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The angle subtended at the center of the arc is 102⁰

Recall that to find the length of an arc on a circle, we can use the formula L = r *, where r is the radius of the circle, is the central angle, and is the angle between the ends of the arc.  If the central angle is measured in degrees, we can use the formula L = r *, where r is the radius of the circle, is the central angle, and is the angle between the ends of the arc.

Lenght of arc = A/360 *2пr

A = angle at center = ?

п = 22/7 r = radius = 840 feet

⇒1500 = A/360  2 *22/7 * 840

1500 = 36960A/2520

3780000= 36960A

making A the subject we have

3780000/36960 = A

A = 102.27

A= 102⁰

The angle is 102⁰

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Answer:

the answer is D. have a nice day :)

The alternative hypothesis should state P1 - P2 > 0 if we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2. The answer is a.

When testing hypotheses about the difference between two population proportions, we want to determine whether there is sufficient evidence to conclude that there is a significant difference between the two proportions.

The null hypothesis for this test states that the difference between the two population proportions is equal to zero, while the alternative hypothesis states that the difference is either greater than or less than zero.

If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, we are specifically looking for evidence that supports the idea that P1 is greater than P2. Therefore, the alternative hypothesis should state P1 - P2 > 0, indicating that the difference between the two proportions is positive.

On the other hand, if we were interested in testing whether the proportion in population 1 is smaller than the proportion in population 2, the alternative hypothesis would be P1 - P2 < 0. Finally, if we simply want to test whether the two proportions are not equal, the alternative hypothesis would be P1 - P2 ≠ 0. The answer is a.

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Question 3: True

Question 4: False

Question 5: True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c.

This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

Question 3: If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c.

True

When the derivative of a function, f'(x), is negative at a point c, it indicates that the function is decreasing at that point. Additionally, if the second derivative, f''(x), exists and is negative at x = c, it implies that the graph of f(x) is concave down at that point.

Question 4: A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0.

False

A local extreme point of a polynomial function can occur when f'(x) = 0, but it is not the only condition. A local extreme point can also occur when f'(x) does not exist (such as at a sharp corner or cusp) or when f'(x) is undefined. Therefore, f'(x) being equal to zero is not the sole requirement for a local extreme point to exist.

Question 5: If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = c.

True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c. This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

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The maximum value of the function f(x) = (x − x²)/(1 + 8x²) is 1/4, and it occurs when x = 1/2.

A function is a mathematical relationship between input and output values.

In this problem, we have a specific function defined as

=> f(x) = (x − x²)/(1 + 8x²).

Let's start by analyzing the expression of the function.

The function is composed of two parts:

=> (x − x²) and (1 + 8x²).

The first part is a simple polynomial expression with degree 2. It represents a parabolic shape with a vertex located at (1/2, 1/4).

The second part, (1 + 8x²), is always positive, so it does not affect the shape of the function.

The maximum value of the function will occur when the first part, (x − x²), is at its maximum. Since this part is a parabolic shape with a vertex at (1/2, 1/4), the maximum value is 1/4.

So, the maximum value of the function

=>  f(x) = (x − x2)/(1 + 8x²) is 1/4.

To find the value of x at which this occurs, we will have to find the x-coordinate of the vertex of the parabolic shape.

This can be done using the formula for the x-coordinate of the vertex of a parabolic equation, which is -b/2a.

Plugging in the values of a and b from the equation (x − x²) gives us

x = 1/2.

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The specified value of n for trapezoidal rule, the midpoint rule, and simpson's rule is 10.36 , 10.72 and 10.52.

Trapezoidal Rule: In Calculus, “Trapezoidal Rule” is one of the important integration rules. The name trapezoidal is because when the area under the curve is evaluated, then the total area is divided into small trapezoids instead of rectangles. This rule is used for approximating the definite integrals where it uses the linear approximations of the functions.

The trapezoidal rule is mostly used in the numerical analysis process. To evaluate the definite integrals, we can also use Riemann Sums, where we use small rectangles to evaluate the area under the curve.

Midpoint rule : In mathematics, the midpoint rule, also known as the midpoint Riemann sum or midpoint method, is a method of estimating the integral of a function or the area under a curve by dividing the area into rectangles of equal width. The midpoint rule formula is. The midpoint method formula works by summing the areas of each of the rectangles to produce an estimate for the area under a curve.

