Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.)
∫xsin(7x²)cos(8x²)dx

Based on Chebyshev's Theorem, we can conclude that the lower bound for the number of bags in a sample of 225 that weigh between 335 and 371 gm is 200 bags.

Chebyshev's Theorem states that for any given number k greater than 1, at least (1 - 1/k²) of the data values in a dataset will fall within k standard deviations of the mean.

In this case, we have a sample size of 225 bags and a mean weight of 353 gm with a standard deviation of 6 gm.

To find a lower bound for the number of bags that weigh between 335 and 371 gm, we need to calculate the range within k standard deviations of the mean.

First, let's find the number of standard deviations for the given range:

Lower range: (335 - 353) / 6 = -3

Upper range: (371 - 353) / 6 = 3

Since we want to find the lower bound, we consider the lower range and use its absolute value: |-3| = 3.

Now, we can use Chebyshev's Theorem to find the lower bound:

(1 - 1/k²) ≤ (1 - 1/3²) = 1 - 1/9 = 8/9

This means that at least 8/9 of the bags will fall within 3 standard deviations of the mean.

To find the lower bound for the number of bags, we multiply this probability by the sample size:

Lower bound = (8/9) * 225 = 200

Therefore, based on Chebyshev's Theorem, we can conclude that the lower bound for the number of bags in a sample of 225 that weigh between 335 and 371 gm is 200 bags.

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The extreme points of the polyhedral set S are {(2, 1), (2, 2), (3, 1), (3, 2), (4, 1), (4, 2)}. There are no extreme directions in this case.

To find the extreme points and extreme directions of the polyhedral set S, we need to analyze the given inequalities.

The inequalities defining the polyhedral set S are:

2x1 + 4x2 > 4

-x1 + x2 < 4

x1 > 0

x2 > 0

Let's solve these inequalities step by step.

2x1 + 4x2 > 4:

Rearranging this inequality, we get x2 > (4 - 2x1) / 4.

This implies that x2 > (2 - x1/2).

-x1 + x2 < 4:

Rearranging this inequality, we get x2 > x1 + 4.

Combining the above two inequalities, we can determine the range of values for x1 and x2. We can draw a graph to visualize this region:

         x2

          ^

          |

     +    |   +

          |

     +----|---------+

          |

     +    |   +

          |

     +----|---------+----> x1

          |

          |

From the graph, we can see that the polyhedral set S is a bounded region with vertices at (2, 1), (2, 2), (3, 1), (3, 2), (4, 1), and (4, 2). These are the extreme points of S.

However, in this case, there are no extreme directions since the polyhedral set S is a finite set with distinct vertices. Extreme directions are typically associated with unbounded regions.

Therefore, the extreme points of S are {(2, 1), (2, 2), (3, 1), (3, 2), (4, 1), (4, 2)}, and there are no extreme directions in this case.

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Answer:

12+18x is the perimeter

Step-by-step explanation:

4+6x+4+6x+1/2(4+6x)+1/2(4+6x)=

3(4+6x)=

12+18x

Answer:

17

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

The answer is 17 because We noticed that 5 is 4 more than 1, 9 is 4 more than 5, and 13 is 4 more than 9. They are all a +4 pattern so you just simply add 4 to 13 which is 13 + 4 + 17 So our answer is 17

Answer:

ax^2 + bx + c = 0

Step-by-step explanation:

The graph the corresponds to the function f(x)=√(x - 1) is plotted and attached

A radical graph, also known as a square root graph, represents the graph of a square root function. A square root function is a mathematical function that calculates the square root of the input value.

key features of a radical graph is the shape: The shape of a square root graph is a concave upward curve. The steepness or flatness of the curve depends on the value of the constant a. A larger value of a results in a steeper curve, while a smaller value of a results in a flatter curve.

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Answers & Explanations:

5x-1=2(x-11)

5x-1=2x-22

3x-1=-22

3x=-21

x=-21/3

x=-7

\(\frac{x+4}{2}\)-\(\frac{x-1}{3}\)=1

\(\frac{3x+12}{6}\)-\(\frac{2x-2}{6}\)=1

\(\frac{3x+12-(2x-2)}{6}\)=1

\(\frac{3x+12-2x+2}{6}\)=1

\(\frac{x+14}{6}\)=1

x+14=6

x=6-14

x=-8

Hope this helps! Comment any questions.

