y = -3x + 1

Comparing this equation with the slope-intercept form, we see that m, the slope of the line, is -3, and c, the y-intercept, is 1.

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The graph of the function g(x) = −|x + 3| − 2 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

g(x) = −|x + 3| − 2

The above expression is an absolute value function that hs the following properties

Next, we plot the graph

See attachment for the graph of the function

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The value of x in the equation 2x² + 10x + 12 = 0 is -2 and -3.

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The standard form of a quadratic equation is:

ax² + bx + c = 0

The quadratic formula is given by:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a} \\\\Given\ the\ equation\ 2x^2+10x+12=0:\\\\a=2;b=10;c=12\\\\x=\frac{-b\pm\sqrt{b^2-4ac} }{2a} \\\\substituting:\\\\x=\frac{-10\pm\sqrt{10^2-4(2)(12)} }{2(2)} \\\\x=-3; and\ x=-2\\[/tex]

The value of x is -2 and -3.

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Answer: 7, 10, 11, 12, 14, 14, 15, 15, 15, 15, 16, 16, 17, 19, 19, 20, 21, 21, 23, 28, 40, 40, 44

To find the mean of Carl Yastrzemski's home run totals, we need to add up all the values and then divide by the number of values.

11 + 19 + 14 + 15 + 20 + 16 + 44 + 23 + 40 + 40 + 15 + 12 + 19 + 15 + 14 + 21 + 28 + 17 + 21 + 15 + 7 + 16 + 10 = 391

There are 23 values in the data set, so we divide by 23:

Mean = 391/23 = 17

Therefore, the mean number of home runs that Carl Yastrzemski hit per season during his career was 17.

To find the median, we need to arrange the values in order from smallest to largest:

7, 10, 11, 12, 14, 14, 15, 15, 15, 16, 16, 17, 19, 19, 20, 21, 21, 23, 28, 40, 40, 44

There are an odd number of values, so the median is the middle value. In this case, the middle value is 16.

Therefore, the median number of home runs that Carl Yastrzemski hit per season during his career was 16.

In summary, the mean number of home runs per season was 17 and the median number of home runs per season was 16. The mean and median are both measures of central tendency, but they represent slightly different things. The mean is the average value and takes into account all the values in the data set. The median is the middle value and is less affected by extreme values. Both measures can be useful in understanding a data set, depending on what information you are looking for.

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The presence of extreme values can cause the standard deviation to be larger than it would be otherwise, indicating greater variability in the data set.

The mean is the measure of central tendency that is most affected by extreme values or outliers. The mean is calculated by adding up all the data points and dividing by the total number of data points. Since extreme values can be significantly different from the other values in the data set, their effect on the mean can be significant.

For example, consider the following data set of salaries for a company: $30,000, $35,000, $40,000, $45,000, $50,000, and $1,000,000. The mean salary for this data set is calculated as:

($30,000 + $35,000 + $40,000 + $45,000 + $50,000 + $1,000,000) ÷ 6 = $193,333.33

Here, the extreme value of $1,000,000 has significantly impacted the mean salary. Even though the other salaries are all within a reasonable range, the mean is skewed by the extreme value.

On the other hand, the median and mode are less affected by extreme values. The median is the middle value in a data set when the data is arranged in order, and the mode is the most frequently occurring value. In the above example, the median salary would be $42,500, and the mode would be undefined as no salary occurs more than once.

The standard deviation is a measure of the spread or dispersion of the data, and is not directly affected by extreme values. However, the presence of extreme values can cause the standard deviation to be larger than it would be otherwise, indicating greater variability in the data set.

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If Mexico, one of our largest trading partners, goes into a recession, it is likely to decrease its demand for our exports. This would shift the aggregate demand (AD) curve leftward, leading to a decrease in equilibrium GDP and price level in the short run.

In the AD/AS model, a decrease in aggregate demand would cause a leftward shift of the AD curve. As a result, the intersection point of the AD and the short-run aggregate supply (SRAS) curves would move to the left, causing a decrease in equilibrium GDP and price level.

In the long run, however, the economy is likely to adjust to the new equilibrium. The decrease in aggregate demand would cause a decrease in prices, which would shift the SRAS curve rightward. Eventually, the new intersection point of the AD and the SRAS curves would be reached, resulting in a new equilibrium GDP and price level.

Overall, a recession in Mexico would likely have a negative impact on the US economy, leading to a decrease in GDP and price level in the short run. However, the economy would eventually adjust to the new equilibrium in the long run.

