Prove that:(cosecA-sinA)(secA-cosA)(tanA+cotA)=1

Answer:

C. The function shown on the graph has a greater rate of change, but a lower starting point.

Step-by-step explanation:

The fourth corner of the rectangle is located at (5, 40.0625).

The fourth corner of the rectangle must have the same y-coordinate (3.5) as the third corner and the same x-coordinate (5) as the second corner. To find the fourth corner, we must use the distance formula. The distance formula is\(d = √[(x2-x1)^2 + (y2-y1)^2]\). We already know the x-coordinate is 5, so we will be solving for the y-coordinate. We will use the coordinates of the first corner and the second corner. Plugging in the coordinates, we get: \(d = √[(5- -4)^2 + (3.5 - -2)^2]\). Simplifying, we get d = \(√[(9)^2 + (5.5)^2] = √[81 + 30.25] = √111.25\). Since we are solving for the y-coordinate, we can use the following equation: \(y=d^2 - (x2-x1)^2 + y1\). Plugging in the values, we get: \(y = (111.25)^2 - (5 - -4)^2 + -2 = 123.0625 - 81 + -2 = 40.0625.\)Thus, the fourth corner of the rectangle is located at (5, 40.0625).

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Answer:

x=20

x=21

x=22

x=23

x=24

Step-by-step explanation:

We are given that

\(19<r\)

\(r<25\)

We have to find value of x which is a solution to both of the given inequalities.

First we find the solution of given inequalities

\(19<r<25\)

The value of r lies between 19 and 25.

Therefore, the possible values of r are

20,21,22,23,24

Hence, the value of x which is the solution of both given inequalities is given by

x=20

x=21

x=22

x=23

x=24

Answer:

254 cm² (to 3 s.f.)

Step-by-step explanation:

Area of shaded region

= area of large circle -area of smaller circle

\(\boxed{area \: of \: circle = \pi {r}^{2} }\)

Radius of large circle= 15cm

Radius of smaller circle= 12cm

Area of shaded region

= π(15²) -π(12²)

= 225π -144π

= 81π

= 81(3.14)

= 254.34

= 254 cm² (3 s.f.)

The encryption method that combines a random value with the plain text to produce the cipher text is: One-time pad.

The one-time pad encryption technique is a form of symmetric encryption where a random key, known as the one-time pad, is combined with the plain text using a bitwise XOR operation. The one-time pad should be at least as long as the plain text and should never be reused.

In this method, each character of the plain text is combined with a corresponding character from the one-time pad, resulting in the cipher text. The one-time pad acts as a random key stream, making the encryption extremely secure if implemented correctly.

Steganography is a different technique that involves hiding information within other seemingly innocuous data, such as images or audio files, without necessarily encrypting it.

Transposition is a method of encryption where the characters of the plain text are rearranged or shuffled without changing the actual characters themselves.

Elliptic Curve is not an encryption method but rather a mathematical framework used in public-key cryptography systems, such as Elliptic Curve Cryptography (ECC), which provide secure communication channels but do not involve combining random values with the plain text to produce the cipher text.

Therefore, the correct answer is: One-time pad.

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Answer:

compound Inequalities.

Answer: 11+23i

Step-by-step explanation:

(i+5)(3+4i)

First foil

3i+4i^2 +15+20i

Then combine like terms

23i+15+4i^2

i^2 = -1 so,

23i+15+4(-1)

11+23i

1. The slope of each object are: a) 0.6. b) 1.375.

2. The slope of the road section is 0.02.

3. No, a wheelchair ramp with a vertical rise of 1.4 m along a horizontal run of 8 m does not satisfy the regulation.

4. The slope of each line segment are: a) 0.6. b) -0.6.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

By substituting the given data points into the formula for the slope of a line, we have the following;

Part 1

Slope of a = 3/5

Slope of a = 0.6

Slope of b = 4.4/3.2

Slope of b = 1.375

Part 2.

Slope of road section = 2.5/152

Slope of road section = 0.0165 ≈ 0.02.