Answer:

jdiejrkduebrhfjdidudjdidudheisuydudud

Step-by-step explanation:

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dhsjeuedieiwjwuejxofi 36

Answer:

11.96

Step-by-step explanation:

We can figure this out by multiplying 17.94 times 2/3, which gives us a total of 11.96

A hypothesis that there is some sort of relationship between the variables is where scientists start their inquiry. The alternative, or null hypothesis, asserts that there is no such relationship. Although the null hypothesis may not appear fascinating, it is a crucial component of research.

The claim can be supported by either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is the same as the value specified in the claim. If the null hypothesis is the assertion, then the alternative hypothesis statement is the antithesis of the null hypothesis. A hypothesis is a well-informed, logically-supported guess about the answer to a scientific question. Although it is the experiment's anticipated outcome, it does not constitute experimental proof. The information obtained may or may not be supported, depending on the information received. Simple hypotheses simply state the relationship between two independent and dependent variables. Examples: If you stay up late, you will feel fatigued the next day.

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Using JMP, the probability P(0 < X < 20) for a random variable X following a Normal distribution with mean 10 and standard deviation 10 is computed to be 0.68.

To compute the probability P(0 < X < 20) for the given Normal distribution, we need to first standardize the distribution to a standard Normal distribution (Z ~ N(0, 1)). The standardization process involves subtracting the mean (10) from both ends of the desired interval and dividing by the standard deviation (10).

For the lower bound:

Z_lower = (0 - 10) / 10 = -1

For the upper bound:

Z_upper = (20 - 10) / 10 = 1

Now, we can use JMP to calculate the probability that a standard Normal random variable is less than 1 and greater than -1. By applying the formula P(0 < X < 20) = P(Z < Z_upper) - P(Z < Z_lower), we obtain:

P(0 < X < 20) = P(Z < 1) - P(Z < -1)

Using JMP or a Z-table, we can find that P(Z < 1) is approximately 0.8413 and P(Z < -1) is approximately 0.1587. Subtracting these values gives us:

P(0 < X < 20) ≈ 0.8413 - 0.1587 = 0.6826

Rounding to the nearest hundredth, the probability P(0 < X < 20) is approximately 0.68 or 68%.

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To find the median d of set M, we first need to arrange the numbers in ascending order and then determine the middle value. Set M contains the numbers 37, 45, 7, 12, 21, 22, and n. We know n is a positive integer.

First, arrange the known numbers: 7, 12, 21, 22, 37, 45. Next, consider the position of n in the sorted sequence:

1. If n ≤ 7, the sorted sequence becomes: n, 7, 12, 21, 22, 37, 45.
2. If 7 < n ≤ 12, the sorted sequence becomes: 7, n, 12, 21, 22, 37, 45.
3. If 12 < n ≤ 21, the sorted sequence becomes: 7, 12, n, 21, 22, 37, 45.
4. If 21 < n ≤ 22, the sorted sequence becomes: 7, 12, 21, n, 22, 37, 45.
5. If 22 < n ≤ 37, the sorted sequence becomes: 7, 12, 21, 22, n, 37, 45.
6. If 37 < n ≤ 45, the sorted sequence becomes: 7, 12, 21, 22, 37, n, 45.
7. If n > 45, the sorted sequence becomes: 7, 12, 21, 22, 37, 45, n.

Since there are 7 numbers in the set, the median d will be the 4th value. In all cases, the 4th value remains 21. Therefore, the value of d is 21.

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The doctor used inductive reasoning because the doctor used various observations to come up with a final conclusion.

Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

In the coordinate axis the point D is located at the position of (5,-2) .

In the given graph of the coordinate axis , we can see that the four points A,B,C and D are located

The coordinates of each point are :

A (-5,-2)

B (-2,5)

C (2,-5)

D (5,-2)

Therefore using the given abscissae and ordinate of the points the point that is located at (5,-2) is D.

A coordinate system in geometry is a way to use one or more integers, or coordinates, to determine the exact placement of points or other geometrical objects on a manifold, such Euclidean space.

The order of the coordinates is crucial, and they are frequently identified by their position in an ordered tuple or by a letter, such as "the x-coordinate." The coordinates are often real values in elementary mathematics, but they could also be complex numbers or parts of a more abstract system, such a commutative ring.

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Step-by-step explanation:

a. The intersection of two open sets is an open set.