Simpson's Rule: Simpson's rule is used to find the value of a definite integral (that is of the form b∫ₐ f(x) dx) by approximating the area under the graph of the function f(x). While using the Riemann sum, we calculate the area under a curve (a definite integral) by dividing the area under the curve into rectangles whereas while using Simpson's rule, we evaluate the area under a curve is by dividing the total area into parabolas. Simpson's rule is also known as Simpson's 1/3 rule (which is pronounced as Simpson's one-third rule).

Now,

a=1,b=4,Δx =(b-a)/n =3/6 =1/2

f(x)=4√(ln(x))

trapezoidal rule:

∫4√(ln(x)) dx =(Δx /2)[f(1)+2*[f(1.5)+f(2)+f(2.5)+f(3)+f(3.5)]+f(4)]

∫4√(ln(x)) dx =((1/2) /2)[4√(ln(1))  +2*[4√(ln(1.5)) +4√(ln(2)) +4√(ln(2.5)) +4√(ln(3)) +4√(ln(3.5))] +4√(ln(4))]

∫4√(ln(x)) dx =10.365336

midpoint rule :

∫4√(ln(x)) dx =(Δx)[f(1.25)+f(1.75)+f(2.25)+f(2.75)+f(3.25)+f(3.75)]]

∫4√(ln(x)) dx =(1/2)[4√(ln(1.25))  +4√(ln(1.75)) +4√(ln(2.25)) +4√(ln(2.75)) +4√(ln(3.25)) +4√(ln(3.75)) ]

∫4√(ln(x)) dx =10.724182

simpsons rule:

∫4√(ln(x)) dx =(Δx /3)[f(1)+4*f(1.5)+ 2*f(2)+ 4*f(2.5)+  2*f(3)+  4*f(3.5)]+f(4)]

∫4√(ln(x)) dx =((1/2) /3)[4√(ln(1))  +4*4√(ln(1.5)) +  2*4√(ln(2))  +4*4√(ln(2.5))  +2*4√(ln(3)) + 4*4√(ln(3.5)) +4√(ln(4))]

∫4√(ln(x)) dx =10.527905

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There are 13,992 integers between 1 and 1,000,000 with a sum of digits equal to 15.

To find the number of integers between 1 and 1,000,000 with a sum of digits equal to 15, we can use a combinatorial approach.

We need to distribute the sum of 15 among the digits of the number. We can think of this as placing 15 indistinguishable balls into 6 distinct boxes (corresponding to the digits).

Using the stars and bars method, the number of ways to distribute the sum of 15 among 6 boxes is given by the combination formula:

C(n + r - 1, r - 1)

where n is the sum (15) and r is the number of boxes (6).

Plugging in the values, we have:

C(15 + 6 - 1, 6 - 1) = C(20, 5)

Calculating this combination, we find:

C(20, 5) = 13,992

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Using proportional relationships, we can say that They will walk 12 laps and run 20 laps for a total of 32 miles.

In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

Given that we know this, they walk 3/8 of the 8 miles that make up the complete distance. Run 5/8 of the route.

The following are the proportional relationships for the distances:

For a total distance of 32 miles, the distances walked and run are given:

therefore, They will walk 12 laps and run 20 laps for a total of 32 miles as per the proportional relation.

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The yy-component of vector a a is -y-direction, which is equal to 0 m/s2.the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.

Given a vector, a⃗ a→ = (5.0 m/s2, −y−direction)Find the yy -component of the given vector a⃗ a→.Solution: The yy-component of the given vector a⃗ a→ = -y-directionTo find the yy-component of the given vector a⃗ a→, we have to take the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.Therefore, the yy-component of vector a⃗ a→ is :a_yy = -y-direction = (-1)(0) = 0 m/s²  Answer: 0 m/s².

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The yy-component of vector a⃗ a→ is -y-direction.

The yy-component of a vector represents the magnitude of the vector in the y-direction.

In this case, the vector a⃗ a→ is given as (5.0 m/s2, −y-direction).

Since the yy-component is the magnitude in the y-direction, the yy-component of the vector a⃗ a→ is -y-direction.

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1945 men and 2849 women register to audition for a singing competition. The number of participants who are not successful in their auditions what’s five times the number of those who are successful. There are 799  participants were successful.

