If the trapezoidal rule is used to approximate the integral[sin x^2] dx with 20 strips, what value of h should be used?
[1] h = 7/20 [2] h = 5/20 [3] h = 10/20
[4] h=5/40

The probability that a 0 is received can be found using conditional probability. Let's denote the event that a 0 is sent as S0, and the event that a 0 is received as R0. We want to find P(R0), the probability that a 0 is received.

Using the law of total probability, we can express P(R0) as the sum of the probabilities of receiving a 0 given that a 0 or a 1 was sent, weighted by the probabilities of sending a 0 or a 1:

\(P(R0) = P(R0|S0)P(S0) + P(R0|S1)P(S1)\)

We are given that the probe sends a 1 one-third of the time and a 0 two-thirds of the time, so we have:

P(S0) = 2/3
P(S1) = 1/3

We are also given the probabilities of receiving a 0 or a 1 correctly or incorrectly, so we have:

P(R0|S0) = 0.6
P(R1|S0) = 0.4
P(R0|S1) = 0.2
P(R1|S1) = 0.8

Plugging these values into the formula for P(R0), we get:

P(R0) = (0.6)(2/3) + (0.8)(1/3)
     = 1/2

Therefore, the probability that a 0 is received is 1/2, or 50%.

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Answer:

a

Step-by-step explanation:

Move 6 to the right by subtracting 6 to both sides of <

7x<4x+18

Now move 4x to the left by subtracting 4x to both sides of <

3x<18

Now divide 3 by both sides of < to solve for x

x<6

If the storage container can hold 896 wooden cube blocks with edge length of 1/4 ft , then the volume of the container is 14 ft³ .

The shape of the storage container is rectangular prism ,

the number of cube blocks that the container can hold is = 896 wooden cube ,

the edge length of each cube is = 1/4 ft ,

we know that the volume of cube is = (edge length)³ ,

So , the volume of the container is = 896 × (1/4)³ ,

= 896 × (1/64) ,

On simplifying ,

we get ,

= 14 .

Therefore , the volume of the cube is 14 ft³ .

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Answer:

a = 20

Step-by-step explanation:

a = (4 + 6) (2)

a = 10 × 2

a = 20

Answer:

The value of a is 20

Step-by-step explanation:

( 4 + 6 ) ( 2 ) a = 0

( 4 + 6 ) ( 2 ) = a

(10)(2) = a

10×2 = a

20 = a

∴ a = 20

The response y(t) graphically, we can first plot the individual functions h(t) and x(t) on a graph, and then determine their convolution to obtain y(t). Let's go step by step:

Plotting h(t):

The function h(t) is defined as h(t) = [u(t-1) - u(t-4)].

The unit step function u(t-a) is 0 for t < a and 1 for t ≥ a. Based on this, we can plot h(t) as follows:

For t < 1, h(t) = [0 - 0] = 0

For 1 ≤ t < 4, h(t) = [1 - 0] = 1

For t ≥ 4, h(t) = [1 - 1] = 0

So, h(t) is 0 for t < 1 and t ≥ 4, and it jumps up to 1 between t = 1 and t = 4. Plotting h(t) on a graph will show a step function with a jump from 0 to 1 at t = 1.

Plotting x(t):

The function x(t) is defined as x(t) = t[u(t) - u(t-2)].

For t < 0, both u(t) and u(t-2) are 0, so x(t) = t(0 - 0) = 0.

For 0 ≤ t < 2, u(t) = 1 and u(t-2) = 0, so x(t) = t(1 - 0) = t.

For t ≥ 2, both u(t) and u(t-2) are 1, so x(t) = t(1 - 1) = 0.

So, x(t) is 0 for t < 0 and t ≥ 2, and it increases linearly from 0 to t for 0 ≤ t < 2. Plotting x(t) on a graph will show a line segment starting from the origin and increasing linearly with a slope of 1 until t = 2, after which it remains at 0.

Obtaining y(t):

To obtain y(t), we need to convolve h(t) and x(t). Convolution is an operation that involves integrating the product of two functions over their overlapping ranges.

In this case, the convolution integral can be simplified because h(t) is only non-zero between t = 1 and t = 4, and x(t) is only non-zero between t = 0 and t = 2.

The convolution y(t) = h(t) * x(t) can be written as:

y(t) = ∫[1,4] h(τ) x(t - τ) dτ

For t < 1 or t > 4, y(t) will be 0 because there is no overlap between h(t) and x(t).

For 1 ≤ t < 2, the convolution integral simplifies to:

y(t) = ∫[1,t+1] 1(0) dτ = 0

For 2 ≤ t < 4, the convolution integral simplifies to:

y(t) = ∫[t-2,2] 1(t - τ) dτ = ∫[t-2,2] (t - τ) dτ

Evaluating this integral, we get:

\(y(t) = 2t - t^2 - (t - 2)^2 / 2,\) for 2 ≤ t < 4

For t ≥ 4, y(t) will be 0 again.