Part 3.

Slope of wheelchair ramp = 1.4/8

Slope of wheelchair ramp = 0.0175 ≈ 0.02.

Part 4.

a) The rise for graph a is 3 units.

The run for graph a is 5 units.

Slope of graph a = 3/5

Slope of graph a = 0.6

b) The rise for graph b is -3 units.

The run for graph b is 5 units.

Slope of graph b = -3/5

Slope of graph b = -0.6

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The table with the scale measurements is given by the image shown at the end of the answer.

The measurements are obtained applying the proportion given for each table.

The symbols are given as follows:

For the first table, we have that every inch on the table represents one feet in real life, hence:

For the second table, we have that every inch on the paper represents two feet in real life, hence the measurements are given as follows:

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Answer:sedan can hold 3 people and a minivan can hold 9 people.

Step-by-step explanation:

Suppose the number of passengers each sedan can carry is A and the number of passengers each minivan can carry is B

So 3A + 2B = 21 and 3A + 3B = 27

If we subtract the equations we can solve for B

3A + 3B = 27

-3A - 2B = 21

___________

B = 6

Now we know Each minivan can hold 6 passengers and we can solve for A.

3A + 3B = 27

3A + 3(6) = 27

3A + 18 = 27

- 18. -18

__________

3A = 9

A =3

You can check this by solving the other equation.

3A + 2B = 21

3(3) + 2(6) = 21

9 + 12 = 21

Hope that helps

The given integral is ∫(0 / x² √(2² + 490)) dx. To solve this integral, we can make a substitution by letting x = 7tan(θ), where θ is between -π/8 and π/8. Then, dx = 2sec²(θ) dθ. The given integral is ∫(0 / x² √(2² + 490)) dx, and after making the substitution x = 7tan(θ), the integral becomes ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

Substituting these expressions in the integral, we have ∫(0 / (7tan(θ))² √(2² + 490))(2sec²(θ)) dθ. Simplifying further, we get ∫(0 / 49tan²(θ) √(4 + 490))(2sec²(θ)) dθ. Rearranging the expression under the square root, we have ∫(0 / 49sec²(θ) √(4(1 + 122.5tan²(θ))))(2sec²(θ)) dθ. This can be simplified to ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

In summary, the given integral is ∫(0 / x² √(2² + 490)) dx, and after making the substitution x = 7tan(θ), the integral becomes ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

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The given integral is ∫(0 / x² √(2² + 490)) dx. To solve this integral, we can make a substitution by letting x = 7tan(θ), where θ is between -π/8 and π/8. Then, dx = 2sec²(θ) dθ. The given integral is ∫(0 / x² √(2² + 490)) dx, and after making the substitution x = 7tan(θ), the integral becomes ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

Substituting these expressions in the integral, we have ∫(0 / (7tan(θ))² √(2² + 490))(2sec²(θ)) dθ. Simplifying further, we get ∫(0 / 49tan²(θ) √(4 + 490))(2sec²(θ)) dθ. Rearranging the expression under the square root, we have ∫(0 / 49sec²(θ) √(4(1 + 122.5tan²(θ))))(2sec²(θ)) dθ. This can be simplified to ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

In summary, the given integral is ∫(0 / x² √(2² + 490)) dx, and after making the substitution x = 7tan(θ), the integral becomes ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

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Answer:

BC=0.87

Step-by-step explanation:

Answer:

Your answer is C. Angle a is congruent to both angles 3 and 1.

Step-by-step explanation:

Using normal distribution, we can expect 26% of Tim Worker's electric bill expenses to fall between $184.00 and $200.00.

Tim Worker's electric bill to calculate the percentage of his expenses in this category that would be expected to fall between $184.00 and $200.00.

Calculate the z-scores for $184.00 and $200.00 using the formula z = (x - μ) / σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

For $184.00: z = ($184.00 - $206.00) / $10.00 = -2.2

For $200.00: z = ($200.00 - $206.00) / $10.00 = -0.6

Look up the percentage of the area associated with each z-score using a standard normal distribution table or a calculator that can calculate normal probabilities.