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The value of w in the similar rectangle is 27 units.

For two rectangles to be similar, their sides have to be proportional (form equal ratios).

Therefore, let's use the proportional relationship of the rectangle to find the value of w in the rectangle as follows:

9 / w = 16 / 48

cross multiply

9 × 48 = 16w

16w = 432

divide both sides by 16

w = 432 / 16

w = 27 units

Hence, the value of w is 27 units

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The table should be completed with the correct key features as follows;

Axis of symmetry (1st graph): x = 1.

Vertex (1st graph): (1, -9).

Minimum (1st graph): -9.

y-intercept (1st graph): (0, -8).

Axis of symmetry (2nd graph): x = 2.

Vertex (2nd graph): (2, 16).

Maximum (2nd graph): 16.

y-intercept (2nd graph): (0, 12).

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first graph of a quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).

Based on the second graph of a quadratic function, we can logically deduce that the graph is a downward parabola because the coefficient of x² is negative and the value of "a" is less than zero (0).

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There will be 15 booths can fit in the beverage area.

C = πd

where C is the circumference, d is the diameter, and π is pi (approximately 3.14).

C = π(50) = 157.1 feet (rounded to the nearest tenth)

Next, we need to subtract the space needed between booths from the total arc length.

157.1 - (10.5x) = 0

where x is the number of booths.

Simplifying the equation, we get:

10.5x = 157.1

x ≈ 14.9

Rounding to the nearest whole number, we get that 15 booths can fit in the beverage area.

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Answer:

To find the critical points, we need to find the derivative of the function:

y' = -2x

Setting y' = 0, we get:

-2x = 0

x = 0

So the only critical point is (0,0).

To determine whether this is a relative maximum, relative minimum, or horizontal point of inflection, we need to look at the second derivative:

y'' = -2

Since y'' is negative at x = 0, this means that the function is concave down and the critical point is a relative maximum.

Therefore, the critical point (0,0) is a relative maximum for the function y = -x^2.

Step-by-step explanation:

Branliest or else

The function y = -x^2 has one critical point at x = 0, and it is a relative maxima. The critical points and determine their nature for the function y = -x^2. Here's a step-by-step explanation:

1. Find the first derivative of y with respect to x:
  y' = dy/dx = -2x

2. Find critical points by setting the first derivative equal to zero:
  -2x = 0
  x = 0

3. Determine the nature of the critical point by examining the second derivative:
  Find the second derivative of y with respect to x:
  y'' = d²y/dx² = -2

4. Since the second derivative is negative (y'' = -2), the critical point at x = 0 corresponds to a relative maxima.

In conclusion, the function y = -x^2 has one critical point at x = 0, and it is a relative maxima.

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The width of the walkway is 3.27 feet.

We have,

Let's assume that the width of the walkway is y feet.

Dimensions of the pool and the walkway can be represented as follows:

Length = 2(x+y) + 13

Width = 2(x+y) + 10

The area of the pool and the walkway.

Area = Length x Width

Area = (2(x+y) + 13) x (2(x+y) + 10)

We know that the total area of the pool and the walkway is 304 square feet.

So,

(2(x+y) + 13) x (2(x+y) + 10) = 304

Expanding the left-hand side and simplifying, we get:

4x² + 28x + 39y + 65 = 304

Rearranging and simplifying, we get:

4x² + 28x + 39y - 239 = 0

We can use the quadratic formula to find the solution:

y = (-b ± √(b² - 4ac)) / 2a

where a = 4, b = 39, and c = -239.

Substituting these values, we get:

y = (-39 ± √(39² - 44(-239))) / 8

Simplifying, we get:

y ≈ 3.27 or y ≈ -18.27 (rejected)

Therefore,

The width of the walkway is 3.27 feet.

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To find the proportion of tiles produced with a surface area less than 16.0 square inches, we'll use the properties of the normal distribution. Here are the steps:

1. Identify the given information: mean (μ) = 16.1 square inches, standard deviation (σ) = 0.2 square inches, and the desired surface area (x) = 16.0 square inches.

2. Calculate the z-score using the formula: z = (x - μ) / σ
  z = (16.0 - 16.1) / 0.2
  z = (-0.1) / 0.2
  z = -0.5

3. Look up the z-score (-0.5) in a standard normal distribution table or use a calculator to find the area to the left of the z-score. This area represents the proportion of tiles with a surface area less than 16.0 square inches.