Maximum value of y(t):

To find the value of t at which y(t) reaches its maximum value, we need to examine the expression for y(t) within the valid range 2 ≤ t < 4. We can graphically determine the maximum by plotting y(t) within this range and identifying the peak.

Plotting y(t) within the range 2 ≤ t < 4 will give you a curve that reaches a maximum at a certain value of t. By visually inspecting the graph, you can determine the specific value of t at which y(t) reaches its maximum.

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(a) The probability that Miranda will have two twin girls is 1/4. (b) The probability that the girls are identical twins is 1/3.

(a) The probability of having two twin girls is determined by the ratio of the different combinations of twin girls. There are four possible combinations: two girls, one girl and one boy, two boys, and one boy and one girl. Since there are two combinations of twin girls, the probability of having two twin girls is 1/4. (b) The probability that the girls are identical twins is determined by the ratio of identical twins to all twins. Since 1/3 of all twins are identical twins, the probability that the girls are identical twins is 1/3.

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Answer:

(-3, -5)

Step-by-step explanation:

When reflected over the x-axis, the x remains the same, and the y change to their opposite sign.

So, the answer is (-3, -5)

Using scientific notation, the number of significant digits of the product is given as follows:

B. 3.

A number in scientific notation is given by:

\(a \times 10^b\)

With the base being \(a \in [1, 10)\).

When two numbers in scientific notation are multiplied, we have that:

For this problem, the product is given by:

\(5.2187 \times 10^{-3} \times 2.05 \times 10^7 \times 3.4 \times 10^3\)

Multiplying the bases and adding the exponents, we have that:

\(5.2187 \times 10^{-3} \times 2.05 \times 10^7 \times 3.4 \times 10^3 = 5.2187 \times 2.05 \times 3.4 \times 10^{-3 + 7 + 3} = 42.8 \times 10^7\)

42.8 has to be divided by 10 to assume for the base have only one digit, thus, to compensate, we have to add one to the exponent(equivalent to multiply by 10), hence:

\(42.8 \times 10^7 = 4.28 \times 10^8\)

Hence, considering the rounding, the number has 3 significant digits(4, 2 and 8), and option B is correct.

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The sentence, using the rational root theorem, is completed as follows:

If a polynomial function f has integer coefficients, then every rational solution of f(x) = 0 has the format p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The rational root theorem states that a polynomial with integer coefficients will have every rational solution following the format p/q.

The variables p and q are defined as follows:

Hence the blanks in this problem are completed, respectively, by:

Constant term and leading coefficent.

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Answer:

$266.60

Step-by-step explanation:

Answer:

  (4, -2)  (see attached)

Step-by-step explanation:

Vector addition on a graph is accomplished by placing the tail of one vector on the nose of the one it is being added to. The negative of a vector is in the direction opposite to the original.

__

The components of the vectors are ...

  u  = (1, -2)

  v = (-6, -6)

Then the components of the vector sum are ...

  2u -1/3v = 2(1, -2) -1/3(-6, -6) = (2 +6/3, -4 +6/3)

  2u -1/3v = (4, -2)

The sum is shown graphically in the attachment. Vector u is added to itself by putting a copy at the end of the original. Then the nose of the second vector is at 2u.

One-third of vector v is subtracted by adding a vector to 2u that is 1/3 the length of v, and in the opposite direction. The nose of this added vector is the resultant: 2u-1/3v.

The resultant is in red in the attachment.

The answer is (4, -2) hope this helps!

To dilate a point at a point, you start by selecting a center of dilation and a scale factor.

Then, for each point that you want to dilate, you do the following:

For example, if you wanted to dilate point P by a scale factor of 2, with the center of dilation at O, you would draw a line segment from O to P, double its length, and then draw a new line segment from O to the new point, using the new length that you calculated. The new point would be the point that you arrive at when you complete this line segment.

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Answer:

240 is the mark down.

Step-by-step explanation:

1 - .20 = 0.8

0.8 x 300 = 240

Answer:

$240

Step-by-step explanation:

Answer:

B) 13°

Step-by-step explanation:

a right angle is 90°. Angle 2 is congruent to 77° so it is 77°. 90° minus 77° gives you the total of 13°. 13 + 77 = 90

Answer: 13. 30

Step-by-step explanation:

13. Area = 18x * 10y = 180xy

Length = 6th

With ?

180xy = 6xy x width

180 x/6xy

Width = 30

14. 3^(9-5)= 3^4 = 81 the truck weighs 81 times as the driver

3^5

In statistics, the "central tendency" refers to a single value which represents middle or center of a set of data. The 3 common measures of central tendency are named as mean, median, and mode.