Let A and B be open sets. To prove that their intersection, A ∩ B, is also an open set, we need to show that for any point x ∈ A ∩ B, there exists an open ball centered at x that is completely contained within A ∩ B.

Since x ∈ A ∩ B, it means that x belongs to both A and B. Since A is open, there exists an open ball centered at x, let's call it B_A(x), such that B_A(x) ⊆ A. Similarly, since B is open, there exists an open ball centered at x, let's call it B_B(x), such that B_B(x) ⊆ B.

Now, consider the open ball B(x) with radius r, where r is the smaller of the radii of B_A(x) and B_B(x). By construction, B(x) ⊆ B_A(x) ⊆ A and B(x) ⊆ B_B(x) ⊆ B. Therefore, B(x) ⊆ A ∩ B.

Since for every point x ∈ A ∩ B, there exists an open ball centered at x that is completely contained within A ∩ B, we conclude that A ∩ B is an open set.

For the first statement, if x is in Cl(A), it means that every neighborhood of x intersects A. Since A ⊆ B, every neighborhood of x also intersects B. Therefore, x is in Cl(B).

b) If A ⊆ B, then Cl(A) ⊆ Cl(B) and int(A ∪ B) ⊆ (int(A) ∪ Cl(B)).

Let A and B be sets, and A ⊆ B. We want to prove two statements:

Cl(A) ⊆ Cl(B): If x is a point in the closure of A, then it belongs to the closure of B.

int(A ∪ B) ⊆ (int(A) ∪ Cl(B)): If x is an interior point of the union of A and B, then either it is an interior point of A or it belongs to the closure of B.

For the second statement, if x is in int(A ∪ B), it means that there exists a neighborhood of x that is completely contained within A ∪ B. This neighborhood can either be completely contained within A (making x an interior point of A) or it can intersect B. If it intersects B, then x is in Cl(B) since every neighborhood of x intersects B. Therefore, x is either in int(A) or in Cl(B). Hence, we have proven that if A ⊆ B, then Cl(A) ⊆ Cl(B) and int(A ∪ B) ⊆ (int(A) ∪ Cl(B)).

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Answer:

Step-by-step explanation:

Step 1: You have the slope so its already y=-4x+b. So you need to find the y intercept.

To find the y intercept, you need to plug the coordinates in. So 2=-4(-3)+b. Then you solve the equation from there.  

Hope this helps!

The area of the parallelogram whose vertices are listed (0,0), (2,8), (7,4), (9,12). The area of the parallelogram is 20 square units.

To find the area of a parallelogram, we need to know the base and height of the parallelogram. One of the sides of the parallelogram will serve as the base, and the height will be the distance between the base and the opposite side.

We can start by drawing the parallelogram using the given vertices:

(0,0)         (7,4)
     *---------*
     |         |
     |         |
     |         |
     *---------*
(2,8)         (9,12)

We can see that the sides connecting (0,0) to (2,8) and (7,4) to (9,12) are parallel, so they are opposite sides of the parallelogram. We can use the distance formula to find the length of one of these sides:

d = √[(9 - 7)^2 + (12 - 4)^2]
 = √[(2)^2 + (8)^2]
 = √68

So the length of one side is √68.

Next, we need to find the height of the parallelogram. We can do this by finding the distance between the line connecting (0,0) and (2,8) and the point (7,4). We can use the formula for the distance between a point and a line to do this:

h = |(7 - 0)(8 - 4) - (2 - 0)(4 - 0)| / √[(2 - 0)^2 + (8 - 0)^2]
 = |28 - 8| / √68
 = 20 / √68

Now we have the base (√68) and the height (20 / √68) of the parallelogram, so we can find the area using the formula:

A = base x height
 = (√68) x (20 / √68)
 = 20

Therefore, the area of the parallelogram is 20 square units.

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The statement that is true abut the slopes of perpendicular lines is that: D. One of the slopes is negative and the other is positive.

If two lines are perpendicular, it means that their slope (which is the change in y over x or rise/run along the line) will be negative reciprocal to each other.

For example, if the slope of one line is 2, the slope of any line that is perpendicular to the line must be negative reciprocal to 2, which is -1/2.

If we multiply their slopes together, we must have -1. I.e. 2 * -1/2 = -1. Therefore, if one is negative the other would be positive.