4. The area to the left of z = -0.5 is approximately 0.3085.

So, the proportion of tiles produced with a surface area less than 16.0 square inches is approximately 0.3085, or 30.85%.

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a) The total amount in Charles' account after ten years is $728,215.72.

b) Charles earns $29,375.31 more by putting his investment into an account that is compounded continuously instead of annually.

c) It will take approximately 17.3 years for Charles' account balance to double.

a. To calculate the total amount in Charles' account after ten years, we use the formula for continuous compound interest:

A = [tex]Pe^{(rt)[/tex]

where A is the amount in the account after t years, P is the initial principal, r is the annual interest rate as a decimal, and e is the constant approximately equal to 2.71828.

Substituting the given values, we get:

A = 500,000[tex]e^{(0.0410)[/tex]

A = $728,215.72

b. To calculate the difference in earnings between continuous and annual compounding, we use the formula:

A = P(1 + r/n)^(nt)

where n is the number of times interest is compounded per year. For continuous compounding, n approaches infinity, so the formula becomes:

A = [tex]Pe^{(rt)[/tex]

Substituting the given values, we get:

A = 500,000[tex]e^{(0.0410)[/tex]

A = $728,215.72

For annual compounding, n = 1, so the formula becomes:

Al = 500,000*[tex](1 + 0.04/1)^{(1*10)[/tex]

Al = $698,840.41

Therefore, the difference in earnings between continuous and annual compounding is:

A - Al = $728,215.72 - $698,840.41 = $29,375.31

c. To find the time it takes for Charles' account balance to double, we use the formula:

A = [tex]Pe^{(rt)[/tex]

We want to find t when A = 2P, so we can write:

2P = [tex]Pe^{(0.04t)[/tex]

Dividing both sides by P and taking the natural logarithm, we get:

ln(2) = 0.04t

Solving for t, we get:

t = ln(2)/0.04

t ≈ 17.3 years

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1. Determine the equilibrium price and quantity: This is the point where the supply curve and the demand curve intersect.
2. This triangle represents the producers' surplus. To find its area, use the formula for the area of a triangle:

(base × height) / 2.

To find the producers' surplus, we need to first determine the equilibrium price at which the supply and demand curves intersect. At this price, the quantity supplied by producers will equal the quantity demanded by consumers.

Once we have the equilibrium price, we can then calculate the area between the supply curve and the equilibrium price. This represents the producers' surplus, which is the amount of profit they make on each unit sold above their cost of production.

Without knowing the specific supply and demand curves, it is not possible to provide an exact answer to this question. However, we can use the formula for producers' surplus to calculate an approximate answer:

Producers' Surplus = (Equilibrium Price - Minimum Supply Price) x Quantity Supplied

For example, if the equilibrium price is $5.50 and the minimum supply price is $3.00, and the quantity supplied is 100 units, the producers' surplus would be:

Producers' Surplus = ($5.50 - $3.00) x 100
Producers' Surplus = $2.50 x 100
Producers' Surplus = $250.00

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Slope tells us that the rate of change in elevation during Ryan's uphill climb was not constant and Average rate of change is 6.67 per minute

The slope of the elevation-time graph represents the rate of change in elevation during Ryan's uphill climb. In this case, the slope can be calculated as:

Slope = (Change in elevation) / (Change in time)

From the given data, the total elevation change during Ryan's uphill climb is:

Total elevation change = 1500 - 300 = 1200 feet

the slope tells us that the rate of change in elevation during Ryan's uphill climb was not constant.

It varied between 15 feet per minute to -40 feet per minute.

A positive slope indicates an increase in elevation over time, while a negative slope indicates a decrease in elevation over time.

The total elevation change of 1200 feet was achieved over a period of 3 hours (180 minutes), so the average rate of change in elevation was:

Average rate of change = Total elevation change / Total time

= 1200 / 180

= 6.67 feet per minute.

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The price should you sell the bracelets at is given by the term of the amount is $64.

The increase in income that comes from selling one more unit of output is known as marginal revenue. Although marginal revenue can remain constant above a certain level of output, it will eventually start to decline as the output level rises due to the law of diminishing returns. According to economic theory, companies that are completely competitive keep on producing goods until marginal revenue and marginal cost are equal.

Price, the sum of money required to purchase a specific good. Price is also a measure of value insofar as it reflects what consumers are willing to pay for a product's worth.

Overall marginal cost (MC) = Explicit (stated) marginal cost + Profit per unit given up = $2 + $6 = $8

Profit is maximized when Marginal revenue (MR) equals Overall MC.