When scores have a central tendency, it means that most of the scores in a set of data are clustered around a particular value.

For Example, if we have a data set of test scores, and most of the scores are around 70, then 70 would be the central tendency of the data set.

The central tendency is an important concept in statistics because it provides a way to summarize a large set of data with a single value.

It can help you understand the overall pattern of the data and make comparisons between different data sets.

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Answer:

c-2x+3+x

Step-by-step explanation:

Answer:

Choice B: \(2x+3=18\)

Step-by-step explanation:

First of all we know that the x will represent the number of pencils that Miguel has. So if it mentioned that Imani has 3 more than twice of Miguel's pencils, that can be made into this expression \(2x+3\). Then it said that both of their pencils added together is 18. So we take the expression and add an equal sign with the 18. So once we put it together it makes Choice B \(2x+3=18\).

The lower confidence bound for the percentage of all such homes that have electrical/environmental problems is 12.8% (rounded to one decimal place). This means we can be 99% confident that the true percentage of all homes with electrical/environmental problems is at least 12.8%.

To calculate the lower confidence bound using a confidence level of 99%, we need to use the formula:
Lower Bound = Sample Proportion - Z-score * Square Root[(Sample Proportion * (1 - Sample Proportion)) / Sample Size]
Here, we need to know the sample proportion, which is the percentage of homes that have electrical/environmental problems. Let's assume that the sample size is 500 and 85 homes out of those have electrical/environmental problems. Then the sample proportion would be:
Sample Proportion = 85/500 = 0.17
Next, we need to find the Z-score for a 99% confidence level. From the Z-tables, we can find that the Z-score for a 99% confidence level is 2.576.
Putting these values in the formula, we get:
Lower Bound = 0.17 - 2.576 * Square Root[(0.17 * (1 - 0.17)) / 500] = 0.128

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Answer: Among the given choices, the largest one that could be used successfully in an epsilon-delta proof of lim (9x + 36) = 9 is:

C. 8 = 2ε

Step-by-step explanation:

To determine the largest choice of 8 that could be used successfully in an epsilon-delta proof, we need to find the maximum value of epsilon (ε) that satisfies the given limit statement.

In an epsilon-delta proof, for a given limit statement lim (9x + 36) = 9, we want to show that for any epsilon (ε) greater than 0, there exists a corresponding delta (δ) such that whenever 0 < |x - a| < δ (where 'a' is the value of x approaching), it implies |(9x + 36) - 9| < ε.

Let's consider each choice of 8:

A. 8 = B: This choice doesn't provide any information about epsilon (ε) and is unrelated to the limit statement.

B. 8 = C: Similarly, this choice doesn't provide any relevant information.

C. 8 = 2ε: Here, we have epsilon (ε) defined as 2ε. In this case, we can choose delta (δ) such that whenever 0 < |x - a| < δ, it implies |(9x + 36) - 9| < 2ε. Therefore, this choice of 8 could be used successfully in the epsilon-delta proof.

D. 8 = 3ε: With this choice, we would need to find a delta (δ) such that |(9x + 36) - 9| < 3ε. However, since the limit statement only requires |(9x + 36) - 9| < ε, this choice is unnecessarily restrictive. Therefore, it is not the largest choice that could be used successfully.

E. 8 = 9ε: Similar to choice D, this choice is overly restrictive and not necessary for the limit statement.

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The statement is false because in a Poisson distribution, the probability of success does not vary from trial to trial.

The Poisson distribution is a discrete probability distribution that describes the number of times an event occurs in a fixed time interval or spatial region, given the average rate of occurrence and assuming that the events are independent and random.

The Poisson distribution has only one parameter, λ, which represents the average rate of occurrence of the event.

The probability of observing k events in the interval is given by the Poisson probability mass function:

P(k) = (e^(-λ) * λ^k) / k!

where e is the base of the natural logarithm, and k is a non-negative integer.

The Poisson distribution assumes that the probability of observing an event at any given point in time or space is constant, and that the events are independent of each other.

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Answer:

0091880102993201019200299219191

\(1 \times 666 = 1000\)

Step-by-step explanation:

1+1

Answer:

B

Step-by-step explanation:

The formula for area of a square is length x width. The x represents the width and the 7x is just the width times 7. this means the length is 7 times the width, If the width is x, then the length is 7x

To find an objective function that has a maximum or minimum value at each indicated vertex, we need to consider the properties of the vertices.

Let's assume we have a set of vertices indicated by \(\(V = \{v_1, v_2, \ldots, v_n\}\).\) To ensure that our objective function has either a maximum or minimum value at each vertex, we can construct a piecewise function that achieves this property.

