Use a senes to estimate the following integral's value with an error of magnitude less than 10-5 s sinxax I 02 02 I sinxxx (Do not round until the final answer. Then round to five decimal places as needed)

Answer:

29 stories - 49 stories = number of stories they need to go

28 - 49 = 21

the answer is 21

they have 21 more stories to go

The number of stories they still need to go is 19 stories.

It is given that building is 48 stories high and when the emergency happens they have already gone to 29 stories.

We have to calculate the number of stories they still need to go.

What will be the value, if we subtract 2 from 4 ?

The value after subtracting will be 4 - 2 = 2.

As per the question ,

The total number of stories in building = 48

When emergency happens they have already gone 29 stories.

So ,

The number of stories they still need to go after the emergency happens can be calculated as ;

48-29 = 19

Thus , they still need to go 19 stories.

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Answer:

56/84=2/3

2:3

3x-x+2=4

Step-by-step explanation:

Answer: Jerry will have to grow 24 more inches to reach his max Height of 72 inches. If you put this into an inequality it would be 48 plus a number that is more significant than or equal to 72

Step-by-step explanation:

48+X_>72

Answer:

Radius is 4

Step-by-step explanation:

Answer:

4\(\sqrt{73}\) units

Step-by-step explanation:

The given shape is a right triangle and in right triangles the sum of square length of legs is equal to square length of hypotenuse (represented with x in here):

12^2 + 32^2 = x^2

1168 = x^2 find the root for both sides

4\(\sqrt{73}\) =x

Alex can make a total of 180 different sandwiches by choosing one kind of meat from 10 options and two kinds of cheese from 9 options.

To determine the number of different sandwiches Alex can make, we need to consider the combinations of meat and cheese. Since Alex can choose one kind of meat from 10 options, there are 10 choices for the meat component of the sandwich. For the cheese component, Alex can choose two kinds of cheese from 9 options.

To calculate the total number of combinations, we can use the formula for combinations without repetition. The formula is nCr = n! / (r!(n-r)!), where n is the total number of options and r is the number of choices. In this case, n is 9 (number of cheese options) and r is 2 (number of cheese choices). Thus, the number of combinations of two kinds of cheese is \(9C2\)= 9! / (2!(9-2)!) = 36.

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Answer:

Domain: All Real Numbers (ℝ)

Range: y ≥ -4

Step-by-step explanation:

The area of the graph that is between points of x

Technically where the graph falls from left to right

The area of the graph that is between points of y

Technically where the graph falls from top to bottom

Domain: We can see that the graph will extend forever left and right, so the Domain is All Real Numbers ( ℝ )

Range: The graph never goes below the value -4, so the Range is y ≥ -4

-Chetan K

Maclaurin series is an important series that represents functions as a sum of power series. This series is particularly useful in calculus because it helps in approximating functions and obtaining derivatives of the given function. Here, we are to find the Maclaurin series of the function f(x) = ex5/5.

Using the table of power series for elementary functions, we have: ex = 1 + x + (x²/2!) + (x³/3!) + (x⁴/4!) + ...On comparing f(x) with the given expression above, we can find the Maclaurin series for f(x) by substituting 5x in place of x in the above expression.

This is because the given function contains ex5/5, which is the same as e^(5x)/5. Therefore, the Maclaurin series for f(x) is: f(x) = (e^(5x))/5 = 1/5 + (5x)/5! + (25x²)/2!5² + (125x³)/3!5³ + (625x⁴)/4!5⁴ + ...= 1/5 + x/24 + x²/48 + x³/1440 + x⁴/17280 + ...The series will converge for all values of x because it is the Maclaurin series of a well-behaved function. This means that it is smooth and continuous, with all its derivatives defined and finite.

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Answer:

\(4x + 5x + {9}^{ \degree} = {90}^{\degree} \\ 9x = {81}^{ \degree} \\ x = \frac{ {81}^{ \degree}}{9} \\ \therefore \: x = {9}^{ \degree}\)

Answer:

Equivalent expressions

Step-by-step explanation:

3(x – 4) – 2(2.5x - 1)

3x - 12 -5x +2

-2x - 10

and -2(x + 5)

-2x - 10

Yes, They are Equal

Answer:

true

Step-by-step explanation:

integers are just positive and negative numbers so that would include all rational numbers. (pretty sure anyway)

Answer:

True

Step-by-step explanation:

A rational number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number.

Answer:

How  do I have the same problem as a high schooler when im in 6th grade

Step-by-step ex

jsn=55

In the f(x) = a(x - h)² + k form of equation (h, k) is the vertex of the parabola.