P = 120 - 2Q

Total revenue (TR) = P x Q = 120Q - 2Q2

MR = dTR/dQ = 120 - 4Q

Equating with Overall MC,

120 - 4Q = 8

4Q = 112

Q = 28

P = 120 - (2 x 28) = 120 - 56 = $64.

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The price should you sell the bracelets at is given by the term of the amount is $64.

The term "marginal revenue" refers to the additional income generated by selling one additional unit of output. Although marginal income can remain constant above a particular output level, it will ultimately start to decrease as the output level increases owing to the law of diminishing returns.

Companies that are entirely competitive continue to produce items until marginal income and marginal cost are equal, according to economic theory. A certain good's price is the amount of money needed to buy it. Insofar as it represents what customers are prepared to pay for a product's worth, price is likewise a measure of value.

Overall marginal cost (MC) = Explicit (stated) marginal cost + Profit per unit given up = $2 + $6 = $8

Profit is maximized when Marginal revenue (MR) equals Overall MC.

P = 120 - 2Q

Total revenue (TR) = P x Q = 120Q - 2Q2

MR = dTR/dQ = 120 - 4Q

Equating with Overall MC,

120 - 4Q = 8

4Q = 112

Q = 28

P = 120 - (2 x 28)

= 120 - 56

= $64.

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(i) To create a tree diagram for the situation, we can split it into two stages: First Selection and Second Selection. Here's a description of the tree diagram:

1. First Selection (FS): Two branches - Blue Ball (BB) with probability 6/7, and Red Ball (RB) with probability 1/7.

2. Second Selection (SS): After each FS branch, add two new branches:
  a. After FS-BB: SS-BB with probability 5/9 (since one blue ball was removed), and SS-RB with probability 4/9 (3 red balls added).
  b. After FS-RB: SS-BB with probability 6/9 (no blue ball was removed), and SS-RB with probability 3/9 (3 red balls added).

(ii) To calculate the chances that Nick only takes one red ball, we need to consider two possibilities:
1. First Selection is a Blue Ball and Second Selection is a Red Ball (FS-BB & SS-RB): (6/7) * (4/9) = 24/63
2. First Selection is a Red Ball and Second Selection is a Blue Ball (FS-RB & SS-BB): (1/7) * (6/9) = 6/63

Add both probabilities: (24/63) + (6/63) = 30/63. Simplify the fraction: 30/63 = 10/21.

The chances that Nick only takes one red ball is 10/21.

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Answer:

400 in²

Step-by-step explanation:

We Know

The formula V = l · w · h

l = 10 in

w = 8 in

h = 5 in

Find the volume of the box.

We Take

10 · 8 · 5 = 400 in²

So, the volume of the box is 400 in²

volume of the box is 400 cubic inches.

The given values are:

l = 10 inches

w = 8 inches

h = 5 inches

Using the formula for the volume of a box:

V = lwh

Substituting the given values:

V = (10 in.)(8 in.)(5 in.)

Multiplying:

V = 400 cubic inches

Therefore, the volume of the box is 400 cubic inches.

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Answer:

x=4, -7

Step-by-step explanation:

4 (x−4)(x+7)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x−4=0x+7=0Set x−4 equal to 0 and solve for x. Set

x+7 equal to 0.x+7=0

Subtract 7 from both sides of the equation. x=−7

The final solution is all the values that make 4(x−4)(x+7)=0 true.

x=4,−7

Solving a system of equations necessarily necessitates the utilization of an appropriate unit system, depending on the equations to be solved.

Here are a few common unit systems employed when attempting to resolve such equations:

Metric System: This involves adhering to the International System of Units (SI), which is used across the world; in this premise, meters, kilograms, and seconds depict length, mass, and time respectively.

Imperial System: Proffered mainly in the United States, this method applies units like feet, pounds, and seconds for sizing, mass and time correspondingly.

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The new angle at which the tree is leaning is approximately 47.56 degrees.

To calculate the new angle of the tree after it leans back, we can use the concept of similar triangles. Initially, you have a shadow of 8 feet while being 5.5 feet tall. The tree's shadow is 48 feet long. Let's denote the height of the tree as H.

Using the initial measurements, we can set up the proportion:

5.5 / 8 = H / 48

Solving for H, we get:

H = (5.5 / 8) * 48 = 33 feet

Now, the tree leans back, and its shadow is now 30 feet long. We can use the tangent function to find the angle at which the tree is leaning:

tan(angle) = opposite / adjacent
tan(angle) = 33 / 30

To find the angle, we can take the inverse tangent:

angle = arctan(33 / 30)

angle ≈ 47.56 degrees

So, the new angle at which the tree is leaning is approximately 47.56 degrees.