First, we need to determine whether each vertex is a maximum or minimum point. Let's denote \(\(v_i\)\) as a maximum vertex if the desired extremum at that vertex is a maximum value, and \(\(v_i\)\) as a minimum vertex if the desired extremum is a minimum value.

For each vertex \(\(v_i\)\), we can construct a quadratic function that achieves the desired extremum at that vertex. The general form of a quadratic function is \(\(f(x) = ax^2 + bx + c\).\)

If \(\(v_i\)\) is a maximum vertex, we choose a negative coefficient for the quadratic term \((\(a < 0\))\) to ensure the function opens downwards and has a maximum value at that vertex. Conversely, if \(\(v_i\)\) is a minimum vertex, we choose a positive coefficient for the quadratic term \((\(a > 0\))\) to ensure the function opens upwards and has a minimum value at that vertex.

By assigning appropriate coefficients for each vertex, we can construct a piecewise function that satisfies the given conditions. The objective function can be defined as follows:

\(\[f(x) = \begin{cases} a_1 x^2 + b_1 x + c_1 & \text{if } x \in \text{Region 1} \\ a_2 x^2 + b_2 x + c_2 & \text{if } x \in \text{Region 2} \\ \ldots & \\ a_n x^2 + b_n x + c_n & \text{if } x \in \text{Region n} \end{cases}\]\)

Here, each region corresponds to a specific vertex \(\(v_i\)\) and has its own set of coefficients (\(\(a_i, b_i, c_i\)\)) chosen to achieve the desired maximum or minimum value at that vertex.

It's important to note that the specific regions and coefficients depend on the given vertices and their corresponding desired extremum values.

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It's (8,-2), (5,-1), (2,0), (-1,1), (-4,2).  Just took it and suffered the fate of the wrong answer.

Answer:

C

Step-by-step explanation:

Answer : The area of the figure composed of a parallelogram, a square and a rectangle is 126 in².

Step-by-step explanation :

Area of composed figure = Area of parallelogram + Area of square + Area of rectangle

First we have to calculate the area of parallelogram.

Area of parallelogram = Base × Height

Given:

Base = 10 in

Height = 3.5 in

Area of parallelogram = 10 in × 3.5 in

Area of parallelogram = 35 in²

Now we have to calculate the area of square.

Area of square = (Side)²

Given:

Side = 4 in

Area of square = (4 in)²

Area of square = 16 in²

Now we have to calculate the area of rectangle.

Area of rectangle = Length × Breadth

Given:

Length = 12.5 in

Breadth = 6 in

Area of rectangle = 12.5 in × 6 in

Area of rectangle = 75 in²

Now we have to calculate the composed figure.

Area of composed figure = Area of parallelogram + Area of square + Area of rectangle

Area of composed figure = 35 in² + 16 in² + 75 in²

Area of composed figure = 126 in²

Therefore, the area of the figure composed of a parallelogram, a square and a rectangle is 126 in².

The area of the given figure is 126in²

The given figure is a composite figure composed of a parallelogram, a square and a rectangle.

Get the area of the square

Area = L²

Area of the square = 4² = 16in²

Area of the rectangle = 6 * 12.5

Area of the rectangle = 75in²

For the parallelogram:

Area of the parallelogram = Base * Height

Area of the parallelogram = 10 * 3.5

Area of the parallelogram  = 35 in²

Area of the figure = 75in² + 35in² + 16in²

Area of the figure = 126in²

Hence the area of the figure is 126in²

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Answer:

Step-by-step explanation:

To determine the sign of the sum of two integers when one integer is positive and the other is negative, we can follow a simple rule based on their magnitudes.

If the magnitude of the positive integer is greater than the magnitude of the negative integer, the sum will be positive. This is because the positive integer outweighs the negative integer, resulting in a positive value.

On the other hand, if the magnitude of the negative integer is greater than the magnitude of the positive integer, the sum will be negative. In this case, the negative integer dominates and determines the sign of the sum.

In both scenarios, the sign of the larger magnitude integer takes precedence and determines the sign of the sum. It is important to note that the sum will always have the sign of the integer with the larger magnitude, regardless of the specific values of the integers involved.

By considering the magnitudes of the integers, we can easily determine the sign of their sum when one integer is positive and the other is negative.

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Answer:

b. 1/9

Step-by-step explanation:

1. 1/6 is the probability of rolling 6

2. 4/6 is the probability of rolling less than 5

3. Multiply them: \(\frac{1}{6} x\frac{2}{3}\)

4. Answer: 1/9

The probability of getting a 6 on the first roll, then a number less than 5 on the second roll should be option b.

since

1/6 should be considered as  the probability of rolling 6

And, 4/6 is the probability of rolling less than 5

So \(= 1\div 6 \times 2\div 3\)

= 1/9

Hence, the option b is correct.

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