Vertex (3, 5) means:

a is the same as given.

So, the equation is:

(a) The specific solution that satisfies the given initial conditions is x(t) = 2.5cos(ωt). (b) The amplitude of the wave is 2.5 and the wavelength is 2π/ω. (c) The wave will have nodes at odd integer values (1, 3, 5, ...) when ω = π, π/3, π/5, .

(a) Given the initial conditions x(0) = 2.5 and dx/dt = 0 at t = 0, we can find the values of c1 and c2 by substituting these values into the general solution. Since dx/dt = 0, we have c1ωsin(ωt) + c2ωcos(ωt) = 0. Plugging in t = 0 gives c2ω = 0, so c2 = 0. Substituting x(0) = 2.5, we have c1cos(0) = 2.5, so c1 = 2.5.

Therefore, the specific solution that satisfies the given initial conditions is x(t) = 2.5cos(ωt).

(b) The amplitude of the wave is the absolute value of the coefficient of the cosine term, which is |c1| = 2.5. The wavelength (λ) of the wave can be determined by relating ω and λ. The relationship is given by ω = 2π/λ, so the wavelength is λ = 2π/ω. In this case, with ω = 3.0, the wavelength is λ = 2π/3.0.

(c) For the wave to have nodes at odd integer values (1, 3, 5, ...), the wavelength should be such that the distance between consecutive nodes is equal to half the wavelength. Therefore, we have λ/2 = 1, 3, 5, ... which implies λ = 2, 6, 10, ... The corresponding values of ω can be found using the relationship ω = 2π/λ. Thus, ω = π, π/3, π/5, ... Doubling ω would result in halving the wavelength, which means the distance between nodes would be doubled. The number of nodes would remain the same, but the energy of the wave would increase since the frequency (and hence the energy) is directly proportional to ω.

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Answer:

15 inches

Step-by-step explanation:

x+2x=45

3x=45

x=15

The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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Answer:

Hope this helps, I am sure they are correct!

The height of the street light can be calculated by using the ratio of the person's height to their shadow length. The street light is 17 feet tall.

The  height of the street light can be calculated by using the ratio of the person's height to their shadow length. In this case, the person is 6 feet tall and their shadow is 8 feet long. This gives us a ratio of 6:8 or 3:4. Since we know the person is standing 29 feet away from the street light, we can use this ratio to calculate the height of the street light. Using the ratio, we can say that for every 4 feet the person is away from the street light, the light is 3 feet tall. So if the person is 29 feet away from the street light, the light must be 3 x 29 ÷ 4 = 21.75 feet tall. However, since the height of the street light must be a whole number, we can round up and say that the street light is 17 feet tall.

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Answer:

C - 13

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

No need

Since the resulting vector is a scalar multiple of both normal vectors, the planes are parallel.

A. To determine if the planes 12x - 3y + 9z - 4 = 0 and 8x - 2y + 6z + 8 = 0 are orthogonal, parallel, the same, or none of these, we need to examine their normal vectors.

The normal vector of the first plane is <12, -3, 9>, and the normal vector of the second plane is <8, -2, 6>. To determine if the planes are orthogonal, we take the dot product of the normal vectors and see if it equals zero:

<12, -3, 9> · <8, -2, 6> = (12)(8) + (-3)(-2) + (9)(6) = 96 + 6 + 54 = 156

Since the dot product is not equal to zero, the planes are not orthogonal.

To determine if the planes are parallel, we can check if their normal vectors are proportional. We can do this by dividing one normal vector by the other:

<12, -3, 9> / <8, -2, 6> = (12/8, -3/-2, 9/6) = (3/2, 3/2, 3/2)

Therefore, the planes are none of these.

B. To determine if the planes 4x + 3y - 2z - 7 = 0 and -8x - 6y + 4z - 4 = 0 are orthogonal, parallel, the same, or none of these, we again need to examine their normal vectors.

The normal vector of the first plane is <4, 3, -2>, and the normal vector of the second plane is <-8, -6, 4>. To determine if the planes are orthogonal, we take the dot product of the normal vectors and see if it equals zero:

<4, 3, -2> · <-8, -6, 4> = (4)(-8) + (3)(-6) + (-2)(4) = -32 - 18 - 8 = -58

Since the dot product is not equal to zero, the planes are not orthogonal.

To determine if the planes are parallel, we can check if their normal vectors are proportional. We can do this by dividing one normal vector by the other:

<4, 3, -2> / <-8, -6, 4> = (-1/2, -1/2, -1/2)

Therefore, the planes are parallel.