The successful  participants  can be calculate by solving a linear equation as follows

First, it's crucial to understand linear equations.

Equation connects the two algebraic expressions with an equal to sign to demonstrate the equality between the two algebraic expressions.

Linear equations are those with one degree.

In this case, a linear equation must be resolved.

1945 for the men's total

Women are present in 2849.

Participants in total: 1945 + 2849 = 4794

Let x be the proportion of participants that were successful.

Men who failed were 5 times as numerous.

Participants in total: 5x + x = 6x

Due to the issue,

The linear formula is

6x = 4794

x = 4794/6

x = 799

799 of the participants had success.

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(b) Yes, the experiment has a control group.

(c) The treatments can be randomly assigned to the experimental units by randomly selecting 20 containers and assigning each of the four treatments to 5 containers.

a) Treatments: Four different concentrations of fungus mixtures (0 ml/L, 1.25 ml/L, 2.5 ml/L, and 3.75 ml/L).

Experimental units: 20 individual containers with a group of insects.

Response variable: Number of insects that are still alive in each container one week after spraying.

(b) A control group is used to compare the results of the treatment group to a group that is not exposed to the treatment.

In this experiment, the control group can be the group of insects that are not exposed to any of the fungus mixtures.

c) The treatments can be randomly assigned to the experimental units by randomly selecting 20 containers and assigning each of the four treatments to 5 containers.

This way, each treatment has the same number of units and the assignment of treatments to units is random, which reduces the risk of bias in the experiment.

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The tree is 34 feet tall.

Ratio of length of the stick to the length of the shadow = 6 : 4.5 = 4:3

Ratio of length of the tree to the length of its shadow   = x : 25 = 4:3

x / 25 = 4 / 3

x = 25 x 4 / 3 = 100/3 = 33.33

Therefore, the length of the tree to the nearest foot is 34 feet (approximately).

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Answer:

the answer is 71

Step-by-step explanation:

423/6

42÷6=7

42-42=0

6÷3=×

30÷6=5

70.5--> 71

Answer:

∠ 6 = 62°

Step-by-step explanation:

∠ 6 and ∠ 8 are corresponding angles and are congruent , so

∠ 6 = ∠ 8 = 62°

Answer:

1/-20 or -0.05

Step-by-step explanation:

Step-by-step explanation:

\(y = 5x \\ y = 9x + 4 \\substitute \:y = 5x \: to \: the \: other \: equation \\ y = 9x + 4 \\5x = 9x + 4 \\ 5x - 9x = 4 \\ - 4x = 4 \\ x = \frac{4}{ - 4} \\ x = - 1\)

Answer:

1. G

2. E

3. C

Step-by-step explanation:

Multiply the number on the outside by both on the inside.

Answer:

C,E,G

Step-by-step explanation:

Multiply the number out of the parenthesis to both of the ones in the parenthesis

The dependent variable in this study is the number of times the students got out of their seats over the course of 2 hours.

The independent variable is the variable that is being manipulated or controlled by the researcher.

It is the variable that is expected to cause a change in the dependent variable which is the variable being measured as the outcome or response to the manipulation of the independent variable.

In the given scenario, the independent variable is the group assignment based on the scores on the sensation-seeking test.

The researcher has divided the students into two groups based on their scores, and this grouping is being used as a way of manipulating or controlling the students' level of sensation-seeking behavior.

The researcher is interested in how this manipulation affects the students' behavior in terms of getting out of their seats.

The dependent variable is the number of times the students got out of their seats over the course of 2 hours.

This variable is expected to vary depending on the level of the independent variable, which is the group assignment based on the sensation-seeking test scores.

The researcher will measure the dependent variable for each group separately and then compare the results to determine if there is a significant difference between the two groups.

In summary,

The independent variable is the grouping of the students based on their scores on the sensation-seeking test and the dependent variable is the number of times the students got out of their seats over the course of 2 hours.

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Probability that at least one of them is a universal donar is 0.5263.

What is probability ?

What is probability explain?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Have given,

Probability of getting a universal donor is 0.072.

X be the “random variable” which “describes the number of universal donors” in the “sample of 10 people”.