For z = -2.2: 48.6%

For z = -0.6: 22.6%

Subtract the percentage of the area associated with the lower z-score from the percentage of the area associated with the higher z-score to get the percentage of expenses between $184.00 and $200.00.

Percentage between $184.00 and $200.00 = 48.6% - 22.6% = 26%

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For a standardized normal distribution, Z, the probability that Z is greater than 1.50 is less than the probability that Z is greater than 2.50. False, is the correct statement regarding the given statement.

In statistics, the standardized normal distribution is a normal distribution with a mean of zero and a standard deviation of one. It is also known as the standard normal distribution. The distribution is entirely defined by its mean and standard deviation. For example, any normal distribution can be standardized by subtracting its mean and dividing by its standard deviation.This distribution is a continuous probability distribution.

A continuous probability distribution is a probability distribution that assigns probabilities to an infinite number of possible outcomes that are not countable. These probabilities are expressed as the area under the curve in a continuous probability distribution. The total area under the curve of a continuous probability distribution is always equal to one.

The statement given "For a standardized normal distribution, Z, the probability that Z is greater than 1.50 is less than the probability that Z is greater than 2.50" is false.

This is because the normal distribution curve is a symmetrical curve and the probability of being greater than a value of 1.50 or 2.50 is the same.

Therefore, the probability of Z being greater than 1.50 is the same as the probability of Z being greater than 2.50. The answer is False.

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Answer:

um 8??

Step-by-step explanation:

For given linear equation x will be 5.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

As given linear equation is

15-x=10

x=15-10

x=5

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Answer:

C

Step-by-step explanation:

Answer:

$26.20

Step-by-step explanation:

first you multiple 2.12 by 10 then you add 6 to get your answer. (2.12×10)+6 (21.2)+6=26.2

After the second outer loop iteration, the list is [6,1,7,8,9].

To determine the list after the second outer loop iteration, let's assume we're working with a simple bubble sort algorithm. Here are the steps:
1. First outer loop iteration:
  - Compare 6 and 9; no swap.
  - Compare 9 and 8; swap to get [6,8,9,1,7].
  - Compare 9 and 1; swap to get [6,8,1,9,7].
  - Compare 9 and 7; swap to get [6,8,1,7,9].
2. Second outer loop iteration:
  - Compare 6 and 8; no swap.
  - Compare 8 and 1; swap to get [6,1,8,7,9].
  - Compare 8 and 7; swap to get [6,1,7,8,9].

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The corresponding CDF is:F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X is 2. d. The variance of the given random variable X is π²/4 + 2π - 6.

The value of the constant A can be obtained by using the normalization condition that the integral of the PDF function over the entire possible range of X must be equal to 1. So, we can write the following integral to solve for

A:(∫f(x) dx) from 0 to π/2=∫A sin(x) dx= A [-cos(x)] evaluated at π/2 and 0= -A(cos(π/2) - cos(0))= A (1 - 0) =1. Therefore, the value of the constant A is 1. b. The CDF of the given random variable X is given as follows:

F(x)=∫f(x)dx from 0 to x, for 0 < x < π/2=∫sin(x) dx from 0 to x= [-cos(x)] evaluated at x and 0= -cos(x) - (-cos(0))= 1 - cos(x) for 0 < x < π/2=1 for x ≥ π/2. So, the corresponding CDF is as follows:

F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X can be obtained using the following formula:

E(X) = ∫xf(x)dx from 0 to π/2=∫x sin(x) dx from 0 to π/2= [-x cos(x)] evaluated at π/2 and 0 - ∫-cos(x) dx from 0 to π/2= -0 + cos(0) - ([-cos(x)] evaluated at π/2 and 0)= 0 + 1 - (-1)= 2. So, the expected value of the given random variable X is 2.

d. The variance of the given random variable X can be obtained using the following formula:

Var(X) = E(X²) - [E(X)]²=∫x² f(x)dx from 0 to π/2 - [E(X)]²=∫x² sin(x)dx from 0 to π/2 - (2)²= [-x² cos(x)] evaluated at π/2 and 0 + ∫2x cos(x)dx from 0 to π/2 - 4= -0 + π²/4 - 4 + (2 sin(x) + 2x cos(x)) evaluated at π/2 and 0= π²/4 - 2 - 4 + 2 + 2π= π²/4 + 2π - 6. So, the variance of the given random variable X is π²/4 + 2π - 6

Hence, the answer is: a. The value of the constant A is 1.b. The corresponding CDF is : F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X is 2. d. The variance of the given random variable X is π²/4 + 2π - 6

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Answer: 489

Step-by-step explanation:

420+69=489

Answer:

The slope of a linear model can be calculated using the formula:

m = Δy / Δx

where:

Δy = change in y (the dependent variable, in this case, total cost)

Δx = change in x (the independent variable, in this case, number of candy bars)

This is essentially the "rise over run" concept from geometry, applied to data points on a graph.

In this case, we can take two points from the table (for instance, the first and last) and calculate the slope.

Let's take the first point (3 candy bars, $6.65) and the last point (25 candy bars, $48.45).

Δy = $48.45 - $6.65 = $41.8

Δx = 25 - 3 = 22

So the slope m would be:

m = Δy / Δx = $41.8 / 22 = $1.9 per candy bar

This suggests that the cost of each candy bar is $1.9 according to this linear model.

Please note that this assumes the relationship between the number of candy bars and the total cost is perfectly linear, which might not be the case in reality.

Answer:

6(1/4) or (25/4) pounds

Step-by-step explanation:

      1       1(1/4)  1(1/2)   1(3/4)          2

<-----|---------|---------|------------|-----------|---->

      X         X        X             X            X

      X         X                                      X

                  X

                  X

                  X

1(1/4) or (5/4)

(5/4) x 5 = 6(1/4) or 25/4 pounds

I hope this helps!

The solution to this problem is the p-value must be higher than 0.05.

A confidence interval in frequentist statistics is a range of estimates for an unobserved parameter. The most common confidence level for computing confidence intervals is 95%, however other levels, including 90% or 99%, are sporadically employed.

Here ,

In this given problem we can see confidence interval has 0 in it.

So,

Since the confidence interval comprises 0, the null hypothesis should be rejected.

When the p-value exceeds the level of significance, the null hypothesis is only rejected.

Since alpha=0.05 in this case, the p-value must be higher than 0.05.

Thus, the p-value must be higher than 0.05.

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The prosecutor claims that there is a 1% chance that the defendant would have the crime blood type if he were innocent, and thus, there is a 99% chance that he is guilty.

This is a fallacy known as the prosecutor's fallacy.The prosecutor's fallacy is an error in statistical reasoning that occurs when the probability of an event occurring given a particular hypothesis is incorrectly equated with the probability of the hypothesis given the event.

It is a common mistake in legal proceedings and forensic science.According to the prosecutor's argument, the probability of the defendant being innocent given the blood evidence is only 1%, while the probability of him being guilty is 99%. This argument is invalid because it equates the conditional probability of the hypothesis (the defendant being innocent or guilty) given the evidence with the inverse probability of the evidence given the hypothesis.

In other words, the prosecutor has taken the likelihood of observing the blood evidence given that the defendant is innocent and used it as evidence that the defendant is guilty. This is a logical fallacy, as it fails to take into account other factors that could account for the presence of the blood evidence and ignores the possibility that the defendant may be innocent. Therefore, the prosecutor's argument is wrong, and his conclusion that the defendant is guilty cannot be justified by the evidence.

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Answer:

70

Step-by-step explanation:

7 x 7 = 49

7 x 10 = 70

check

49/70

49 ÷ 7 = 7

70 ÷ 7 = 10

7/10

49/70 = 7/10