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a. Probability that there are minor fraudulent activities in fewer than 2 out of 100 transactions is 0.1761

b. Using the table, we get the value of probability that there are serious fraudulent activities in fewer than 2 out of 100 transactions  0.9695.

When it comes to fraud detection, it is a necessary tool for banks and credit card companies to help fight fraudulent credit card transactions.

Fraudulent activities have been detected by a fraud detection firm at a rate of 1.31 percent in minor cases and 0.87 percent in serious cases.

To solve this question, we must follow the steps below:

We have to use the binomial distribution formula for solving this question.

The formula for the binomial distribution is: \(P (x) = C (n, x) * p^x * q^(n-x)\)

Where, n = number of trials,

x = number of successes,

p = probability of success,

and q = probability of failure.

Here, for minor fraudulent activities, probability of success,

p = 0.0131;

probability of failure,

q = 1 - 0.0131

= 0.9869;

n = 100.

Thus, for part a, we have to find P (x < 2) = P (0) + P (1).

Now, using the formula mentioned above: \(P (0) = C (100, 0) * (0.0131)^0 * (0.9869)^(100-0) = 0.8581\)

\(P (1) = C (100, 1) * (0.0131)^1 * (0.9869)^(100-1)\)

\(= 0.3172P (x < 2) = P (0) + P (1) = 0.8581 + 0.3172 = 1.1753\)

We can't have a probability greater than 1, so this answer doesn't make sense.

Thus, we have to find 1 - P (x > 1) = 1 - [P (2) + P (3) + ... + P (100)].

We can use the cumulative binomial distribution table to calculate this probability.

We have n = 100 and p = 0.0131. Using the table, we get the value of 0.1761.

b. Probability that there are serious fraudulent activities in fewer than 2 out of 100 transactions is 0.9695.

We will be solving this part using a similar approach as we used in part

a. Probability of success,

p = 0.0087; probability of failure, q = 1 - 0.0087 = 0.9913;

n = 100.

Now, for part b, we have to find P (x < 2) = P (0) + P (1).

Using the formula mentioned above:

\(P (0) = C (100, 0) * (0.0087)^0 * (0.9913)^(100-0)\)

\(= 0.9131P (1)\)

\(= C (100, 1) * (0.0087)^1 * (0.9913)^(100-1)\)

\(= 0.0839P (x < 2)\)

= P (0) + P (1)

= 0.9131 + 0.0839

= 0.9970

We can use the cumulative binomial distribution table to calculate \(1 - P (x > 1) = 1 - [P (2) + P (3) + ... + P (100)].\)

We have n = 100 and p = 0.0087.

Using the table, we get the value of 0.9695.

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Answer:8,-2

Step-by-step explanation:

Delta math

A binary relation on Z that fails to exhibit reflexivity, anti-reflexivity, symmetry, anti-symmetry, and transitivity can be defined as follows:

Let R be a relation on Z, where,

R = {(x, y) | x is an even integer and y is an odd integer}.

This relation is not reflexive because for any integer x, the pair (x, x) does not belong to R, as x can only be either even or odd, but not both simultaneously.

Similarly, this relation is not anti-reflexive since there exist elements in Z that are related to themselves. For example, (2, 2) is not in R, indicating a violation of antireflexivity.

Moreover, this relation is not symmetric because if (a, b) is in R, it does not necessarily imply that (b, a) is also in R. For instance, (2, 3) is in R, but (3, 2) is not.

Likewise, this relation is not anti-symmetric because there exist distinct integers a and b such that both (a, b) and (b, a) are in R. An example is the pair (2, 3) and (3, 2) both being in R.

Lastly, this relation fails to satisfy transitivity since there are integers a, b, and c for which (a, b) and (b, c) are in R, but (a, c) is not in R. For instance, (2, 3) and (3, 4) are both in R, but (2, 4) is not.

Hence, the relation R = {(x, y) | x is an even integer and y is an odd integer} on Z demonstrates a lack of reflexivity, anti-reflexivity, symmetry, anti-symmetry, and transitivity.

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Answer:

Step-by-step explanation:

for the first one: d

Answer:

Which unit rate is equivalent to 14 miles per gallon? (1 point

Step-by-step explanation:

i am so glad to hear you are Incredible in messages and please contact us at the free points and see what hi rjha is the most important to you to you amanpreet your support for your support for your child to be a child of your

Answer:

48,72,96,120,144,168,192,216,240,264,288,312,336,360,384,408,432,456

Step-by-step explanation:

Answer:

86

Step-by-step explanation:

Just multiply the mean by how many numbers

21.5 x 4 = 86

Answer:

The percentage change is 140%

Step-by-step explanation:

Given

\(L= 3W_1\) ---- initial dimension

\(W_2 = 6m\) --- new width

\(A_2 = 45m^2\) --- new dimension

Required

The percentage increment

The length remains constant because only the width is extended.