X follows a “binomial distribution” with n=10 and p=0.072

P(X=x) = (\({n}C^{x}\))*(\(p^{x}\))*(\(q^{n-x}\)) ; x=1(1)10 ; q=1-p

Required probability,

P(X≥1)= 1 - P(X=0)

= 1 - (10C0)*(\(0.072^{0}\))*(\(0.928^{10}\))

= 1 - 0.4737 = 0.5263

Probability that at least one of them is a universal donar is 0.5263.

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There are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

In this problem, we want to find the number of ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

Since every man must be diametrically opposite a woman, we can pair each man with one woman. There are 5 men and 9 women, so there are 5 pairs. We need to find the number of ways to seat these 5 pairs of people in a circle.

To do this, we can first seat one pair in any position. Then, we can seat the second pair anywhere but opposite the first pair. This gives us 11 positions for the second pair. Continuing in this way, we see that there are 11 * 6 * 5 * 4 * 3 = 7920 ways to seat the 5 pairs of people in a circle.

So, there are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

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Assuming 14 people, 5 men and 9 women, how many ways can they sit in a circle such that every man is diametrically opposite a woman?

The segment AB is a radius and the notation is ↔ AB

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

The circle

On the circle, we can see that

The segment AB goes from the center of the circle to a point on the circle

A line that goes from the center of the circle to a point on the circle is the radius of the circle

This means that the segment AB is a radius and the notation is ↔ AB

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Solve for x

|2x -4| + 6 =8

subtract 6 from both sides, then solve

|2x - 4| = 2                                   and                                 |2x -4| = -2

2x - 4 = 2                                                                           2x - 4 = -2

     +4   +4                                                                                +4  +4

2x = 6                                                                                   2x = 2

divide by 2 to isolate the variable

x = 3                                                                                    x = 1

in the Golden Balls game, there is only one pure strategy Nash equilibrium, which is (Split, Split).

In the Golden Balls game, there are two players, Player 1 and Player 2. Each player can choose to either "Split" or "Steal." The payoffs for each possible combination of actions are as follows:

If both players choose Split, they both receive a payoff of 50.

If Player 1 chooses Steal and Player 2 chooses Split, Player 1 receives 100, and Player 2 receives 0.

If Player 1 chooses Split and Player 2 chooses Steal, Player 1 receives 0, and Player 2 receives 100.

If both players choose Steal, they both receive a payoff of 0.

To find all the pure strategy Nash equilibria, we need to identify any strategies where neither player has an incentive to deviate unilaterally.

Pure Strategy Nash Equilibria:

(Split, Split): This is a pure strategy Nash equilibrium because if both players choose Split, neither player can improve their payoff by unilaterally changing their strategy to Steal.

Now let's consider mixed strategy Nash equilibria, where players randomize between their available strategies.

Mixed Strategy Nash Equilibrium:

To find the mixed strategy Nash equilibrium, we need to examine whether there exists a probability distribution over strategies that maximizes the expected payoff for each player, given the other player's strategy.

In this case, there is no mixed strategy Nash equilibrium since Player 2's expected payoff from choosing Split is always lower than the expected payoff from choosing Steal, regardless of the probabilities assigned to each strategy by Player 1. Similarly, Player 1's expected payoff from choosing Split is always lower than the expected payoff from choosing Steal, regardless of the probabilities assigned to each strategy by Player 2.

Therefore, in the Golden Balls game, there is only one pure strategy Nash equilibrium, which is (Split, Split).

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Answer:

1. Sine ratio of angle ∠C = 12/13

2. cos ratio for ∠C = 6/10

Step-by-step explanation:

1. sin = perpendicular /hypotuse

=> 12/13

2. cos = base / hypotuse

=> 6/10

Answer:

x = 7

Step-by-step explanation:

Lets do the brackets first,

6 × 2x = 12

6 × -11 = -66

------

Calculate the x constant:

12x - 3x = 9x

-------

Then the ones with no x:

-66 + 15 = -51

51 + 12 = 63

-------

Lastly, divide

63 ÷ 9 = 7

-------

Have a good day :)

Answer:

degree 3

Step-by-step explanation:

To get the degree, we open up the bracket

We have this as;

f(x) = x(x-2x^2)

f(x) = x^2 - 2x^3

3 is the highest power of x and thus, it is our degree

Answer:-1 as said in the bottom of the equation

Step-by-step explanation: it is at the bottom of the equation if wrong sorry.

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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