The correct answer is: D. One of the slopes is negative and the other is positive.

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Answer:

\(n = \frac{l-a}{d}+1\)

Step-by-step explanation:

\(l= a+(n-1)d\\\)

\(l -a =(n+1)d\)

Divide both sides of the equation by d

\(\frac{l-a}{d} = \frac{(n-1)}{d}\\ \\\frac{l-a}{d} = n-1\\\\\frac{l-a}{d}+1 = n\)

Percentages greater than 100% can be expressed as x% where x is any real number

As a general rule, percentages are represented by %

Take for instance

x% is pronounced x percentage

Where x is any real number

Whether x is greater than 100 or not, the format of the expression remains the same

i.e. 150 percent is written as 150% and 25 percent is written as 25%

Hence, percentages greater than 100% can be expressed as x% where x is any real number

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answer : 1 = P/2 - 2

w = (P - 2)/2

What is the value of w in an equation of P = 2(1 + w)?

P = 2(1 + w)

P = 2 + 2w

Reverse the equation,

2 + 2w = P

2w = P - 2

w = (P - 2)/2

w = (P - 2)/2

(a) To calculate the area surrounding the swimming pool, we need to consider the width of the cement around all sides of the pool. Since the cement has a uniform width of 4m on all sides, we need to add 4m to the length and width of the pool.

The length of the pool with the surrounding cement is 10m + 2(4m) = 10m + 8m = 18m.

The width of the pool with the surrounding cement is 5m + 2(4m) = 5m + 8m = 13m.

The area surrounding the swimming pool is the difference between the area of the larger rectangle (with the cement) and the area of the pool itself.

Area surrounding pool = Area of larger rectangle - Area of pool

= (18m) x (13m) - (10m) x (5m)

= 234m² - 50m²

= 184m².

(b) The cost to install the cement is determined by multiplying the area surrounding the pool by the cost per square meter, which is $50.

Cost to install cement = Area surrounding pool × Cost per square meter

= 184m² × $50/m²

= $9,200.

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since y=AsinKx.......1

so amplitude =|A|=1

Answer:

umm... i need a problem or anything bud

Step-by-step explanation:

"y" will represent the total cost per month

"x" will represent the number of movies watched in one month

There are two streaming plans:

Plan A

Has a monthly fee of $16 plus $2 per movie watched.

→ So if he watches no movies in a month, he will pay $16 and for each movie watched he will pay an extra $2

You can represent the monthly cost of plan A as follows:

Plan B

Has a monthly fee of $12 plus $3 for every movie watched.

The monthly cost of the plan can be expressed as follows:

For both equations the y-interceot represents the monthly fee of the plan and the slope of the line is the cost per movie.

To determine the number of movies (x) that would make both plans cost the same for one month using a graph, you have to draw both lines and determine the point where they intercept. The x-coordinate of said point will be the number of movies that make both plans cost the same.

To draw the lines you have to determine at least two points of the line.

The easiest point will be the y-intercept, for the second point, choose any value of x, replace it in the formula and calculate the corresponding value of y. Then plot both points and draw the line.

For plan A

y-intercept, x=0

The coordinates are (0,16)

Second point, for example, for x= 2 movies

The coordinates are (2,20)

For plan B

y-intercept, x=0

The coordinates are (0,12)

Second point, for example, for x=3

The coordinates are (3,21)

The red line represents the cost with respect to the number of movies for plan A

The purple line represents the cost with respect to the number of movies for plan B

Where both lines intercept indicates the point when both plans cost the same. Said point is (4,24), which means that when you watch x=4 movies both plans will cost $24 that month.

The value of x that makes the equation x³ = -64 true is x = -4.

To find the value of x that satisfies the equation x³ = -64, we need to solve for x.

We can rewrite the equation as x³+ 64 = 0. By applying the cube root to both sides of the equation, we get x + 4 = 0, which simplifies to x = -4.

Substituting x = -4 back into the original equation, we have (-4)³= -64. Evaluating the left side of the equation, we get -64 = -64, which confirms that x = -4 is the solution.

When x equals -4, the equation x³ = -64 holds true, satisfying the given condition.

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Answer:

31,536,000,000

Step-by-step explanation:

Have a nice day/night:)

Answer:

x^2+22x+121

Step-by-step explanation:

(x)^2+2*x*11+11^2

=x^22x+121