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Gursant would measure an angle of approximately 29º (rounded to the nearest degree) from the ground to the top of the monument.

To solve this problem, we will use the formula d = rt, where d is the distance traveled, r is the rate (or speed), and t is the time.

First, we need to convert the time of 90 minutes to hours by dividing by 60: 90/60 = 1.5 hours.

Let's call the distance traveled by Suban "d1" and the distance traveled by Jas "d2". We want to find the distance between them, which we can call "d".

Using trigonometry, we can find that d1 = 12*cos(38º)1.5 = 11.513 km (rounded to 3 decimal places) and d2 = 14sin(38º)*1.5 = 8.307 km (rounded to 3 decimal places).

Now we can find the distance between them using the Pythagorean theorem: d^2 = d1^2 + d2^2.

Plugging in the values we found, we get d^2 = (11.513 km)^2 + (8.307 km)^2 = 221.93 km^2.

Taking the square root of both sides, we get d = 14.899 km (rounded to 3 decimal places).

Therefore, the two friends are approximately 14.899 km apart after riding for 90 minutes.

Let's call the distance from Gursant to the monument "x". Since Leo is standing 3.5 m closer to the monument, his distance from the monument is "x - 3.5".

Using trigonometry, we can set up the following equation:

tan(41º) = 6/x

Solving for x, we get:

x = 6/tan(41º) = 7.967 m (rounded to 3 decimal places)

Now we can find the angle that Gursant would measure from the ground to the top of the monument using the following equation:

tan(theta) = 6/(x + 3.5)

Plugging in the value we found for x, we get:

tan(theta) = 6/11.467

Solving for theta, we get:

theta = arctan(6/11.467) = 28.52º (rounded to the nearest degree)

Therefore, Gursant would measure an angle of approximately 29º (rounded to the nearest degree) from the ground to the top of the monument.

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The circle relation C defined on the set of real numbers is not reflexive and transitive but it is symmetric.

(a) C is not reflexive. To be reflexive, for every real number, xCx must hold true, meaning [tex]x^{2} + x^{2}[/tex]= 1. This is false. For example, let x=0. In this case, [tex]x^{2} + x^{2}[/tex] = 0, which does not equal 1. Therefore, C is not reflexive.

(b) C is symmetric.  If xCy then yCx, for all real numbers x and y. If we see the definition of C, this means that if [tex]x^{2} + y^{2}[/tex] = 1, then [tex]y^{2} + x^{2}[/tex] = 1. This is true due to the commutative property of addition ([tex]x^{2} + y^{2} = y^{2} + x^{2}[/tex] for all real numbers x and y). Thus, C is symmetric.

(c) C is not transitive. To be transitive, if xCy and yCz, then xCz must hold true for all real numbers x, y, and z. This means that if [tex]x^{2} + y^{2}[/tex] = 1 and [tex]y^{2} + z^{2}[/tex] = 1, then [tex]x^{2} + z^{2}[/tex]must equal 1. This is not always true. Let's take an example (x, y, z) = (1, 0, -1). Then [tex]x^{2} + y^{2}[/tex] = 1, [tex]y^{2} + z^{2}[/tex]= 1, but [tex]x^{2} + z^{2}[/tex] = 2, not 1. Thus, C is not transitive.

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The acceleration of the box is 0.4 m/s².

The magnitude of the force that Rory applies is 20.12 N.

(a)

The acceleration of the box can be calculated using the formula:

[tex]a = (v_f^2 - v_i^2) / (2d)[/tex]

where vf is the final velocity, vi is the initial velocity, and d is the distance traveled.

Substituting the given values, we get:

a = (1.2² - 0²) / (2 x 1.8)

a = 0.4 m/s²

(b)

To find the magnitude of the force that Rory applies, we can use Newton's second law, which states that the net force on an object is equal to its mass times its acceleration:

F(net) = ma

The resistance force is acting in the opposite direction to the force applied by Rory.

F(applied) - F(resistance) = ma

Substituting the given values.

F(applied) - 19 = 2.8 x 0.4

F(applied) = 19 + 1.12 = 20.12 N

Therefore, the magnitude of the force that Rory applies is 20.12 N.

Thus,

The acceleration of the box is 0.4 m/s².

The magnitude of the force that Rory applies is 20.12 N.

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