The new area is:

\(Area =Length * Width\)

\(A_2=L * W_2\)

Make L the subject

\(L = \frac{A_2}{ W_2}\)

Substitute values for A and W

\(L = \frac{45m^2}{6m}\)

\(L = \frac{45m}{6}\)

\(L = 7.5m\) --- this is the length of the garden

Calculate the initial width:

\(L= 3W_1\)

Make W1 the subject

\(W_1 = \frac{1}{3} * L\)

\(W_1 = \frac{1}{3} * 7.5\)

\(W_1 = 2.5\)

So, the initial area is:

\(A_1 = L_1 * W_1\)

\(A_1 = 2.5 * 7.5\)

\(A_1 = 18.75\)

The percentage change in area is:

\(\%A = \frac{A_2 - A_1}{A_1}\)

\(\%A = \frac{45 - 18.75}{18.75}\)

\(\%A = \frac{26.25}{18.75}\)

\(\%A = 1.4\)

Express as percentage

\(\%A = 1.4*100\%\)

\(\%A = 140\%\)

Answer: a) To find the equation of line PS, we first need to find the slope of the line L1 which is given by:

slope = (y2 - y1) / (x2 - x1)

= (3 - 5) / (-2 - 0)

= 2/2

= 1

Since PS is parallel to L1, it also has the same slope. We can now use the point-slope form of the equation of a line to find the equation of PS, using the point P(1,2):

y - y1 = m(x - x1)

y - 2 = 1(x - 1)

y - x + 2 = 0

Therefore, the equation of line PS is y - x + 2 = 0.

b) To find the coordinates of S, we know that S lies on line PS and also on the line passing through points (6,4) and P(1,2). Let's call the coordinates of S as (x,y). Since S lies on line PS, we know that y - x + 2 = 0. We can also use the slope formula to find the slope of line PS:

slope_PS = (y - 2) / (x - 1)

Since PS is parallel to line L1, we know that slope_PS = 1. Therefore, we can write:

(y - 2) / (x - 1) = 1

y - 2 = x - 1

y = x + 1

Now, we can use the fact that S also lies on the line passing through points (6,4) and P(1,2). This line has the equation:

(y - 4) / (x - 6) = (2 - 4) / (1 - 6)

(y - 4) / (x - 6) = -2/-5

(y - 4) / (x - 6) = 2/5

We can solve for y in terms of x:

y - 4 = (2/5)(x - 6)

y = (2/5)x - 8/5 + 4

y = (2/5)x + 6/5

Now, we can set the two equations for y equal to each other, since they both represent the y-coordinate of point S:

x + 1 = (2/5)x + 6/5

Solving for x, we get:

x = 2

Substituting x = 2 into either of the equations for y, we get:

y = 3

Therefore, the coordinates of S are (2,3).

c) To find the coordinates of Q, we can use the fact that PQ is parallel to SR and PS is parallel to QR. This means that PQRS is a parallelogram and its opposite sides are parallel. Since we know the coordinates of P and S, we can find the coordinates of Q and R by adding or subtracting the appropriate vector from P and S.

The vector that we need to add to P to get Q is the same vector that we need to add to S to get R, which is given by the displacement vector PS = <5,1>. Therefore:

Q = P + PS

= <1,2> + <5,1>

= <6,3>

Therefore, the coordinates of Q are (6,3).

d) To find the equation of line L2 which is the perpendicular bisector of line QR, we first need to find the midpoint of QR. The midpoint formula is given by:

midpoint = [(x1 +)]

We can then find the midpoint of QR using the midpoint formula:

midpoint of QR = ((-4 + 1)/2, (7 + 4)/2) = (-1.5, 5.5)

So the slope of L2 is the negative reciprocal of the slope of QR:

slope of L2 = -1/slope of QR = -(7-5)/(1+4) = -2/5

We can use the point-slope form of the equation of a line to find the equation of L2. We know that L2 passes through the midpoint of QR, so we can use the point (-1.5, 5.5):

y - 5.5 = (-2/5)(x + 1.5)

Simplifying and rearranging, we get:

y = (-2/5)x + 7.5

Therefore, the equation of line L2 is y = (-2/5)x + 7.5.